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Previous Seminars

ThursdayDec 13, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Manuel Stadlbauer Title:Exponential decay of quotients of Ruelle operatorsAbstract:opens in new windowin html    pdfopens in new window

Ruelle's operator theorem states that the Ruelle operator $L$, which is a positive operator acting on Holder functions, is conjugated to $P+R$ where $R$ is a one-dimensional projection and the norm of $R$ is smaller than 1. This decomposition, also known as spectral gap, is of interest as it allows to characterise the underlying dynamical system through, e.g., central limit theorems or continuous response to perturbations. However, the conjugation depends on the existence of a positive eigenfunction of $L$, which might not exist in more general, fibred situations due to purely functorial reasons. A possibility to circumvent this problem is to consider quotients of operators of the form $f \mapsto \frac{L^m(f L^n (1))}{L^{m+n}(1)}.$ In fact, it is possible to provide reasonable conditions such that their dual operators contract the Wasserstein distance exponentially in $m$. The result gives rise, for example, to a law of the iterated logarithm for continued fractions with sequentially restricted entries or a topology on the set of equilibrium states for semigroups of expanding maps. This is joint work with Paulo Varandas and Xuan Zhang.

ThursdayDec 13, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Tali Dekel Title:Re-rendering RealityAbstract:opens in new windowin html    pdfopens in new window

We all capture the world around us through digital data such as images, videos and sound. However, in many cases, we are interested in certain properties of the data that are either not available or difficult to perceive directly from the input signal. My goal is to "Re-render Reality", i.e., develop algorithms that analyze digital signals and then create a new version of it that allows us to see and hear better. In this talk, I'll present a variety of methodologies aimed at enhancing the way we perceive our world through modified, re-rendered output. These works combine ideas from signal processing, optimization, computer graphics, and machine learning, and address a wide range of applications. More specifically, I'll demonstrate how we can automatically reveal subtle geometric imperfection in images, visualize human motion in 3D, and use visual signals to help us separate and mute interference sound in a video. Finally, I'll discuss some of my future directions and work in progress.

BIO: Tali is a Senior Research Scientist at Google, Cambridge, developing algorithms at the intersection of computer vision and computer graphics. Before Google, she was a Postdoctoral Associate at the Computer Science and Artificial Intelligence Lab (CSAIL) at MIT, working with Prof. William T. Freeman. Tali completed her Ph.D studies at the school of electrical engineering, Tel-Aviv University, Israel, under the supervision of Prof. Shai Avidan, and Prof. Yael Moses. Her research interests include computational photography, image synthesize, geometry and 3D reconstruction.

ThursdayDec 13, 201811:30
Computer Science Seminar
Speaker: Sampath KannanTitle: Fairness in Algorithmic Decision MakingAbstract:opens in new windowin html    pdfopens in new windowWOLFSON AUDITORIUM

In this talk we survey some formulations of fairness requirements for decision making under uncertainty. We then discuss results from 3 recent papers:

  1. Treating individuals fairly is not in conflict with long-term scientific learning goals if the population is sufficiently diverse.
  2. When there is a pipeline of decisions, end-to-end fairness is impossible to achieve even in a very simple model.
  3. Exploiting the knowledge acquired by others can unfairly advantage the free rider.

These papers are joint work with a number of co-authors:

Christopher Jung, Neil Lutz, Jamie Morgenstern, Aaron Roth, Bo Waggoner, Steven Wu, and Juba Ziani

WednesdayDec 12, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Roy SchwartzTitle:Towards Interpretable Deep Learning for Natural Language ProcessingAbstract:opens in new windowin html    pdfopens in new window

Despite their superb empirical performance, deep learning models for natural language processing (NLP) are often considered black boxes, as relatively little is known as to what accounts for their success. This lack of understanding turns model development into a slow and expensive trial-and-error process, which limits many researchers from developing state-of-the-art models. Customers of deep learning also suffer from this lack of understanding, because they are using tools that they cannot interpret. In this talk I will show that many deep learning models are much more understandable than originally thought. I will present links between several deep learning models and classical NLP models: weighted finite-state automata. As the theory behind the latter is well studied, these findings allow for the development of more interpretable and better-performing NLP models. As a case study, I will focus on convolutional neural networks (ConvNets), one of the most widely used deep models in NLP. I will show that ConvNets are mathematically equivalent to a simple, linear chain weighted finite-state automaton. By uncovering this link, I will present an extension of ConvNets that is both more robust and more interpretable than the original model. I will then present similar observations regarding six recently introduced recurrent neural network (RNN) models, demonstrating the empirical benefits of these findings to the performance of NLP systems.

This is joint work with Hao Peng, Sam Thomson and Noah A. Smith

TuesdayDec 11, 201816:00
Seminar in Geometry and TopologyRoom 1
Speaker:Karim RakhimovTitle:Dynamical properties of geodesics of meromorphic connections on Riemann surfacesAbstract:opens in new windowin html    pdfopens in new window
MondayDec 10, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Nir BitanskyTitle:Weak Zero Knowledge Beyond the Black Box BarrierAbstract:opens in new windowin html    pdfopens in new window

Zero knowledge protocols are spectacular, allowing to prove NP statements without revealing anything but their validity. An essential element that enables this wonder is interaction. But how much interaction exactly is needed? This question has long challenged cryptographers and is yet to be settled under standard assumptions. In fact, the question appears to be equally challenging also for natural relaxations of the zero knowledge requirement. The difficulty in answering the round complexity question stems from that of a foundational question in cryptography --- what is the power of non-black-box reductions?

In this talk, I will explain this difficulty and present a new non-black-box technique that resolves, under standard assumptions, the round complexity of weak zero knowledge protocols (Dwork-Naor-Reingold-Stockmeyer '98). Specifically, assuming quasipolynomial hardness of the Learning with Errors problem and fully-homomorphic encryption, we construct a two message protocol, a setting where (full-fledged) zero knowledge is impossible.

The talk will assume no prior knowledge in cryptography. It is based on joint work with Dakshita Khurana and Omer Paneth (the paper can be found on

https://eprint.iacr.org/2018/895.pdf).

ThursdayDec 06, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Boaz SlomkaTitle:Improved bounds for Hadwiger’s covering problem via thin-shell estimatesAbstract:opens in new windowin html    pdfopens in new window

A long-standing open problem, known as Hadwiger's covering problem, asks what is the smallest natural number $N(n)$ such that every convex body in {\mathbb R}^n can be covered by a union of the interiors of at most $N(n)$ of its translates. Despite continuous efforts, the best general upper bound known for this number remains as it was more than sixty years ago, of the order of ${2n \choose n} \ln n$.

In this talk, I will discuss some history of this problem and present a new result in which we improve this bound by a sub-exponential factor. Our approach combines ideas from previous work, with tools from Asymptotic Geometric Analysis. As a key step, we use thin-shell estimates for isotropic log-concave measures to prove a new lower bound for the maximum volume of the intersection of a convex body $K$ with a translate of $-K$. We further show that the same bound holds for the volume of $K\cap(-K)$ if the center of mass of $K$ is at the origin.

If time permits we shall discuss some other methods and results concerning this problem and its relatives.

Joint work with H. Huang, B. Vritsiou, and T. Tkocz

ThursdayDec 06, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Yuval BahatTitle:Exploiting Deviations from Ideal Visual RecurrenceAbstract:opens in new windowin html    pdfopens in new window

Visual repetitions are abundant in our surrounding physical world: small image patches tend to reoccur within a natural image, and across different rescaled versions thereof. Similarly, semantic repetitions appear naturally inside an object class within image datasets, as a result of different views and scales of the same object. In my thesis I studied deviations from these expected repetitions, and demonstrated how this information can be exploited to tackle both low-level and high-level vision tasks. These include “blind” image reconstruction tasks (e.g. dehazing, deblurring), image classification confidence estimation, and more.

TuesdayDec 04, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Shai ShechterTitle:Approximating the Representation Zeta Functions of Finite Groups of Lie-TypeAbstract:opens in new windowin html    pdfopens in new window
ThursdayNov 29, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Amir Dembo Title:Large deviations of subgraph counts for sparse random graphsAbstract:opens in new windowin html    pdfopens in new window

For fixed t>1 and L>3 we establish sharp asymptotic formula for the log-probability that the number of cycles of length L in the Erdos - Renyi random graph G(N,p) exceeds its expectation by a factor t,  assuming only that p >> log N/sqrt(N). We obtain such sharp upper tail  bounds also for the Schatten norms of the corresponding adjacency matrices, and in a narrower range of p=p(N), also for general subgraph counts. In this talk, based on a recent joint work with Nick Cook, I will explain our approach and in particular our quantitative refinement of Szemeredi's regularity lemma for sparse random graphs in the large deviations regime.

ThursdayNov 29, 201812:15
Vision and Robotics SeminarRoom 155
Speaker:Yair Weiss Title:Why do deep convolutional networks generalize so poorly to small image transformations?Abstract:opens in new windowin html    pdfopens in new window

Deep convolutional network architectures are often assumed to guarantee generalization for small image translations and deformations. In this paper we show that modern CNNs (VGG16, ResNet50, and InceptionResNetV2) can drastically change their output when an image is translated in the image plane by a few pixels, and that this failure of generalization also happens with other realistic small image transformations. Furthermore,  we see these failures to generalize more frequently in more modern networks. We show that these failures are related to the fact that the architecture of modern CNNs ignores the classical sampling theorem so that generalization is not guaranteed. We also show that biases in the statistics of commonly used image datasets makes it unlikely that CNNs will learn to be invariant to these transformations. Taken together our results suggest that the performance of CNNs in object recognition falls far short of the generalization capabilities of humans.
Joint work with Aharon Azulay

ThursdayNov 29, 201811:30
Computer Science Seminar
Speaker: Noam NisanTitle:The Communication Complexity of Cake CuttingAbstract:opens in new windowin html    pdfopens in new windowWOLFSON AUDITORIUM

This talk concerns the well-studied model of "cake-cutting" for studying questions regarding notions of fair division of resources. We focus on discrete versions rather than using infinite-precision real values, specifically, focusing on the communication complexity. Using general discrete simulations of classical infinite-precision protocols (Robertson-Webb and moving-knife), we roughly partition the various fair-allocation problems into 3 classes: "easy" (constant number of rounds of logarithmic many bits), "medium" (poly-log total communication), and "hard".

Our main technical result concerns two of the "medium" problems (perfect allocation for 2 players and equitable allocation for any number of players) which we prove are not in the "easy" class. Our main open problem is to separate the "hard" from the "medium" classes.

Joint work with Simina Branzei

WednesdayNov 28, 201814:00
Foundations of Computer Science SeminarRoom 208
Speaker:Nicolas ReschTitle:Lossless dimension expanders via linearized polynomials and subspace designs Abstract:opens in new windowin html    pdfopens in new windowNote special time and place

For a vector space F^n over a field F, an (η, ß)-dimension expander of degree d is a collection of d linear maps Γ_j : F^n \to F^n such that for every subspace U of F^n of dimension at most ηn, the image of U under all the maps, ∑_{j=1}^d Γ_j(U), has dimension at least ßdim(U). Over a finite field, a random collection of d=O(1) maps Γ_j over excellent “lossless” expansion with high probability: ß ≈ d for η ≥ Ω(1/\eta). When it comes to a family of explicit constructions (for growing n), however, achieving even expansion factor β = 1 + ε with constant degree is a non-trivial goal. We present an explicit construction of dimension expanders over finite fields based on linearized polynomials and subspace designs, drawing inspiration from recent progress on list decoding in the rank-metric. Our approach yields the following:

  • Lossless expansion over large fields; more precisely ß ≥ (1–ε)d and η ≥ (1–ε)/d with d=O_ε(1), when |F| ≥ Ω(n).
  • Optimal up to constant factors expansion over fields of arbitrarily small polynomial size; more precisely ß ≥ Ω(δd) and η ≥ Ω(1/(δd)) with d = O_δ(1), when |F| ≥ n^δ.

Previously, an approach reducing to monotone expanders (a form of vertex expansion that is highly non-trivial to establish) gave (Ω(1), 1+Ω(1))-dimension expanders of constant degree over all fields. An approach based on “rank condensing via subspace designs” led to dimension expanders with ß ≥ Ω(√d) over large finite fields. Ours is the first construction to achieve lossless dimension expansion, or even expansion proportional to the degree. Based on joint work with Venkatesan Guruswami and Chaoping Xing.

WednesdayNov 28, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Michael KimTitle:Fairness through Computationally-Bounded AwarenessAbstract:opens in new windowin html    pdfopens in new window

As algorithmic prediction systems have become more widespread, so too have concerns that these systems may be discriminatory against groups of people protected by laws and ethics. We present a recent line of work that takes a complexity theoretic perspective towards combating discrimination in prediction systems. We'll focus on fair classification within the versatile framework of Dwork et al. [ITCS'12], which assumes the existence of a metric that measures similarity between pairs of individuals. Unlike earlier work, we do not assume that the entire metric is known to the learning algorithm; instead, the learner can query this metric a bounded number of times. We propose a new notion of fairness called *metric multifairness* and show how to achieve this notion in our setting. Metric multifairness is parameterized by a similarity metric d on pairs of individuals to classify and a rich collection C of (possibly overlapping) "comparison sets" over pairs of individuals. At a high level, metric multifairness guarantees that *similar subpopulations are treated similarly*, as long as these subpopulations are identified within the class C.

MondayNov 26, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Dana RonTitle:Title: 2,3,…,k: From approximating the number of edges to approximating the number of k-cliques (with a sublinear number of queries)Abstract:opens in new windowin html    pdfopens in new window

In this talk I will present an algorithms for approximating the number of k-cliques in a graph when given query access to the graph. This problem was previously studied for the cases of k=2 (edges) and k=3 (triangles). We give an algorithm that works for any k >= 3, and is actually conceptually simpler than the k=3 algorithm. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let n denote the number of vertices in the graph, m the number of edges, and C_k the number of k-cliques. We design an algorithm that outputs a (1+\epsilon)-approximation (with high probability) for C_k, whose expected query complexity and running time are O (\frac{n}{C_k^{1/k}}+\frac{m^{k/2}}{C_k}) poly (\log n, 1/\epsilon,k).

Hence, the complexity of the algorithm is sublinear in the size of the graph for C_k = \omega(m^{k/2-1}). Furthermore, we prove a lower bound showing that the query complexity of our algorithm is essentially optimal (up to the dependence on \log n, 1/\epsilon and k).

This is joint work with Talya Eden and C. Seshadhri.

ThursdayNov 22, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Yehuda Dar Title:System-Aware Compression: Optimizing Imaging Systems from the Compression StandpointAbstract:opens in new windowin html    pdfopens in new window

In typical imaging systems, an image/video is first acquired, then compressed for transmission or storage, and eventually presented to human observers using different and often imperfect display devices. While the resulting quality of the perceived output image may severely be affected by the acquisition and display processes, these degradations are usually ignored in the compression stage, leading to an overall sub-optimal system performance. In this work we propose a compression methodology to optimize the system's end-to-end reconstruction error with respect to the compression bit-cost. Using the alternating direction method of multipliers (ADMM) technique, we show that the design of the new globally-optimized compression reduces to a standard compression of a "system adjusted" signal. Essentially, we propose a new practical framework for the information-theoretic problem of remote source coding. The main ideas of our method are further explained using rate-distortion theory for Gaussian signals. We experimentally demonstrate our framework for image and video compression using the state-of-the-art HEVC standard, adjusted to several system layouts including acquisition and rendering models. The experiments established our method as the best approach for optimizing the system performance at high bit-rates from the compression standpoint.
In addition, we relate the proposed approach also to signal restoration using complexity regularization, where the likelihood of candidate solutions is evaluated based on their compression bit-costs.
Using our ADMM-based approach, we present new restoration methods relying on repeated applications of standard compression techniques. Thus, we restore signals by leveraging state-of-the-art models designed for compression. The presented experiments show good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards.
* Joint work with Prof. Alfred Bruckstein and Prof. Michael Elad.
** More details about the speaker and his research work are available at  http://ydar.cswp.cs.technion.ac.il/

 

 

ThursdayNov 22, 201811:30
Computer Science Seminar
Speaker:Amos FiatTitle:C-single crossing Interdependent valuationsAbstract:opens in new windowin html    pdfopens in new windowWOLFSON AUDITORIUM

We consider the goal of social welfare maximization where a single item is to be assigned to one of to n potential agents with interdependent values.

That is, each agent has her own private signal, and the valuation of each agent is a known function of all n private signals. This captures settings such as valuations for artwork, oil drilling rights, broadcast rights, and many more. In the interdependent value setting, all previous work has assumed a so-called single-crossing condition. Single-crossing means that the impact of agent i’s private signal, s_i, on her own valuation is greater than the impact of s_ii on the valuation of any other agent. It is known that without the single-crossing condition an efficient outcome cannot be obtained. We study welfare maximization for interdependent valuations through the lens of approximation.

We show that, in general, without the single-crossing condition, one cannot hope to approximate the optimal social welfare any better than the approximation given by assigning the item to a random bidder. Consequently, we introduce a relaxed version of single-crossing, c-single-crossing, parameterized by c ≥ 1, which means that the impact of s_i on the valuation of agent i is at least 1/c times the impact of s_i on the valuation of any other agent (c = 1 is single-crossing). Using this parameterized notion, we obtain a host of positive results. We also consider interdependent settings when valuations are concave and give improved results.

Joint work with Alon Eden, Michal Feldman, and Kira Goldner.

MondayNov 19, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Natan RubinTitle:Hitting Convex Sets with PointsAbstract:opens in new windowin html    pdfopens in new window

Given an underlying finite point set P in the plane, we seek a small set Q that would hit any convex set that contains at least an Epsilon-fraction of P. Such a set Q is called a weak Epsilon-net. The study of Epsilon-nets is central to Computational and Combinatorial Geometry, and it bears important connections to Statistical Learning Theory, Extremal Combinatorics, Discrete Optimization, and other areas.

It is an outstanding open problem to determine tight asymptotic bounds on weak Epsilon-nets with respect to convex sets. For any underlying point set in the plane we describe such a net whose cardinality is roughly proportional to Epsilon^{-3/2}. This is the first improvement of the over-25-year-old bound of Alon, Barany, Furedi, and Kleitman.

WednesdayNov 14, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Kfir LevyTitle:Beyond SGD: Data Adaptive Methods for Machine Learning Abstract:opens in new windowin html    pdfopens in new window

The tremendous success of the Machine Learning paradigm heavily relies on the development of powerful optimization methods. The canonical algorithm for training learning models is SGD (Stochastic Gradient Descent), yet this method has its limitations. It is often unable to exploit useful statistical/geometric structure, it might degrade upon encountering prevalent non-convex phenomena, and it is hard to parallelize. In this talk I will discuss an ongoing line of research where we develop alternative methods that resolve some of SGD"s limitations. The methods that I describe are as efficient as SGD, and implicitly adapt to the underlying structure of the problem in a data dependent manner.

In the first part of the talk, I will discuss a method that is able to take advantage of hard/easy training samples. In the second part, I will discuss a method that enables an efficient parallelization of SGD. Finally, I will briefly describe a method that implicitly adapts to the smoothness and noise properties of the learning objective.

MondayNov 12, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Michal Dory Title:Distributed Approximation of k-edge-connected SubgraphsAbstract:opens in new windowin html    pdfopens in new window

In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. In this talk, I will present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model.

ThursdayNov 08, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Snir Ben-Ovadia Title:What are SRB and GSRB measures, and a new characterisation of their existence.Abstract:opens in new windowin html    pdfopens in new window

SRB measures are an important object in dynamical systems and mathematical physics. Named after Sinai , Ruelle and Bowen, these measures have important properties of being equilibrium states which describe chaotic behaviour, yet may also describe the asymptotic of ``observable” events in the phase space. An open and important question, is in what generality do systems admit SRB measures?

We present the notion of generalised SRB measures (GSRB in short), mention some of their important properties, and present a new condition to characterise their existence on a general setup.

The first part of the talk will describe some of the motivation leading to define and to study SRB measures; and so we will define GSRB measures and compare their properties with the properties sought for SRB measures. We will also describe a case study of examples motivating to study GSRB measures. Our new result is a characterisation of systems admitting GSRB measures.

In the second part of the talk, as much as time permits, we will present some key steps in the construction of GSRB measures.

ThursdayNov 08, 201811:30
Computer Science Seminar
Speaker: Shai Shalev-ShwartzTitle:Formalizing the “Duty of Care” for self-driving carsAbstract:opens in new windowin html    pdfopens in new windowWOLFSON AUDITORIUM

The "Duty of Care"is a legal obligation requiring one to adhere to a standard of reasonable care while performing acts that could harm others. We propose a formal, mathematical interpretation of the duty of care in the context of "being cautious while driving". The framework enables tackling moral questions in a formal way and is an example of a new research field which we call regulatory science.

Joint work with Shaked Shammah and Amnon Shashua.

WednesdayNov 07, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Tamir Bendory Title:Estimation in extreme noise levels with application to cryo-electron microscopyAbstract:opens in new windowin html    pdfopens in new window

Single-particle cryo-electron microscopy (cryo-EM) is an innovative technology for elucidating structures of biological molecules at atomic-scale resolution. In a cryo-EM experiment, tomographic projections of a molecule, taken at unknown viewing directions, are embedded in highly noisy images at unknown locations. The cryo-EM problem is to estimate the 3-D structure of a molecule from these noisy images.

Inspired by cryo-EM, the talk will focus on two estimation problems: multi-reference alignment and blind deconvolution. These problems abstract away much of the intricacies of cryo-EM, while retaining some of its essential features. In multi-reference alignment, we aim to estimate a signal from its noisy, rotated observations. While the rotations and the signal are unknown, the goal is only to estimate the signal. In the blind deconvolution problem, the goal is to estimate a signal from its convolution with an unknown, sparse signal in the presence of noise. Focusing on the low SNR regime, I will propose the method of moments as a computationally efficient estimation framework for both problems and will introduce its properties. In particular, I will show that the method of moments allows estimating the sought signal accurately in any noise level, provided sufficiently many observations are collected, with only one pass over the data. I will then argue that the same principles carry through to cryo-EM, show examples, and draw potential implications.

TuesdayNov 06, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Erez LapidTitle:Results and conjectures about irreducibility of parabolic induction of representations of the general linear group over a local non-archimedean fieldAbstract:opens in new windowin html    pdfopens in new window

The representation theory of GL(n,F), F non-archimedean is a classical subject initiated by Bernstein and Zelevinsky in the 1970s.

I will review some recent results and conjectures which aim to characterize irreducibility of parabolic induction, in terms of geometry. Joint with Alberto Minguez

MondayNov 05, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Moni NaorTitle:White- box vs. black-box search problems: a cryptographic perspectiveAbstract:opens in new windowin html    pdfopens in new window

Ramsey theory assures us that in any graph there is a clique or independent set of a certain size, roughly logarithmic in the graph size. But how difficult is it to find the clique or independent set? If the graph is given explicitly, then it is possible to do so while examining a linear number of edges. If the graph is given by a black-box, where to figure out whether a certain edge exists the box should be queried, then a large number of queries must be issued. But what if one is given a program or circuit for computing the existence of an edge? What if we are assured that the program is small without being given explicitly?

In this talk I will explore recent work on the complexity of search problems with guaranteed solution (the class TFNP) and the tight relationship with cryptographic assumptions and techniques.

Based on joint works with Pavel Hubacek, Ilan Komargodski and Eylon Yogev

ThursdayNov 01, 201811:30
Computer Science Seminar
Speaker:Adi ShamirTitle:Machine Learning in Security: Applications and ImplicationsAbstract:opens in new windowin html    pdfopens in new windowWolfson Auditorium

In this talk I will survey the way machine learning research is affecting the field of security, and the way security research Is affecting the field of machine learning. After giving several examples of each type, I will discuss some of the latest developments In adversarial machine learning research, which are used by hackers to defeat security mechanisms based on regular machine learning techniques

ThursdayOct 25, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Daniel Dadush Title:Balancing vectors in any normAbstract:opens in new windowin html    pdfopens in new window

In the vector balancing problem, we are given N vectors v_1,..., v_N in an n-dimensional normed space, and our goal is to assign signs to them, so that the norm of their signed sum is as small as possible. The balancing constant of the vectors is the smallest number beta, such that any subset of the vectors can be balanced so that their signed sum has norm at most beta.
The vector balancing constant generalizes combinatorial discrepancy, and is related to rounding problems in combinatorial optimization, and to the approximate Caratheodory theorem. We study the question of efficiently approximating the vector balancing constant of any set of vectors, with respect to an arbitrary norm. We show that the vector balancing constant can be approximated in polynomial time to within factors logarithmic in the dimension, and is characterized by (an appropriately optimized version of) a known volumetric lower bound. Our techniques draw on results from geometric functional analysis and the theory of Gaussian processes. Our results also imply an improved approximation algorithm for hereditary discrepancy.
Joint work with Aleksandar Nikolov, Nicole Tomczak-Jaegermann and Kunal Talwar.

WednesdayOct 17, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Alexander Elashvili Title:Cyclic elements in semisimple Lie algebrasAbstract:opens in new windowin html    pdfopens in new window

In the talk I will tell about a theory of cyclic elements in semisimple Lie algebras. This notion was introduced by Kostant, who associated a cyclic element with the principal nilpotent and proved that it is regular semisimple. In particular, I will tell about the classification of all nilpotents giving rise to semisimple and regular semisimple cyclic elements. The results are from my joint work with V. Kac and E. Vinberg.

WednesdayOct 17, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Adam KapelnerTitle:Harmonizing Fully Optimal Designs with Classic Randomization in Fixed Trial ExperimentsAbstract:opens in new windowin html    pdfopens in new window

There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in advance and subjects can be divided optimally into two groups based on a criterion of homogeneity or "imbalance" between the two groups. These designs are far from random. This talk seeks to understand the benefits and the costs over classic randomization in the context of different performance criterions such as Efron's worst-case analysis. In the criterion that we motivate, randomization beats optimization. However, the optimal design is shown to lie between these two extremes. Much-needed further work will provide a procedure to find this optimal designs in different scenarios in practice. Until then, it is best to randomize.

ThursdaySep 13, 201813:30
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Maria GorelikTitle:Bounded modules for finite-dimensional Lie superalgebras.Abstract:opens in new windowin html    pdfopens in new window
Let g be a basic classical Lie superalgebra. A weight module is called bounded if the dimensions of its weight spaces are uniformly bounded. Theorems of Fernando-Futorny and Dimitrov-Matheiu-Penkov reduce the classification of irreducible bounded modules to the classification of irreducible bounded highest weight modules L(\lambda). For Lie algebras the bounded modules L(\lambda) were classified by O. Mathieu. They exist only for the series A and C. For Lie superalgebras L(\lambda) have been classified in all cases except for five series of low-rank orthosymplectic superalgebras. Using the Enright functor, I will show how the boundness of L(\lambda) over g can be reduced to the boundness over simple Lie algebras and the orthosymplectic algebra osp(1|2n). This work is a joint project with D. Grantcharov.
ThursdaySep 13, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Maria GorelikTitle:Enright functor without long formulae.Abstract:opens in new windowin html    pdfopens in new window

I will define the Enright functor for contragredient Lie superalgebras and discuss its properties. If time permits, we may discuss a proof of Arakawa's Theorem for osp(1|2l).
This work is a joint project with V. Serganova.

ThursdaySep 06, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Arkady Berenstein Title:Noncommutative clustersAbstract:opens in new windowin html    pdfopens in new window

The goal of my talk (based on joint work with Vladimir Retakh) is to introduce noncommutative clusters and their mutations, which can be viewed as generalizations of both classical and quantum cluster structures.

Each noncommutative cluster S is built on a torsion-free group G and a certain collection of its automorphisms. We assign to S a noncommutative algebra A(S) related to the group algebra of G, which is an analogue of the cluster algebra, and establish a noncommutative version of Laurent Phenomenon in some algebras A(S).  

"Cluster groups" G for which the Noncommutative Laurent Phenomenon holds include triangular groups of marked surfaces (closely related to the fundamental groups of their ramified double covers), free group of rank 2, and principal noncommutative tori which exist for any exchange matrix B.

TuesdaySep 04, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Nir GadishTitle:Stable character theory and representation stability.Abstract:opens in new windowin html    pdfopens in new window

Various algebraic and topological situations give rise to compatible sequences of representations of different groups, such as the symmetric groups, with stable asymptotic behavior. Representation stability is a recent approach to studying such sequences, which has proved effective for extracting important invariants. Coming from this point of view, I will introduce the associated character theory, which formally explains many of the approach's strengths (in char 0). Central examples are simultaneous characters of all symmetric groups, or of all Gl(n) over some finite field. Their mere existence gives applications to statistics of random matrices over finite fields, and raises many combinatorial questions.

ThursdayAug 30, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Assaf Naor Title:Coarse (non)Universality of Alexandrov SpacesAbstract:opens in new windowin html    pdfopens in new window

We will show that there exists a metric space that does not admit a coarse embedding into any Alexandrov space of global nonpositive curvature, thus answering a question of Gromov (1993). In contrast, any metric space embeds coarsely into an Alexandorv space of nonnegative curvature. Based on joint works with Andoni and Neiman, and Eskenazis and Mendel.

TuesdayAug 28, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Mattias Jonsson Title:Degenerations of p-adic volume forms.Abstract:opens in new windowin html    pdfopens in new window

Let $X$ be an $n$-dimensional smooth projective variety over a non-Archimedean local field $K$, such as the $p$-adic numbers, and let $\omega$ be an global $n$-form on $X$. The set $X(K)$ of $K$-points on $X$ has the structure of a $K$-analytic manifold, and $\omega$ induces a measure $|\omega|$ on $X(K)$. For any finite extension $K'$ of $K$, there is a natural continuous map from $X(K')$ to the Berkovich analytification $X^{\mathrm{an}}$ of $X$. We study the asymptotics of the images of the measures $|\omega\otimes_KK'|$ on $X^{\mathrm{an}}$ as $K'$ runs through towers of finite extensions of $K$. This is joint work with Johannes Nicaise.

ThursdayAug 16, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:David Ellis Title:Random graphs with constant r-ballsAbstract:opens in new windowin html    pdfopens in new window

Let F be a fixed infinite, vertex-transitive graph. We say a graph G is `r-locally F' if for every vertex v of G, the ball of radius r and centre v in G is isometric to the ball of radius r in F. For each positive integer n, let G_n be a graph chosen uniformly at random from the set of all unlabelled, n-vertex graphs that are r-locally F. We investigate the properties that the random graph G_n has with high probability --- i.e., how these properties depend on the fixed graph F.

We show that if F is a Cayley graph of a torsion-free group of polynomial growth, then there exists a positive integer r_0 such that for every integer r at least r_0, with high probability the random graph G_n = G_n(F,r) defined above has largest component of size between n^{c_1} and n^{c_2}, where 0 < c_1 < c_2 < 1 are constants depending upon F alone, and moreover that G_n has a rather large automorphism group. This contrasts sharply with the random d-regular graph G_n(d) (which corresponds to the case where F is replaced by the infinite d-regular tree).

Our proofs use a mixture of results and techniques from group theory, geometry and combinatorics.

We obtain somewhat more precise results in the case where F is L^d (the standard Cayley graph of Z^d): for example, we obtain quite precise estimates on the number of n-vertex graphs that are r-locally L^d, for r at least linear in d.

Many intriguing open problems remain: concerning groups with torsion, groups with faster than polynomial growth, and what happens for more general structures than graphs.

This is joint work with Itai Benjamini (WIS).

TuesdayJul 31, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Roberto Rubio Title:On exceptional symmetric Gelfand pairsAbstract:opens in new windowin html    pdfopens in new window
A pair of a reductive linear algebraic group G and a subgroup H is said to be a Gelfand pair when, roughly speaking, the representation of G on $\mathcal{C}^\infty(G/H)$ is multiplicity free. Symmetric pairs, those where H is the fixed-point set of an involution on G, give many examples of Gelfand pairs. The Aizenbud-Gourevitch criterion, based on a previous distributional criterion by Gelfand and Kazhdan, was introduced to prove that many classical symmetric pairs are Gelfand pairs. For complex symmetric pairs, it says that the Gelfand property holds if the pair and all its descendants (centralizers of admissible semisimple elements) satisfy a certain regularity condition (expressed in terms of invariant distributions). In this talk we will focus on the twelve exceptional complex symmetric pairs and combine the Aizenbud-Gourevitch criterion with Lie-theoretic techniques. We will first introduce the concept of a pleasant pair, which will allow us to prove regularity for many pairs. We will then show how to compute descendants visually, thanks to the Satake diagram. The combination of these results with the criterion yields that nine out of the twelve pairs are Gelfand, and that the Gelfand property for the remaining three is equivalent to the regularity of one exceptional and two classical symmetric pairs.
TuesdayJul 31, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Edriss S. TitiTitle:On Recent Advances of the 3D Euler Equations by Means of ExamplesAbstract:opens in new windowin html    pdfopens in new window

abstract

ThursdayJul 26, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Eliran Subag Title:Free energy landscapes in spherical spin glassesAbstract:opens in new windowin html    pdfopens in new window

I will describe a new approach to the study of spherical spin glass models via free energy landscapes, defined by associating to interior points of the sphere the free energy computed only over the spherical band around them.
They are closely related to several fundamental objects from spin glass theory: the TAP free energy, pure states decomposition, overlap distribution, and temperature chaos. I will explain some of of those connections.

TuesdayJul 17, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Anthony JosephTitle:Some comments on the lowest degree appearances of representations.Abstract:opens in new windowin html    pdfopens in new window

TBA

TuesdayJul 10, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Anthony JosephTitle:Some comments on the lowest degree appearances of representations.Abstract:opens in new windowin html    pdfopens in new window

TBA

ThursdayJul 05, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Jonathan Hermon Title:The exclusion process (usually) mixes faster than independent particles.Abstract:opens in new windowin html    pdfopens in new window
The exclusion process is one of the most basic and best studied processes in the literature on interacting particle systems, with connections to card shuffling and statistical mechanics. It has been one of the major examples driving the study of mixing-times. In the exclusion process on an n-vertex graph we have k black particles and n-k white particles, one per site. Each edge rings at rate 1. When an edge rings, the particles occupying its end-points switch positions. Oliveira conjectured that the order of the mixing time of the process is at most that of the mixing-time of k independent particles. Together with Richard Pymar we verify this up to a constant factor for d-regular (or bounded degree) graphs 1 in various cases: (1) the degree d is at least logarithmic in n, or (2) the spectral-gap of a single walk is small (at most log number of vertices to the power 4) or (3) when the number of particles k is roughly n^a for some constant 0 n^c $) is within a $\log \log n$ factor from Oliveira's conjecture. As applications we get new mixing bounds: (a) $O(\log n \log \log n)$ for expanders, (b) order $ \log (dk) $ for the hypercube ${0,1}^d$ and (c) order $(diameter)^2 \log k $ for vertex-transitive graphs of moderate growth and for the giant component of supercritical percolation on a torus
ThursdayJul 05, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Netalee Efrat Title:Beyond the limitations of sensors and displaysAbstract:opens in new windowin html    pdfopens in new window

In this talk I explore various limitations of sensors and displays, and suggest new ways to overcome them.
These include:

  1. The limited 2D displays of today's screens - I will show how we can design new displays that enable us to see in 3D *without* any glasses.
  2. The limited spatial resolution of images - I will discuss the crucial factors for successful Super-Resolution.
  3. The poor image quality due to motion blur (due to camera motion or scene motion) - I will present a new approach for Blind Non-Uniform Deblurring.
WednesdayJul 04, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Alexander Volfovsky Title:Causal inference from complex observational data Abstract:opens in new windowin html    pdfopens in new window

A classical problem in causal inference is that of matching treatment units to control units in an observational dataset. This problem is distinct from simple estimation of treatment effects as it provides additional practical interpretability of the underlying causal mechanisms that is not available without matching. Some of the main challenges in developing matching methods arise from the tension among (i) inclusion of as many covariates as possible in defining the matched groups, (ii) having matched groups with enough treated and control units for a valid estimate of average treatment effect in each group, (iii) computing the matched pairs efficiently for large datasets, and (iv) dealing with complicating factors such as non-independence among units. We propose the Fast Large-scale Almost Matching Exactly (FLAME) framework to tackle these problems for categorical covariates. At its core this framework proposes an optimization objective for match quality that captures covariates that are integral for making causal statements while encouraging as many matches as possible. We demonstrate that this framework is able to construct good matched groups on relevant covariates and further extend the methodology to incorporate continuous and other complex covariates. related papers: https://arxiv.org/abs/1707.06315, https://arxiv.org/abs/1806.06802

TuesdayJul 03, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Moshe KamenskyTitle:Fields with free operators in positive characteristicAbstract:opens in new windowin html    pdfopens in new window

Moosa and Scanlon defined a general notion of  "fields with operators'', that generalizes those of difference and differential fields. In the case of  "free'' operators in characteristic zero they also analyzed the basic model-theoretic properties of the theory of such fields. In particular, they showed in this case the existence of the model companion, a construction analogous to that of algebraically closed fields for usual fields. In positive characteristic, they provided an example showing that the model companion need not exist.
 
I will discuss work, joint with Beyarslan, Hoffman and Kowalski, that completes the description of the free case, namely, it provides a full classification of those free operators for which the model companion exists. Though the motivating question is model theoretic, the description and the proof are completely algebraic and geometric. If time permits, I will discuss additional properties, such as quantifier elimination. All notions related to model theory and to fields with operators will be explained (at least heuristically).

SPECIAL NOTE: this will be part of a model theory day. Thus, the talk will be preceded by an introduction to algebraic geometry by the same speaker, 10-10:45 (in Room 1) and followed by a talk by Nick Ramsey " Classification Theory and the Construction of PAC Fields" , 14-16 (in Room 155). See https://mt972.weebly.com/ for more information

MondayJul 02, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Ariel Procaccia Title:Extreme DemocracyAbstract:opens in new windowin html    pdfopens in new window

Technological advances have changed every aspect of our lives in recent decades, yet, for the most part, the same systems of democratic decision making have been in place for centuries. I will argue that computer scientists can help rethink the practice of democracy, as well as its potential applications. I will focus on three emerging paradigms that go far beyond your run-of-the-mill election: (i) liquid democracy, an approach that allows voters to transitively delegate their votes; (ii) participatory budgeting, whereby residents collectively decide how to spend their local government's budget; and (iii) virtual democracy, which employs instant elections among machine learning models of real voters to address the grand AI challenge of ethical decision making.

ThursdayJun 28, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Omer BobrowskiTitle:Homological connectivity and percolation in random geometric complexesAbstract:opens in new windowin html    pdfopens in new window
Connectivity and percolation are two well studied phenomena in random graphs. In this talk we will discuss higher-dimensional analogues of connectivity and percolation that occur in random simplicial complexes. Simplicial complexes are a natural generalization of graphs, consisting of vertices, edges, triangles, tetrahedra, and higher dimensional simplexes. We will mainly focus on random geometric complexes. These complexes are generated by taking the vertices to be a random point process, and adding simplexes according to their geometric configuration. Our generalized notions of connectivity and percolation use the language of homology - an algebraic-topological structure representing cycles of different dimensions. In this talk we will review some recent progress in characterizing and analyzing these phenomena, as well as describing related phase transitions.
ThursdayJun 28, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Ariel EphratTitle:Looking to Listen at the Cocktail Party: A Speaker-Independent Audio-Visual Model for Speech SeparationAbstract:opens in new windowin html    pdfopens in new window

We present a joint audio-visual model for isolating a single speech signal from a mixture of sounds such as other speakers and background noise. Solving this task using only audio as input is extremely challenging and does not provide an association of the separated speech signals with speakers in the video. In this paper, we present a deep network-based model that incorporates both visual and auditory signals to solve this task. The visual features are used to "focus" the audio on desired speakers in a scene and to improve the speech separation quality. To train our joint audio-visual model, we introduce AVSpeech, a new dataset comprised of thousands of hours of video segments from the Web. We demonstrate the applicability of our method to classic speech separation tasks, as well as real-world scenarios involving heated interviews, noisy bars, and screaming children, only requiring the user to specify the face of the person in the video whose speech they want to isolate. Our method shows clear advantage over state-of-the-art audio-only speech separation in cases of mixed speech. In addition, our model, which is speaker-independent (trained once, applicable to any speaker), produces better results than recent audio-visual speech separation methods that are speaker-dependent (require training a separate model for each speaker of interest).

Joint work with Inbar Mosseri, Oran Lang, Tali Dekel, Kevin Wilson, Avinatan Hassidim, Bill Freeman and Miki Rubinstein of Google Research.

WednesdayJun 27, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Tamir Bendory Title:Estimation in low SNR environment and under group action with application to cryo-EMAbstract:opens in new windowin html    pdfopens in new window

Cryo-electron microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology, enabling reconstruction of molecules at near-atomic resolution.  
Cryo-EM produces a large number of noisy two-dimensional tomographic projection images of a molecule, taken at unknown viewing directions. 
The extreme levels of noise make classical tasks in statistics and signal processing, such as alignment, detection and clustering, very challenging. 
I will start the talk by studying the multi-reference alignment problem, which can be interpreted as a simplified model for cryo-EM. In multi-reference alignment, we aim to estimate multiple signals from circularly-translated, unlabeled, noisy copies. 
In high noise regimes, the measurements cannot be aligned or clustered. Nonetheless, accurate and efficient estimation can be achieved via group-invariant representations (invariant polynomials). Furthermore, such estimators achieve the optimal estimation rate. 
Then, I will show how this framework can be applied to the problem of 2-D classification in cryo-EM. In the last part of the talk, I will introduce the analog invariants of the cryo-EM problem and discuss how they can be used for ab initio modeling.
 

TuesdayJun 26, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Siddhartha SahiTitle:The Capelli eigenvalue problem for Lie superalgebrasAbstract:opens in new windowin html    pdfopens in new window
TBA
TuesdayJun 26, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Horacio G. RotsteinTitle:Network resonance: impedance interactions and frequency response alternating maps (FRAM)Abstract:opens in new windowin html    pdfopens in new window

generation of neuronal network oscillations are not well understood. We view this process as the individual neurons' oscillations being communicated among the nodes in the network, mediated by the impedance profiles of the isolated (uncoupled) individual neurons. In order to test this idea, we developed a mathematical tool that we refer to as the Frequency Response Alternating Map (FRAM). The FRAM describes how the impedances of the individual oscillators interact to generate network responses to oscillatory inputs. It consists of decoupling the non-autonomous part of the coupling term and substituting the reciprocal coupling by a sequence of alternating one-directional forcing effects (cell 1 forces cell 2, which in turn forces cell 1 and so on and so forth). The end result is an expression of the network impedance for each node (in the network) as power series, each term involving the product of the impedances of the autonomous part of the individual oscillators. For linear systems we provide analytical expressions of the FRAM and we show that its convergence properties and limitations.  We illustrate numerically that this convergence is relatively fast. We apply the FRAM to the phenomenon of network resonance to the simplest type of oscillatory network:  two non-oscillatory nodes receiving oscillatory inputs in one or the two nodes. We discuss extensions of the FRAM to include non-linear systems and other types of network architectures.

MondayJun 25, 201816:00
Machine Learning and Statistics SeminarRoom 155
Speaker:Ariel Jaffe / Phd defenceTitle:Spectral methods for unsupervised ensemble learning and latent variable modelsAbstract:opens in new windowin html    pdfopens in new windowNOTE SPECIAL DATE, TIME AND ROOM

The use of latent variables in probabilistic modeling is a standard approach in numerous data analysis applications. In recent years, there has been a surge of interest in spectral methods for latent variable models, where inference is done by analyzing the lower order moments of the observed data. In contrast to iterative approaches such as the EM algorithm, under appropriate conditions spectral methods are guaranteed to converge to the true model parameters given enough data samples.
The focus of the seminar is the development of novel spectral based methods for two problems in statistical machine learning. In the first part, we address unsupervised ensemble learning, where one obtains predictions from different sources or classifiers, yet without knowing the reliability and expertise of each source, and with no labeled data to directly assess it. We develop algorithms to estimate the reliability of the classifiers based on a common assumption that different classifiers make statistically independent errors. In addition, we show how one can detect subsets of classifiers that strongly violate the model of independent errors, in a fully unsupervised manner.
In the second part of the seminar we show how one can use spectral methods to learn the parameters of binary latent variable models. This model has many applications such as overlapping clustering and Gaussian-Bernoulli restricted Boltzmann machines. Our methods are based on computing the eigenvectors of both the second and third moments of the observed variables.
For both problems, we show that spectral based methods can be applied effectively, achieving results that are state of the art in various problems in computational biology and population genetics.

ThursdayJun 21, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Danielle Ezuz Title:Reversible Harmonic MapsAbstract:opens in new windowin html    pdfopens in new window

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. This talk describes a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g. point landmarks, a dense map or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state-of-the-art, while succeeding in correctly mapping key features of the input shapes.

TuesdayJun 19, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Nadav DymTitle:Linear algorithms for computing conformal mappingsAbstract:opens in new windowin html    pdfopens in new window

(joint with Noam Aigerman, Raz Sluzky and Yaron Lipman)
Computing homeomorphisms between surfaces is an important task in shape analysis fields such as computer graphics, medical imaging and  morphology. A fundamental tool for these tasks is solving Dirichlet's problem on an arbitrary Jordan domain with disc topology, where the boundary of the domain is mapped homeomorphically to the boundary of a specific target domain: A convex polygon. By the Rado-Kneser-Choquet Theorem such harmonic mappings are homeomorphisms onto the convex polygon. Standard finite element approximations of harmonic mappings lead to  discrete harmonic mappings, which have been proven to be homeomorphisms as well. Computing the discrete harmonic mappings is very efficient and reliable as the mappings are obtained as the solution of a sparse linear system of equations.

In this talk we show that the methodology above, can be used to compute *conformal* homeomorphisms, for domains with either disc or sphere topology:

By solving Dirichlet's problem with correct boundary conditions, we can compute conformal homeomorphisms from arbitrary Jordan domains to a specific canonical domain- a triangle. The discrete conformal mappings we compute are homeomorphisms, and approximate the conformal homeomorphism uniformly and in H^1. Similar methodology can also be used to conformally map a sphere type surface to a planar Jordan domain, whose edges are identified so that the planar domain has the topology of a sphere.

ThursdayJun 14, 201816:00
Special Guest LectureRoom 1
Speaker:Don ZagierTitle:Units, K-theory, and knotsAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE THE CHANGE IN TIME

  In knot theory and more generally the theory of 3-manifolds various "quantum invariants" like the Witten-Reshetikhin-Turaev or the Kashaev invariant have been much studied in recent years,  in particular because of the famous "volume conjecture" related to the asymptotic growth of the Kashaev invariant.  Rather surprisingly, it transpired a few years ago that these invariants  also have very non-trivial number-theoretical properties, including a kind of weak invariance under the modular group SL(2,Z) ("quantum modular forms") and the experimental discovery of the appearance of certain units in cyclotomic extensions as factors in the asymptotic expansions.  The talk will report on this and specifically on recent joint work with Frank Calegari and Stavros Garoufalidis that constructs such units in a purely algebraic way starting from elements in algebraic K-theory or in the more elementary "Bloch group".  As an unexpected application, this result led to the proof of a well-known conjecture of Nahm on the modularity of certain q-hypergeometric series.

ThursdayJun 14, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Emanuel Milman Title:The Gaussian Double-Bubble and Multi-Bubble ConjecturesAbstract:opens in new windowin html    pdfopens in new window

The classical Gaussian isoperimetric inequality, established in the 70's independently by Sudakov-Tsirelson and Borell, states that the optimal way to decompose $\mathbb{R}^n$ into two sets of prescribed Gaussian measure, so that the (Gaussian) area of their interface is minimal, is by using two complementing half-planes. This is the Gaussian analogue of the classical Euclidean isoperimetric inequality, and is therefore referred to as the "single-bubble" case.

A natural generalization is to decompose $\mathbb{R}^n$ into $q \geq 3$ sets of prescribed Gaussian measure. It is conjectured that when $q \leq n+1$, the configuration whose interface has minimal (Gaussian) area is given by the Voronoi cells of $q$ equidistant points. For example, for $q=3$ (the "double-bubble"conjecture) in the plane ($n=2$), the interface is conjectured to be a "tripod" or "Y" - three rays meeting at a single point in 120 degree angles. For $q=4$ (the "triple-bubble" conjecture) in $\mathbb{R}^3$, the interface is conjectured to be a tetrahedral cone.

We confirm the Gaussian double-bubble and, more generally, multi-bubble conjectures for all $3 \leq q \leq n+1$. The double-bubble case $q=3$ is simpler, and we will explain why.

None of the numerous methods discovered over the years for establishing the classical $q=2$ case seem amenable to the $q \geq 3$ cases, and our method consists of establishing a Partial Differential Inequality satisfied by the isoperimetric profile. To treat $q > 3$, we first prove that locally minimimal configurations must have flat interfaces, and thus convex polyhedral cells. Uniqueness of minimizers up to null-sets is also established.

This is joint work with Joe Neeman (UT Austin).

TuesdayJun 12, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Adi Ditkowski Title:Error inhibiting schemes for differential equations Abstract:opens in new windowin html    pdfopens in new window

Typically, when semi-discrete approximations to time-dependent partial differential equations (PDE) or schemes for ordinary differential equation (ODE) are constructed they are derived such that they are stable and have a specified truncation error $\tau$. Under these conditions, the Lax-Richtmyer equivalence theorem assures that the scheme converges and that the error is, at most, of the order of $|| \tau ||$. In most cases, the error is in indeed of the order of $|| \tau ||$. We demonstrate that schemes can be constructed, whose truncation errors are $\tau$, however, the actual errors are much smaller. This error reduction is made by constructing the schemes such that they inhibit the accumulation of the local errors; therefore they are called Error Inhibiting Schemes (EIS).

MondayJun 11, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Roy Schwartz Title:Trees for Vertex Cuts, Hypergraph Cuts and Minimum Hypergraph BisectionAbstract:opens in new windowin html    pdfopens in new window

In the Minimum Hypergraph Bisection problem, the vertex set of a hypergraph has to be partitioned into two parts of equal size so that the number of hyperedges intersecting both parts is minimized.
This problem is a natural generalization of the well-studied Minimum Bisection problem in graphs.
We present a sharp distinction between Minimum Bisection in hypergraphs and graphs.
Whereas it is well-known that all bi-criteria approximation algorithms for Minimum Bisection in graphs can be extended to hypergraphs with the exact same guarantees, we prove that this is not the case when considering true (i.e., non bi-criteria) approximation algorithms.
Specifically, we show that Minimum Hypergraph Bisection admits an $\tilde{\mathcal{O}}(\sqrt{n})$ approximation algorithm.
However, we also show that any $\alpha$-approximation algorithm for Minimum Hypergraph Bisection implies an approximation of $\Omega(\alpha^{-2})$ for Densest $k$-Subgraph.
Thus, assuming the exponential time hypothesis there is no efficient approximation algorithm for Minimum Hypergraph Bisection with an approximation ratio $n^{poly(\log{\log{n}})}$.

In particular, Minimum Hypergraph Bisection is much harder to approximate than Minimum Bisection in graphs, for which a logarithmic approximation algorithm exists.
If time permits, the problem of constructing trees that are cut sparsifiers for hypergraph and vertex cuts will also be discussed.
While similar trees lie at the heart of powerful algorithms for Minimum Bisection in graphs, we prove that this is not the case for hypergraphs.
Joint work with Harald R\"{a}cke and Richard Stotz.

ThursdayJun 07, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Ohad Feldheim (HUJI) and Eviatar Procaccia (Texas A&M) Title:Double seminarAbstract:opens in new windowin html    pdfopens in new window

Ohad Feldheim: Convergence of a quantile admission processes
Abstract: Consider the following stochastic model for a growing set. At time 0 the model consists of the singleton S = {-infty}. At every subsequent time, two i.i.d. samples, distributed according to some distribution D on R, are suggested as candidates for S. If the smaller among the two is closer to at least a fraction of r of the current elements of S (in comparison with the larger one), then it is admitted into S.
How will the distribution of the members of S evolve over time as a function of r and D?
This model was suggested by Alon, Feldman, Mansour, Oren and Tennenholtz as a model for the evolution of an exclusive social group. We'll show that the empirical distribution of the elements of S converges to a (not-necessarily deterministic) limit distribution for any r and D.
This we do by relating the process to a random walk in changing environment. The analysis of this random walk involves various classical exponential concentration inequalities as well as a new general inequality concerning mean and minimum of independent random variables.
Joint work with Naomi Feldheim

Eviatar Procaccia:  Stabilization of Diffusion Limited Aggregation in a Wedge
Abstract: We prove a discrete Beurling estimate for the harmonic measure in a wedge in $\mathbf{Z}^2$, and use it to show that Diffusion Limited Aggregation (DLA) in a wedge of angle smaller than $\pi/4$ stabilizes. This allows to consider the infinite DLA and questions about the number of arms, growth and dimension. I will present some conjectures and open problems.

ThursdayJun 07, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Mark Sheinin Title:Leveraging Hidden Structure in Unstructured IlluminationAbstract:opens in new windowin html    pdfopens in new window

Artificial illumination plays a vital role in human civilization. In computer vision, artificial light is extensively used to recover 3D shape, reflectance, and further scene information. However, in most computer vision applications using artificial light, some additional structure is added to the illumination to facilitate the task at hand. In this work, we show that the ubiquitous alternating current (AC) lights already have a valuable inherent structure that stems from bulb flicker. By passively sensing scene flicker, we reveal new scene information which includes: the type of bulbs in the scene, the phases of the electric grid up to city scale, and the light transport matrix. This information yields unmixing of reflections and semi-reflections, nocturnal high dynamic range, and scene rendering with bulbs not observed during acquisition. Moreover, we provide methods that enable capturing scene flicker using almost any off-the-shelf camera, including smartphones.

In underwater imaging, similar structures are added to illumination sources to overcome the limited imaging range. In this setting, we show that by optimizing camera and light positions while taking the effect of light propagation in scattering media into account we achieve superior imaging of underwater scenes while using simple, unstructured illumination.

MondayJun 04, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Or SattathTitle:Quantum Tokens for Digital SignaturesAbstract:opens in new windowin html    pdfopens in new window

The fisherman caught a quantum fish. "Fisherman, please let me go", begged the fish, "and I will grant you three wishes". The fisherman agreed. The fish gave the fisherman a quantum computer, three quantum signing tokens and his classical public key. The fish explained: "to sign your three wishes, use the tokenized signature scheme on this quantum computer, then show your valid signature to the king, who owes me a favor".
The fisherman used one of the signing tokens to sign the document "give me a castle!" and rushed to the palace. The king executed the classical verification algorithm using the fish's public key, and since it was valid, the king complied.
The fisherman's wife wanted to sign ten wishes using their two remaining signing tokens. The fisherman did not want to cheat, and secretly sailed to meet the fish. "Fish, my wife wants to sign ten more wishes". But the fish was not worried: "I have learned quantum cryptography following the previous story (The Fisherman and His Wife by the brothers Grimm). The quantum tokens are consumed during the signing. Your polynomial wife cannot even sign four wishes using the three signing tokens I gave you".
"How does it work?" wondered the fisherman. "Have you heard of quantum money? These are quantum states which can be easily verified but are hard to copy. This tokenized quantum signature scheme extends Aaronson and Christiano's quantum money scheme, and a variant by Zhandry, which is why the signing tokens cannot be copied".
"Does your scheme have additional fancy properties?" the fisherman asked. "Yes, the scheme has other security guarantees: revocability, testability and everlasting security. Furthermore, if you're at sea and your quantum phone has only classical reception, you can use this scheme to transfer the value of the quantum money to shore", said the fish, and swam away.

Joint work with Shalev Ben-David. https://arxiv.org/abs/1609.09047

ThursdayMay 31, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Bhaswar Bhattacharya (UPenn) and Elliot Paquette (Ohio) Title:Double SeminarAbstract:opens in new windowin html    pdfopens in new window

Bhaswar Bhattacharya: Large Deviation Variational Problems in Random Combinatorial Structures

The upper tail problem in the Erdos-Renyi random graph $G\sim\mathcal{G}_{n,p}$, where every edge is included independently with probability $p$, is to estimate the probability that the number of copies of a graph $H$ in $G$ exceeds its expectation by a factor of $1+\delta$. The arithmetic analog of this problem counts the number of $k$-term arithmetic progressions in a random subset of $\{1, 2, \ldots, N\}$, where every element is included independently with probability $p$. The recently developed framework of non-linear large deviations (Chatterjee and Dembo (2016) and Eldan (2017)) shows that the logarithm of these tail probabilities can be reduced to a natural variational problem on the space of weighted graphs/functions. In this talk we will discuss methods for solving these variational problems in the sparse regime ($p \rightarrow 0$), and show how the solutions are often related to extremal problems in combinatorics. (This is based on joint work with Shirshendu Ganguly, Eyal Lubetzky, Xuancheng Shao, and Yufei Zhao.)

Elliot Paquette: Random matrix point processes via stochastic processes

In 2007, Virag and Valko introduced the Brownian carousel, a dynamical system that describes the eigenvalues of a canonical class of random matrices. This dynamical system can be reduced to a diffusion, the stochastic sine equation, a beautiful probabilistic object requiring no random matrix theory to understand. Many features of the limiting eigenvalue point process, the Sine--beta process, can then be studied via this stochastic process. We will sketch how this stochastic process is connected to eigenvalues of a random matrix and sketch an approach to two questions about the stochastic sine equation: deviations for the counting Sine--beta counting function and a functional central limit theorem.

TuesdayMay 29, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Max Gurevich Title:Branching laws for non-generic representationsAbstract:opens in new windowin html    pdfopens in new window

The celebrated Gan-Gross-Prasad conjectures aim to describe the branching behavior of representations of classical groups, i.e., the decomposition of irreducible representations when restricted to a lower rank subgroup.

These conjectures, whose global/automorphic version bear significance in number theory, have thus far been formulated and resolved for the generic case.

In this talk, I will present a newly formulated rule in the p-adic setting (again conjectured by G-G-P) for restriction of representations in non-generic Arthur packets of GL_n.

Progress towards the proof of the new rule takes the problem into the rapidly developing subject of quantum affine algebras. These techniques use a version of the Schur-Weyl duality for affine Hecke algebras, combined with new combinatorial information on parabolic induction extracted by Lapid-Minguez.

MondayMay 28, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Kevin Leyton-Brown Title:Learning as a Tool for Algorithm Design and Beyond-Worst-Case AnalysisAbstract:opens in new windowin html    pdfopens in new window

All known algorithms for solving NP-complete problems require exponential time in the worst case; however, these algorithms nevertheless solve many problems of practical importance astoundingly quickly, and are hence relied upon in a broad range of applications. This talk is built around the observation that "Empirical Hardness Models" - statistical models that predict algorithm runtime on novel instances from a given distribution - work surprisingly well. These models can serve as powerful tools for algorithm design, specifically by facilitating automated methods for algorithm design and for constructing algorithm portfolios. They also offer a statistical alternative to beyond-worst-case analysis and a starting point for theoretical investigations.

bio at http://www.cs.ubc.ca/~kevinlb/bio.html

 

TuesdayMay 22, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Itay Glazer Title:On singularity properties of convolution of algebraic morphisms Abstract:opens in new windowin html    pdfopens in new window

In analysis, a convolution of two functions usually results in a smoother, better behaved function. Given two morphisms f,g from algebraic varieties X,Y to an algebraic group G, one can define a notion of convolution of these morphisms. Analogously to the analytic situation, this operation yields a morphism (from X x Y to G) with improved smoothness properties.

In this talk, I will define a convolution operation and discuss some of its properties. I will then present a recent result; if G is an algebraic group, X is smooth and absolutely irreducible, and f:X-->G is a dominant map, then after finitely many self convolutions of f, we obtain a morphism with the property of being flat with fibers of rational singularities (a property which we call (FRS)).

Moreover, Aizenbud and Avni showed that the (FRS) property has an equivalent analytic characterization, which leads to various applications such as counting points of schemes over finite rings, representation growth of certain compact p-adic groups and arithmetic groups of higher rank, and random walks on (algebraic families of) finite groups. We will discuss some of these applications, and maybe some of the main ideas of the proof of the above result.

Joint with Yotam Hendel.

ThursdayMay 17, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Ron Peled Title:The fluctuations of random surfacesAbstract:opens in new windowin html    pdfopens in new window

Random surfaces in statistical physics are commonly modeled by a real-valued function phi on a lattice, whose probability density penalizes nearest-neighbor fluctuations. Precisely, given an even function V, termed the potential, the energy H(phi) is computed as the sum of V over the nearest-neighbor gradients of phi, and the probability density of phi is set proportional to exp(-H(phi)). The most-studied case is when V is quadratic, resulting in the so-called Gaussian free field. Brascamp, Lieb and Lebowitz initiated in 1975 the study of the global fluctuations of random surfaces for other potential functions and noted that understanding is lacking even in the case of the quartic potential, V(x)=x^4. We will review the state of the art for this problem and present recent work with Alexander Magazinov which finally settles the question of obtaining upper bounds for the fluctuations for the quartic and many other potential functions.

ThursdayMay 17, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Matan Sela Title:Deep Semi-supervised 3D Face ReconstructionAbstract:opens in new windowin html    pdfopens in new window

Fast and robust three-dimensional reconstruction of facial geometric structure from a single image is a challenging task with numerous applications in computer vision and graphics. We propose to leverage the power of convolutional neural networks (CNNs) to produce highly detailed face reconstruction directly from a single image. For this purpose, we introduce an end-to-end CNN framework which constructs the shape in a coarse-to-fine fashion. The proposed architecture is composed of two main blocks, a network which recovers the coarse facial geometry (CoarseNet), followed by a CNN which refines the facial features of that geometry (FineNet). To alleviate the lack of training data for face reconstruction, we train our model using synthetic data as well as unlabeled facial images collected from the internet. The proposed model successfully recovers facial geometries from real images, even for faces with extreme expressions and under varying lighting conditions. In this talk, I will summarize three papers that were published at 3DV 2016, CVPR 2017 (as an oral presentation), and ICCV 2017.

Bio: Matan Sela holds a Ph.D in Computer Science from the Technion - Israel Institute of Technology. He received B.Sc. and M.Sc. (both with honors) in electrical engineering, both from The Technion - Israel Institute of Technology in 2012 and 2015, respectively. During summer 2017, he was a research intern at Google, Mountain View, California. His interests are Machine Learning, Computer Vision, Computer Graphics, Geometry Processing and any combination of thereof.

TuesdayMay 15, 201816:00
Seminar in Geometry and TopologyRoom 1
Speaker:Midory Komatsudanu QuispeTitle:On the Generic Rank of the Baum-Bott MapAbstract:opens in new windowin html    pdfopens in new window

The Baum-Bott indexes are important local invariants for singular holomorphic foliations by curves with isolated singularities. On a compact complex manifold, we consider foliations with fixed cotangent bundle. Then, the Baum-Bott map associates to a foliation its Baum-Bott indexes on its singularities. We focus on foliations on the projective space and we are interested in the generic rank of that map. The generic rank for foliations on the projective plane is known. For high-dimensional projectives spaces, we give an upper bound and in some cases we determine the generic rank.

TuesdayMay 15, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Leonard Schulman Title:Explicit Binary Tree Codes with Polylogarithmic Size AlphabetAbstract:opens in new windowin html    pdfopens in new windowNOTE SPECIAL DAY (TUESDAY)

This paper makes progress on the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size.

For every constant delta < 1 we give an explicit binary tree code with distance delta and alphabet size poly(log n), where n is the depth of the tree. This is the first improvement over a two-decade-old construction that has an exponentially larger alphabet of size poly(n).

As part of the analysis, we prove a bound on the number of positive integer roots a real polynomial can have in terms of its sparsity with respect to the Newton basis---a result of independent interest.

Joint work with G. Cohen and B. Haeupler

ThursdayMay 10, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:David Jerison (MIT) and Ron Rosenthal (Technion)Title:DOUBLE TALKAbstract:opens in new windowin html    pdfopens in new window

David Jerison: Localization of eigenfunctions via an effective potential
We discuss joint work with Douglas Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator $L u = - \mbox{div} (A \nabla u) + Vu$ on a Lipschitz domain $\Omega$ and, more generally, on a manifold with or without boundary. The eigenfunctions of $L$ are often localized, as a result of disorder of the potential $V$, the matrix of coefficients $A$, irregularities of the boundary, or all of the above. In earlier work, Filoche and Mayboroda introduced the function $u$ solving $Lu = 1$, and showed numerically that it strongly reflects this localization. Here, we deepen the connection between the eigenfunctions and this {\em landscape} function $u$ by proving that its reciprocal $1/u$ acts as an {\em effective potential}. The effective potential governs the exponential decay of the eigenfunctions of the system and delivers information on the distribution of eigenvalues near the bottom of the spectrum.

Ron Rosenthal: Eigenvector correlation in the complex Ginibre ensemble
The complex Ginibre ensemble is a non-Hermitian random matrix on C^N with i.i.d. complex Gaussian entries normalized to have mean zero and variance 1=N. Unlike the Gaussian unitary ensemble, for which the eigenvectors are orthogonal, the geometry of the eigenbases of the Ginibre ensemble are not particularly well understood. We will discuss a some results regarding the analytic and algebraic structure of eigenvector correlations in this matrix ensemble. In particular, we uncover an extended algebraic structure which describes the asymptotic behavior (as N goes to infinity) of these correlations. Our work extends previous results of Chalker and Mehlig [CM98], in which the correlation for pairs of eigenvectors was computed. Based on a joint work with Nick Crawford.

ThursdayMay 10, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Lihi Zelnik-ManorTitle:Maintaining Internal Image Statistics in Synthesized ImagesAbstract:opens in new windowin html    pdfopens in new window

Recent work has shown impressive success in automatically creating new images with desired properties such as transferring painterly style, modifying facial expressions or manipulating the center of attention of the image. In this talk I will discuss two of the standing challenges in image synthesis and how we tackle them:
- I will describe our efforts in making the synthesized images more photo-realistic.
- I will further show how we can broaden the scope of data that can be used for training synthesis networks, and with that provide a solution to new applications.

WednesdayMay 09, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Richard Olshen Title:V(D)J Diversity of Subsets of T and B Cells, Statistics and Probability Abstract:opens in new windowin html    pdfopens in new window

This talk will include an introduction to the topic of V(D)J rearrangements of particular subsets of T cells and B cells of the adaptive human immune system, in particular of IgG heavy chains. There are many statistical problems that arise in trying to understand these cells. They involve estimating aspects of functionals of discrete probabilities on (random) finite sets. Topics include but are not limited to exchangeability, estimating non-centrality parameters, and estimating covariance matrices from what are called "replicates" that have been amplified by the PCR process and (partially) sequenced.

I have received considerable assistance from Lu Tian, and also Yi Liu; as well, I have been helped considerably by Andrew Fire and Scott Boyd, and also Jorg Goronzy

TuesdayMay 08, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Leah Edelstein-KeshetTitle:Coupling mechanics and chemical signaling in cells: from single cell to the collectiveAbstract:opens in new windowin html    pdfopens in new window

Single cells and cells in a tissue respond to stimuli by deforming, changing their shape, and/or moving. Some of these responses can be understood from the underlying biochemical signaling, a topic that has been of interest to both biologists and modelers. In our recent work, my group has studied the link between mechanical tension on cells and their internal chemical signaling. (Our primary focus has been, and remains, that of Rho proteins.) Here I will describe a simple "toy model" that captures key aspects of what is known biologically. The model is simple enough to understand mathematically, and yet capable fo displaying several regimes of behavior consistent with experimental observations. I describe how we investigated the model in a single cell, and how this was then used to capture multiple cells that interact with one another mechanically. We find waves of expansion and contraction that sweep through the model "tissue" is certain parameter regimes. This work is joint with Cole Zmurchok and Dhanajay Bhaskar.

MondayMay 07, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Yuval Dagan Title:Detecting Correlations with Little Memory and CommunicationAbstract:opens in new windowin html    pdfopens in new window

We study the problem of identifying correlations in multivariate data, under information constraints:
Either on the amount of memory that can be used by the algorithm, or the amount of communi- cation when the data is distributed across several machines. We prove a tight trade-off between the memory/communication complexity and the sample complexity, implying (for example) that to detect pairwise correlations with optimal sample complexity, the number of required mem-ory/communication bits is at least quadratic in the dimension. Our results substantially improve those of Shamir (2014), which studied a similar question in a much more restricted setting. To the best of our knowledge, these are the first provable sample/memory/communication trade-offs for a practical estimation problem, using standard distributions, and in the natural regime where the memory/communication budget is larger than the size of a single data point. To derive our theorems, we prove a new information-theoretic result, which may be relevant for studying other information-constrained learning problems.
Joint work with Ohad Shamir

TuesdayMay 01, 201814:30
Foundations of Computer Science SeminarRoom Pekeris
Speaker:Igor Shinkar Title:Probabilistic Checking against Non-Signaling Strategies from Linearity TestingAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DATE AND ROOM

Non-signaling strategies are collections of distributions with certain non-local correlations that have been studied recently in the context of delegation of computation.
In this talk I will discuss a recent result showing that the Hadamard based PCP of [ALMSS'92] is sound against non-signaling strategies. As part of the proof, we study the classical problem of linearity testing [BLR'93] in the setting of non-signaling strategies, and prove that any no-signaling strategy that passes the linearity test with high probability must be close to a quasi-distribution over linear functions.

Joint work with Alessandro Chiesa and Peter Manohar (UC Berkeley).

ThursdayApr 26, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Anirban Basak Title:Local weak limits of Ising and Potts measures on locally tree-like graphsAbstract:opens in new windowin html    pdfopens in new window

Consider a sequence of growing graphs converging locally weakly to an infinite (possibly random) tree. As there are uncountably many Ising and Potts Gibbs measures on the limiting tree in the low-temperature regime it is not apriori clear whether the local weak limit of such measures exists and if so, identifying the limit remains a challenge. In this talk, I will describe these limits. The talk is based on joint works with Amir Dembo and Allan Sly.

ThursdayApr 26, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Sharon Fogel (Tel-Aviv University) and Hadar Averbuch-Elor (Tel Aviv University and Amazon AI) Title:Clustering-driven Deep Embedding with Pairwise ConstraintsAbstract:opens in new windowin html    pdfopens in new window

Recently, there has been increasing interest to leverage the competence of neural networks to analyze data. In particular, new clustering methods that employ deep embeddings have been presented.

In this talk, we depart from centroid-based models and suggest a new framework, called Clustering-driven deep embedding with PAirwise Constraints (CPAC), for non-parametric clustering using a neural network. We present a clustering-driven embedding based on a Siamese network that encourages pairs of data points to output similar representations in the latent space. Our pair-based model allows augmenting the information with labeled pairs to constitute a semi-supervised framework. Our approach is based on analyzing the losses associated with each pair to refine the set of constraints.
We show that clustering performance increases when using this scheme, even with a limited amount of user queries.
We present state-of-the-art results on different types of datasets and compare our performance to parametric and non-parametric techniques.

MondayApr 23, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Lior Gishboliner Title:A Generalized Turan Problem and Its ApplicationsAbstract:opens in new windowin html    pdfopens in new window

Our first theorem is a hierarchy theorem for the query complexity of testing graph properties with one-sided error; more precisely, we show that for every sufficiently fast-growing function f from (0,1) to the natural numbers, there is a graph property whose one-sided-error query complexity is precisely f(\Theta(\epsilon)). No result of this type was previously known for any f which is super-polynomial. Goldreich [ECCC 2005] asked to exhibit a graph property whose query complexity is exponential in 1/\epsilon. Our hierarchy theorem partially resolves this problem by exhibiting a property whose one-sided-error query complexity is exponential in 1/\epsilon. We also use our hierarchy theorem in order to resolve a problem raised by Alon and Shapira [STOC 2005] regarding testing relaxed versions of bipartiteness.

Our second theorem states that for any function f there is a graph property whose one-sided-error query complexity is at least f(\epsilon) while its two-sided-error query complexity is only polynomial in 1/\epsilon. This is the first indication of the surprising power that two-sided-error testing algorithms have over one-sided-error ones, even when restricted to properties that are testable with one-sided error. Again, no result of this type was previously known for any f that is super-polynomial.

The above theorems are derived from a graph theoretic result which we think is of independent interest, and might have further applications. Alon and Shikhelman [JCTB 2016] introduced the following generalized Turan problem: for fixed graphs H and T, and an integer n, what is the maximum number of copies of T, denoted by ex(n,T,H), that can appear in an n-vertex H-free graph? This problem received a lot of attention recently, with an emphasis on T = C_3, H=C_{2m+1}. Our third theorem gives tight bounds for ex(n,C_k,C_m) for all the remaining values of k and m.
Joint work with Asaf Shapira.

TuesdayApr 17, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Cy Maor Title:Elasticity and curvature: the elastic energy of non-Euclidean thin bodiesAbstract:opens in new windowin html    pdfopens in new window

Non-Euclidean, or incompatible elasticity is an elastic theory for bodies that do not have a reference (stress-free) configuration. It applies to many systems, in which the elastic body undergoes inhomogeneous growth (e.g. plants, self-assembled molecules). Mathematically, it is a question of finding the "most isometric" immersion of a Riemannian manifold (M,g) into Euclidean space of the same dimension, by minimizing an appropriate energy functional.

Much of the research in non-Euclidean elasticity is concerned with elastic bodies that have one or more slender dimensions (such as leaves), and finding appropriate dimensionally-reduced models for them.

In this talk I will give an introduction to non-Euclidean elasticity, and then focus on thin bodies and present some recent results on the relations between their elastic behavior and their curvature.

Based on a joint work with Asaf Shachar.

MondayApr 16, 201814:30
Foundations of Computer Science SeminarRoom 155
Speaker:Iftach HaitnerTitle:Computational Two-Party Correlation Abstract:opens in new windowin html    pdfopens in new window

We prove a dichotomy theorem for two-party protocols, and show that for every poly-time two-party protocol with single-bit output, at least one of following holds:

  • The protocol can be used to construct a key-agreement protocol.
  • For every constant ρ > 0 the parties' output is ρ -uncorrelated: let (X; Y; T) denote the parties' outputs and the protocol's transcript respectively. A protocol is &rho -uncorrelated if there exists an efficient "decorralizer" algorithm Decor, that when given a random transcript T, produces two numbers PA; PB, such that no efficient algorithm can distinguish (UPS ;UPB ; T) (where Up denotes a biassed coin with bias ρ from (X; Y; T), with distinguishing advantage larger than ρ.

Namely, if the protocol cannot be used to construct key-agreement, then its output distribution (X; Y; T) is trivial: it can be simulated non-interactively by the parties given public randomness (used to sample T). (The precise statement also has qualifiers of the form: "on infinitely many choices of the security parameter").
We use the above characterization to prove that (α= 24ε2)-correct differentially private symmetric protocol for computing XOR, implies the existence of key-agreement protocol. The above dependency between α and &epsilon is tight since an θ( ε2)-correct "-differentially private protocol for computing XOR is known to exists unconditionally. It also improves, in the ( ε,α)dependency aspect, upon Goyal et al. [ICALP '16] who showed that, for some constant c > 0, a c-correct "-differentially private protocol for computing XOR implies oblivious transfer. Our result extends to a weaker notion of di erential privacy in which the privacy only requires to hold against external observer. Interestingly, the reductions used for proving the above results are non black box.

Joint work with: Eran Omri and Kobbi Nissim and Ronen Shaltiel and Jad Silbak

ThursdayApr 12, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:David Ellis (Queen Mary U) Benjamin Fehrman (Max Planck Institute)Title:** Double Seminar **Abstract:opens in new windowin html    pdfopens in new window

Talk 1: David Ellis (Queen Mary U)
Title: The edge-isoperimetric problem for antipodally symmetric subsets of the discrete cube.
Abstract: A major open problem in geometry is to solve the isoperimetric problem for n-dimensional real projective space, i.e. to determine, for each real number V, the minimum possible size of the boundary of a (well-behaved) set of volume V, in n-dimensional real projective space. We study a discrete analogue of this question: namely, among all antipodally symmetric subsets of {0,1}^n of fixed size, which sets have minimal edge-boundary? We obtain a complete answer to the second question. This is joint work with Imre Leader (Cambridge)

Talk 2:  Benjamin Fehrman (Max Planck Institute)
Title: Well-posedness of stochastic porous media equations with nonlinear, conservative noise.
Abstract: In this talk, which is based on joint work with Benjamin Gess, I will describe a pathwise well-posedness theory for stochastic porous media equations driven by nonlinear, conservative noise. Such equations arise in the theory of mean field games, as an approximation to the Dean-Kawasaki equation in fluctuating hydrodynamics, to describe the fluctuating hydrodynamics of a zero range process, and as a model for the evolution of a thin film in the regime of negligible surface tension. Our methods are loosely based on the theory of stochastic viscosity solutions, where the noise is removed by considering a class of test functions transported along underlying stochastic characteristics. We apply these ideas after passing to the equation's kinetic formulation, for which the noise enters linearly and can be inverted using the theory of rough paths.

ThursdayApr 12, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Yoav LevineTitle:Bridging Many-Body Quantum Physics and Deep Learning via Tensor NetworksAbstract:opens in new windowin html    pdfopens in new window

The harnessing of modern computational abilities for many-body wave-function representations is naturally placed as a prominent avenue in contemporary condensed matter physics. Specifically, highly expressive computational schemes that are able to efficiently represent the entanglement properties which characterize many-particle quantum systems are of interest. In the seemingly unrelated field of machine learning, deep network architectures have exhibited an unprecedented ability to tractably encompass the convoluted dependencies which characterize hard learning tasks such as image classification or speech recognition. However, theory is still lagging behind these rapid empirical advancements, and key questions regarding deep learning architecture design have no adequate answers. In the presented work, we establish a Tensor Network (TN) based common language between the two disciplines, which allows us to offer bidirectional contributions. By showing that many-body wave-functions are structurally equivalent to mappings of convolutional and recurrent arithmetic circuits, we construct their TN descriptions in the form of Tree and Matrix Product State TNs, and bring forth quantum entanglement measures as natural quantifiers of dependencies modeled by such networks. Accordingly, we propose a novel entanglement based deep learning design scheme that sheds light on the success of popular architectural choices made by deep learning practitioners, and suggests new practical prescriptions. Specifically, our analysis provides prescriptions regarding connectivity (pooling geometry) and parameter allocation (layer widths) in deep convolutional networks, and allows us to establish a first of its kind theoretical assertion for the exponential enhancement in long term memory brought forth by depth in recurrent networks. In the other direction, we identify that an inherent re-use of information in state-of-the-art deep learning architectures is a key trait that distinguishes them from TN based representations. Therefore, we suggest a new TN manifestation of information re-use, which enables TN constructs of powerful architectures such as deep recurrent networks and overlapping convolutional networks. This allows us to theoretically demonstrate that the entanglement scaling supported by state-of-the-art deep learning architectures can surpass that of commonly used expressive TNs in one dimension, and can support volume law entanglement scaling in two dimensions with an amount of parameters that is a square root of that required by Restricted Boltzmann Machines. We thus provide theoretical motivation to shift trending neural-network based wave-function representations closer to state-of-the-art deep learning architectures.

WednesdayApr 11, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Ethan Fetaya Title:Neural Relational Inference for Interacting Systems Abstract:opens in new windowin html    pdfopens in new window

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. In this talk I will introduce our neural relational inference model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks.

WednesdayApr 11, 201811:00
Mathematical Analysis and Applications SeminarRoom Pekeris
Speaker:Jean-Pierre Eckmann Title:Breathers as Metastable States for the Discrete NLS equationAbstract:opens in new windowin html    pdfopens in new windowNOTE SPECIAL TIME AND PLACE

I will describe work with C.E.Wayne in which we study how dissipation leads to a very slow drift in secular parameters for the Non-linear Schroedinger equation. The nice thing about this model is that one can describe a relatively complex phenomenon in almost explicit terms as a perturbation from an integrable Hamiltonian system

MondayApr 09, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Shlomi Dolev Title:Overlay Security and Quantum Safe Public Key InfrastructureAbstract:opens in new windowin html    pdfopens in new window

The advancement in quantum computing, where Google, IBM, Microsoft, Intel are competing in the (exponentially growing) number of qubits in their (some already) commercial quantum computers that they produce, requires the reexamination of the Internet Security, and the public key infrastructure. The talk will describe the concept of overlay security together with blockchain based directories for establishing symmetric keys. When combined with nested Lamport signature and Merkle trees for digital signatures the result is a complete, easily implementable architecture with information theoretically secure communication, and hash based signatures.

ThursdayMar 29, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Mark Rudelson (UMich), Yinon Spinka (TAU)Title:*** Double Seminar ***Abstract:opens in new windowin html    pdfopens in new window

Mark Rudelson (UMich)
Title: Invertibility of the adjacency matrices of random graphs.
Abstract: Consider an adjacency matrix of a bipartite, directed, or undirected Erdos-Renyi random graph. If the average degree of a vertex is large enough, then such matrix is invertible with high probability. As the average degree decreases, the probability of the matrix being singular increases, and for a sufficiently small average degree, it becomes singular with probability close to 1. We will discuss when this transition occurs, and what the main reason for the singularity of the adjacency matrix is.
This is a joint work with Anirban Basak.

Yinon Spinka (TAU)
Title: Finitary codings of Markov random fields
Abstract: Let X be a stationary Z^d-process. We say that X can be coded by an i.i.d. process if there is a(deterministic and translation-invariant) way to construct a realization of X from i.i.d. variables associated to the sites of Z^d. That is, if there is an i.i.d. process Y and a measurable map F from the underlying space of Y to that of X, which commutes with translations of Z^d and satisfies that F(Y)=X in distribution. Such a coding is called finitary if, in order to determine the value of X at a given site, one only needs to look at a finite (but random) region of Y.
It is known that a phase transition (existence of multiple Gibbs states) is an obstruction for the existence of such a finitary coding. On the other hand, we show that when X is a Markov random field satisfying certain spatial mixing conditions, then X can be coded by an i.i.d. process in a finitary manner. Moreover, the coding radius has exponential tails, so that typically the value of X at a given site is determined by a small region of Y.
We give applications to models such as the Potts model, proper colorings and the hard-core model.

ThursdayMar 29, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Tomer MichaeliTitle:The Perception-Distortion TradeoffAbstract:opens in new windowin html    pdfopens in new window

Image restoration algorithms are typically evaluated by some distortion measure (e.g. PSNR, SSIM, IFC, VIF) or by human opinion scores that quantify perceived perceptual quality. In this work, we prove mathematically that distortion and perceptual quality are at odds with each other. Specifically, we study the optimal probability for correctly discriminating the outputs of an image restoration algorithm from real images. We show that as the mean distortion decreases, this probability must increase (indicating worse perceptual quality). As opposed to the common belief, this result holds true for any distortion measure, and is not only a problem of the PSNR or SSIM criteria. However, as we show experimentally, for some measures it is less severe (e.g. distance between VGG features). We also show that generative-adversarial-nets (GANs) provide a principled way to approach the perception-distortion bound. This constitutes theoretical support to their observed success in low-level vision tasks. Based on our analysis, we propose a new methodology for evaluating image restoration methods, and use it to perform an extensive comparison between recent super-resolution algorithms. Our study reveals which methods are currently closest to the theoretical perception-distortion bound.
* Joint work with Yochai Blau.

MondayMar 26, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Gal Shahaf Title:Oblivious routing via random walksAbstract:opens in new windowin html    pdfopens in new window

We present novel oblivious routing algorithms for the splittable and the unsplittable multicommodity flow settings. Our algorithms for both models improve upon the state-of-the-art, in terms of running time and performance with respect to graphs that exhibit good expansion guarantees. As an intermediate step towards the unsplittable setting, we present a novel generalization of Valiant's classical load balancing scheme for packet-switched networks to arbitrary graphs, which is of independent interest. Our approach relies on diffusing traffic throughout the network and then regathering it to its destination, via iterative applications of the random walk operator. Consequently, the performance guarantees of our algorithms are derived from the convergence of the random walk operator to the stationary distribution and are expressed in terms of the spectral gap of the graph (which dominates the mixing time).

ThursdayMar 22, 201812:30
Guest SeminarRoom 108
Speaker:Mark BorodovskyTitle:Genome Decoding: Learning and Following Sequence PatternsAbstract:opens in new windowin html    pdfopens in new window

Genome-wide forces of mutation and selection create local and global sequence patterns that carry information on functional role of genomic DNA. I will describe algorithmic approaches to genome analysis that decode sequence patterns and identify features of structural gene organization and gene expression (e.g. leaderless transcription). The algorithms make unsupervised inference of the structure of underlying graphical model and its parameters. 
The subsequently developed software tools were, among other applications, used at NCBI (Bethesda, MD) to annotate and re-annotate 2,500+ fungal genomes and 130,000+ prokaryotic genomes. Yet another algorithm was employed by DOE JGI (Walnut Creek, CA) to annotate the largest collection of metagenomes. 

Speaker s short Bio
Mark Borodovsky, PhD, a Regents' Professor at the Joint Georgia Tech and Emory University Department of Biomedical Engineering and the School of Computational Science and Engineering. Since 1990 when he arrived to Atlanta from Moscow, Dr Borodovsky had also joint faculty appointments at the School of Biology and the School of Mathematics. Dr. Borodovsky is a Founder of the Georgia Tech Bioinformatics graduate program.
 

MondayMar 19, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:William Hoza Title:Typically-Correct Derandomization for Small Time and SpaceAbstract:opens in new windowin html    pdfopens in new window

Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. An immediate corollary is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also discuss additional complexity-theoretic applications of our technique.

SundayMar 18, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Amir RosenfeldTitle:Striving for Adaptive Representations in Neural NetworksAbstract:opens in new windowin html    pdfopens in new windowPlease note the Special Date!!
Some sub-problems in visual recognition already enjoy very impressive performance. However, the deep-learning solutions that underlie them require large training data, are brittle to domain shift and incur a large cost in parameters for adapting to new domains - all in stark contrast to what is observed in human beings. I will talk about my recent work on this area, including (1) introduce a new dataset on which the strongest of learned representations perform very poorly in mimicking human perceptual similarity (2) discuss recent results hinting that the parameters in neural networks are under-utilized and show an alternative method for transfer learning without forgetting at a small parameter cost and (3) show some recent work on conditional computation, inspired by the psychophysical phenomena of visual priming in humans.
ThursdayMar 15, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Elie Aidekon Title:Points of infinite multiplicity of a planar Brownian motionAbstract:opens in new windowin html    pdfopens in new window

Points of infinite multiplicity are particular points which the Brownian motion visits infinitely often. Following a work of Bass, Burdzy and Khoshnevisan, we construct and study a measure carried by these points. Joint work with Yueyun Hu and Zhan Shi.

ThursdayMar 15, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Aviad Levis Title:Three-Dimensional Scatterer TomographyAbstract:opens in new windowin html    pdfopens in new window

Scattering effects in images, including those related to haze, fog, and appearance of clouds, are fundamentally dictated by microphysical characteristics of the scatterers. We define and derive recovery of these characteristics, in a three-dimensional heterogeneous medium. Recovery is based on a novel tomography approach. Multiview (multi-angular) and multi-spectral data are linked to the underlying microphysics using 3D radiative transfer, accounting for multiple-scattering. Despite the nonlinearity of the tomography model, inversion is enabled using a few approximations that we describe. As a case study, we focus on passive remote sensing of the atmosphere, where scatterer retrieval can benefit modeling and forecasting of weather, climate, and pollution.

TuesdayMar 13, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Giuliano GagliardiTitle:Smoothness of spherical varieties via toric degenerationsAbstract:opens in new windowin html    pdfopens in new window
Spherical varieties are a natural generalization of toric, symmetric, and flag varieties and form a rich class of algebraic varieties with an action of a reductive group. We combine the theory of toric degenerations of spherical varieties using representation theory with a recent result by Brown-McKernan-Svaldi-Zong, which characterises toric varieties using log pairs, in order to study the geometry of (horo-)spherical varieties. This is joint work in progress with Johannes Hofscheier.
ThursdayMar 08, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Erwin Bolthausen Title:On the high temperature phase in mean-field spin glassesAbstract:opens in new windowin html    pdfopens in new window

We present a new way to derive the replica symmetric solution for the free energy in mean-field spin glasses. Only the Sherrington-Kirpatrick case has been worked out in details, but the method also works in other cases, for instance for the perceptron (work in progress), and probably also for the Hopfield net. The method is closely related to the TAP equations (for Thouless-Anderson-Palmer). It does not give any new results, presently, but it gives a new viewpoint, and it looks to be quite promising. As the TAP equations are widely discussed in the physics literature, also at low temperature, it is hoped that the method could be extended to this case, too. But this is open, and probably very difficult.

TuesdayFeb 27, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Professor Amnon NeemanTitle:Approximability in derived categoriesAbstract:opens in new windowin html    pdfopens in new window

We will introduce the (new) notion of approximability in triangulated categories and show its power.

The brief summary is that the derived category of quasicoherent sheaves on a separated, quasicompact scheme is an approximable triangulated category.
As relatively easy corollaries one can: (1) prove an old conjecture of Bondal and Van den Bergh, about strong generation in D^{perf}(X), (2) generalize an old theorem of of Rouquier about strong generation in D^b_{coh}(X). Rouquier proved the result only in equal characteristic, we can extend to mixed characteristic, and (3) generalize a representability theorem of Bondal and Van den Bergh,from proper schemes of finite type over fields to proper schemes of finite type over any noetherian rings.

After stating these results and explaining what they mean, we will (time permitting) also mention structural theorems. It turns out that approximable triangulated categories have a fair bit of intrinsic, internal structure that comes for free.

TuesdayFeb 20, 201810:00
Guest SeminarRoom 1
Speaker:Prof. David SontagTitle:AI for Health Needs CausalityAbstract:opens in new windowin html    pdfopens in new window

Recent success stories of using machine learning for diagnosing skin cancer, diabetic retinopathy, pneumonia, and breast cancer may give the impression that artificial intelligence (AI) is on the cusp of radically changing all aspects of health care. However, many of the most important problems, such as predicting disease progression, personalizing treatment to the individual, drug discovery, and finding optimal treatment policies, all require a fundamentally different way of thinking. Specifically, these problems require a focus on *causality* rather than simply prediction. Motivated by these challenges, my lab has been developing several new approaches for causal inference from observational data. In this talk, I describe our recent work on the deep Markov model (Krishnan, Shalit, Sontag AAAI '17) and TARNet (Shalit, Johansson, Sontag, ICML '17).

TuesdayFeb 20, 201810:00
Guest SeminarRoom 1
Speaker:Prof. David SontagTitle:AI for Health Needs CausalityAbstract:opens in new windowin html    pdfopens in new window

Recent success stories of using machine learning for diagnosing skin cancer, diabetic retinopathy, pneumonia, and breast cancer may give the impression that artificial intelligence (AI) is on the cusp of radically changing all aspects of health care. However, many of the most important problems, such as predicting disease progression, personalizing treatment to the individual, drug discovery, and finding optimal treatment policies, all require a fundamentally different way of thinking. Specifically, these problems require a focus on *causality* rather than simply prediction. Motivated by these challenges, my lab has been developing several new approaches for causal inference from observational data. In this talk, I describe our recent work on the deep Markov model (Krishnan, Shalit, Sontag AAAI '17) and TARNet (Shalit, Johansson, Sontag, ICML '17).

TuesdayFeb 13, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Yasmine Fittouhi Title:The intricate relationship between the Mumford system and the Jacobians of singular hyperelliptic curvesAbstract:opens in new windowin html    pdfopens in new window

The generalized Jacobian Jac_m(C ') of a smooth hyperelliptic curve C'  associated with a module m is an algebraic group that  can be described by using lines bundle of the curve C' or by using a  symmetric product  of the curve C' provided with a law of composition. This second definition of the Jacobian Jac_m(C') is directly related to the fibres of a  Mumford system. To be precise it is a subset of the compactified Jac_m(C') which is related to the fibres. This presentation will help us to demystify the relationship of these two mathematical objects.

TuesdayFeb 13, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dmitry TuraevTitle:On Herman's positive metric entropy conjectureAbstract:opens in new windowin html    pdfopens in new window

We show that any area-preserving Cr-diffeomorphism of a two-dimensional surface displaying an elliptic fxed point can be Cr-perturbed to one exhibiting a chaotic island whose metric entropy is positive, for every 1 ≤ r≤ 1. This proves a conjecture of Herman stating that the identity map of the disk can be C-perturbed to a conservative di eomorphism with positive metric entropy. This implies also that the Chirikov standard map for large and small parameter values can be C- approximated by a conservative diffeomorphisms displaying a positive metric entropy (a weak version of Sinai's positive metric entropy conjecture). Finally, this sheds light onto a Herman's question on the density of Cr-conservative di eomorphisms displaying a positive metric entropy: we show the existence of a dense set formed by conservative diffeomorphisms which either are weakly stable (so, conjecturally, uniformly hyperbolic) or display a chaotic island of positive metric entropy.
This is a joint work with Pierre Berger.

MondayFeb 12, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Alisha ZachariahTitle:Sub-Linear Channel Estimation and the Heisenberg group Abstract:opens in new windowin html    pdfopens in new window

Multiple wireless sensing tasks, e.g. radar detection for driver safety, involve estimating the "channel" or relationship between signal transmitted and received.

In this talk I will tell about the standard math model for the radar channel. In the case where the channel is sparse, I will demonstrate a channel estimation algorithm that is sub-linear in sampling and arithmetic complexity (and convince you of the need for such).

The main ingredients in the algorithm will be the use of an intrinsic algebraic structure known as the Heisenberg group and recent developments in the theory of the sparse Fast Fourier Transform (sFFT, due to Indyk et al.)

The talk will assume minimal background knowledge.

 

WednesdayFeb 07, 201811:00
The Chaim Leib Pekeris Memorial Lecture
Speaker:Professor Christos PapadimitriouTitle:A Computer Scientist Thinks about the BrainAbstract:opens in new windowin html    pdfopens in new windowDolfi and Lola Ebner Auditorium

Understanding the ways in which the Brain gives rise to the Mind (memory, behavior, cognition, intelligence, language) is the most challengingproblem facing science today. As the answer seems likely to be at least partly computational, computer scientists should work on this problem --- except there is no obvious place to start. I shall recount recent work (with W. Maass and S. Vempala) on a model for the formation and association of memories in humans, and reflect on why it may be a clue about language.

ThursdayFeb 01, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Justin Solomon Title:Geometric Optimization Algorithms for Variational ProblemsAbstract:opens in new windowin html    pdfopens in new window

 Variational problems in geometry, fabrication, learning, and related applications lead to structured numerical optimization problems for which generic algorithms exhibit inefficient or unstable performance.  Rather than viewing the particularities of these problems as barriers to scalability, in this talk we embrace them as added structure that can be leveraged to design large-scale and efficient techniques specialized to applications with geometrically structure variables.  We explore this theme through the lens of case studies in surface parameterization, optimal transport, and multi-objective design

MondayJan 29, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Robert KrauthgamerTitle:Streaming Symmetric Norms via Measure ConcentrationAbstract:opens in new windowin html    pdfopens in new window

A long line of research studies the space complexity of estimating a norm l(x) in the data-stream model, i.e., when x is the frequency vector of an input stream consisting of insertions and deletions of items of n types. I will focus on norms l (in R^n) that are *symmetric*, meaning that l is invariant under sign-flips and coordinate-permutations, and show that the streaming space complexity is essentially determined by the measure-concentration characteristics of l. These characteristics are known to govern other phenomena in high-dimensional spaces, such as the critical dimension in Dvoretzky's Theorem. 

The family of symmetric norms contains several well-studied norms, such as all l_p norms, and indeed we provide a new explanation for the disparity in space complexity between p<=2 and p>2. We also obtain bounds for other norms that are useful in applications. 

Joint work with Jaroslaw Blasiok, Vladimir Braverman, Stephen R. Chestnut, and Lin F. Yang.

ThursdayJan 25, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Hallel Bunis Title:Caging Polygonal Objects Using Minimalistic Three-Finger HandsAbstract:opens in new windowin html    pdfopens in new window

Multi-finger caging offers a robust approach to object grasping. To securely grasp an object, the fingers are first placed in caging regions surrounding a desired immobilizing grasp. This prevents the object from escaping the hand, and allows for great position uncertainty of the fingers relative to the object. The hand is then closed until the desired immobilizing grasp is reached.

While efficient computation of two-finger caging grasps for polygonal objects is well developed, the computation of three-finger caging grasps has remained a challenging open problem. We will discuss the caging of polygonal objects using three-finger hands that maintain similar triangle finger formations during the grasping process. While the configuration space of such hands is four dimensional, their contact space which represents all two and three finger contacts along the grasped object's boundary forms a two-dimensional stratified manifold.

We will present a caging graph that can be constructed in the hand's relatively simple contact space. Starting from a desired immobilizing grasp of the object by a specific triangular finger formation, the caging graph is searched for the largest formation scale value that ensures a three-finger cage about the object. This value determines the caging regions, and if the formation scale is kept below this value, any finger placement within the caging regions will guarantee a robust object grasping.

TuesdayJan 23, 201816:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Carl TiplerTitle:Quantization of extremal metrics and applicationsAbstract:opens in new windowin html    pdfopens in new window

An extremal metric, as defined by Calabi, is a canonical Kahler metric: it minimizes the curvature within a given Kahler class. According to the Yau-Tian-Donaldson conjecture, polarized Kahler manifolds admitting an extremal metric should correspond to stable manifolds in a Geometric Invariant Theory sense.
In this talk, we will explain that a projective extremal Kahler manifold is asymptotically relatively Chow stable. This fact was conjectured by Apostolov and Huang, and its proof relies on quantization techniques. We will explain various implications, such that unicity or splitting results for extremal metrics.
Joint work with Yuji Sano ( Fukuoka University). 

MondayJan 22, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Ofer Grossman Title:Reproducibility in Randomized Log-spaceAbstract:opens in new windowin html    pdfopens in new window

A curious property of randomized log-space search algorithms is that their outputs are often longer than their workspace. One consequence is that there is no clear way to reproduce the same output when running the algorithm twice on the same input. It is not feasible to store the random bits (or the output) of the previous run in log-space, and using new random bits in another execution can result in a different output. This leads to the question: how can we reproduce the results of a randomized log space computation of a search problem?

We will give a precise definition of this notion of "reproducibility". Then we will show that every problem in search-RL has a randomized log-space algorithm where the output can be reproduced. Reproducibility can be thought of as an extension of pseudo-determinism. Indeed, for some problems in search-RL we show pseudo-deterministic algorithms whose running time significantly improve on known deterministic algorithms.

Joint work with Yang Liu.

ThursdayJan 18, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Oren Louidor (Technion) and Alexander Glazman (Tel Aviv).Title:Double SeminarAbstract:opens in new windowin html    pdfopens in new window

Oren Louidor (Technion)
Title: Dynamical freezing in a spin-glass with logarithmic correlations.
Abstract: We consider a continuous time random walk on the 2D torus, governed by the exponential of the discrete Gaussian free field acting as potential. This process can be viewed as Glauber dynamics for a spin-glass system with logarithmic correlations. Taking temperature to be below the freezing point, we then study this process both at pre-equilibrium and in-equilibrium time scales. In the former case, we show that the system exhibits aging and recover the arcsine law as asymptotics for a natural two point temporal correlation function. In the latter case, we show that the dynamics admits a functional scaling limit, with the limit given by a variant of Kolmogorov's K-process, driven by the limiting extremal process of the field, or alternatively, by a super-critical Liouville Brownian motion. Joint work with A. Cortines, J. Gold and A. Svejda.

Alexander Glazman (Tel Aviv)
Title: Level lines of a random Lipschitz function
Abstract: We consider the uniform distribution on Lipschitz functions on the triangular lattice, i.e. all integer-valued functions which differ by 0 or 1 on any two adjacent vertices. We show that with a positive probability such a function exhibits macroscopic level lines. Instead of working directly with Lipschitz functions we map this model to the loop $O(2)$ model with parameter $x=1$. The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model.
A main tool in the proof is a positive association (FKG) property that was recently shown to hold when $n \ge 1$ and $0<x\le\frac{1}{\sqrt{n}}$. Though the case $n=2$, $x=1$ is not in the FKG regime, it turns out that when loops are assigned one of two colours independently the marginal on loops of either of the colours does satisfy the FKG property. The colouring of loops allows to view the loop $O(2)$ model with $x=1$ as coupling of two percolation configurations. Studying each of them independently and using the XOR operation we establish existence of macroscopic loops, i.e. level lines in the original setting.
(Based on a joint work with H. Duminil-Copin, and I. Manolescu)

ThursdayJan 18, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Sagie BenaimTitle:One-Sided Unsupervised Domain Mapping via Distance CorrelationsAbstract:opens in new windowin html    pdfopens in new window

In unsupervised domain mapping, the learner is given two unmatched datasets A and B. The goal is to learn a mapping G_AB that translates a sample in A to the analog sample in B. Recent approaches have shown that when learning simultaneously both G_AB and the inverse mapping G_BA, convincing mappings are obtained. In this work, we present a method of learning G_AB without learning G_BA. This is done by learning a mapping that maintains the distance between a pair of samples. Moreover, good mappings are obtained, even by maintaining the distance between different parts of the same sample before and after mapping. We present experimental results that the new method not only allows for one sided mapping learning, but also leads to preferable numerical results over the existing circularity-based constraint.

ThursdayJan 18, 201811:00
Guest SeminarRoom 290C
Speaker:Shaull Almagor Title:Automated Verification of Infinite-State Systems with Certifiable AlgorithmsAbstract:opens in new windowin html    pdfopens in new window

In formal verification, one uses mathematical tools in order to prove that a system satisfies a given specification.
In this talk I consider three limitations of traditional formal verification:
The first is the fact that treating systems as finite-state machines is problematic, as systems become more complex, and thus we must consider infinite-state machines.
The second is that Boolean specifications are not rich enough to specify properties required by today's systems. Thus, we need to go beyond the Boolean setting.
The third concerns certifying the results of verification: while a verifier may answer that a system satisfies its specification, a designer often needs some palpable evidence of correctness.

I will present several works addressing the above limitations, and the mathematical tools involved in overcoming them.

No prior knowledge is assumed. Posterior knowledge is guaranteed.

WednesdayJan 17, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Pavel Etingof Title:Semisimplification of tensor categoriesAbstract:opens in new windowin html    pdfopens in new window

We develop the theory of semisimplifications of tensor categories defined by Barrett and Westbury. By definition, the semisimplification of a tensor category is its quotient by the tensor ideal of negligible morphisms, i.e., morphisms f such that Tr(fg)=0 for any morphism g in the opposite direction. In particular, we compute the semisimplification of the category of representations of a finite group in characteristic p in terms of representations of the normalizer of its Sylow p-subgroup. This allows us to compute the semisimplification of the representation category of the symmetric group S_{n+p} in characteristic p, where n=0,...,p-1, and of the Deligne category Rep^{ab} S_t, t in N. We also compute the semisimplification of the category of representations of the Kac-De Concini quantum group of the Borel subalgebra of sl_2. Finally, we study tensor functors between Verlinde categories of semisimple algebraic groups arising from the semisimplification construction, and objects of finite type in categories of modular representations of finite groups (i.e., objects generating a fusion category in the semisimplification).
This is joint work with Victor Ostrik.

MondayJan 15, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Eylon Yogev Title:Distributed Computing Made Secure: A New Cycle Cover Theorem Abstract:opens in new windowin html    pdfopens in new window

In the area of distributed graph algorithms a number of network's entities with local views solve some computational task by exchanging messages with their neighbors. Quite unfortunately, an inherent property of most existing distributed algorithms is that throughout the course of their execution, the nodes get to learn not only their own output but rather learn quite a lot on the inputs or outputs of many other entities. This leakage of information might be a major obstacle in settings where the output (or input) of network's individual is a private information (e.g. distributed networks of selfish agents, decentralized digital currency such as Bitcoin, voting systems).
While being quite unfamiliar notion in the classical distributed setting, the notion of secure multi-party computation (MPC) is one of the main themes in the Cryptography community. Yet despite all extensive work in the area, no existing algorithm fits the framework of classical distributed models in which there are no assumptions on the graph topologies and only messages of bounded size are sent on the edges in each round.

In this work, we introduce a new framework for \emph{secure distributed graph algorithms} and provide the first \emph{general compiler} that takes any "natural" non-secure distributed algorithm that runs in $r$ rounds, and turns it into a secure algorithm that runs in $\widetilde{O}(r \cdot D \cdot poly(\Delta))$ rounds where $\Delta$ is the maximum degree in the graph and $D$ is its diameter. This round complexity is nearly optimal for bounded degree graphs.
The main technical part of our compiler is based on a new cycle cover theorem: We show that the edges of every bridgeless graph $G$ of diameter $D$ can be covered by a collection of cycles such that each cycle is of length $\widetilde{O}(D)$ and each edge of the graph $G$ appears in $\widetilde{O}(1)$ many cycles. This provides the basis for additional combinatorial constructions required by our compiler and might be of independent combinatorial and algorithmic interest.
Joint work with Merav Parter.

ThursdayJan 11, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Oren SalzmanTitle:Computational Challenges and Algorithms in Planning for Robotic SystemsAbstract:opens in new windowin html    pdfopens in new window

In recent years, robots have played an active role in everyday life: medical robots assist in complex surgeries, low-cost commercial robots clean houses and fleets of robots are used to efficiently manage warehouses. A key challenge in these systems is motion planning, where we are interested in planning a collision-free path for a robot in an environment cluttered with obstacles. While the general problem has been studied for several decades now, these new applications introduce an abundance of new challenges.

In this talk I will describe some of these challenges as well as algorithms developed to address them. I will overview general challenges such as compression and graph-search algorithms in the context of motion planning. I will show why traditional Computer Science tools are ill-suited for these problems and introduce alternative algorithms that leverage the unique characteristics of robot motion planning. In addition, I will describe domains-specific challenges such as those that arise when planning for assistive robots and for humanoid robots and overview algorithms tailored for these specific domains.

WednesdayJan 10, 201811:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Yonatan BelinkovTitle:Understanding Internal Representations in Deep Learning Models for Language and Speech ProcessingAbstract:opens in new windowin html    pdfopens in new window

Language technology has become pervasive in everyday life, powering applications like Apple's Siri or Google's Assistant. Neural networks are a key component in these systems thanks to their ability to model large amounts of data. Contrary to traditional systems, models based on deep neural networks (a.k.a. deep learning) can be trained in an end-to-end fashion on input-output pairs, such as a sentence in one language and its translation in another language, or a speech utterance and its transcription. The end-to-end training paradigm simplifies the engineering process while giving the model flexibility to optimize for the desired task. This, however, often comes at the expense of model interpretability: understanding the role of different parts of the deep neural network is difficult, and such models are often perceived as "black-box". In this work, we study deep learning models for two core language technology tasks: machine translation and speech recognition. We advocate an approach that attempts to decode the information encoded in such models while they are being trained. We perform a range of experiments comparing different modules, layers, and representations in the end-to-end models. Our analyses illuminate the inner workings of end-to-end machine translation and speech recognition systems, explain how they capture different language properties, and suggest potential directions for improving them. The methodology is also applicable to other tasks in the language domain and beyond.

TuesdayJan 09, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Efrat Bank Title:Correlation between primes in short intervals on curves over finite fieldsAbstract:opens in new windowin html    pdfopens in new window

In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields. 
I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial setting. 
I will give a sketch of the proof which includes a computation of a certain Galois group, and a counting argument, namely, Chebotarev density type theorem. 

This is a joint work with Tyler Foster.
 

MondayJan 08, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Omer PanethTitle:Cryptography Outside the Black BoxAbstract:opens in new windowin html    pdfopens in new window

Computational problems whose input is a program are central in Cryptography, as well as Complexity, Learning, and Optimization. The nature of such problems crucially depends on the way the program is accessed -- as a black box or explicitly by its implementation.

In which settings can we exploit code to gain an advantage over black-box access? In Cryptography, we explore this question from two opposing perspectives:

Protecting Code: Can we obfuscate a program's code so that its functionality is preserved but it is otherwise unintelligible? Intuitively, such obfuscated code reveals nothing more than black-box access to the program. Obfuscation is, therefore, a powerful tool with numerous applications in software protection and Cryptography.

Exploiting Code: Most security proofs in cryptography consist of a reduction that translates any potential attacker into an algorithm solving some underlying hard problem. While most security reductions only require black-box access to the attacker, for many applications black-box reductions are provably insufficient. Can we exploit the attacker's code to prove security where black-box reductions fail?

In this talk, I will describe new techniques for protecting and exploiting code, taking advantage of the inherent tension between these two tasks. I will also demonstrate applications of these techniques in and beyond cryptography.

ThursdayJan 04, 201813:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Sebastien Bubeck (Microsoft Research) and Percy Deift (Courant Institute)Title:Double SeminarAbstract:opens in new windowin html    pdfopens in new window

Sebastien Bubeck (Microsoft Research)

Title: k-server via multiscale entropic regularization
Abstract: I will start by describing how mirror descent is a natural strategy for online decision making, specifically in online learning and metrical task systems. To motivate the k-server problem I will also briefly recall what we know and what we don't know for structured state/action spaces in these models. Using the basic mirror descent calculations I will show how to easily obtain a log(k)-competitive algorithm for k-paging. I will then introduce our new parametrization of fractional k-server on a tree, and explain how to analyze the movement cost of entropy-regularized mirror descent on this parametrization. This leads to a depth*log(k)-competitive (fractional) algorithm for general trees, and log^2(k) for HSTs. I will also briefly mention dynamic embeddings to go beyond the standard log(n) loss in the reduction from general metrics to HSTs.
Joint work with Michael B. Cohen, James R. Lee, Yin Tat Lee, and Aleksander Madry.

Percy Deift (Courant Institute )

Title: Universality in numerical analysis with some examples of cryptographic algorithms.
Abstract: We show that a wide variety of numerical algorithms with random data exhibit universality. Most of the results are computational, but in some important cases universality is established rigorously. We also discuss universality for some cryptographic algorithms.
Joint work with C. Pfrany, G. Menon, S. Olver, T. Trogdan and S. Miller.

ThursdayJan 04, 201812:15
Vision and Robotics SeminarRoom 1
Speaker:Guy Gilboa Title:Processing images using nonlinear transformsAbstract:opens in new windowin html    pdfopens in new window
Recent studies of convex functionals and their related nonlinear eigenvalue problems show surprising analogies to harmonic analysis based on classical transforms (e.g. Fourier). In this talk the total-variation transform will be introduced along with some theoretical results. Applications related to image decomposition, texture processing and face fusion will be shown. Extensions to graphs and a new interpretation of gradient descent will also be discussed.
WednesdayJan 03, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker: Dmitry VaintrobTitle:Characters of inadmissible representationsAbstract:opens in new windowin html    pdfopens in new window

Given a p-adic group G, number theorists are interested in producing admissible representations of G: representations which have a well-defined character functional. One way to produce such representations is by "Jacquet induction" from smaller groups, whose characters can be understood inductively. The complementary space of "new" characters which are not obtained by induction (complementary with respect to a natural metric on the space of characters) is given by what is called "elliptic" characters. Given a representation V of G, the "new" input from its character is captured by the operator Ax(V), with A (the Bernstein-Deligne-Kazhdan A-operator) the projector to the elliptic component (note that this is different from the component of the character lattice valued in elliptic elements). I will talk about my ongoing work with Xuhua He on extending this operator to a trace functional Ax(V) for V a finitely-generated representation (whose Grothendieck group is well understood), which works by first constructing a virtual elliptic admissible representation from any finitely generated representation.

TuesdayJan 02, 201816:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Or HershkovitsTitle:The Mean Curvature flow and its applicationsAbstract:opens in new windowin html    pdfopens in new window

Being the gradient flow of the area functional, the mean curvature flow can be thought of as a greedy algorithm for simplifying embedded shapes. But how successful is this algorithm?
In this talk, I will describe three examples for how mean curvature flow, as well as its variants and weak solutions, can be used to achieve this desired simplification.

The first is a short time smoothing effect of the flow, allowing to smooth out some rough, potentially fractal initial data.

The second is an application of mean curvature flow with surgery to smooth differential topology, allowing to conclude Schoenflies-type theorems about the moduli space of smooth embedded spheres and tori, satisfying some curvature conditions.

The third is an application of (weak,modified) mean curvature flow to differential geometry, allowing to relate bounds on the gaussian entropy functional to the topology of a closed hypersurface.

In this talk, which will assume no prior knowledge in PDE or mean curvature flow, I will try to highlight the relation between the analysis of the flow and in particular, its singularity formation, to both ''time dependent'' and  "classical" geometry.

Some of the results described in this talk are joint works with Reto Buzano, Robert Haslhofer and Brian White.

TuesdayJan 02, 201811:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Adam Gal Title:Higher Hall algebrasAbstract:opens in new windowin html    pdfopens in new window

We recall the notion of a hall algebra associated to a category, and explain how this construction can be done in a way that naturally includes a higher algebra structure, motivated by work of Toen and Dyckerhoff-Kapranov. We will then explain how this leads to new insights about the bi-algebra structure and related concepts.

TuesdayJan 02, 201811:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dima BatenkovTitle:Soft extrapolation of band-limited functionsAbstract:opens in new windowin html    pdfopens in new window

The problem of computational super-resolution asks to recover high-frequency features of an object from the noisy and blurred/band-limited samples of its Fourier transform, based on some a-priori information about the object class. A core theoretical question is to quantify the possible amount of bandwidth extension and the associated stability of recovering the missing frequency components, as a function of the sample perturbation level and the object prior.

In this work we assume that the object has a compact space/time extent in one dimension (but otherwise can be fairly arbitrary), while the low-pass window can have a super-exponentially decaying "soft" shape (such as a Gaussian). In contrast, previously known results considered only the ideal "hard" window (a characteristic function of the band) and objects of finite energy. The super-resolution problem in this case is equivalent to a stable analytic continuation of an entire function of finite exponential type. We show that a weighted least-squares polynomial approximation with equispaced samples and a judiciously chosen number of terms allows one to have a super-resolution factor which scales logarithmically with the noise level, while the pointwise extrapolation error exhibits a Holder-type continuity with an exponent derived from weighted potential theory. The algorithm is asymptotically minimax, in the sense that there is essentially no better algorithm yielding meaningfully lower error over the same smoothness class.

The results can be considered as a first step towards analyzing the much more realistic model of a sparse combination of compactly-supported "approximate spikes", which appears in applications such as synthetic aperture radar, seismic imaging and direction of arrival estimation, and for which only limited special cases are well-understood.

Joint work with L.Demanet and H.Mhaskar.

MondayJan 01, 201814:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Yael Tauman Kalai Title:Using the PIR Heuristic to Enhance Secrecy Abstract:opens in new windowin html    pdfopens in new window

The use of a computational PIR scheme has been instrumental in reducing interaction from interactive proofs, and in converting multi-prover interactive proofs to (single prover) 2-message computationally sound proofs (also known as arguments).

In this talk we will focus on the secrecy guarantees of this transformation.
We show that if we start with an interactive proof which is only *honest-verifier* zero-knowledge, and we use a quasi-poly secure *symmetric* PIR scheme (or a 2-message OT scheme) to reduce interaction, then the resulting 2-message argument is witness indistinguishable, and in the delayed-input setting it is distributional weak zero-knowledge (which implies strong witness indistinguishable and witness hiding in the delayed input setting). Moreover, under the same assumption (which can be instantiated from quasi-poly DDH/QR/N'th residuosity assumption), we construct a two-message argument with (similar) *statistical* secrecy guarantees. For the latter, we apply the PIR heuristic on a computationally sound proof, which is honest-verifier statistical zero-knowledge.

This is based on joint works with Abhishek Jain, Dakshita Khurana, Ron Rothblum and Amit Sahai.

SundayDec 31, 201714:30
Foundations of Computer Science SeminarRoom 208
Speaker:Shay Solomon Title:Dynamic graph matching and related problemsAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY (SUNDAY) AND PLACE (ROOM 208)

Graph matching is one of the most well-studied problems in combinatorial optimization, with applications ranging from scheduling and object recognition to numerical analysis and computational chemistry.

Nevertheless, until recently very little was unknown about this problem in real-life **dynamic networks**, which aim to model the constantly changing physical world.

In the first part of the talk we'll discuss our work on dynamic graph matching, and in the second part we'll highlight our work on a few related problems.

ThursdayDec 28, 201713:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Amir Dembo (Stanford) and Yuval Peres (Microsoft)Title:DOUBLE TALKAbstract:opens in new windowin html    pdfopens in new window

Talk 1: Amir Dembo (Stanford) 

Title: Large deviations theory for chemical reaction networks.
The microscopic dynamics of well-stirred networks of chemical reactions are modeled as jump Markov processes. At large volume, one may expect in this framework to have a straightforward application of large deviation theory. This is not at all true, for the jump rates are typically neither globally Lipschitz, nor bounded away from zero, with both blowup and absorption as quite possible scenarios. In joint work with Andrea Agazzi and Jean-Pierre Eckman, we utilize Lyapunov stability theory to bypass this challenge and to characterize a large class of network topologies that satisfy the full Wentzell-Freidlin theory of asymptotic rates of exit from domains of attraction.

Talk 2: Yuval Peres (Microsoft)
Title: Trace reconstruction for the deletion channel
Abstract: In the trace reconstruction problem, an unknown string $x$ of $n$ bits is observed through the deletion channel, which deletes each bit with some constant probability q, yielding a contracted string. How many independent outputs (traces) of the deletion channel are needed to reconstruct $x$ with high probability?
The best lower bound known is linear in $n$. Until 2016, the best upper bound was exponential in the square root of $n$. We improve the square root to a cube root using statistics of individual output bits and some inequalities for Littlewood polynomials on the unit circle. This bound is sharp for reconstruction algorithms that only use this statistical information. (Similar results were obtained independently and concurrently by De O'Donnell and Servedio). If the string $x$ is random, we can show a subpolynomial number of traces suffices by comparison to a random walk. (Joint works with Fedor Nazarov, STOC 2017, with Alex Zhai, FOCS 2017 and with Nina Holden & Robin Pemantle, preprint (2017).)

ThursdayDec 28, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Greg ShakhnarovichTitle:Discriminability loss for learning to generate descriptive image captionsAbstract:opens in new windowin html    pdfopens in new window

Image captioning -- automatic production of text describing a visual scene -- has received a lot of attention recently. However, the objective of captioning, evaluation metrics, and the training protocol remain somewhat unsettled. The general goal seems to be for machines to describe visual signal like humans do. We pursue this goal by incorporating a discriminability loss in training caption generators. This loss is explicitly "aware" of the need for the caption to convey information, rather than appear fluent or reflect word distribution in the human captions. Specifically, the loss in our work is tied to discriminative tasks: producing a referring expression (text that allows a recipient to identify a region in the given image) or producing a discriminative caption which allows the recipient to identify an image within a set of images. In both projects, use of the dscriminability loss does not require any additional human annotations, and relies on collaborative training between the caption generator and a comprehension model, which is a proxy for a human recipient. In experiments on standard benchmarks, we show that adding discriminability objectives not only improves the discriminative quality of the generated image captions, but, perhaps surprisingly, also makes the captions better under a variety of traditional metrics.

Joint work with Ruotian Luo (TTIC), Brian Price and Scott Cohen (Adobe).

WednesdayDec 27, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Ehud MeirTitle:Generalized Harish-Chandra functors for general linear groups over nite local ringsAbstract:opens in new windowin html    pdfopens in new window

Let K be a commutative ring. Consider the groups GLn(K). Bernstein and Zelevinsky have studied the representations of the general linear groups in case the ring K is a nite eld. Instead of studying the representations of GLn(K) for each n separately, they have studied all the representations of all the groups GLn(K) si- multaneously. They considered on R := nR(GLn(K)) structures called parabolic (or Harish-Chandra) induction and restriction, and showed that they enrich R with a structure of a so called positive self adjoint Hopf algebra (or PSH algebra). They use this structure to reduce the study of representations of the groups GLn(K) to the following two tasks:
1. Study a special family of representations of GLn(K), called cuspidal representa- tions. These are representations which do not arise as direct summands of parabolic induction of smaller representations.
2. Study representations of the symmetric groups. These representation also has a nice combinatorial  description, using partitions.
In this talk I will discuss the study of representations of GLn(K) where K is a nite quotient of a discrete valuation ring (such as Z=pr or k[x]=xr, where k is a nite eld). One reason to study such representation is that all continuous complex representations of the groups GLn(Zp) and GLn(k[[x]]) (where Zp denotes the p-adic integers) arise from these nite quotients. I will explain why the natural generalization of the Harish-Chandra functors do not furnish a PSH algebra in this case, and how is this related to the Bruhat decomposition and Gauss elimination. In order to overcome this issue we have constructed a generalization of the Harish-Chandra functors. I will explain this generalization, describe some of the new functors properties, and explain how can they be applied to studying complex representations.
 The talk will be based on a joint work with Tyrone Crisp and Uri Onn.
 

TuesdayDec 26, 201712:30
Distinguished Lecture SeriesRoom 1
Speaker:Walter StraussTitle:Steady Water WavesAbstract:opens in new windowin html    pdfopens in new window
The mathematical study of water waves became possible after the derivation of the basic mathematical equations of fluids by Euler in 1752. Later, water waves, with a free boundary at the air interface, played a central role in the work of Poisson, Cauchy, Stokes, Levi-Civita and many others. It has seen greatly renewed interest among mathematicians in recent years. I will consider classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, one can prove that there exist many such waves. They are exact smooth solutions of the Euler equations with the physical boundary conditions. Some of the waves are quite tall and steep and some are overhanging. There are periodic ones and solitary ones. I will also exhibit some numerical computations of such waves. Many fundamental problems remain open.
TuesdayDec 26, 201711:15
Distinguished Lecture SeriesRoom 1
Speaker:Allen TannenbaumTitle:Optimal Mass Transport and the Robustness of Complex NetworksAbstract:opens in new windowin html    pdfopens in new window

Today's technological world is increasingly dependent upon the reliability, robustness, quality of service and timeliness of networks including those of power distribution, financial, transportation, communication, biological, and social. For the time-critical functionality in transferring resources and information, a key requirement is the ability to adapt and reconfigure in response to structural and dynamic changes, while avoiding disruption of service and catastrophic failures. We will outline some of the major problems for the development of the necessary theory and tools that will permit the understanding of network dynamics in a multiscale manner.

Many interesting networks consist of a finite but very large number of nodes or agents that interact with each other. The main challenge when dealing with such networks is to understand and regulate the collective behavior. Our goal is to develop mathematical models and optimization tools for treating the Big Data nature of large scale networks while providing the means to understand and regulate the collective behavior and the dynamical interactions (short and long-range) across such networks.

The key mathematical technique will be based upon the use optimal mass transport theory and resulting notions of curvature applied to weighted graphs in order to characterize network robustness. Examples will be given from biology, finance, and transportation.

TuesdayDec 26, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Eyal Subag Title:Algebraic Families of Harish-Chandra Modules and their ApplicationAbstract:opens in new windowin html    pdfopens in new window

I shall review the framework of algebraic families of Harish-Chandra modules, introduced recently, by Bernstein, Higson, and the speaker. Then, I shall describe three of their applications.

The first is contraction of representations of Lie groups. Contractions are certain deformations of representations with applications in mathematical physics.

The second is the Mackey bijection, this is a (partially conjectural) bijection between the admissible dual of a real reductive group and the admissible dual of its Cartan motion group.

The third is the hidden symmetry of the hydrogen atom as an algebraic family of Harish-Chandra modules.

MondayDec 25, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Or Meir Title:Prediction from Partial Information and Hindsight, with Application to Circuit Lower BoundsAbstract:opens in new windowin html    pdfopens in new window

Consider a random sequence of n bits that has entropy at least n-k, where k << n. A commonly used observation is that an average coordinate of this random sequence is close to being uniformly distributed, that is, the coordinate "looks random''. In this work, we prove a stronger result that says, roughly, that the average coordinate looks random to an adversary that is allowed to query about n/k other coordinates of the sequence, even if the adversary is non-deterministic.
As an application of this result, we prove a new result on depth-3 circuits, which recovers as a direct corollary the known lower bounds for the parity and majority functions, as well as a lower bound on sensitive functions due to Boppana.

ThursdayDec 21, 201713:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Nadav YeshaTitle:CLT for small scale mass distribution of toral Laplace eigenfunctionsAbstract:opens in new windowin html    pdfopens in new window

 In this talk we discuss the fine scale $L^2$-mass distribution of toral Laplace eigenfunctions with respect to random position. For the 2-dimensional torus, under certain flatness assumptions on the Fourier coefficients of the eigenfunctions and generic restrictions on energy levels, both the asymptotic shape of the variance and the limiting Gaussian law are established, in the optimal Planck-scale regime. We also discuss the 3-dimensional case, where the asymptotic behaviour of the variance is analysed in a more restrictive scenario. This is joint work with Igor Wigman.

ThursdayDec 21, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Assaf ShocherTitle:“Zero-Shot” Super-Resolution using Deep Internal LearningAbstract:opens in new windowin html    pdfopens in new window

Deep Learning has led to a dramatic leap in Super-Resolution (SR) performance in the past few years. However, being supervised, these SR methods are restricted to specific training data, where the acquisition of the low-resolution (LR) images from their high-resolution (HR) counterparts is predetermined (e.g., bicubic downscaling), without any distracting artifacts (e.g., sensor noise, image compression, non-ideal PSF, etc). Real LR images, however, rarely obey these restrictions, resulting in poor SR results by SotA (State of the Art) methods. In this paper we introduce "Zero-Shot" SR, which exploits the power of Deep Learning, but does not rely on prior training. We exploit the internal recurrence of information inside a single image, and train a small image-specific CNN at test time, on examples extracted solely from the input image itself. As such, it can adapt itself to different settings per image. This allows to perform SR of real old photos, noisy images, biological data, and other images where the acquisition process is unknown or non-ideal. On such images, our method outperforms SotA CNN-based SR methods, as well as previous unsupervised SR methods. To the best of our knowledge, this is the first unsupervised CNN-based SR method.

WednesdayDec 20, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Lenny Makar-Limanov Title:A Bavula conjectureAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL TIME AND ROOM

Abstract. As is well known and easy to prove the Weyl algebras A_n over a field of characteristic zero are simple. Hence any non-zero homomorphism from A_n to A_m is an embedding and m \geq n. V. Bavula conjectured that the same is true over the fields with finite characteristic. It turned out that exactly one half of his conjecture is correct (m \geq n but there are homomorphisms which are not embeddings).
If we replace the Weyl algebra by its close relative symplectic Poisson algebra (polynomial algebra with F[x_1, ..., x_n; y_1, ..., y_n] variables and Poisson bracket given by {x_i, y_i} =1 and zero on the rest of the pairs), then independently of characteristic all homomorphisms are embeddings.

TuesdayDec 19, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Avner Segal Title:L-function of cuspidal representations of G_2 and their polesAbstract:opens in new windowin html    pdfopens in new window

In this talk I will describe a family of integral representations for the standard twisted L-function of a cuspidal representation of the exceptional group of type G_2. This integral representations. These integral representations are unusual in the sense that they unfold with a non-unique model. A priori this integral is not Eulerian but using remarkable machinery proposed by I. Piatetski-Shapiro and S. Rallis we prove that in fact the integral does factor. In the course of the plocal unramified calculation we use another non-standard method, approximations of generating functions. I will then describe a few applications of these integral representations to the study of the analytic behaviour of the this L-function and to various functorial lifts associated with the group G_2.

MondayDec 18, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Avishay Tal Title:Improved Pseudorandomness for Unordered Branching Programs through Local MonotonicityAbstract:opens in new windowin html    pdfopens in new window

We present an explicit pseudorandom generator with polylog(n) seed length for read-once constant-width branching programs that can read their $n$ input bits in any order. This improves upon the work of Impagliazzo, Meka, and Zuckerman (FOCS, 2012), where they required seed length $n^{1/2+o(1)}$.

A central ingredient in our work is a bound on the Fourier spectrum of constant-width branching programs, settling a conjecture posed by Reingold, Steinke, and Vadhan (RANDOM, 2013).

Our analysis crucially uses a notion of local monotonicity on the edge labeling of the branching program. We carry critical parts of our proof under the assumption of local monotonicity and show how to deduce our results for unrestricted branching programs.

(Joint work with Eshan Chattopadhyay, Pooya Hatami, and Omer Reingold)

 

WednesdayDec 13, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Roi Livni Title:Overcoming Intractability in LearningAbstract:opens in new windowin html    pdfopens in new window

Machine learning has recently been revolutionized by the introduction of Deep Neural Networks. However, from a theoretical viewpoint these methods are still poorly understood. Indeed the key challenge in Machine Learning today is to derive rigorous results for optimization and generalization in deep learning. In this talk I will present several tractable approaches to training neural networks. At the second part I will discuss a new sequential algorithm for decision making that can take into account the structure in the action space and is more tuned with realistic decision making scenarios.

I will present our work that provides some of the first positive results and yield new, provably efficient, and practical algorithms for training certain types of neural networks. In a second work I will present a new online algorithm that learns by sequentially sampling random networks and asymptotically converges, in performance, to the optimal network. Our approach improves on previous random features based learning in terms of sample/computational complexity, and expressiveness. In a more recent work we take a different perspective on this problem. I will provide sufficient conditions that guarantee tractable learning, using the notion of refutation complexity. I will then discuss how this new idea can lead to new interesting generalization bounds that can potentially explain generalization in settings that are not always captured by classical theory.

In the setting of reinforcement learning I will present a recently developed new algorithm for decision making in a metrical action space. As an application, we consider a dynamic pricing problem in which a seller is faced with a stream of patient buyers. Each buyer buy at the lowest price in a certain time window. We use our algorithm to achieve an optimal regret, improving on previously known regret bound.

TuesdayDec 12, 201716:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Ary ShavivTitle:Tempered Manifolds and Schwartz Functions on ThemAbstract:opens in new windowin html    pdfopens in new window

Schwartz functions are classically defined as smooth functions such that they, and all their (partial) derivatives, decay at infinity faster than the inverse of any polynomial. This was formulated on $\mathbb{R}^n$ by Laurent Schwartz, and later on Nash manifolds  (smooth semi-algebraic varieties) by Fokko du Cloux and by Rami Aizenbud and Dima Gourevitch. In a joint work with Boaz Elazar we have extended the theory of Schwartz functions to the category of (possibly singular) real algebraic varieties. The basic idea is to define Schwartz functions on a (closed) algebraic subset of $\mathbb{R}^n$ as restrictions of Schwartz functions on $\mathbb{R}^n$.

Both in the Nash and the algebraic categories there exists a very useful characterization of Schwartz functions on open subsets, in terms of Schwartz functions on the embedding space: loosely speaking, Schwartz functions on an open subset are exactly restrictions of Schwartz functions on the embedding space, which are zero "to infinite order" on the complement to this open subset. This characterization suggests a very intuitive way to attach a space of Schwartz functions to an arbitrary (not necessarily semi-algebraic) open subset of $\mathbb{R}^n$.

In this talk, I will explain this construction, and more generally the construction of the category of tempered smooth manifolds. This category is in a sense the "largest" category whose objects "look" locally like open subsets of $\mathbb{R}^n$ (for some $n$), and on which Schwartz functions may be defined. In the development of this theory some classical results of Whitney are used, mainly Whitney type partition of unity (this will also be explained in the talk). As time permits, I will show some properties of Schwartz functions, and describe some possible applications. This is a work in progress.

MondayDec 11, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Tomer Koren Title:Interplays between Machine Learning and OptimizationAbstract:opens in new windowin html    pdfopens in new windowJoint Foundations of Computer Science & Machine Learning and Statistics Seminar

Over the past two decades, machine learning has rapidly evolved and emerged as a highly influential discipline of computer science and engineering. One of the pillars of machine learning is mathematical optimization, and the connection between the two fields has been a primary focus of research. In this talk, I will present two recent works that contribute to this study, focusing on online learning---a central model in machine learning for sequential decision making and learning under uncertainty. In the first part of the talk, I will describe a foundational result concerned with the power of optimization in online learning, and give answer to the question: does there exist a generic and efficient reduction from online learning to black-box optimization? In the second part, I will discuss a recent work that employs online learning techniques to design a new efficient and adaptive preconditioned algorithm for large-scale optimization. Despite employing preconditioning, the algorithm is practical even in modern optimization scenarios such as those arising in training state-of-the-art deep neural networks. I will present the new algorithm along with its theoretical guarantees and demonstrate its performance empirically.

ThursdayDec 07, 201713:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Matan Harel Title:Discontinuity of the phase transition for the planar random-cluster and Potts models with $q > 4$Abstract:opens in new windowin html    pdfopens in new window

The random-cluster model is a dependent percolation model where the weight of a configuration is proportional to q to the power of the number of connected components. It is highly related to the ferromagnetic q-Potts model, where every vertex is assigned one of q colors, and monochromatic neighbors are encouraged. Through non-rigorous means, Baxter showed that the phase transition is first-order whenever $q > 4$ - i.e. there are multiple Gibbs measures at criticality. We provide a rigorous proof of this claim. Like Baxter, our proof uses the correspondence between the above models and the six-vertex model, which we analyze using the Bethe ansatz and transfer matrix techniques. We also prove Baxter's formula for the correlation length of the models at criticality.
This is joint work with Hugo Duminil-Copin, Maxime Gangebin, Ioan Manolescu, and Vincent Tassion.

ThursdayDec 07, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Dotan KaufmanTitle:Temporal Tessellation: A Unified Approach for Video AnalysisAbstract:opens in new windowin html    pdfopens in new window

We present a general approach to video understanding, inspired by semantic transfer techniques that have been successfully used for 2D image analysis. Our method considers a video to be a 1D sequence of clips, each one associated with its own semantics. The nature of these semantics -- natural language captions or other labels -- depends on the task at hand. A test video is processed by forming correspondences between its clips and the clips of reference videos with known semantics, following which, reference semantics can be transferred to the test video. We describe two matching methods, both designed to ensure that (a) reference clips appear similar to test clips and (b), taken together, the semantics of the selected reference clips is consistent and maintains temporal coherence. We use our method for video captioning on the LSMDC'16 benchmark, video summarization on the SumMe and TVSum benchmarks, Temporal Action Detection on the Thumos2014 benchmark, and sound prediction on the Greatest Hits benchmark. Our method not only surpasses the state of the art, in four out of five benchmarks, but importantly, it is the only single method we know of that was successfully applied to such a diverse range of tasks.

TuesdayDec 05, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Victor Ivrii Title:Spectral asymptotic for Steklov’s problem in domains with edges (work in progress)Abstract:opens in new windowin html    pdfopens in new window
We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacle for deriving the second term
TuesdayDec 05, 201711:00
Vision and Robotics SeminarRoom 290C
Speaker:Amit BermanoTitle:Geometry Processing Methods and Their Real-Life ApplicationsAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DAY AND TIME

Digital geometry processing (DGP) is one of the core topics of computer graphics, and has been an active line of research for over two decades. On one hand, the field introduces theoretical studies in topics such as vector-field design, preservative maps and deformation theory. On the other hand, the tools and algorithms developed by this community are applicable in fields ranging from computer-aided design, to multimedia, to computational biology and medical imaging. Throughout my work, I have sought to bridge the gap between the theoretical aspects of DGP and their applications. In this talk, I will demonstrate how DGP concepts can be leveraged to facilitate real-life applications with the right adaptation. More specifically, I will portray how I have employed deformation theory to support problems in animation and augmented reality. I will share my thoughts and first taken steps to enlist DGP to the aid of machine learning, and perhaps most excitingly, I will discussion my own and the graphics community's contributions to computational fabrication field, as well as my vision for its future.

Bio: Dr. Amit H. Bermano is a postdoctoral Researcher at the Princeton Graphics Group, hosted by Professor Szymon Rusinkiewicz and Professor Thomas Funkhouser. Previously, he was a postdoctoral researcher at Disney Research Zurich in the computational materials group, led by Dr. Bernhard Thomaszewski. He conducted his doctoral studies at ETH Zurich under the supervision of Prof. Dr. Markus Gross, in collaboration with Disney Research Zurich. His Masters and Bachelors degrees were obtained at The Technion - Israel Institute of Technology under the supervision of Prof. Craig Gotsman. His research focuses on connecting the geometry processing field with other fields in computer graphics and vision, mainly by using geometric methods to facilitate other applications. His interests in this context include computational fabrication, animation, augmented reality, medical imaging and machine learning.

MondayDec 04, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Uri Stemmer Title:Practical Locally Private Heavy HittersAbstract:opens in new windowin html    pdfopens in new window

We present new heavy-hitters algorithms satisfying local-differential-privacy, with optimal or near-optimal worst-case error, running time, and memory. In our algorithms, the server running time is $\tilde O(n)$ and user running time is $\tilde O(1)$, hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring $O(n^{5/2})$ server time and $O(n^{3/2})$ user time. With a typically large number of participants in local algorithms ($n$ in the millions), this reduction in time complexity is crucial for making locally-private heavy-hitters algorithms usable in practice.

Joint work with Raef Bassily, Kobbi Nissim, and Abhradeep Thakurta.

ThursdayNov 30, 201713:30
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Fanny Augeri Title:Large deviations principles for random matricesAbstract:opens in new windowin html    pdfopens in new windowPlease note that the seminar's starting time has been permanently changed to 13:30

In this talk, I will try to present some techniques to handle the problem of large deviations of the spectrum of random matrices. I will focus on the case of macroscopic statistics of the spectrum of Hermitian matrices - in particular Wigner matrices - as the empirical distribution of the eigenvalues, the largest eigenvalue or the traces of powers.

In a first part, I will be concerned with the so-called "objective method''. Coined by David Aldous, this method consists in introducing, given a sequence of random objects, like random finite graphs, a new infinite random object from which one can deduce asymptotic properties of the original sequence. In the context of random matrices, this method has been mainly advertised by Balint Virag, and proven effective in showing universality results for the so-called beta-ensembles. Regarding large deviations of random matrices, this "objective method'' amounts to embed our sequence of matrices with growing size into an appropriate space on which one is able to understand the large deviations, and carry out a contraction principle. I will review several large deviations principles obtained by this method, given by interpretations of random matrices as either dense or sparse graphs, and point out the limits of this strategy.

WednesdayNov 29, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Roy Lederman Title:Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)Abstract:opens in new windowin html    pdfopens in new window

Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. "hyper-molecules", the first mathematical formulation of truly continuously heterogeneous molecules, 2. The optimal representation of objects that are highly concentrated in both the spatial domain and the frequency domain using high-dimensional prolate spheroidal functions, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.

TuesdayNov 28, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Yuanqing Cai Title:Weyl group multiple Dirichlet seriesAbstract:opens in new windowin html    pdfopens in new window

Weyl group multiple Dirichlet series are Dirichlet series in r complex variables which initially converge on a cone in C^r, possess analytic continuation to a meromorphic function on the whole complex space, and satisfy functional equations whose action on C^r is isomorphic to the Weyl group of a reduced root system. I will review different constructions of such series and discuss the relations between them.

MondayNov 27, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Yakov Babichenko Title:Informational Bounds on Approximate Nash EquilibriaAbstract:opens in new windowin html    pdfopens in new window

The talk will discuss informational lower bounds of approximate Nash equilibrium in two complexity models: Query Complexity and Communication Complexity.
For both models we prove exponential (in the number of players) lower bound on the complexity of computing ε -Nash equilibrium, for constant value of approximation ε .

ThursdayNov 23, 201714:10
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Naomi Feldheim Title:Persistence of Gaussian Stationary ProcessesAbstract:opens in new windowin html    pdfopens in new window

Consider a real Gaussian stationary process, either on Z or on R.
What is the probability that it remains positive on [0,N] for large N?

The relation between this probability, known as the persistence probability, and the covariance kernel of the process has been investigated since the 1950s with motivations stemming from probability, engineering and mathematical physics. Nonetheless, until recently, good estimates were known only for particular cases, or when the covariance kernel is either non-negative or summable.

In the first hour of the talk we will discuss new spectral methods which greatly simplify the analysis of persistence. We will then describe its qualitative behavior in a very general setting.

In the second hour, we will describe (very) recent progress. In particular we will show the proof of the "spectral gap conjecture'', which states: if the spectral measure vanishes on an interval containing 0 then the persistence is less then e^{-cN^2}, and this bound is tight if the measure is non-singular and compactly supported. 
Time permitting, we will also discuss "tiny persistence'' phenomena (of the order of e^{-e^{cN}}).

Based on joint works with Ohad Feldheim, Benjamin Jaye, Fedor Nazarov and Shahaf Nitzan.

ThursdayNov 23, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Aviv GabbayTitle:Seeing Through Noise: Visually Driven Speaker Separation and EnhancementAbstract:opens in new windowin html    pdfopens in new window

Isolating the voice of a specific person while filtering out other voices or background noises is challenging when video is shot in noisy environments, using a single microphone. For example, video conferences from home or office are disturbed by other voices, TV reporting from city streets is mixed with traffic noise, etc. We propose audio-visual methods to isolate the voice of a single speaker and eliminate unrelated sounds. Face motions captured in the video are used to estimate the speaker's voice, which is applied as a filter on the input audio. This approach avoids using mixtures of sounds in the learning process, as the number of such possible mixtures is huge, and would inevitably bias the trained model.

In the first part of this talk, I will describe a few techniques to predict speech signals by a silent video of a speaking person. In the second part of the talk, I will propose a method to separate overlapping speech of several people speaking simultaneously (known as the cocktail-party problem), based on the speech predictions generated by video-to-speech system.

WednesdayNov 22, 201716:15
Special Guest LectureRoom 290C
Speaker:Dalia TerhesiuTitle:The pressure function for infinite equilibrium Abstract:opens in new windowin html    pdfopens in new window

 Assume that $(X,f)$ is a dynamical system and $\phi$ is a real non negative potential such that the corresponding $f$-invariant measure $\mu_\phi$ measure is infinite.  Under assumptions of good inducing schemes, we give conditions under which the pressure of $f$ for a perturbed potential $\phi+s\psi$ relates to the pressure of the induced system term.
This extends some of Sarig's results to the setting of infinite "equilibrium states".
In addition, limit properties of the family of measures $\mu_{\phi+s\psi}$ as $s\to 0$ are studied and statistical properties (e.g. correlation coefficients) under the limit measure are derived. I will discuss several examples.
This is based on joint work with H. Bruin and M. Todd.

WednesdayNov 22, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Alexander Elashvili Title:About Index of Lie AlgebrasAbstract:opens in new windowin html    pdfopens in new window
In my talk I plan to give overview of results about of index of biparaboic subalgebras of classical Lie algebras and formulate conjecture about asymptotic biheviar of lieandric numbers.
TuesdayNov 21, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Raf Cluckers Title:Uniform p-adic integration and applications Abstract:opens in new windowin html    pdfopens in new window

As a concrete variant of motivic integration, I will discuss uniform p-adic integration and constructive aspects of results involved. Uniformity is in the p-adic fields, and, for large primes p, in the fields F_p((t)) and all their finite field extensions. Using real-valued Haar measures on such fields, one can study integrals, Fourier transforms, etc. We follow a line of research that Jan Denef started in the eighties, with in particular the use of model theory to study various questions related to p-adic integration. A form of uniform p-adic quantifier elimination is used. Using the notion of definable functions, one builds constructively a class of complex-valued functions which one can integrate (w.r.t. any of the variables) without leaving the class. One can also take Fourier transforms in the class. Recent applications in the Langlands program are based on Transfer Principles for uniform p-adic integrals, which allow one to get results for F_p((t)) from results for Q_p, once p is large, and vice versa. These Transfer Principles are obtained via the study of general kinds of loci, some of them being zero loci. More recently, these loci are playing a role in the uniform study of p-adic wave front sets for (uniformly definable) p-adic distributions, a tool often used in real analysis.
This talk contains various joint works with Gordon, Hales, Halupczok, Loeser, and Raibaut, and may mention some work in progress with Aizenbud about WF-holonomicity of these distributions, in relation to a question raized by Aizenbud and Drinfeld.

WednesdayNov 15, 201714:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Liran ShaulTitle:Injective modules in higher algebraAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DAY AND TIME
The notion of an Injective module is one of the most fundamental notions in homological algebra over rings. In this talk, we explain how to generalize this notion to higher algebra. The Bass-Papp theorem states that a ring is left noetherian if and only if an arbitrary direct sum of left injective modules is injective. We will explain a version of this result in higher algebra, which will lead us to the notion of a left noetherian derived ring. In the final part of the talk, we will specialize to commutative noetherian rings in higher algebra, show that the Matlis structure theorem of injective modules generalize to this setting, and explain how to deduce from it a version of Grothendieck's local duality theorem over commutative noetherian local DG rings.
WednesdayNov 15, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Ilya SoloveychikTitle:Group Symmetric Robust Covariance EstimationAbstract:opens in new windowin html    pdfopens in new window

Covariance matrix estimation is essential in many areas of modern Statistics and Machine Learning including Graphical Models, Classification/Discriminant Analysis, Principal Component Analysis, and many others. Classical statistics suggests using Sample Covariance Matrix (SCM) which is a Maximum Likelihood Estimator (MLE) in the Gaussian populations. Real world data, however, usually exhibits heavy-tailed behavior and/or contains outliers, making the SCM non-efficient or even useless. This problem and many similar ones gave rise to the Robust Statistics field in early 60s, where the main goal was to develop estimators stable under reasonable deviations from the basic Gaussian assumptions. One of the most prominent robust covariance matrix estimators was introduced and thoroughly studied by D. Tyler in the mid-80s. This important representative of the family of M-estimators can be defined as an MLE of a certain population. The problem of robust covariance estimation becomes even more involved in the high-dimensional scenario, where the number of samples n is of the order of the dimension p, or even less. In such cases, prior knowledge, often referred to as structure, is utilized to decrease the number of degrees of freedom and make the estimation possible. Unlike the Gaussian setting, in Tyler's case even imposition of linear structure becomes challenging due to the non-convexity of the negative log-likelihood. Recently, Tyler's target function was shown to become convex under a certain change of metric (geodesic convexity), which stimulated further investigation of the estimator.

In this work, we focus on the so-called group symmetry structure, which essentially means that the true covariance matrix commutes with a group of unitary matrices. In engineering applications such structures appear due to the natural symmetries of the physical processes; examples include circulant, perHermitian, proper quaternion matrices, etc. Group symmetric constraints are linear, and thus convex in the regular Euclidean metric. We show that they are also convex in the geodesic metric. These properties allow us to develop symmetric versions of the SCM and Tyler's estimator and build a general framework for their performance analysis. The classical results claim that at least n = p and n = p+1 samples in general position are necessary to ensure the existence and uniqueness of the SCM and Tyler's estimator, respectively. We significantly improve the sample complexity requirements for both estimators under the symmetry structure and show that in some cases even 1 or 2 samples are enough to guarantee the existence and uniqueness regardless of the ambient dimension.

TuesdayNov 14, 201716:15
Geometry and Topology Seminar & Mathematical Analysis and Applications SeminarRoom 290C
Speaker:Ran TesslerTitle:Integrable hierarchies, wave functions and open intersection theoriesAbstract:opens in new windowin html    pdfopens in new window
I will Describe KP hierarchy, its reductions KdV and r-GD, tau functions and wave functions. Witten's conjectured that the tau functions are the generating functions of intersection numbers over the moduli of curves/ r-spin curves (these conjectures are now Kontsevich's theorem and Faber-Shadrin-Zvonkine theorem resp.). Recently the following was conjectured: a. The KdV wave function is a generating function of intersection numbers on moduli of "Riemann surfaces with boundary" (Pandharipande-Solomon-T,Solomon-T,Buryak). b. The r-th GD wave function is the generating function of intersection numbers on moduli of "r-spin Riemann surfaces with boundary" (Buryak-Clader-T). I will describe the conjectures, and sketch the proof of conjecture (a) (Pandharipande-Solomon-T in genus 0, T,Buryak-T for the general case). If there will be time, I'll describe a conjectural generalization by Alexandrov-Buryak-T, and explain why the proof of (b) in high genus seems currently unreachable.
TuesdayNov 14, 201711:15
Distinguished Lecture SeriesRoom 1
Speaker:Prof. Yakov PesinTitle:The Dynamical Systems Approach to Coupled Map LatticesAbstract:opens in new windowin html    pdfopens in new window
Coupled Map Lattices (CML) of an unbounded media appear as a result of time and space discretization of evolutional partial differential equations but can also be viewed as original phenomenological models of the medium. I will present the dynamical systems approach to study the global behavior of solutions of CML. In particular, I will describe the dynamics of the evolution operator on the set of traveling wave solutions of CML and discuss the phenomenon known as spatio-temporal chaos. I will illustrate this phenomenon in the particular example of CML associated with the famous FitzHue-Nagumo equation that describes propagation of voltage impulse through a nerve axon. When the leading parameter of this equation varies the dynamics undergoes several stages presenting Morse-Smale type dynamics, strange attractors and Smale horseshoes.
MondayNov 13, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Eric Balkanski Title:The Adaptive Complexity of Maximizing a Submodular FunctionAbstract:opens in new windowin html    pdfopens in new window

In this paper we study the adaptive complexity of submodular optimization. Informally, the adaptive complexity of a problem is the minimal number of sequential rounds required to achieve a constant factor approximation when polynomially-many queries can be executed in parallel at each round. Adaptivity is a fundamental concept that is heavily studied in computer science, largely due to the need for parallelizing computation. Somewhat surprisingly, very little is known about adaptivity in submodular optimization. For the canonical problem of maximizing a monotone submodular function under a cardinality constraint, to the best of our knowledge, all that is known to date is that the adaptive complexity is between 1 and Ω(n).Our main result in this paper is a tight characterization showing that the adaptive complexity of maximizing a monotone submodular function under a cardinality constraint is, up to lower order terms, θ(log n):We describe an algorithm which requires O(log n) sequential rounds and achieves an approximation that is arbitrarily close to 1/3; We show that no algorithm can achieve an approximation better than O(1 / log n) with fewer than O(log n / log log n) rounds. Thus, when allowing for parallelization, our algorithm achieves a constant factor approximation exponentially faster than any known existing algorithm for submodular maximization.  Importantly, the approximation algorithm is achieved via adaptive sampling and complements a recent line of work on optimization of functions learned from data. In many cases, we do not know the functions we optimize and learn them from labeled samples. Recent results show that no algorithm can obtain a constant factor approximation guarantee using polynomially-many labeled samples as in the PAC and PMAC models, drawn from any distribution. Since learning with non-adaptive samples over any distribution results in a sharp impossibility, we consider learning with adaptive samples where the learner obtains poly(n) samples drawn from a distribution of her choice in every round. Our result implies that in the realizable case, where there is a true underlying function generating the data, θ(log n) batches, up to lower order terms, of adaptive samples are necessary and sufficient to approximately "learn to optimize" a monotone submodular function under a cardinality constraint. This is joint work with Yaron Singer.

ThursdayNov 09, 201714:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Ilya GoldsheidTitle:Real and complex eigenvalues of the non-self-adjoint Anderson model.Abstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL TIME
TBA
MondayNov 06, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Scott AaronsonTitle:New Results on Learning and Reconstruction of Quantum StatesAbstract:opens in new windowin html    pdfopens in new window

Given an unknown D-dimensional quantum state rho, as well as M two-outcome measurements E_1,...,E_M, how many copies of rho do we need, if we want to learn the approximate probability that E_i accepts rho for *every* i? In this talk, I'll prove the surprising result --I didn't believe it myself at first -- that one can achieve this using a number of copies that's polylogarithmic in both M and D. So, e.g., one can learn whether *every* size-n^3 quantum circuit accepts or rejects an n-qubit state, given only poly(n) copies of the state. To prove this will require first surveying previous results on measuring quantum states and succinctly describing them, including my 2004 postselected learning theorem, and my 2006 "Quantum OR Bound" (with an erroneous proof fixed in 2016 by Harrow, Lin, and Montanaro).

As time permits, I'll also discuss new joint work with Xinyi Chen, Elad Hazan, and Ashwin Nayak, which takes my 2006 result on PAC-learnability of quantum states, and extends to the setting of online learning. Here we show that, given a sequence of T two-outcome measurements on an n-qubit state, even if the sequence is chosen adversarially, one can still learn to predict the outcomes of those measurements with total regret O(n) (in the "realizable" case) or O(sqrt(Tn)) (in the "non-realizable" case).

No quantum computing background will be assumed.

WednesdayNov 01, 201711:15
Vision and Robotics SeminarRoom 1
Speaker:Tal HassnerTitle:A Decade of Faces in the WildAbstract:opens in new windowin html    pdfopens in new windowJOINT VISION AND MACHINE LEARNING SEMINAR
Faces are undoubtedly one of the most rigorously studied object classes in computer vision and recognizing faces from their pictures is one of the classic problems of the field. Fueled by applications ranging from biometrics and security to entertainment and commerce, massive research efforts were directed at this problem from both academia and industry. As a result, machine capabilities rose to the point where face recognition systems now claim to surpass even the human visual system. My own work on this problem began nearly a decade ago. At that time, the community shifted its interests from the (largely) solved problem of recognizing faces appearing in controlled, high quality images to images taken in the wild, where no control is assumed over how the faces are viewed. In this talk, I will provide my perspectives on this problem and the solutions proposed to solve it. I will discuss the rationale which drove the design of our methods, their limitations, and breakthroughs. In particular, I will show how classical computer vision methods and, surprisingly, elementary computer graphics, work together with modern deep learning in the design of our state of the art face recognition methods.
TuesdayOct 31, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Walter Gubler Title:The non-Archimedean Monge-Ampere problemAbstract:opens in new windowin html    pdfopens in new window

Calabi conjectured that the complex Monge-Ampere equation on compact Kaehler manifolds has a unique solution.
This was solved by Yau in 1978. In this talk, we present a non-archimedean version on projective Berkovich spaces.
In joint work with Burgos, Jell, Kunnemann and Martin, we improve a result of  Boucksom, Favre and Jonsson in the equicharacteristic 0 case. We give also a result in positive equicharacteristic using test ideals.

TuesdayOct 17, 201716:15
Geometry and Topology Seminar & Mathematical Analysis and Applications SeminarRoom 290C
Speaker:Gabriel Katz Title:Holography of traversing flows and its applications to the inverse scattering problemsAbstract:opens in new windowin html    pdfopens in new window

We study the non-vanishing gradient-like vector fields $v$ on smooth compact manifolds $X$ with boundary. We call such fields traversing. With the help of a boundary generic field $v$, we divide the boundary $\d X$ of $X$ into two complementary compact manifolds, $\d^+X(v)$ and $\d^-X(v)$. Then we introduce the causality map $C_v: \d^+X(v) \to \d^-X(v)$, a distant relative of the Poincare return map. Let $\mathcal F(v)$ denote the oriented 1-dimensional foliation on $X$, produced by a traversing $v$-flow.

Our main result, the Holography Theorem, claims that, for boundary generic traversing vector fields $v$, the knowledge of the causality map $C_v$ is allows for a reconstruction of the pair $(X, \mathcal F(v))$, up to a homeomorphism $\Phi: X \to X$ which is the identity on the boundary $\d X$. In other words, for a massive class of ODE's, we show that the topology of their solutions, satisfying a given boundary value problem, is rigid. We call these results ``holographic" since the $(n+1)$-dimensional $X$ and the un-parameterized dynamics of the flow on it are captured by a single correspondence $C_v$ between two $n$-dimensional screens, $\d^+X(v)$ and $\d^-X(v)$.

This holography of traversing flows has numerous applications to the dynamics of general flows. Time permitting, we will discuss some applications of the Holography Theorem to the geodesic flows and the inverse scattering problems on Riemannian manifolds with boundary.

WednesdaySep 06, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Thorsten HeidersdorfTitle:Reductive groups attached to representations of the general linear supergroup GL(m|n)Abstract:opens in new windowin html    pdfopens in new window

Let Rep(GL(m|n)) denote the category of finite-dimensional algebraic representations of the supergroup Gl(m|n). Nowadays the abelian structure (Ext^1 between irreducibles, block description,...) is well understood. Kazhdan-Lusztig theory gives an algorithmic solution for the character problem, and in special cases even explicit character formulas. However we understand the monoidal structure hardly at all (e.g. the decomposition of tensor products into the indecomposable constituents). I will talk about the problem of decomposing tensor products "up to superdimension 0", i.e. about the structure of Rep(GL(m|n))/N where N is the ideal of indecomposable representations of superdimension 0.

MondaySep 04, 201714:00
Vision and Robotics SeminarRoom 1
Speaker:Ita LifshitzTitle:Hand-object interaction: a step towards action recognitionAbstract:opens in new windowin html    pdfopens in new windowNOTE THE UNUSUAL TIME AND DAY

When dealing with a highly variable problem such as action recognition, focusing on a small area, such as the hand's region, makes the problem more manageable, and enables us to invest relatively high amount of resources needed for interpretation in a small but highly informative area of the image. In order to detect this region of interest in the image and properly analyze it, I have built a process that includes several steps, starting with a state of the art hand detector, incorporating both detection of the hand by appearance and by estimation of human body pose. The hand detector is built upon a fully convolutional neural network, detecting hands efficiently and accurately. The human body pose estimation starts with a state of the art head detector and continues with a novel approach where each location in the image votes for the position of each body keypoint, utilizing information from the whole image. Using dense, multi-target votes enables us to compute image-dependent joint keypoint probabilities by looking at consensus voting, and accurately estimates the body pose. Once the detection of the hands is complete, an additional step of segmentation of the hand and fingers is made. In this step each hand pixel in the image is labeled using a dense fully convolutional network. Finally, an additional step is made to segment and identify the held object. Understanding the hand-object interaction is an important step toward understanding the action taking place in the image. These steps enable us to perform fine interpretation of hand-object interaction images as an essential step towards understanding the human-object interaction and recognizing human activities.

TuesdayJul 11, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Jasmine Fittouhi Title:The uncovering of fibers’ Mumford systemAbstract:opens in new windowin html    pdfopens in new window
This talk is dedicate to the description of the fibers resulting from the Mumford system of degree g>0. Each fiber is linked to a hyperelliptic curve; we will focus our description more specifically to the ones linked to singular hyperelliptic curves. These fibers are arranged hierarchically by stratification which allows us to provide a geometrical as well as an algebraic understanding of fibers that result in an isomorphism between a fiber and a part of a commutative algebraic group associated to its singular hyperelliptic curves in other words the generalized Jacobian.
MondayJul 10, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Rohit Gurjar Title:Derandomizing Isolation Lemma: a geometric approachAbstract:opens in new windowin html    pdfopens in new window
We present a geometric approach towards derandomizing the Isolation lemma for a given family, i.e., deterministically constructing a weight assingnment which ensures a unique minimum weight set in the family. The idea is to work with a polytope corresponding to the family of sets. In this talk, we present the approach in terms of general polytopes and describe a sufficient condition on the polytope for this approach to work. The approach gives a quasi-polynomially bounded weight assignment. Finally, we show that two specific families - perfect matchings in bipartite graphs and common base sets of two matroids - satisfy the required condition and thus, we get an isolating weight assignment for these cases. This also puts the two problems in quasi-NC. Based on joint works with Stephen Fenner and Thomas Thierauf.
ThursdayJul 06, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Tammy Riklin-Raviv Title:Big data - small training sets: biomedical image analysis bottlenecks, some strategies and applications Abstract:opens in new windowin html    pdfopens in new window

Recent progress in imaging technologies leads to a continuous growth in biomedical data, which can provide better insight into important clinical and biological questions. Advanced machine learning techniques, such as artificial neural networks are brought to bear on addressing fundamental medical image computing challenges such as segmentation, classification and reconstruction, required for meaningful analysis of the data. Nevertheless, the main bottleneck, which is the lack of annotated examples or 'ground truth' to be used for training, still remains.

In my talk, I will give a brief overview on some biomedical image analysis problems we aim to address, and suggest how prior information about the problem at hand can be utilized to compensate for insufficient or even the absence of ground-truth data. I will then present a framework based on deep neural networks for the denoising of Dynamic contrast-enhanced MRI (DCE-MRI) sequences of the brain. DCE-MRI is an imaging protocol where MRI scans are acquired repetitively throughout the injection of a contrast agent, that is mainly used for quantitative assessment of blood-brain barrier (BBB) permeability. BBB dysfunctionality is associated with numerous brain pathologies including stroke, tumor, traumatic brain injury, epilepsy. Existing techniques for DCE-MRI analysis are error-prone as the dynamic scans are subject to non-white, spatially-dependent and anisotropic noise. To address DCE-MRI denoising challenges we use an ensemble of expert DNNs constructed as deep autoencoders, where each is trained on a specific subset of the input space to accommodate different noise characteristics and dynamic patterns. Since clean DCE-MRI sequences (ground truth) for training are not available, we present a sampling scheme, for generating realistic training sets with nonlinear dynamics that faithfully model clean DCE-MRI data and accounts for spatial similarities. The proposed approach has been successfully applied to full and even temporally down-sampled DCE-MRI sequences, from two different databases, of stroke and brain tumor patients, and is shown to favorably compare to state-of-the-art denoising methods.

WednesdayJul 05, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Ronen TalmonTitle:Common Manifold Learning with Alternating DiffusionAbstract:opens in new windowin html    pdfopens in new window

We consider the problem of hidden common manifold extraction from multiple data sets, which have observation-specific distortions and artifacts. A new manifold learning method is presented based on alternating products of diffusion operators and local kernels. We provide theoretical analysis showing that our method is able to build a variant of the Laplacian of the hidden common manifold, while suppressing the observation-specific artifacts. The generality of this method is demonstrated in data analysis applications, where different types of devices are used to measure the same activity. In particular, we present applications to problems in biomedicine, neuroscience, and audio analysis. 
This is joint work with Roy Lederman and Hau-tieng Wu.

TuesdayJul 04, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Claude BardosTitle:Some remarks about Fractional Laplacian in connection with kinetic theoryAbstract:opens in new windowin html    pdfopens in new window
This talk will contain some remarks on the different aspects of the fractional Laplacian and a derivation of fractional diffusion from Kinetic Models inspired by the work of Mellet and illustrated by an example of Uriel and Helene Frisch on radiative transfert which goes back to 1977.
MondayJul 03, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Omri WeinsteinTitle:Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower BoundsAbstract:opens in new windowin html    pdfopens in new window

We prove the first super-logarithmic lower bounds on the cell probe complexity of dynamic *boolean* (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new technique and use it to prove a ~ log^{1.5}(n) lower bound on the operational time of a wide range of boolean data  structure problems, most notably, on the query time of dynamic range counting *over F_2* ([Patrascu07]). Proving a super-logarithmic lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai Patrascu's obituary [Tho13]. This result also implies the first super-logarithmic lower bound for the classical 2D range counting problem,one of the most fundamental data structure problems in computational geometry and spatial databases. We derive similar lower bounds for boolean versions of dynamic polynomial evaluation and 2D "rectangle stabbing", and for the (non-boolean) problems of range selection and range median. Our technical centerpiece is a new way of "weakly" simulating dynamic data structures using efficient *one-way* communication protocols with small advantage over random guessing. This simulation involves a surprising excursion to low-degree (Chebychev) polynomials which may be of independent interest, and offers an entirely new algorithmic angle on the "cell sampling" method of Panigrahy et al. [PTW10].

Joint work with Kasper Green-Larsen and Huacheng Yu.

ThursdayJun 29, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Shai AvidanTitle:Co-occurrence FilterAbstract:opens in new windowin html    pdfopens in new window
Co-occurrence Filter (CoF) is a boundary preserving filter. It is based on the Bilateral Filter (BF) but instead of using a Gaussian on the range values to preserve edges it relies on a co-occurrence matrix. Pixel values that co-occur frequently in the image (i.e., inside textured regions) will have a high weight in the co-occurrence matrix. This, in turn, means that such pixel pairs will be averaged and hence smoothed, regardless of their intensity differences. On the other hand, pixel values that rarely co-occur (i.e., across texture boundaries) will have a low weight in the co-occurrence matrix. As a result, they will not be averaged and the boundary between them will be preserved. The CoF therefore extends the BF to deal with boundaries, not just edges. It learns co-occurrences directly from the image. We can achieve various filtering results by directing it to learn the co-occurrence matrix from a part of the image, or a different image. We give the definition of the filter, discuss how to use it with color images and show several use cases. Joint work with Roy Jevnisek
ThursdayJun 29, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Amir Dembo Title:The criticality of a randomly-driven front.Abstract:opens in new windowin html    pdfopens in new window
Consider independent continuous-time random walks on the integers to the right of a front R(t). Starting at R(0)=0, whenever a particle attempts to jump into the front, the latter instantaneously advances k steps to the right, absorbing all particles along its path. Sly (2016) resolves the question of Kesten and Sidoravicius (2008), by showing that for k=1 the front R(t) advances linearly once the particle density exceeds 1, but little is known about the large t asymptotic of R(t) at critical density 1. In a joint work with L-C Tsai, for the variant model with k taken as the minimal random integer such that exactly k particles are absorbed by the move of R(t), we obtain both scaling exponent and the random scaling limit for the front at the critical density 1. Our result unveils a rarely seen phenomenon where the macroscopic scaling exponent is sensitive to the initial local fluctuations (with the scaling limit oscillating between instantaneous super and sub-critical phases).
MondayJun 26, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Ilan CohenTitle:Randomized Online Matching in Regular GraphsAbstract:opens in new windowin html    pdfopens in new window

We study the classic bipartite matching problem in the online setting,  first introduced in the seminal work of Karp, Vazirani and Vazirani. Specifically, we consider the problem for the well-studied class of regular graphs. Matching in this class of graphs was studied extensively in the offline setting. In the online setting, an optimal deterministic algorithm, as well as efficient algorithms under stochastic input assumptions were known. In this work, we present a novel randomized algorithm with competitive ratio tending to one on this family of graphs, under adversarial arrival order. Our main contribution is a novel algorithm which achieves competitive ratio 1-O(\sqrt{\log d}/\sqrt{d}) in expectation on d-regular graphs. In contrast, we show that all previously-known online algorithms, such as the generally worst-case optimal ranking algorithm of Karp et al., are restricted to a competitive ratio strictly bounded away from one, even as d grows. Moreover, we show the convergence rate of our algorithm's competitive ratio to one is nearly tight, as no algorithm achieves competitive ratio better than 1-O(1/\sqrt{d}). Finally, we show that our algorithm yields a similar competitive ratio with high probability, as well as guaranteeing each offline vertex a probability of being matched tending to one.

ThursdayJun 22, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Haggai MaronTitle:Convolutional Neural Networks on Surfaces via Seamless Toric CoversAbstract:opens in new windowin html    pdfopens in new window

The recent success of convolutional neural networks (CNNs) for image processing tasks is inspiring research efforts attempting to achieve similar success for geometric tasks. One of the main challenges in applying CNNs to surfaces is defining a natural convolution operator on surfaces. In this paper we present a method for applying deep learning to sphere-type shapes using a global seamless parameterization to a planar flat-torus, for which the convolution operator is well defined. As a result, the standard deep learning framework can be readily applied for learning semantic, high-level properties of the shape. An indication of our success in bridging the gap between images and surfaces is the fact that our algorithm succeeds in learning semantic information from an input of raw low-dimensional feature vectors. 

We demonstrate the usefulness of our approach by presenting two applications: human body segmentation, and automatic landmark detection on anatomical surfaces. We show that our algorithm compares favorably with competing geometric deep-learning algorithms for segmentation tasks, and is able to produce meaningful correspondences on anatomical surfaces where hand-crafted features are bound to fail.

Joint work with: Meirav Galun, Noam Aigerman, Miri Trope, Nadav Dym, Ersin Yumer, Vladimir G. Kim and Yaron Lipman.
 

WednesdayJun 21, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Raja Giryes Title:On the relationship between structure in the data and what deep learning can learnAbstract:opens in new windowin html    pdfopens in new window

The past five years have seen a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for feature learning and classification. However, the mathematical reasons for this success remain elusive. In this talk we will briefly survey some existing theory of deep learning. In particular, we will focus on data structure based theory and discuss two recent developments. 
The first work studies the generalization error of deep neural network. We will show how the generalization error of deep networks can be bounded via their classification margin. We will also discuss the implications of our results for the regularization of the networks. For example, the popular weight decay regularization guarantees the margin preservation, but it leads to a loose bound to the classification margin. We show that a better regularization strategy can be obtained by directly controlling the properties of the network's Jacobian matrix. 
The second work focuses on solving minimization problems with neural networks. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence of certain iterative algorithms with an error related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing and deep learning. In particular, it provides an explanation for the successful approximation of the ISTA (iterative shrinkage and thresholding algorithm) solution by neural networks with layers representing iterations. 

Joint work with Guillermo Sapiro, Miguel Rodrigues, Jure Sokolic, Alex Bronstein and Yonina Eldar. 

TuesdayJun 20, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 141
Speaker:Luc IllusieTitle:Revisiting vanishing cycles and duality in étale cohomologyAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL ROOM
Abstract: In the early 1980's Gabber proved compatibility of nearby cycles with duality and Beilinson compatibility of vanishing cycles with duality. I will explain new insights and results on this topic, due to Beilinson, Gabber, and Zheng.
ThursdayJun 15, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Ron KimmelTitle:On Learning Invariants and Representation Spaces of Shapes and FormsAbstract:opens in new windowin html    pdfopens in new window
We study the power of the Laplace Beltrami Operator (LBO) in processing and analyzing geometric information. The decomposition of the LBO at one end, and the heat operator at the other end provide us with efficient tools for dealing with images and shapes. Denoising, segmenting, filtering, exaggerating are just few of the problems for which the LBO provides an efficient solution. We review the optimality of a truncated basis provided by the LBO, and a selection of relevant metrics by which such optimal bases are constructed. Specific example is the scale invariant metric for surfaces that we argue to be a natural selection for the study of articulated shapes and forms. In contrast to geometry understanding there is a new emerging field of deep learning. Learning systems are rapidly dominating the areas of audio, textual, and visual analysis. Recent efforts to convert these successes over to geometry processing indicate that encoding geometric intuition into modeling, training, and testing is a non-trivial task. It appears as if approaches based on geometric understanding are orthogonal to those of data-heavy computational learning. We propose to unify these two methodologies by computationally learning geometric representations and invariants and thereby take a small step towards a new perspective on geometry processing. I will present examples of shape matching, facial surface reconstruction from a single image, reading facial expressions, shape representation, and finally definition and computation of invariant operators and signatures.
ThursdayJun 15, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Piotr Nayar Title:Gaussian mixtures with applications to entropy inequalities and convex geometryAbstract:opens in new windowin html    pdfopens in new window
We say that a symmetric random variable X is a Gaussian mixture if X has the same distribution as YG, where G is a standard Gaussian random variable, and Y is a positive random variable independent of G. In the first part of the talk we use this simple notion to study the Shannon entropy of sums of independent random variables. In the second part we investigate, using Gaussian mixtures, certain topics related to the geometry of B_p^n balls, including optimal Khinchine-type inequalities and Schur-type comparison for volumes of section and projections of these sets. In the third part we discuss extensions of Gaussian correlation inequality to the case of p-stable laws and uniform measure on the Euclidean sphere. Based on a joint work with Alexandros Eskenazis and Tomasz Tkocz.
ThursdayJun 15, 201711:00
Foundations of Computer Science SeminarRoom 141
Speaker:Ariel Procaccia Title:Computational Social Choice: For the PeopleAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY, TIME AND ROOM

Computational social choice deals with algorithms for aggregating individual preferences or opinions towards collective decisions. AI researchers (including myself) have long argued that such algorithms could play a crucial role in the design and implementation of multiagent systems. However, in the last few years I have come to realize that the "killer app" of computational social choice is helping people -- not software agents -- make joint decisions. I will illustrate this theme through two recent endeavors: Spliddit.org, a website that offers provably fair solutions to everyday problems; and Robovote.org, which provides optimization-driven voting methods.

Throughout the talk, I will devote special attention to the theoretical foundations and results that make these services possible.

ThursdayJun 08, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Nadav CohenTitle:Expressive Efficiency and Inductive Bias of Convolutional Networks: Analysis and Design through Hierarchical Tensor DecompositionsAbstract:opens in new windowin html    pdfopens in new windowJOINT VISION AND MACHINE LEARNING SEMINAR
The driving force behind convolutional networks - the most successful deep learning architecture to date, is their expressive power. Despite its wide acceptance and vast empirical evidence, formal analyses supporting this belief are scarce. The primary notions for formally reasoning about expressiveness are efficiency and inductive bias. Efficiency refers to the ability of a network architecture to realize functions that require an alternative architecture to be much larger. Inductive bias refers to the prioritization of some functions over others given prior knowledge regarding a task at hand. Through an equivalence to hierarchical tensor decompositions, we study the expressive efficiency and inductive bias of various architectural features in convolutional networks (depth, width, pooling geometry and more). Our results shed light on the demonstrated effectiveness of convolutional networks, and in addition, provide new tools for network design. The talk is based on a series of works published in COLT, ICML, CVPR and ICLR (as well as several new preprints), with collaborators Or Sharir, Ronen Tamari, David Yakira, Yoav Levine and Amnon Shashua.
ThursdayJun 08, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Nishant ChandgotiaTitle:Irrational rotations, random affine transformations and the central limit theoremAbstract:opens in new windowin html    pdfopens in new window
It is a well-known result from Hermann Weyl that if alpha is an irrational number in [0,1) then the number of visits of successive multiples of alpha modulo one in an interval contained in [0,1) is proportional to the size of the interval. In this talk we will revisit this problem, now looking at finer joint asymptotics of visits to several intervals with rational end points. We observe that the visit distribution can be modelled using random affine transformations; in the case when the irrational is quadratic we obtain a central limit theorem as well. Not much background in probability will be assumed. This is in joint work with Jon Aaronson and Michael Bromberg.
TuesdayJun 06, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Klaus KunnemannTitle:Positivity properties of metrics in non-archimedean geometryAbstract:opens in new windowin html    pdfopens in new window
We describe the Calabi-Yau problem on complex manifolds and its analog in non-archimedean geometry. We discuss positivity properties of metrics on line bundles over non-archimedean analytic spaces and applications to the solution of the non-archimedean Calabi-Yau problem in the equicharacteristic zero case.
ThursdayJun 01, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Nir Sharon Title:Synchronization over Cartan motion groupsAbstract:opens in new windowin html    pdfopens in new window
The mathematical problem of group synchronization deals with the question of how to estimate unknown group elements from a set of their mutual relations. This problem appears as an important step in solving many real-world problems in vision, robotics, tomography, and more. In this talk, we present a novel solution for synchronization over the class of Cartan motion groups, which includes the special important case of rigid motions. Our method is based on the idea of group contraction, an algebraic notion origin in relativistic mechanics.
TuesdayMay 30, 201711:15
Algebraic Geometry and Representation Theory Seminar
Speaker:Siddhartha Sahi Title:Multivariate Hypergeometric functions with a parameterAbstract:opens in new windowin html    pdfopens in new windowDe Picciotto Building, Room 25

The theory of hypergeometric functions with matrix argument was developed in the 1950s by S. Bochener for Hermitian matrices, and by C. Herz for symmetric matrices. This theory admits a common generalization to the setting of symmetric cones, which is discussed in the book by Faraut-Koranyi. It also has applications to the study of non-central distributions in statistics and to the theory of random matrices.

In the 1980s, I.G. Macdonald introduced a one parameter family of multivariate hypergeometric functions, which, for special values of the parameter, are the *radial* parts of the matrix hypergeometric functions. He also formulated a number of natural conjectures about these functions, which in the matrix case can be proved by appropriate integral formulas. However this technique is unavailable in the general setting and as a result these conjectures have remained open.


In recent work with G. Olafsson we have solved most of these conjectures, using ideas from the theory of Cherednik algebras and Jack polynomials. Among other results we obtain sharp estimates for the exponential kernel that allow us to establish a rigorous theory of the Fourier and Laplace transforms, and we prove an explicit formula for the Laplace transform of a Jack polynomial conjectured by Macdonald. This opens the door for several future developments in the associated harmonic analysis, some of which we also treat. This includes (1) the Paley-Wiener theorem, (2) Laplace transform identities for hypergeometric functions, and (3) the "so-called" Ramanujan master theorem.

 

Note the unusual room [De Picciotto Building, Room 25]

MondayMay 29, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Amnon Ta-Shma Title:Almost Optimal eps biasAbstract:opens in new windowin html    pdfopens in new window
The question of finding an epsilon-biased set with close to optimal support size, or, equivalently, finding an explicit binary code with distance 1/2-epsilon and rate close to the Gilbert-Varshamov bound, attracted a lot of attention in recent decades. In this paper we solve the problem almost optimally and show an explicit epsilon-biased set over k bits with support size O(k/epsilon^{2+o(1)}). This improves upon all previous explicit constructions which were in the order of k^2/epsilon^2, k/epsilon^3 or (k/epsilon^2)^{5/4}. The result is close to the Gilbert-Varshamov bound which is O(k/epsilon^2) and the lower bound which is $Omega(k/epsilon^2 log(1/epsilon)). The main technical tool we use is bias amplification with the s-wide replacement product. The sum of two independent samples from a biased set is epsilon^2 biased. Rozenman and Wigderson showed how to amplify the bias more economically by choosing two samples with an expander. Based on that they suggested a recursive construction that achieves sample size O(k/epsilon^4). We show that amplification with a long random walk over the s-wide replacement product reduces the bias almost optimally.
ThursdayMay 25, 201714:30
Foundations of Computer Science SeminarRoom 208
Speaker:Swastik Kopparty Title:Locally testable and locally correctable codes approaching the Gilbert-Varshamov boundAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY AND ROOM

We show that there exist binary locally testable codes (for all rates) and locally correctable codes (for low rates) with rate and distance approaching the Gilbert-Varshamov bound (which is the best rate-distance tradeoff known for general binary error-correcting codes). Our constructions use a number of ingredients: Thommesen's random concatenation technique, the Guruswami-Sudan-Indyk strategy for list-decoding concatenated codes, the Alon-Edmonds-Luby distance amplification method, and the local list-decodability and local testability of Reed-Muller codes. Interestingly, this seems to be the first time that local testability is used in the construction of locally correctable codes.

Joint work with Sivakanth Gopi, Rafael Oliveira, Noga Ron-Zewi and Shubhangi Saraf 
 

ThursdayMay 25, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Rafi MalachTitle:Neuronal "Ignitions" underlying stable representations in a dynamic visual environmentAbstract:opens in new windowin html    pdfopens in new window
The external world is in a constant state of flow- posing a major challenge to neuronal representations of the visual system that necessitate sufficient time for integration and perceptual decisions. In my talk I will discuss the hypothesis that one solution to this challenge is implemented by breaking the neuronal responses into a series of discrete and stable states. I will propose that these stable points are likely implemented through relatively long lasting "ignitions" of recurrent neuronal activity. Such ignitions are a pre-requisite for the emergence of a perceptual image in the mind of the observer. The self-sustained nature of the ignitions endows them with stability despite the dynamically changing inputs. Results from intracranial recordings in patients conducted for clinical diagnostic purposes during rapid stimulus presentations, ecological settings, blinks and saccadic eye movements will be presented in support of this hypothesis.
TuesdayMay 23, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 141
Speaker:Yakov Varshavsky Title:On the depth r Bernstein projector.Abstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE THE UNUSUAL ROOM

This is a joint work with Bezrukavnikov and Kazhdan. The goal of my talk is to give an explicit formula for the Bernstein projector to representations of depth $\leq r$. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth $r$ Bernstein projector is stable. Moreover, for integral depths our proof is purely local.

ThursdayMay 18, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Michael Elad Title:Regularization by Denoising (RED)Abstract:opens in new windowin html    pdfopens in new window

Image denoising is the most fundamental problem in image enhancement, and it is largely solved: It has reached impressive heights in performance and quality -- almost as good as it can ever get. But interestingly, it turns out that we can solve many other problems using the image denoising "engine". I will describe the Regularization by Denoising (RED) framework: using the denoising engine in defining the regularization of any inverse problem. The idea is to define an explicit image-adaptive regularization functional directly using a high performance denoiser. Surprisingly, the resulting regularizer is guaranteed to be convex, and the overall objective functional is explicit, clear and well-defined. With complete flexibility to choose the iterative optimization procedure for minimizing this functional, RED is capable of incorporating any image denoising algorithm as a regularizer, treat general inverse problems very effectively, and is guaranteed to converge to the globally optimal result.

* Joint work with Peyman Milanfar (Google Research) and Yaniv Romano (EE-Technion).

WednesdayMay 17, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Aryeh KontorovichTitle:Mixing Time Estimation in Reversible Markov Chains from a Single Sample PathAbstract:opens in new windowin html    pdfopens in new window

We propose a procedure (the first of its kind) for computing a fully data-dependent interval that traps the mixing time t_mix of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge.

The interval is constructed around the relaxation time t_relax, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a sqrt{n} rate, where n is the length of the sample path. Upper and lower bounds are given on the number of samples required to achieve constant-factor multiplicative accuracy. The lower bounds indicate that, unless further restrictions are placed on the chain, no procedure can achieve this accuracy level before seeing each state at least \Omega(t_relax) times on the average. Future directions of research are identified. Time permitting, we will mention some recent further developments by D. Levin and Y. Peres.

Joint work with Daniel Hsu and Csaba Szepesvari.

MondayMay 15, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Daniel KerenTitle:Monitoring Properties of Large, Distributed, Dynamic GraphsAbstract:opens in new windowin html    pdfopens in new window

Graphs that are prevalent in current applications (the Internet, Facebook etc.) are not only very large and highly dynamic, but also distributed between many servers, none of which sees the graph in its entirety. The distributed monitoring problem deals with the question of imposing conditions on the local graphs, such that as long as they hold, it is guaranteed that some desired property holds for the global graph.
While defining local conditions for linear properties (e.g. average degree) is relatively easy, they are more difficult to derive for non-linear functions over the graph. We propose a solution and a general definition of solution optimality, and demonstrate how to  apply it to two important graph properties -- spectral gap and number of triangles.  We also define an absolute lower bound on the communication overhead for distributed monitoring, and compare our algorithm to it, with good results. Performance improves as the graph becomes larger and denser -- that is, when distributing it is more important.

MondayMay 08, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Amos KormanTitle:From Ants to Query ComplexityAbstract:opens in new windowin html    pdfopens in new window

I will talk about my recent adventures with ants. Together with biologists we study P. longicornis ants as they collaboratively transport a large food item to their nest. This collective navigation process is guided by pheromones which are laid by individual ants. Using a new methodology to detect scent marks, we identify a new kind of ant trail characterized by very short and dynamic pheromone markings and highly stochastic navigation response to them. We argue that such a trail can be highly beneficial in conditions in which knowledge of individual ants regarding the underlying topological structure is unreliable. This gives rise to a new theoretical search model on graphs under unreliable guiding instructions, which is of independent computational interest. To illustrate the model, imagine driving a car in an unknown country that is in the aftermath of a major hurricane which has randomly flipped a certain small fraction of the road-signs. Under such conditions of unreliability, how can you still reach your destination fast? I will discuss the limits of unreliability that allow for efficient navigation. In trees, for example, there is a phase transition phenomenon that occurs roughly around the inverse of the square root of the maximal degree. That is, if noise is above this threshold then any algorithm cannot avoid finding the target in exponential time (in the original distance), while below the threshold we identify an optimal, almost linear, walking algorithm. Finally, I will discuss algorithms that under such a noisy model aim to minimize the number of queries to find a target (rather than the number of moves).

This talk is based on joint works with biologists from the Weizmann Institute: Ofer Feinerman, Udi Fonio, and others, and with CS researchers: Lucas Bockowski, Adrian Kosowski, and Yoav Rodeh.

 

ThursdayApr 27, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Tamar FlashTitle:Motion compositionality and timing: combined geometrical and optimization approachesAbstract:opens in new windowin html    pdfopens in new window
In my talk I will discuss several recent research directions that we have taken to explore the different principles underlying the construction and control of complex human upper arm and gait movements. One important topic is motor compositionality, exploring the nature of the motor primitives underlying the construction of complex movements at different levels of the motor hierarchy. The second topic which we focused on is motion timing, investigating what principles dictate the durations of complex sequential behaviors both at the level of the internal timing of different motion segments and the total durations of different types of movement. Finally I will discuss the topic of motor coordination and the mapping between end-effector and joint motions both during arm and leg movements using various dimension reduction approaches. The mathematical models we have used to study the above topics combine geometrical approaches with optimization models to derive motion invariants, optimal control principles and different conservations laws.
TuesdayApr 25, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Crystal Hoyt Title:A new category of sl(infinity)-modules related to Lie superalgebras Abstract:opens in new windowin html    pdfopens in new window
The (reduced) Grothendieck group of the category of finite-dimensional representations of the Lie superalgebra gl(m|n) is an sl(infinity)-module with the action defined via translation functors, as shown by Brundan and Stroppel. This module is indecomposable and integrable, but does not lie in the tensor category, in other words, it is not a subquotient of the tensor algebra generated by finitely many copies of the natural and conatural sl(infinity)-modules. In this talk, we will introduce a new category of sl(infinity)-modules in which this module is injective, and describe the socle filtration of this module. Joint with: I. Penkov, V. Serganova
MondayApr 24, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Luca TrevisanTitle:Some simple distributed network processesAbstract:opens in new windowin html    pdfopens in new window
We will describe network processes in which, at each step, each node communicates with its neighbors, or a random subset of neighbors, and it updates its state to be "more like" the state of the neighbors. In a discrete setting, where there is a finite set of possible states, each node node updates to the state held by a plurality of sampled neighbors. Here we show that, in a complete communication network, there is a quick convergence to a consensus, regardless of the initial configuration and even in the presence of adversarial faults. If the set of possible states is ordered, and nodes update to the median of neighbors, convergence was known to be even faster, but less robust to adversarial tampering. In a continuous setting, each node holds a bounded real number, and it updates to the average of sampled neighbors. Here we show that if the graph has a clustered structure, such as the one generated by the stochastic block model, the nodes can identify the cluster they belong to based on the evolution of the local state. This holds even in an asynchronous model in which only two nodes are active at a time, and the study of the latter setting leads to interesting questions about the concentration of the product of iid random matrices. (Based on joint work with Luca Becchetti, Andrea Clementi, Pasin Manurangsi, Emanuele Natale, Francesco Pasquale and Prasad Raghavendra.)
ThursdayApr 20, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Lihi Zelnik-Manor Title:Separating the Wheat from the Chaff in Visual DataAbstract:opens in new windowin html    pdfopens in new window
By far, most of the bits in the world are image and video data. YouTube alone gets 300 hours of video uploaded every minute. Adding to that personal pictures, videos, TV channels and the gazillion of security cameras shooting 24/7 one quickly sees that the amount of visual data being recorded is colossal. In the first part of this talk I will discuss the problem of "saliency prediction" - separating between the important parts of images/videos (the "wheat") from the less important ones (the "chaff"). I will review work done over the last decade and its achievements. In the second part of the talk I will discuss one particular application of saliency prediction that our lab is interested in: making images and videos accessible to the visually impaired. Our plan is to convert images and videos into tactile surfaces that can be "viewed" by touch. As it turns out, saliency estimation and manipulation both play a key factor in this task.
WednesdayApr 19, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Naftali TishbyTitle:A Deeper Understanding of Deep LearningAbstract:opens in new windowin html    pdfopens in new window

By analytical and numerical studies of Deep Neural Networks (using standard TensorFlow) in the "Information Plane" - the Mutual Information the network layers preserve on the input and the output variables - we obtain the following new insights.

  1. The training epochs, for each layer, are divided into two phases: (1) fitting the training data - increasing the mutual information on the labels; (2) compressing the representation - reducing the mutual information on the inputs. The layers are learnt hierarchically, from the bottom to the top layer, with some overlaps.
  2. Most (~80%) of the training time  - optimization with SGD -  is spent on compressing the representation (the second phase) - NOT on fitting the training data labels, even when the training has no regularization or terms that directly aim at such compression.  
  3. The convergence point, FOR EVERY HIDDEN LAYER, lies on or very close to the Information Bottleneck IB) theoretical bound. Thus, the mappings from the input to the hidden layer and from the hidden layer to the output obey the IB self-consistent equations for some value of the compression-prediction tradeoff.
  4. The main benefit of adding more hidden layers is in the optimization/training time, as the compression phase for each layer amounts to relaxation to a Maximum conditional Entropy state, subject to the proper constraints on the error/information on the labels. As such relaxation takes super-linear time in the compressed entropy, adding more hidden layers dramatically reduces the training time. There is also benefit in sample complexity to adding hidden layers, but this is a smaller effect.

I will explain these new observations and the benefits of exploring Deep Learning in the "Information Plane", and discuss some of the exciting theoretical and practical consequences of our analysis.

Joint work with Ravid Ziv and Noga Zaslavsky.

TuesdayApr 18, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Mikhail IgnatyevTitle:Coadjoint orbits, Kostant–Kumar polynomials and tangent cones to Schubert varietiesAbstract:opens in new windowin html    pdfopens in new window
TBA
ThursdayApr 06, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Simon KormanTitle:Occlusion-Aware Template Matching via Consensus Set MaximizationAbstract:opens in new windowin html    pdfopens in new window

We present a novel approach to template matching that is efficient, can handle partial occlusions, and is equipped with provable performance guarantees. A key component of the method is a reduction that transforms the problem of searching a nearest neighbor among N high-dimensional vectors, to searching neighbors among two sets of order sqrt(N) vectors, which can be done efficiently using range search techniques. This allows for a quadratic improvement in search complexity, that makes the method scalable when large search spaces are involved. 
For handling partial occlusions, we develop a hashing scheme based on consensus set maximization within the range search component. The resulting scheme can be seen as a randomized hypothesize-and-test algorithm, that comes with guarantees regarding the number of iterations required for obtaining an optimal solution with high probability. 
The predicted matching rates are validated empirically and the proposed algorithm shows a significant improvement over the state-of-the-art in both speed and robustness to occlusions.
Joint work with Stefano Soatto.

MondayApr 03, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Udi WiederTitle:Circuit based PSI via Cuckoo HashingAbstract:opens in new windowin html    pdfopens in new window

While there has been a lot of progress in designing efficient custom protocols for computing Private Set Intersection (PSI), there has been less research on using generic MPC protocols for this task. However, there are many variants of the set intersection functionality which seem hard to compute with existing custom protocols and are easy to compute with generic MPC based solutions (for example comparing the cardinality of the intersection with a threshold or measuring ad conversion rates). Generic protocols work over circuits which compute the intersection. For sets of size n the best known circuit constructions compute O(n  log n) comparisons.  In this work we propose new circuit-based protocols for computing variants of the intersection, with circuits computing only O(n) comparisons. Our constructions are based on a new variant of Cuckoo hashing in two dimensions. We employ several optimizations and determine experimentally the  required sizes of tables and circuits, and measure the runtime, showing that our protocol is more efficient in concrete terms than existing constructions. The proof technique is new and can be generalized to analyzing simple Cuckoo hashing as well as new variants.

ThursdayMar 30, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Lior WolfTitle:Unsupervised Cross-Domain Image GenerationAbstract:opens in new windowin html    pdfopens in new window

We study the ecological use of analogies in AI. Specifically, we address the problem of transferring a sample in one domain to an analog sample in another domain. Given two related domains, S and T, we would like to learn a generative function G that maps an input sample from S to the domain T, such that the output of a given representation function f, which accepts inputs in either domains, would remain unchanged. Other than f, the training data is unsupervised and consist of a set of samples from each domain, without any mapping between them. The Domain Transfer Network (DTN) we present employs a compound loss function that includes a multiclass GAN loss, an f preserving component, and a regularizing component that encourages G to map samples from T to themselves. We apply our method to visual domains including digits and face images and demonstrate its ability to generate convincing novel images of previously unseen entities, while preserving their identity.

Joint work with Yaniv Taigman and Adam Polyak

MondayMar 27, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Prahladh Harsha Title:On polynomial approximations to AC0Abstract:opens in new windowin html    pdfopens in new window
In this talk, we will discuss some questions related to polynomial approximations of AC0. A classic result due to Tarui (1991) and Beigel, Reingold, and Spielman (1991), states that any AC0 circuit of size s and depth d has an ε-error probabilistic polynomial over the reals of degree at most (log(s/ ε))^O(d). We will have a re-look at this construction and show how to improve the bound to (log s)^{O(d)} ·log(1/ ε), which is much better for small values of ε. As an application of this result, we show that (log s)^{O(d)}· log(1/ ε)-wise independence fools AC0, improving on Tal's strengthening of Braverman's theorem that (log(s/ ε))^{O(d)}-wise independence fools AC0. Time permitting, we will also discuss some lower bounds on the best polynomial approximations to AC0.

Joint work with Srikanth Srinivasan.

ThursdayMar 09, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Sasha ShamovTitle:Conditional determinantal processes are determinantalAbstract:opens in new windowin html    pdfopens in new window

A determinantal point process governed by a locally trace class Hermitian contraction kernel on a measure space $E$ remains determinantal when conditioned on its configuration on an arbitrary measurable subset $B \subset E$. Moreover, the conditional kernel can be chosen canonically in a way that is "local" in a non-commutative sense, i.e. invariant under "restriction" to closed subspaces $L^2(B) \subset P \subset L^2(E)$.

Using the properties of the canonical conditional kernel we establish a conjecture of Lyons and Peres: if $K$ is a projection then almost surely all functions in its image can be recovered by sampling at the points of the process.

TuesdayMar 07, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Leonid Parnovski Title:Local density of states and the spectral function for almost-periodic operators.Abstract:opens in new windowin html    pdfopens in new window

I will discuss the asymptotic behaviour (both on and off the diagonal) of the spectral function of a Schroedinger operator with smooth bounded potential when energy becomes large. I formulate the conjecture that the local density of states (i.e. the spectral function on the diagonal) admits the complete asymptotic expansion and discuss the known results, mostly for almost-periodic potentials.

TuesdayFeb 21, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Stephen LichtenbaumTitle:A conjectured cohomological description of special values of zeta-functions.Abstract:opens in new windowin html    pdfopens in new window

Let X be a regular scheme, projective and flat over Spec Z. We give a conjectural formula in terms of motivic cohomology, singular cohomology and de Rham cohomology  for the special value of the zeta-function of X at any rational integer. We will explain how this reduces to the standard formula for the residue of the Dedekind zeta-function at s = 1. 

TuesdayFeb 14, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dimitry Turaev Title:Averaging over a non-ergodic systemAbstract:opens in new windowin html    pdfopens in new window

A classical theorem by Anosov states that the slow motion of a slow-fast system where the fast subsystem is ergodic with respect to a smooth invariant measure can be approximated, in a well-defined sense, by the slow subsystem averaged over the fast variables. We address the question of what happens if the fast system is not ergodic. We discuss a theory which is developing in joint works with V. Gelfreich, T. Pereira, V. Rom-Kedar and K. Shah, and suggest that in the non-ergodic case the behavior of the slow variables is approximated by a random process, and not a single, deterministic averaged system. We also discuss the question of the relevance of ergodicity to the foundations of statistical mechanics.

MondayFeb 13, 201716:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Mikhail KarpukhinTitle:Eigenvalue bounds on surfaces: some recent advancesAbstract:opens in new windowin html    pdfopens in new window
We will give an overview of some recent results on Laplace and Steklov eigenvalue estimates on Riemannian surfaces. In particular, we will present an upper bound on the first Laplace eigenvalue for non-orientable surfaces, extending some classical inequalities due to Yang, Li and Yau. We will also discuss the Steklov eigenvalue problem that has attracted a lot of attention in the past decade. In particular, geometric estimates on Steklov eigenvalues of arbitrary index will be presented.
ThursdayFeb 09, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Tomer MichaeliTitle:Deformation-aware image processingAbstract:opens in new windowin html    pdfopens in new window

Image processing algorithms often involve a data fidelity penalty, which encourages the solution to comply with the input data. Existing fidelity measures (including perceptual ones) are very sensitive to slight misalignments in the locations and shapes of objects. This is in sharp contrast to the human visual system, which is typically indifferent to such variations. In this work, we propose a new error measure, which is insensitive to small smooth deformations and is very simple to incorporate into existing algorithms. We demonstrate our approach in lossy image compression. As we show, optimal encoding under our criterion boils down to determining how to best deform the input image so as to make it "more compressible". Surprisingly, it turns out that very minor deformations (almost imperceptible in some cases) suffice to make a huge visual difference in methods like JPEG and JPEG2000. Thus, by slightly sacrificing geometric integrity, we gain a significant improvement in preservation of visual information.

We also show how our approach can be used to visualize image priors. This is done by determining how images should be deformed so as to best conform to any given image model. By doing so, we highlight the elementary geometric structures to which the prior resonates. Using this method, we reveal interesting behaviors of popular priors, which were not noticed in the past.

Finally, we illustrate how deforming images to possess desired properties can be used for image "idealization" and for detecting deviations from perfect regularity.

 

Joint work with Tamar Rott Shaham, Tali Dekel, Michal Irani, and Bill Freeman.

ThursdayFeb 09, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Alexander FishTitle:The values of quadratic forms on difference sets, measure rigidity and equidistributionAbstract:opens in new windowin html    pdfopens in new window

Given a quadratic form Q in d variables over the integers, e.g. Q(x,y,z) = xy - z^2, and a set of positive density E in Z^d, we investigate what kind of structure can be found in the set Q(E-E). 
We will see that if d >= 3, and Q is indefinite, then the measure rigidity, due to Bourgain-Furman-Lindenstrauss-Mozes or Benoist-Quint, of the action of the group of the symmetries of Q implies that there exists k >=1 such that  k^2*Q(Z^d) is a subset of Q(E-E). 
We will give an alternative proof of the theorem for the case Q(x,y,z) = xy - z^2 that uses more classical equidistribution results of Vinogradov, and Weyl, as well as a more recent result by Frantzikinakis-Kra. The latter proof extends the theorem to other polynomials having a much smaller group of symmetries. Based on joint works with M. Bjorklund (Chalmers), and K. Bulinski (Sydney). 

WednesdayFeb 08, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Haim AvronTitle:Large-scale and Non-approximate Kernel Methods Using Random FeaturesAbstract:opens in new windowin html    pdfopens in new window
Kernel methods constitute a mathematically elegant framework for general-purpose infinite-dimensional non-parametric statistical inference. By providing a principled framework to extend classical linear statistical techniques to non-parametric modeling, their applications span the entire spectrum of statistical learning. However, training procedures naturally derived via this framework scale poorly and with limited opportunities for parallelization. This poor scalability poses a significant barrier for the use of kernel methods in big data applications. As such, with the growth in data across a multitude of applications, scaling up kernel methods has acquired renewed and somewhat urgent significance. Random feature maps, such as random Fourier features, have recently emerged as a powerful technique for speeding up and scaling the training of kernel-based methods. However, random feature maps only provide crude approximations to the kernel function, so delivering state-of-the-art results requires huge amount of random features. Nevertheless, in some cases, even when the number of random features is driven to be as large as the training size, full recovery of the generalization performance of the exact kernel method is not attained. In the talk I will show how random feature maps can be used to efficiently perform non-approximate kernel ridge regression, and thus there is no need to compromise between quality and running time. The core idea is to use random feature maps to form preconditioners to be used in solving kernel ridge regression to high accuracy. I will describe theoretical conditions on when this yields an effective preconditioner, and empirically evaluate the method and show it is highly effective for datasets of up to one million training examples.
MondayFeb 06, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Yannai A. GonczarowskiTitle:Efficient Empirical Revenue Maximization in Single-Parameter Auction EnvironmentsAbstract:opens in new windowin html    pdfopens in new window
We present a polynomial-time algorithm that, given samples from the unknown valuation distribution of each bidder, learns an auction that approximately maximizes the auctioneer's revenue in a variety of single-parameter auction environments including matroid environments, position environments, and the public project environment. The valuation distributions may be arbitrary bounded distributions (in particular, they may be irregular, and may differ for the various bidders), thus resolving a problem left open by previous papers. The analysis uses basic tools, is performed in its entirety in value-space, and simplifies the analysis of previously known results for special cases. Furthermore, the analysis extends to certain single-parameter auction environments where precise revenue maximization is known to be intractable, such as knapsack environments. Joint work with Noam Nisan.
FridayFeb 03, 201710:30
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Vadim Schechtman Title:Fourier transformation and hyperplane arrangementsAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY
Linear algebra problems related to the Fourier transformation of perverse sheaves smooth along a hyperplane arrangement in an affine space, together with some examples coming from the representation theory will be discussed.
WednesdayFeb 01, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Ran Gilad-Bachrach Title:CryptoNets: Applying Neural Networks to Encrypted Data with High Throughput and AccuracyAbstract:opens in new windowin html    pdfopens in new window
Applying machine learning to a problem which involves medical, financial, or other types of sensitive data, not only requires accurate predictions but also careful attention to maintaining data privacy and security. Legal and ethical requirements may prevent the use of cloud-based machine learning solutions for such tasks. In this work, we will present a method to convert learned neural networks to CryptoNets, neural networks that can be applied to encrypted data. This allows a data owner to send their data in an encrypted form to a cloud service that hosts the network. The encryption ensures that the data remains confidential since the cloud does not have access to the keys needed to decrypt it. Nevertheless, we will show that the cloud service is capable of applying the neural network to the encrypted data to make encrypted predictions, and also return them in encrypted form. These encrypted predictions can be sent back to the owner of the secret key who can decrypt them. Therefore, the cloud service does not gain any information about the raw data nor about the prediction it made. We demonstrate CryptoNets on the MNIST optical character recognition tasks. CryptoNets achieve 99% accuracy and can make around 59000 predictions per hour on a single PC. Therefore, they allow high throughput, accurate, and private predictions. This is a joint work with Nathan Dowlin, Kim Laine, Kristin Lauter, Michael Naehrig, John Wernsing.
TuesdayJan 31, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Iosif Polterovich Title:Sloshing, Steklov and cornersAbstract:opens in new windowin html    pdfopens in new window
The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.
TuesdayJan 31, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Boris Tsygan Title:What do algebras form? (Revisited)Abstract:opens in new windowin html    pdfopens in new window
We will start with the observation that assocciative algebras form a two-category with a trace functor where one-morphisms are bimodules, two-morphisms are bimodule homomorphisms, and the trace of an (A,A) bimodule M is M/[M,A]. We then explain in what sense the derived version of the above is true, I.e. what happens when one replaces bimodule homomorrphisms and the trace by their derived functors that are Hochschild (com)homology. We will explain how the beginnings of noncommutative differential calculus can bee deduced from the above. This is a continuation of a series of works of MacClure and Smith, Tamarkin, Lurie, and others, and a joint work with Rebecca Wei.
MondayJan 30, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Laszlo Babai Title:Graph Isomorphism in quasipolynomial timeAbstract:opens in new windowin html    pdfopens in new window

The algorithm referred to in the title builds on Luks's powerful group-theoretic divide-and-conquer method (1980) and addresses the bottleneck situation where Luks's method fails to "divide".
Luks will continue to "conquer" if an alternative method "divides"; we develop such a partitioning technique.
In the talk we shall outline the algorithm and explain in some detail its group theoretic core, the "Unaffected Stabilizers Lemma" and the "Local Certificates" routine.  The Lemma is used to construct, somewhat implausibly, global automorphisms out of local information -- a key step toward the construction of combinatorial structures to which the partitioning method from the previous day's lecture will be applied, providing the required "divide" step.

 

SundayJan 29, 201711:00
The Chaim Leib Pekeris Memorial Lecture
Speaker:Laszlo BabaiTitle:Hidden irregularity versus hidden symmetryAbstract:opens in new windowin html    pdfopens in new windowEbner Auditorium

Symmetry is defined in terms of structure-preserving transformations (automorphisms); regularity in terms of numerical invariants. Symmetry always implies regularity but there are many highly regular combinatorial objects (such as "strongly regular graphs") with no symmetry.  The opposite of irregularity is regularity, not symmetry.  Yet we show that in a well-defined sense, the opposite of hidden irregularity is hidden symmetry, and in fact hidden symmetry of a particularly robust kind.
The symmetry of a circle is easily destroyed: just "individualize" two non-opposite points -- color one of them red, the other blue -- and all the symmetry is gone.   In fact, the resulting structure is completely irregular: every point is uniquely identified by a pair of numerical invariants, namely, its pair of distances to the two individualized points. We shall say that the circle has a high degree of hidden irregularity.
In contrast, Johnson graphs are objects with robust symmetry: individualizing a small number of vertices of a Johnson graph hardly makes a dent in its symmetry.  
Recent work on the algorithmic problem of Graph Isomorphism has revealed that Johnson graphs are unique in this regard: Every finite relational structure of small arity either has a measurable (say 10%) hidden irregularity (revealed by individualizing a polylogarithmic number of elements) or has a large degree of hidden symmetry, manifested in a canonically embedded Johnson graph on more than 90% of the underlying set.
This dichotomy is the key Divide-and-Conquer tool in recent progress on the worst-case complexity of the Graph Isomorphism problem.
This subject is purely combinatorial and does not require advanced mathematical apparatus.  The group theoretic aspects of the new Graph Isomorphism test will be discussed in a follow-up seminar on January 30.

ThursdayJan 26, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Vardan PapyanTitle:Signal Modeling: From Convolutional Sparse Coding to Convolutional Neural NetworksAbstract:opens in new windowin html    pdfopens in new window

Within the wide field of sparse approximation, convolutional sparse coding (CSC) has gained increasing attention in recent years. This model assumes a structured-dictionary built as a union of banded Circulant matrices. Most attention has been devoted to the practical side of CSC, proposing efficient algorithms for the pursuit problem, and identifying applications that benefit from this model. Interestingly, a systematic theoretical understanding of CSC seems to have been left aside, with the assumption that the existing classical results are sufficient.
In this talk we start by presenting a novel analysis of the CSC model and its associated pursuit. Our study is based on the observation that while being global, this model can be characterized and analyzed locally. We show that uniqueness of the representation, its stability with respect to noise, and successful greedy or convex recovery are all guaranteed assuming that the underlying representation is locally sparse. These new results are much stronger and informative, compared to those obtained by deploying the classical sparse theory.
Armed with these new insights, we proceed by proposing a multi-layer extension of this model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers. This, in turn, is shown to be tightly connected to Convolutional Neural Networks (CNN), so much so that the forward-pass of the CNN is in fact the Thresholding pursuit serving the ML-CSC model. This connection brings a fresh view to CNN, as we are able to attribute to this architecture theoretical claims such as uniqueness of the representations throughout the network, and their stable estimation, all guaranteed under simple local sparsity conditions. Lastly, identifying the weaknesses in the above scheme, we propose an alternative to the forward-pass algorithm, which is both tightly connected to deconvolutional and recurrent neural networks, and has better theoretical guarantees.

WednesdayJan 25, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Amir Globerson Title:Variational Conditional ProbabilitiesAbstract:opens in new windowin html    pdfopens in new window
Predicting the label Y of an object X is a core task in machine learning. From a probabilistic perspective, this involves reasoning about conditional probabilities p(y|x). However, it is hard to obtain reliable estimates for these probabilities. Here we show how to obtain lower and upper bounds on p(y|x) given statistical information, and show how it can be used within various learning setups. We also extend this formulation to the structured case, where y can be multivariate.
TuesdayJan 24, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Shamgar Gurevich Title:“Size" of a representation of a finite group controls the size of its character valuesAbstract:opens in new windowin html    pdfopens in new window

Many problems about finite groups (e.g., convergence of random walks, properties of word maps, spectrum of Cayley graphs, etc.) can be approached in terms of sums of group characters. More precisely, what intervenes in such sums are the character ratios: 
X_r(g) / dim(r),       g in G, 
where r is an irreducible representation of G, and X_r is its character. This leads to the quest for good estimates on the character ratios.
In this talk I will introduce a precise notion of "size" for representations of finite classical groups and show that it tends to put together those with character ratios of the same order of magnitude.
As an application I will show how one might generalize to classical groups the following result of Diaconis-Shahshahani (for k=2) and Berestycki -Schramm -Zeitouni (for general k): The mixing time for the random walk on the group G=S_n using the cycles of length k is (1/k) n log(n).
The talk should be accessible for beginning graduate students, and is part from our joint project with Roger Howe (Yale and Texas A&M).

TuesdayJan 24, 201710:00
Guest SeminarRoom 208
Speaker:Yair FieldTitle:Detecting human genetic adaptation in historical timescalesAbstract:opens in new windowin html    pdfopens in new window

Detecting genetic adaptation in recent human history is a major challenge of population genetics. The fundamental problem is to infer historical changes in the frequency of genetic variants (alleles), from data of contemporary genomes. With this we can identify unusual changes that are unlikely to have occurred in the absence of selective pressures. However, a generally applicable method to infer recent allele frequency changes is lacking. Instead, present methods can only detect frequency changes under very restrictive assumptions on the model of selection. Moreover, their time resolution is generally limited to prehistoric scales, on the order of the past 25-75 thousand years. To address these gaps we developed a novel statistical method, Singleton Density Score (SDS), that infers the recent changes in allele frequencies from local variation in contemporary genome sequences with specificity to historical timescales. Applied to data of ~3000 genomes from the UK10K project, SDS reveals that human genetic adaptation continued well into historical times. Over the past ~2000-3000 years, ancestors of modern Britons genetically evolved over a range of phenotypes related to diet, immunity, and physical appearance. Notably, we found that polygenic adaptation, whereby selection acting on many small-effect variants across the genome that together determine a single trait, has played a pervasive, previously undetected role in shaping present genotypic and phenotypic variation.
Reference:
Field et al, Science 2016, Detection of human adaptation during the past 2000 years. https://www.ncbi.nlm.nih.gov/pubmed/27738015

MondayJan 23, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Kira GoldnerTitle:The FedEx ProblemAbstract:opens in new windowin html    pdfopens in new window
Consider the following setting: a customer has a package and is willing to pay up to some value v to ship it, but needs it to be shipped by some deadline d. Given the joint prior distribution from which (v, d) pairs are drawn, we characterize the auction that yields optimal revenue, contributing to the very limited understanding of optimal auctions beyond the single-parameter setting. Our work further demonstrates the importance of 'ironing' in revenue maximization, helping to illustrate why randomization is necessary to achieve optimal revenue. Finally, we strengthen the emerging understanding that duality is useful for both the design and analysis of optimal auctions in multi- parameter settings. Joint work with Amos Fiat, Anna Karlin, and Elias Koutsoupias.
SundayJan 22, 201712:15
Foundations of Computer Science SeminarRoom 290C
Speaker:Merav Parter Title:Graph Algorithms for Distributed NetworksAbstract:opens in new windowin html    pdfopens in new window

I will describe two branches of my work related to algorithms for distributed networks. The main focus will be devoted for Fault-Tolerant (FT) Network Structures. 
The undisrupted operation of structures and services is a crucial requirement in modern day communication networks. As the vertices and edges of the network may occasionally fail or malfunction, it is desirable to make those structures robust against failures.
FT Network Structures are low cost highly resilient structures, constructed on top of a given network, that satisfy certain desirable performance requirements concerning, e.g., connectivity, distance or capacity. We will overview some results on fault tolerant graph structures with a special focus on FT Breadth-First-Search.
The second part of the talk will discuss distributed models and algorithms for large-scale networks. Towards the end, we will see some connections between distributed computing and other areas such as EE and Biology.

ThursdayJan 19, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:David Held Title:Robots in Clutter: Learning to Understand Environmental ChangesAbstract:opens in new windowin html    pdfopens in new window
Robots today are confined to operate in relatively simple, controlled environments. One reason for this is that current methods for processing visual data tend to break down when faced with occlusions, viewpoint changes, poor lighting, and other challenging but common situations that occur when robots are placed in the real world. I will show that we can train robots to handle these variations by modeling the causes behind visual appearance changes. If robots can learn how the world changes over time, they can be robust to the types of changes that objects often undergo. I demonstrate this idea in the context of autonomous driving, and I will show how we can use this idea to improve performance for every step of the robotic perception pipeline: object segmentation, tracking, velocity estimation, and classification. I will also present some preliminary work on learning to manipulate objects, using a similar framework of learning environmental changes. By learning how the environment can change over time, we can enable robots to operate in the complex, cluttered environments of our daily lives.
ThursdayJan 19, 201711:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Jay Rosen Title:Tightness for the Cover Time of S^2 Abstract:opens in new windowin html    pdfopens in new window

Let M be a smooth, compact, connected two-dimensional, Riemannian manifold without boundary, and let  C_epsilon be  the amount of time needed for the Brownian motion to come within (Riemannian) distance epsilon of all points in M. The first order asymptotics of C_epsilon as epsilon goes to 0 are known. We show that for the two dimensional sphere 

\sqrt{C_epsilon}-2\sqrt{2}\( \log \epsilon^{-1}- \frac{1}{4}\log\log \epsilon^{-1}\) is tight.

Joint work with David Belius and  Ofer Zeitouni.

TuesdayJan 17, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Tali Pinsky Title:Minimal representatives and the Lorenz equationsAbstract:opens in new windowin html    pdfopens in new window
A minimal representative for a dynamical system is a system that has the simplest possible dynamics in its topological equivalence class. This is very much related to "dynamical forcing": when existence of certain periodic orbits forces existence of others. This is quite useful in the analysis of chaotic systems. I'll give examples of minimal representatives in dimensions one, two and three. In dimension three, I'll show that the minimal representative for the chaotic Lorenz equations (for the correct parameters) is the geodesic flow on the modular surface. This will be an introductory talk.
ThursdayJan 12, 201711:00
Guest SeminarRoom 208
Speaker:Amir AbboudTitle:Hardness in PAbstract:opens in new windowin html    pdfopens in new window
The class P attempts to capture the efficiently solvable computational tasks. It is full of practically relevant problems, with varied and fascinating combinatorial structure. In this talk, I will give an overview of a rapidly growing body of work that seeks a better understanding of the structure within P. Inspired by NP-hardness, the main tool in this approach are combinatorial reductions. Combining these reductions with a small set of plausible conjectures, we obtain tight lower bounds on the time complexity of many of the most important problems in P.
ThursdayJan 12, 201711:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Ran Tessler and Assaf Naor Title:Double lecture !Abstract:opens in new windowin html    pdfopens in new window

First Speaker: Ran Tessler (ETH)
Time: 11:00
Title: A sharp threshold for Hamiltonian spheres in a random 2-complex.
Abstract: We define the notion of Hamiltonian sphere - a 2-complex homeomorphic to a sphere which uses all vertices. We prove an explicit sharp threshold for the appearance of Hamiltonian spheres in the Linial-Meshulam model for random 2-complexes. The proof combines combinatorial, probabilistic and geometric arguments. Based on a joint work with Zur Luria.

Second Speaker: Assaf Naor (Princeton)
Time: 12:00
Title: A new vertical-versus-horizontal isoperimetric inequality on the Heisenberg group, with applications to metric geometry and approximation algorithms
Abstract: In this talk we will show that for every measurable subset of the Heisenberg group of dimension at least 5, an appropriately defined notion of its "vertical perimeter" is at most a constant multiple of its horizontal (Heisenberg) perimeter. We will explain how this new isoperimetric-type inequality solves open questions in analysis (an endpoint estimate for a certain singular integral on W^{1,1}), metric geometry (sharp nonembeddability into L_1) and approximation algorithms (asymptotic evaluation of the performance of the Goemans-Linial algorithm for the Sparsest Cut problem). Joint work with Robert Young.

TuesdayJan 10, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Jianrong LiTitle:Finite-dimensional representations of quantum affine algebrasAbstract:opens in new windowin html    pdfopens in new window
I will talk about finite dimensional representations of quantum affine algebras. The main topics are Chari and Pressley's classification of finite-dimensional simple modules over quantum affine algebras, Frenkel and Reshetikhin's theory of q-characters of finite dimensional modules, Frenkel-Mukhin algorithm to compute q-characters, T-systems, Hernandez-Leclerc's conjecture about the cluster algebra structure on the ring of a subcategory of the category of all finite dimensional representations of a quantum affine algebra. I will also talk about how to obtain a class of simple modules called minimal affinizations of types A, B using mutations (joint work with Bing Duan, Yanfeng Luo, Qianqian Zhang).
MondayJan 09, 201716:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Gal BinyaminiTitle:Wilkie's conjecture for restricted elementary functionsAbstract:opens in new windowin html    pdfopens in new window

Let X be a set definable in some o-minimal structure. The Pila-Wilkie theorem (in its basic form) states that the number of rational points in the transcendental part of X grows sub-polynomially with the height of the points. The Wilkie conjecture stipulates that for sets definable in $R_\exp$, one can sharpen this asymptotic to polylogarithmic.
I will describe a complex-analytic approach to the proof of the Pila-Wilkie theorem for subanalytic sets. I will then discuss how this approach leads to a proof of the "restricted Wilkie conjecture", where we replace $R_\exp$ by the structure generated by the restrictions of $\exp$ and $\sin$ to the unit interval (both parts are joint work with Dmitry Novikov). If time permits I will discuss possible generalizations and applications.

MondayJan 09, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Ofer GrossmanTitle:Bipartite Perfect Matching in Pseudo-Deterministic NCAbstract:opens in new windowin html    pdfopens in new window

Pseudo-deterministic algorithms are randomized search algorithms that on different executions on the same input, output the same solution with high probability.
We will discuss how pseudo-deterministic algorithms bridge the gap  between randomized search and decision problems for problems in P and  in NC. Next, we will show a pseudo-deterministic NC algorithm for bipartite matching. Finally, we will show how pseudo-determinism can be used to save on  random bits used by classical randomized algorithms, and apply the  method to obtain an algorithm for RNC depth first search using only  O(log^2 n) random bits. This is joint work with Shafi Goldwasser.
 

ThursdayJan 05, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Shai AvidanTitle:Taking Pictures in Scattering MediaAbstract:opens in new windowin html    pdfopens in new window
Pictures taken under bad weather conditions or underwater often suffer from low contrast and limited visibility. Restoring colors of images taken in such conditions is extremely important for consumer applications, computer vision tasks, and marine research. The common physical phenomena in these scenarios are scattering and absorption - the imaging is done either under water, or in a medium that contains suspended particles, e.g. dust (haze) and water droplets (fog). As a result, the colors of captured objects are attenuated, as well as veiled by light scattered by the suspended particles. The amount of attenuation and scattering depends on the objects' distance from the camera and therefore the color distortion cannot be globally corrected. We propose a new prior, termed Haze-Line, and use it to correct these types of images. First, we show how it can be used to clean images taken under bad weather conditions such as haze or fog. Then we show how to use it to automatically estimate the air light.Finally, we extend it to deal with underwater images as well. The proposed algorithm is completely automatic and quite efficient in practice. Joint work with Dana Berman (TAU) and Tali Treibitz (U.of Haifa)
ThursdayJan 05, 201711:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Amir DemboTitle:Walking within growing domains: recurrence versus transience Abstract:opens in new windowin html    pdfopens in new window
When is simple random walk on growing in time d-dimensional domains recurrent? For domain growth which is independent of the walk, we review recent progress and related universality conjectures about a sharp recurrence versus transience criterion in terms of the growth rate. We compare this with the question of recurrence/transience for time varying conductance models, where Gaussian heat kernel estimates and evolving sets play an important role. We also briefly contrast such expected universality with examples of the rich behavior encountered when monotone interaction enforces the growth as a result of visits by the walk to the current domain's boundary. This talk is based on joint works with Ruojun Huang, Ben Morris, Yuval Peres, Vladas Sidoravicius and Tianyi Zheng.
WednesdayJan 04, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Sivan SabatoTitle:Active Nearest-Neighbor Learning in Metric SpacesAbstract:opens in new windowin html    pdfopens in new window
We propose a pool-based non-parametric active learning algorithm for general metric spaces, which outputs a nearest-neighbor classifier. We give prediction error guarantees that depend on the noisy-margin properties of the input sample, and are competitive with those obtained by previously proposed passive learners. We prove that the label complexity of the new algorithm is significantly lower than that of any passive learner with similar error guarantees. Our algorithm is based on a generalized sample compression scheme and a new label-efficient active model-selection procedure. Based on joint work with Aryeh Kontorovich and Ruth Urner.
TuesdayJan 03, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Varga KalantarovTitle:On blow up and preventing of blow up of solutions of nonlinear dissipative PDE’sAbstract:opens in new windowin html    pdfopens in new window
We are going to discuss the impact of convective terms on the global solvability or finite time blow up of solutions of initial boundary value problems for nonlinear dissipative PDEs. We will consider the model examples of 1D Burger's type equation, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation, generalized KdV type equations, and establish that sufficiently strong convective terms prevent solutions from blowing up in a finite time and make the considered systems globally well-posed and dissipative. We will also show that solutions of corresponding equations with weak enough convective terms may blow up in a finite time.
TuesdayJan 03, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Elena Gal Title:A geometric approach to Hall algebrasAbstract:opens in new windowin html    pdfopens in new windowNOTE CHANGE IN DATE TO JAN.03 2017, room 155
The Hall algebra associated to a category can be constructed using the Waldhausen S-construction. We will give a systematic recipe for this and show how one can use it to construct higher associativity data. We will discuss a natural extension of this construction providing a bi-algebraic structure for Hall algebra. As a result we obtain a more transparent proof of Green's theorem about the bi-algebra structure on the Hall algebra.
MondayJan 02, 201714:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Gil CohenTitle:Recent advances in randomness extractors and their applicationsAbstract:opens in new windowin html    pdfopens in new window
We present recent developments in randomness extractors theory and applications to classical, long-standing, open problems such as Ramsey graphs constructions and privacy amplification protocols. This exciting progress heavily relies on two new pseudo-random primitives we call correlation breakers and independence-preserving mergers, which we discuss.
ThursdayDec 29, 201611:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Alon Nishry Title:Gaussian complex zeros on the hole event: the emergence of a forbidden regionAbstract:opens in new windowin html    pdfopens in new window

Consider the Gaussian Entire Function (GEF) whose Taylor coefficients are independent complex-valued Gaussian variables, and the variance of the k-th coefficient is 1/k!. This random Taylor series is distinguished by the invariance of its zero set with respect to the isometries of the complex plane.
I will show that the law of the zero set, conditioned on the GEF having no zeros in a disk of radius r, and properly normalized, converges to an explicit limiting Radon measure in the plane, as r goes to infinity. A remarkable feature of this limiting measure is the existence of a large 'forbidden region' between a singular part supported on the boundary of the (scaled) hole and the equilibrium measure far from the hole. This answers a question posed by Nazarov and Sodin, and is in stark contrast to the corresponding result known to hold in the random matrix setting, where such a gap does not appear.
The talk is based on a joint work with S. Ghosh.

TuesdayDec 27, 201616:00
Seminar in Geometry and TopologyRoom 208
Speaker:Boris ZilberTitle:On algebraic and diophantine geometry in characteristic 1Abstract:opens in new windowin html    pdfopens in new window
I will start with a motivation of what algebraic (and model-theoretic) properties an algebraically closed field of characteristic 1 is expected to have. Then I will explain how a search of similar properties lead to a well-known now Hrushovski's construction and then formulate very precise properties that such a construction produces and so the field must satisfy. The axioms have a form of diophantine and valuation-theoretic statements in positive characteristics and the consistency of those remain an open problem. A special case of the axioms has been confirmed by a theorem of F.Bogomolov.
TuesdayDec 27, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Martine MarionTitle:Global existence for systems describing multicomponent reactive flowAbstract:opens in new windowin html    pdfopens in new window
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws for the chemical species. The nonlinear diffusion coefficients are obtained by resolution of the so-called Stefan-Maxwell equations. We prove the existence of weak solutions for the corresponding system of equations which involves coupling between the incompressible Navier-Stokes and equations for temperature and species concentrations.
TuesdayDec 27, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Vera SerganovaTitle:P (n) via categorification of Temperley- Lieb algebra and Sp(infinity)Abstract:opens in new windowin html    pdfopens in new window
MondayDec 26, 201616:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Boris KhesinTitle:Optimal transport and geodesics on diffeomorphism groupsAbstract:opens in new windowin html    pdfopens in new window
We revisit how the Euler and Burgers equations arise as geodesics on the groups of diffeomorphisms. It turns out that the Euler hydrodynamics is in a sense dual to problems of optimal mass transport. We also describe L^2 and H^1 versions of the the Wasserstein space of volume forms. It turns out that for the homogeneous H^1 metric the Wasserstein space is isometric to (a piece of) an infinite-dimensional sphere and it leads to an integrable generalization of the Hunter-Saxton equation.
MondayDec 26, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Avi WigdersonTitle:Theory and applications of operator scalingAbstract:opens in new windowin html    pdfopens in new window

The Operator Scaling problem asks whether a set of complex matrices can be jointly moved to a certain canonical (isotropic) position. This problem has a remarkable number of myriad incarnations:  non-commutative algebra, invariant theory, arithmetic complexity, quantum information theory, analytic inequalities and more. We will describe an efficient algorithm solving all these related problems, and explain how their analysis combines ideas from all these areas. 
Through these connections, the algorithm can be shown to solve some  non-convex optimization problems, some systems of quadratic equations,  and some linear programs with exponentially many inequalities - all  these, and concrete examples we will give, suggest that it might be a  powerful algorithmic tool via reductions to these problems.
No special background will be assumed!
Joint on two joint works with Ankit Garg, Leonid Gurvits and Rafael Olivera.
This talk is longer than usual and has a two-hour slot.

MondayDec 26, 201611:45
Machine Learning and Statistics SeminarRoom 141
Speaker:Elad Hazan Title:A Non-generative Framework and Convex Relaxations for Unsupervised LearningAbstract:opens in new windowin html    pdfopens in new windowNote unusual time and place
We will describe a novel theoretical framework for unsupervised learning which is not based on generative assumptions. It is comparative, and allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficiently learned in our framework by convex optimization. These includes dictionary learning and learning of algebraic manifolds. Joint work with Tengyu Ma. === Bio === Elad Hazan is a professor of computer science at Princeton university. His research focuses on the design and analysis of algorithms for basic problems in machine learning and optimization. Amongst his contributions are the co-development of the AdaGrad algorithm for training learning machines, and the first sublinear-time algorithms for convex optimization. He is the recipient of (twice) the IBM Goldberg best paper award in 2012 for contributions to sublinear time algorithms for machine learning, and in 2008 for decision making under uncertainty, a European Research Council grant, a Marie Curie fellowship and a Google Research Award (twice). He served on the steering committee of the Association for Computational Learning and has been program chair for COLT 2015.
ThursdayDec 22, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Greg Shakhnarovich Title:Image colorization and its role in visual learningAbstract:opens in new windowin html    pdfopens in new window
I will present our recent and ongoing work on fully automatic image colorization. Our approach exploits both low-level and semantic representations during colorization. As many scene elements naturally appear according to multimodal color distributions, we train our model to predict per-pixel color histograms. This intermediate output can be used to automatically generate a color image, or further manipulated prior to image formation to "push" the image in a desired direction. Our system achieves state-of-the-art results under a variety of metrics. Moreover, it provides a vehicle to explore the role the colorization task can play as a proxy for visual understanding, providing a self-supervision mechanism for learning representations. I will describe the ability of our self-supervised network in several contexts, such as classification and semantic segmentation. On VOC segmentation and classification tasks, we present results that are state-of-the-art among methods not using ImageNet labels for pretraining. Joint work with Gustav Larsson and Michael Maire.
TuesdayDec 20, 201616:00
Seminar in Geometry and TopologyRoom A
Speaker:Boaz Elazar Title:Schwartz functions on real algebraic varietiesAbstract:opens in new windowin html    pdfopens in new window
We define Schwartz functions and tempered functions on affine real algebraic varieties, which might be singular. We prove that some of the important classical properties of these functions, such as partition of unity, characterization on open subsets, etc., continue to hold in this case. Some of our proves are based on the works of Milman, Bierstone and Pawlucki on Whitney's extension problem and composite differentiable functions. Joint work with Ary Shaviv.
TuesdayDec 20, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Emanuel A. Lazar Title:Dynamical Cell Complexes: Evolution, Universality, and StatisticsAbstract:opens in new windowin html    pdfopens in new window
Many physical and biological systems are cellular in nature -- soap foams, biological tissue, and polycrystalline metals are but a few examples that we encounter in everyday life. Many of these systems evolve in a manner that changes their geometries and topologies to lower some global energy. We use computer simulations to study how mean curvature flow shapes cellular structures in two and three dimensions. This research touches on discrete geometric flows, combinatorial polyhedra and their symmetries, and the quantification of topological features of large cellular systems. If time permits, I will also describe some exact results in 1 dimension.
TuesdayDec 20, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Leonid Makar-LimanovTitle:On a bizarre geometric property of a counterexample to the Jacobian conjectureAbstract:opens in new windowin html    pdfopens in new window

If f, g are two polynomials in C[x,y] such that J(f,g)=1, but C[f,g] does not coincide with C[x,y], then the mapping  given by these polynomials ( (x,y) maps to (f(x,y), g(x,y)) ) has a rather unexpected property which will be discussed in the talk.  

TuesdayDec 20, 201611:00
Guest SeminarRoom 208
Speaker:Uri Shalit Title:Learning to act from observational dataAbstract:opens in new windowin html    pdfopens in new window

The proliferation of data collection in the health, commercial, and economic spheres, brings with it opportunities for extracting new knowledge with concrete policy implications. Examples include individualizing medical practices based on electronic healthcare records, and understanding the implications of job training programs on employment and income.
The scientific challenge lies in the fact that standard prediction models such as supervised machine learning are often not enough for decision making from this so-called "observational data": Supervised learning does not take into account causality, nor does it account for the feedback loops that arise when predictions are turned into actions. On the other hand, existing causal-inference methods are not adapted to dealing with the rich and complex data now available, and often focus on populations, as opposed to individual-level effects.
The problem is most closely related to reinforcement learning and bandit problems in machine learning, but with the important property of having no control over experiments and no direct access to the actor's model.
In my talk I will discuss how we apply recent ideas from machine learning to individual-level causal-inference and action. I will introduce a novel generalization bound for estimating individual-level treatment effect, and further show how we use representation learning and deep temporal generative models to create new algorithms geared towards this problem. Finally, I will show experimental results using data from electronic medical records and data from a job training program.

MondayDec 19, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Shachar Lovett Title:Robust sensitivityAbstract:opens in new windowin html    pdfopens in new window

The sensitivity conjecture is a famous open problem in the theory of boolean functions. Let f be a boolean function defined on the hypercube. The sensitivity of a node x is the number of its neighbours in the hypercube, for which f give the opposite value as that it does on x. The sensitivity conjecture speculates that if all nodes have low sensitivity, then the function f must be simple. Concretely, all its Fourier mass is supported on levels with low hamming weight.

Recently, Gopalan et al [CCC 2016] conjectured a robust analogue of the sensitivity conjecture: if most of the nodes have low sensitivity, then most of the Fourier mass is supported on levels with low hamming weight. They also prove it under the stronger assumption that all nodes have low sensitivity. In this work, we prove this conjecture, with near tight quantitative bounds.

Joint work with Avishay Tal (IAS) and Jiapeng Zhang (UCSD).

 

ThursdayDec 15, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Gil Ben-Artzi Title:Calibration of Multi-Camera Systems by Global Constraints on the Motion of SilhouettesAbstract:opens in new windowin html    pdfopens in new window
Computing the epipolar geometry between cameras with very different viewpoints is often problematic as matching points are hard to find. In these cases, it has been proposed to use information from dynamic objects in the scene for suggesting point and line correspondences. We introduce an approach that improves by two orders of magnitude the performance over state-of-the-art methods, by significantly reducing the number of outliers in the putative matches. Our approach is based on (a) a new temporal signature: motion barcode, which is used to recover corresponding epipolar lines across views, and (b) formulation of the correspondences problem as constrained flow optimization, requiring small differences between the coordinates of corresponding points over consecutive frames. Our method was validated on four standard datasets providing accurate calibrations across very different viewpoints.
ThursdayDec 15, 201611:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Snir Ben OvadiaTitle:Symbolic dynamics for non uniformly hyperbolic diffeomorphisms of compact smooth manifolds Abstract:opens in new windowin html    pdfopens in new window

Given a dynamical system, a partition of the space induces a mapping to the space of sequences of the partition elements (a point is mapped to the partition elements containing its orbit terms). Such a duality is called Symbolic Dynamics, Markov partitions are an important tool, as the symbolic dynamics they induce enfold many of the important dynamical properties of the original system, and they allow an easier studying of them.
We show that general non uniformly hyperbolic C^{1+epsilon} diffeomorphism on compact manifolds of any dimension admit countable Markov partitions. Previously this was only known in dimension 2.

WednesdayDec 14, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Alon CohenTitle:Online Learning with Feedback Graphs Without the GraphsAbstract:opens in new windowin html    pdfopens in new window

We study an online learning framework introduced by Mannor and Shamir (2011) in which the feedback is specified by a graph, in a setting where the graph may vary from round to round and is \emph{never fully revealed} to the learner. We show a large gap between the adversarial and the stochastic cases. In the adversarial case, we prove that even for dense feedback graphs, the learner cannot improve upon a trivial regret bound obtained by ignoring any additional feedback besides her own loss. In contrast, in the stochastic case we give an algorithm that achieves $\widetilde \Theta(\sqrt{\alpha T})$ regret over $T$ rounds, provided that the independence numbers of the hidden feedback graphs are at most $\alpha$. completely unlearnable. We also extend our results to a more general feedback model, in which the learner does not necessarily observe her own loss, and show that, even in simple cases, concealing the feedback graphs might render the problem unlearnable.

TuesdayDec 13, 201616:00
Seminar in Geometry and TopologyRoom 208
Speaker:Ilya Kossovskiy Title:On the Gevrey regularity of CR-mappingsAbstract:opens in new windowin html    pdfopens in new window

Cauchy-Riemann maps (shortly: CR-maps) occur in complex analysis as boundary values of maps holomorphic in a domain in complex space. As a rule, CR-mappings of real-analytic hypersurfaces appear to be analytic as well. However, we recently showed in a joint work with Rasul Shafikov the existence of Stokes Phenomenon in CR-geometry: there exist real-analytic hypersurfaces, which are equivalent formally, but not holomorphically. 
Despite of this, it appears that in complex dimension 2, CR-maps necessarily posses appropriate weaker regularity properties. Namely, components of such maps necessarily belong to the well known Gevrey classes. The latter statement has the following remarkable application: if two real-analytic hypersurfaces in complex two-space are equivalent formally, then they are also equivalent smoothly. 
The proof of all these facts employs the recent multi-summability theory in Dynamical Systems. It as well employs the recent CR-DS technique that we developed, which connects CR-manifolds and certain Dynamical Systems. In this talk, I will outline the technique, as well as some details of the proof.

TuesdayDec 13, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Cy MaorTitle:Non-Euclidean elasticity and asymptotic rigidity of manifoldsAbstract:opens in new windowin html    pdfopens in new window

Liouville's rigidity theorem (1850) states that a map $f:\Omega\subset R^d \to R^d$ that satisfies $Df \in SO(d)$ is an affine map. Reshetnyak (1967) generalized this result and showed that if a sequence $f_n$ satisfies $Df_n \to SO(d)$ in $L^p$, then $f_n$ converges to an affine map.

In this talk I will discuss generalizations of these theorems to mappings between manifolds, present some open questions, and describe how these rigidity questions arise in the theory of elasticity of pre-stressed materials (non-Euclidean elasticity).
If time permits, I will sketch the main ideas of the proof, using Young measures and harmonic analysis techniques, adapted to Riemannian settings.

Based on a joint work with Asaf Shachar and Raz Kupferman.

 

TuesdayDec 13, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Arkady Berenstein Title:Canonical bases in quantum Schubert cellsAbstract:opens in new windowin html    pdfopens in new window
The goal of my talk (based on a recent joint paper with Jacob Greenstein) is to provide an elementary construction of the canonical basis B(w) in each quantum Schubert cell U_q(w) and to establish its invariance under Lusztig's symmetries. In particular, I will explain how to directly construct the upper global basis B^up, will show that B(w) is contained in B^up, and that a large part of the latter is preserved by the (modified) Lusztig's symmetries.
MondayDec 12, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Ran GellesTitle:Optimal Resilience for Short-Circuit Noise in FormulasAbstract:opens in new windowin html    pdfopens in new window

We show an efficient method for converting a logic circuit of gates with fan-out 1 into an equivalent circuit that works even if some fraction of its gates are short-circuited, i.e., their output is short-circuited to one of their inputs. Our conversion can be applied to any circuit with fan-in k>= 2, yielding a resilient circuit whose size is polynomial in the size of the (non-resilient) input circuit.

The resilient circuit gives the correct output as long as less than 1/3 of the gates in any of its input-to-output paths are corrupted. Furthermore, we prove that a resilience level of 1/3 is optimal (maximal) for this type of faulty gates. This fully answers an open question by Kalai et al. (FOCS 2012).

Joint work with Mark Braverman and Michael Yitayew.

ThursdayDec 08, 201612:00
Guest SeminarRoom 1
Speaker:Shachar ItzhakyTitle:From Programming Languages to Programming Systems – Software Development by RefinementAbstract:opens in new windowin html    pdfopens in new window

Everyone wants to program with "high-level concepts", rather than meddle with the fine details of the implementation, such as pointers, network packets, and asynchronous callbacks. This is usually achieved by introducing layers of abstraction - but every layer incurs some overhead, and when they accumulate, this overhand becomes significant and sometimes prohibitive. Optimizing the program often requires to break abstractions, which leads to suboptimal design, higher maintenance costs, and subtle hard-to-trace bugs.
I will present two recent projects that attempt to address this difficulty. STNG is an automated lifting compiler that can synthesize high-level graphics code for computing stencils over matrices, from low-level legacy code written in Fortran. Its output is expressed in Halide, a domain-specific language for image processing that can take advantage of modern GPUs. The result is therefore code that is both easier to understand and more efficient than the original code.
Bellmania is a specialized tool for accelerating dynamic-programming algorithms by generating recursive divide-and-conquer implementations of them. Recursive divide-and-conquer is an algorithmic technique that was developed to obtain better memory locality properties. Bellmania includes a high-level language for specifying dynamic programming algorithms and a calculus that facilitates gradual transformation of these specifications into efficient implementations. These transformations formalize the divide-and-conquer technique; a visualization interface helps users to interactively guide the process, while an SMT-based back-end verifies each step and takes care of low-level reasoning required for parallelism.
The lesson is that synthesis techniques are becoming mature enough to play a role in the design and implementation of realistic software systems, by combining the elegance of abstractions with the performance gained by optimizing and tuning the fine details.

TuesdayDec 06, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Crystal Hoyt Title:The Duflo-Serganova functor and character rings of Lie superalgebrasAbstract:opens in new windowin html    pdfopens in new window
MondayDec 05, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Dor Minzer Title:Grassmann Graphs, Vertex Cover and 2-to-2 gamesAbstract:opens in new windowin html    pdfopens in new window

We discuss recent progress on hardness of 2-to-2 games, with  applications to the inapproximability of the Vertex-Cover problem.
A 2-to-2 game (which is a variant of Khot's well known unique  games), is defined by a graph where there is a variable in each node,  and a constraint of a specific structure defined on each edge. While  in unique games each edge- constraint must be a one-to-one  correspondence -- i.e. for each assignment to one node there is  exactly one assignent to the other node that satisfies the constraint -- in 2-to-2 games the correspondence has a "two-to-two" structure.
The goal is to distinguish between instances in which almost all of  the edge- constraints can be satisfied, and instances in which almost none of them can be satisfied simultaneously.
We present a new combinatorial hypothesis regarding Grassmann graphs,  and show that it implies that 2-to-2 games are NP-hard *in a certain sense*. As a consequence, the hypothesis implies that it is NP-hard to distinguish between graphs that have an independent set of fractional  size (1- 1/sqrt{2}), and graphs with no independent sets of any constant fractional size. This easily implies that it is NP-hard to  approximate the Vertex Cover problem within a factor \sqrt{2} - o(1).
The talk is mostly based on a joint work with Subhash Khot and Muli  Safra, nevertheless, we will also mention results from a more recent  extension, which is a joint work with Irit Dinur, Subhash Khot, Guy Kindler and Muli Safra.

ThursdayDec 01, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Michael (Miki) Lustig Title:Applications of Subspace and Low-Rank Methods for Dynamic and Multi-Contrast Magnetic Resonance Imaging Abstract:opens in new windowin html    pdfopens in new window
There has been much work in recent years to develop methods for recovering signals from insufficient data. One very successful direction are subspace methods that constrain the data to live in a lower dimensional space. These approaches are motivated by theoretical results in recovering incomplete low-rank matrices as well as exploiting the natural redundancy of multidimensional signals. In this talk I will present our research group's efforts in this area. I will start with describing a new decomposition that can represent dynamic images as a sum of multi-scale low-rank matrices, which can very efficiently capture spatial and temporal correlations in multiple scales. I will then describe and show results from applications using subspace and low-rank methods for highly accelerated multi-contrast MR imaging and for the purpose of motion correction.
TuesdayNov 29, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Volodymyr Derkach Title:Boundary triples and Weyl functions of symmetric operatorsAbstract:opens in new windowin html    pdfopens in new window

Selfadjoint extensions of a closed symmetric operator A in a Hilbert space with equal deficiency indices were described by in the 30's by J. von Neumann. Another approach, based on the notion of abstract boundary triple originates in the work of J.W. Calkin and was developed by M. I. Visik, G. Grubb, F. S. Rofe-Beketov, M. L. Gorbachuck, A .N. Kochubei and others. 

By Calkin's approach, all selfadjoint extensions of the symmetric operator A can be parametrized via "multivalued" selfadjoint operators in an auxiliary Hilbert space. Spectral properties of these extensions can be characterized in terms of the abstract Weyl function, associated to the boundary triple. In the present talk some recent developments in the theory of boundary triples will be presented. Applications to boundary value problems for Laplacian operators in bounded domains with smooth and rough boundaries will be discussed. 

TuesdayNov 29, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Dmitry GourevitchTitle:Whittaker supports of representations of reductive groupsAbstract:opens in new windowin html    pdfopens in new window
MondayNov 28, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Shahar DobzinskiTitle:Computational Efficiency Requires Simple TaxationAbstract:opens in new windowin html    pdfopens in new window

We characterize the communication complexity of truthful mechanisms. Our departure point is the well known taxation principle. The taxation principle asserts that every truthful mechanism can be interpreted as follows: every player is presented with a menu that consists of a price for each bundle (the prices depend only on the valuations of the other players). Each player is allocated a bundle that maximizes his profit according to this menu. We define the taxation complexity of a truthful mechanism to be the logarithm of the maximum number of menus that may be presented to a player.

Our main finding is that in general the taxation complexity essentially equals the communication complexity. The proof consists of two main steps. First, we prove that for rich enough domains the taxation complexity is at most the communication complexity. We then show that the taxation complexity is much smaller than the communication complexity only in "pathological" cases and provide a formal description of these extreme cases.

Our approach yields several applications, including strengthening the solution concept with low communication overhead, fast computation of prices, and hardness of approximation by computationally efficient truthful mechanisms.

SundayNov 27, 201612:15
Foundations of Computer Science SeminarRoom 290C
Speaker:Julia Chuzhoy Title:New Hardness Results for Routing on Disjoint PathsAbstract:opens in new windowin html    pdfopens in new windowPlease note unusual day/time.

 In the classical Node-Disjoint Paths (NDP) problem, the input consists of an undirected n-vertex graph G, and a collection M of pairs of its vertices, called source-destination, or demand, pairs. The goal is to route the largest possible number of the demand pairs via node-disjoint paths. The best current approximation for the problem is achieved by a simple greedy algorithm, whose approximation factor is O(\sqrt n), while the best current negative result is a roughly \Omega(log^{1/2}n)-hardness of approximation. Even seemingly simple special cases of the problem are still poorly understood: when the input graph is a grid, the best current algorithm achieves a \tilde{O}(n^{1/4})- approximation, and when it is a general planar graph, the best current approximation ratio of an efficient algorithm is \tilde{O}(n^{9/19}). The best currently known lower bound for both these versions of the problem is APX- hardness.
In this talk we will show that NDP is 2^{\Omega(\log n)}-hard to approximate, unless all problems in NP have algorithms with running time n^{O(\log n)}. Our result holds even when the underlying graph is a planar graph with maximum vertex degree 3, and all source vertices lie on the boundary of a single face. We extend this result to the closely related Edge-Disjoint Paths problem, showing the same hardness of approximation ratio even for sub-cubic planar graphs with all sources lying on the boundary of a single face.
This is joint work with David H.K. Kim and Rachit Nimavat.

TuesdayNov 22, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Michael Grinfeld Title:Mathematical Challenges in Submonolayer DepositionAbstract:opens in new windowin html    pdfopens in new window
Submonolayer deposition (SD) is a blanket term used to describe the initial stages of processes, such as molecular beam epitaxy, in which material is deposited onto a surface, diffuses and forms large-scale structures. It is easy to simulate using Monte Carlo methods, but theoretical results are few and far between. I will discuss various approaches to SD in the 1-dimensional situation, focusing on open mathematical problems and the difficulty of passing to the 2-dimensional case, which is of most applied interest. This is mainly joint work with Paul Mulheran.
TuesdayNov 22, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Michael Chmutov Title:An affine version of Robinson-Schensted Correspondence for Kazhdan-Lusztig theoryAbstract:opens in new windowin html    pdfopens in new window
In his study of Kazhdan-Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson-Schensted Correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combinatorial realization of Shi's algorithm. As a byproduct, we also give a way to realize the affine correspondence via the usual Robinson-Schensted bumping algorithm. Next, inspired by Honeywill, we extend the algorithm to a bijection between the extended affine symmetric group and collection of triples (P, Q, r) where P and Q are tabloids and r is a dominant weight.
MondayNov 21, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Adi ShamirTitle:Memory-Efficient Algorithms for Finding Needles in HaystacksAbstract:opens in new windowin html    pdfopens in new window

One of the most common tasks in cryptography and cryptanalysis is to find some interesting event (a needle) in an exponentially large collection (haystack) of N=2^n possible events, or to demonstrate that no such event is likely to exist. In particular, we are interested in finding needles which are defined as events that happen with an unusually high probability of p>>1/N in a haystack which is an almost uniform distribution on N possible events. When the search algorithm can only sample values from this distribution, the best known time/memory tradeoff for finding such an event requires O(1/Mp^2) time given O(M) memory.

In this talk I will describe much faster needle searching algorithms in the common cryptographic setting in which the distribution is defined by applying some deterministic function f to random inputs. Such a distribution can be modeled by a random directed graph with N vertices in which almost all the vertices have O(1) predecessors while the vertex we are looking for has an unusually large number of O(pN) predecessors. When we are given only a constant amount of memory, we propose a new search methodology which we call NestedRho. As p increases, such random graphs undergo several subtle phase transitions, and thus the log-log dependence of the time complexity T on p becomes a piecewise linear curve which bends four times. Our new algorithm is faster than the O(1/p^2) time complexity of the best previous algorithm in the full range of 1/N < p < 1 , and in particular it improves the previous time complexity by a significant factor of \sqrt{N} for any p in the range N^(- 0.75) < p < N^(-0.5). When we are given more memory, we show how to combine the NestedRho technique with the parallel collision search technique in order to further reduce its time complexity. Finally, we show how to apply our new search technique to more complicated distributions with multiple peaks when we want to find all the peaks whose probabilities are higher than p.

Joint work with Itai Dinur, Orr Dunkelman and Nathan Keller.

MondayNov 21, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Emanuele Rodola', Or LitanyTitle:Spectral Approaches to Partial Shape MatchingAbstract:opens in new windowin html    pdfopens in new window
In this talk we will present our recent line of work on (deformable) partial shape correspondence in the spectral domain. We will first introduce Partial Functional Maps (PFM), showing how to robustly formulate the shape correspondence problem under missing geometry with the language of functional maps. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. We will show further extensions to deal with the presence of clutter (deformable object-in-clutter) and multiple pieces (non-rigid puzzles). In the second part of the talk, we will introduce a novel approach to the same problem which operates completely in the spectral domain, avoiding the cumbersome alternating optimization used in the previous approaches. This allows matching shapes with constant complexity independent of the number of shape vertices, and yields state-of-the-art results on challenging correspondence benchmarks in the presence of partiality and topological noise.
ThursdayNov 17, 201611:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Anirban Basak Title:Invertibility of sparse random matricesAbstract:opens in new windowin html    pdfopens in new window
We consider a class of sparse random matrices of the form $A_n =(\xi_{i,j}\delta_{i,j})_{i,j=1}^n$, where $\{\xi_{i,j}\}$ are i.i.d.~centered random variables, and $\{\delta_{i,j}\}$ are i.i.d.~Bernoulli random variables taking value $1$ with probability $p_n$, and prove a quantitative estimate on the smallest singular value for $p_n = \Omega(\frac{\log n}{n})$, under a suitable assumption on the spectral norm of the matrices. This establishes the invertibility of a large class of sparse matrices. We also find quantitative estimates on the smallest singular value of the adjacency matrix of a directed Erdos-Reyni graph whenever its edge connectivity probability is above the critical threshold $\Omega(\frac{\log n}{n})$. This is joint work with Mark Rudelson.
WednesdayNov 16, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Dan Garber Title:Faster Projection-free Machine Learning and OptimizationAbstract:opens in new windowin html    pdfopens in new window

Projected gradient descent (PGD), and its close variants, are often considered the methods of choice for solving a large variety of machine learning optimization problems, including empirical risk minimization, statistical learning, and online convex optimization. This is not surprising, since PGD is often optimal in a very appealing information-theoretic sense. However, for many problems PGD is infeasible both in theory and practice since each step requires to compute an orthogonal projection onto the feasible set. In many important cases, such as when the feasible set is a non-trivial polytope, or a convex surrogate for a low-rank structure, computing the projection is computationally inefficient in high-dimensional settings. An alternative is the conditional gradient method (CG), aka Frank-Wolfe algorithm, that replaces the expensive projection step with a linear optimization step over the feasible set. Indeed in many problems of interest, the linear optimization step admits much more efficient algorithms than the projection step, which is the reason to the substantial regained interest in this method in the past decade. On the downside, the convergence rates of the CG method often fall behind that of PGD and its variants. 
In this talk I will survey an ongoing effort to design CG variants that on one hand enjoy the cheap iteration complexity of the original method, and on the other hand converge provably faster, and are applicable to a wider variety of machine learning settings. In particular I will focus on the cases in which the feasible set is either a polytope or a convex surrogate for low-rank matrices. Results will be demonstrated on applications including: LASSO, video co-localization, optical character recognition, matrix completion, and multi-class classification.

MondayNov 14, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Benny ApplebaumTitle:Algebraic Attacks against Random Local Functions and Their CountermeasuresAbstract:opens in new windowin html    pdfopens in new window

Suppose that you have n truly random bits X=(X1,...,Xn) and you wish to use them to generate m>>n pseudorandom bits Y=(Y1,..., Ym) using a local mapping, i.e., each Yi should depend on at most d=O(1) bits of x. In the polynomial regime of m=n^s, s>1, the only known solution, originates from (Goldreich, ECCC 2000), is based on Random Local Functions: Compute Yi by applying some fixed (public) d-ary predicate P to a random (public) tuple of distinct inputs. In this talk, we will try to understand, for any value of s, how the pseudorandomness of the resulting sequence depends on the choice of the underlying predicate.
Based on joint work with Shachar Lovett.

ThursdayNov 10, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Yedid HoshenTitle:End-to-End Learning: Applications in Speech, Vision and CognitionAbstract:opens in new windowin html    pdfopens in new window

One of the most exciting possibilities opened by deep neural networks is end-to-end learning: the ability to learn tasks without the need for feature engineering or breaking down into sub-tasks. This talk will present three cases illustrating how end-to-end learning can operate in machine perception across the senses (Hearing, Vision) and even for the entire perception-cognition-action cycle.

The talk begins with speech recognition, showing how acoustic models can be learned end-to-end. This approach skips the feature extraction pipeline, carefully designed for speech recognition over decades.

Proceeding to vision, a novel application is described: identification of photographers of wearable video cameras. Such video was previously considered anonymous as it does not show the photographer.

The talk concludes by presenting a new task, encompassing the full perception-cognition-action cycle: visual learning of arithmetic operations using only pictures of numbers. This is done without using or learning the notions of numbers, digits, and operators.

The talk is based on the following papers:

Speech Acoustic Modeling From Raw Multichannel Waveforms, Y. Hoshen, R.J. Weiss, and K.W. Wilson, ICASSP'15

An Egocentric Look at Video Photographer Identity, Y. Hoshen, S. Peleg, CVPR'16

Visual Learning of Arithmetic Operations, Y. Hoshen, S. Peleg, AAAI'16

ThursdayNov 03, 201611:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:David Ellis Title:Some applications of the $p$-biased measure to Erd\H{o}s-Ko-Rado type problemsAbstract:opens in new windowin html    pdfopens in new window

If $X$ is a finite set, the $p$-biased measure on the power-set of $X$ is defined as follows: choose a subset $S$ of $X$ at random by including each element of $X$ independently with probability $p$. If $\mathcal{F}$ is a family of subsets of $X$, one can consider the {\em $p$-biased measure} of $\mathcal{F}$, denoted by $\mu_p(\mathcal{F})$, as a function of $p$; if $\mathcal{F}$ is closed under taking supersets, then this function is an increasing function of $p$. Seminal results of Friedgut and Friedgut-Kalai give criteria for this function to have a 'sharp threshold'. A careful analysis of the behaviour of this function also yields some rather strong results in extremal combinatorics which do not explicitly mention the $p$-biased measure - in particular, in the field of {\em Erd\H{o}s-Ko-Rado type problems}, which concern the sizes of families of objects in which any two (or three...) of the objects 'agree' or 'intersect' in some way. We will discuss some of these, including a recent proof of an old conjecture of Frankl that a symmetric three-wise intersecting family of subsets of $\{1,2,\ldots,n\}$ has size $o(2^n)$, and some 'stability' results characterizing the structure of 'large' $t$-intersecting families of $k$-element subsets of $\{1,2,\ldots,n\}$. Based on joint work with (subsets of) Nathan Keller, Noam Lifshitz and Bhargav Narayanan.

TuesdayNov 01, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Anthony JosephTitle:S-graphs, trails and identities in Demazure modulesAbstract:opens in new windowin html    pdfopens in new window
MondayOct 31, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Guy RothblumTitle:Constant-Round Interactive Proofs for Delegating ComputationAbstract:opens in new windowin html    pdfopens in new window

Interactive proofs have had a dramatic impact on Complexity Theory and Cryptography. The celebrated IP=PSPACE Theorem [LFKN92,Shamir92] allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity of extremely complicated statements (as long as they can be evaluated using polynomial space). The interactive proof system designed for this purpose requires a polynomial number of communication rounds. This talk will focus on studying the power of more efficient interactive proof systems.

Our main result is that for every statement that can be evaluated in polynomial time and bounded-polynomial space, there exists an interactive proof that satisfies the following strict efficiency requirements:

(1) The honest prover runs in polynomial time.

(2) The verifier is almost linear time (and under some conditions even sub linear).

(3) The interaction consists of only a constant number of communication rounds.

To obtain this result, we introduce and study several new notions for interactive proofs, which may be of independent interest. One of these notions is that of unambiguous interactive proofs, where the prover has a unique successful strategy. Another notion is that of probabilistically checkable interactive proofs (PCIPs) where the verifier only reads a few bits of the transcript in checking the proof (this could be viewed as an interactive extension of PCPs).

Joint work with Omer Reingold and Ron Rothblum.

MondaySep 26, 201614:00
Vision and Robotics SeminarRoom 1
Speaker:Achuta KadambiTitle:From the Optics Lab to Computer Vision Abstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DAY AND TIME

Computer science and optics are usually studied separately -- separate people, in separate departments, meet at separate conferences. This is changing. The exciting promise of technologies like virtual reality and self-driving cars demand solutions that draw from the best aspects of computer vision, computer graphics, and optics. Previously, it has proved difficult to bridge these communities. For instance, the laboratory setups in optics are often designed to image millimeter-size scenes in a vibration-free darkroom. 

This talk is centered around time of flight imaging, a growing area of research in computational photography. A time of flight camera works by emitting amplitude modulated (AM) light and performing correlations on the reflected light. The frequency of AM is in the radio frequency range (like a Doppler radar system), but the carrier signal is optical, overcoming diffraction limited challenges of full RF systems while providing optical contrast. The obvious use of such cameras is to acquire 3D geometry. By spatially, temporally and spectrally coding light transport we show that it may be possible to go "beyond depth", demonstrating new forms of imaging like photography through scattering media, fast relighting of photographs, real-time tracking of occluded objects in the scene (like an object around a corner), and even the potential to distinguish between biological molecules using fluorescence. We discuss the broader impact of this design paradigm on the future of 3D depth sensors, interferometers, computational photography, medical imaging and many other applications. 

WednesdaySep 21, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Jian-Rong Li Title:Introduction to cluster algebras (continuation)Abstract:opens in new windowin html    pdfopens in new windowcorrect date 21/09/2016
Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky in 2000. I will give an introductory talk about cluster algebras. The main examples are the cluster algebra of type A2, the coordinate ring of $SL_4/N$, and the homogeneous coordinate ring of the Grassmannian $Gr_{2,n+3}(\mathbb{C})$.
WednesdaySep 14, 201614:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Assaf NaorTitle:The Lipschitz extension problem for finite dimensional normed spacesAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY
WednesdaySep 14, 201611:00
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Jian-Rong Li Title:Introduction to cluster algebrasAbstract:opens in new windowin html    pdfopens in new window

Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky in 2000. I will give an introductory talk about cluster algebras. The main examples are the cluster algebra of type A2, the coordinate ring of $SL_4/N$, and the homogeneous coordinate ring of the Grassmannian $Gr_{2,n+3}(\mathbb{C})$.  

ThursdaySep 08, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Tali Dekel Title:Exploring and Modifying Spatial Variations in a Single ImageAbstract:opens in new windowin html    pdfopens in new window
Structures and objects, captured in image data, are often idealized by the viewer. For example, buildings may seem to be perfectly straight, or repeating structures such as corn's kernels may seem almost identical. However, in reality, such flawless behavior hardly exists. The goal in this line of work is to detect the spatial imperfection, i.e., departure of objects from their idealized models, given only a single image as input, and to render a new image in which the deviations from the model are either reduced or magnified. Reducing the imperfections allows us to idealize/beautify images, and can be used as a graphic tool for creating more visually pleasing images. Alternatively, increasing the spatial irregularities allow us to reveal useful and surprising information that is hard to visually perceive by the naked eye (such as the sagging of a house's roof). I will consider this problem under two distinct definitions of idealized model: (i) ideal parametric geometries (e.g., line segments, circles), which can be automatically detected in the input image. (ii) perfect repetitions of structures, which relies on the redundancy of patches in a single image. Each of these models has lead to a new algorithm with a wide range of applications in civil engineering, astronomy, design, and materials defects inspection.
TuesdayAug 23, 201616:00
Seminar in Geometry and TopologyRoom 290C
Speaker:Misha Verbitsky Title:Homogeneous dynamic, hyperbolic geometry and cone conjectureAbstract:opens in new windowin html    pdfopens in new window
Hyperbolic manifold is a Riemannian manifold of constant negative curvature and finite volume. Let S be a set of geodesic hypersurfaces in a hyperbolic manifold of dimension >2. Using Ratner theory, we prove that either S is dense, or it is finite. This is used to study the Kahler cone of a holomorphically symplectic manifold. It turns out that the shape of the Kahler cone is encoded in the geometry of a certain polyhedron in a hyperbolic manifold. I will explain how this correspondence works, and how it is used to obtain the cone conjecture of Kawamata and Morrison. This is a joint work with Ekaterina Amerik.
ThursdayAug 04, 201611:30
Vision and Robotics SeminarRoom 1
Speaker:Michael RabinovichTitle:Scalable Locally Injective MappingsAbstract:opens in new windowin html    pdfopens in new window
We present a scalable approach for the optimization of flip-preventing energies in the general context of simplicial mappings, and specifically for mesh parameterization. Our iterative minimization is based on the observation that many distortion energies can be optimized indirectly by minimizing a simpler proxy energy and compensating for the difference with a reweighting scheme. Our algorithm is simple to implement and scales to datasets with millions of faces. We demonstrate our approach for the computation of maps that minimize a conformal or isometric distortion energy, both in two and three dimensions. In addition to mesh parameterization, we show that our algorithm can be applied to mesh deformation and mesh quality improvement.
WednesdayAug 03, 201610:30
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Siddhartha SahiTitle:The Capelli problem for gl(m|n) and the spectrum of invariant differential operatorsAbstract:opens in new windowin html    pdfopens in new window
The "generalized" Capelli operators form a linear basis for the ring of invariant differential operators on symmetric cones, such as GL/O and GL/Sp. The Harish-Chandra images of these operators are specializations of certain polynomials defined by speaker and studied together with F. Knop. These "Knop-Sahi" polynomials are inhomogeneous polynomials characterized by simple vanishing conditions; moreover their top homogeneous components are Jack polynomials, which in turn are common generalizations of spherical polynomials on symmetric cones. In the talk I will describe joint work with Hadi Salmasian that extends these results to the setting of the symmetric super-cones GL/OSp and (GLxGL)/GL.
ThursdayJul 21, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Ethan FetayaTitle:PhD Thesis Defense: Learning with limited supervision Abstract:opens in new windowin html    pdfopens in new window
The task of supervised learning, performing predictions based on a given labeled dataset, is well-understood theoretically and for which many practical algorithms exist. In general, the more complex the hypothesis space is, the larger the amount of samples we will need so that we do not overfit. The main issue is that obtaining a large labeled dataset is a costly and tedious process. An interesting and important question is what can be done when only a small amount of labeled data, or no data, is available. I will go over several approaches, learning with a single positive example, as well as unsupervised representation learning.
MondayJul 18, 201611:30
Vision and Robotics SeminarRoom 290C
Speaker:Emanuel A. LazarTitle:Voronoi topology analysis of structure in spatial point setsAbstract:opens in new windowin html    pdfopens in new window
Atomic systems are regularly studied as large sets of point-like particles, and so understanding how particles can be arranged in such systems is a very natural problem. However, aside from perfect crystals and ideal gases, describing this kind of "structure" in an insightful yet tractable manner can be challenging. Analysis of the configuration space of local arrangements of neighbors, with some help from the Borsuk-Ulam theorem, helps explain limitations of continuous metric approaches to this problem, and motivates the use of Voronoi cell topology. Several short examples from materials research help illustrate strengths of this approach.
ThursdayJul 14, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Netalee Efrat and Meirav GalunTitle:SIGGRAPH Dry-Runs Abstract:opens in new windowin html    pdfopens in new window

This Thursday we will have two SIGGRAPH rehearsal talks in the Vision Seminar, one by Netalee Efrat  and one by  Meirav Galun. Abstracts are below. Each talk will be about 15 minutes (with NO interruptions), followed by 10 minutes feedback.

Talk1  (Netalee Efrat):   Cinema 3D: Large scale automultiscopic display  

While 3D movies are gaining popularity, viewers in a 3D cinema still need to wear cumbersome glasses in order to enjoy them. Automultiscopic displays provide a better alternative to the display of 3D content, as they present multiple angular images of the same scene without the need for special eyewear. However, automultiscopic displays cannot be directly implemented in a wide cinema setting due to variants of two main problems: (i) The range of angles at which the screen is observed in a large cinema is usually very wide, and there is an unavoidable tradeoff between the range of angular images supported by the display and its spatial or angular resolutions. (ii) Parallax is usually observed only when a viewer is positioned at a limited range of distances from the screen. This work proposes a new display concept, which supports automultiscopic content in a wide cinema setting. It builds on the typical structure of cinemas, such as the fixed seat positions and the fact that different rows are located on a slope at different heights. Rather than attempting to display many angular images spanning the full range of viewing angles in a wide cinema, our design only displays the narrow angular range observed within the limited width of a single seat. The same narrow range content is then replicated to all rows and seats in the cinema. To achieve this, it uses an optical construction based on two sets of parallax barriers, or lenslets, placed in front of a standard screen. This paper derives the geometry of such a display, analyzes its limitations, and demonstrates a proof-of-concept prototype.

*Joint work with Piotr Didyk, Mike Foshey, Wojciech Matusik, Anat Levin

Talk 2  (Meirav Galun):   Accelerated Quadratic Proxy for Geometric Optimization 

We present the Accelerated Quadratic Proxy (AQP) - a simple first order algorithm for the optimization of geometric energies defined over triangular and tetrahedral meshes. The main pitfall encountered in the optimization of geometric energies is slow convergence. We observe that this slowness is in large part due to a Laplacian-like term existing in these energies. Consequently, we suggest to exploit the underlined structure of the energy  and to locally use a quadratic polynomial proxy, whose Hessian is taken to be the Laplacian. This improves stability and convergence, but more importantly allows incorporating acceleration in an almost universal way, that is independent of mesh size and of the specific energy considered. Experiments with AQP show it is rather insensitive to mesh resolution and requires a nearly constant number of iterations to converge; this is in strong contrast to other popular optimization techniques used today such as Accelerated Gradient Descent and Quasi-Newton methods, e.g., L-BFGS.  We have tested AQP for mesh deformation in 2D and 3D as well as for surface parameterization, and found it to provide a considerable speedup over common baseline techniques.

*Joint work with Shahar Kovalsky and Yaron Lipman

WednesdayJun 29, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Michal ZydorTitle:The singular transfer for the Jacquet-Rallis trace formulaAbstract:opens in new windowin html    pdfopens in new window

The Jacquet-Rallis relative trace formula was introduced as a tool towards solving the global conjectures of Gan-Gross-Prasad for unitary groups. I will present some recent progress in developing the full formula.
I will show how to extend the transfer of regular orbital integrals to singular geometric terms using a mix of local and global methods.
(Joint with Pierre-Henri Chaudouard)

SundayJun 26, 201614:30
Foundations of Computer Science SeminarRoom B
Speaker:Yi-Jun ChangTitle:An Exponential Separation Between Randomized and Deterministic Complexity in the LOCAL ModelAbstract:opens in new windowin html    pdfopens in new window

Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least exponentially faster than the best deterministic algorithm. In this paper we prove that these exponential gaps are necessary and establish connections between the deterministic and randomized complexities in the LOCAL model. Each result has a very compelling take-away message:

1. Fast Δ-coloring of trees requires random bits: Building on the recent lower bounds of Brandt et al., we prove that the randomized complexity of Δ-coloring a tree with maximum degree Δ≥55 is Θ(log_Δ log n), whereas its deterministic complexity is Θ(log_Δ n) for any Δ≥3. This also establishes a large separation between the deterministic complexity of Δ-coloring and (Δ+1)-coloring trees.

2. Randomized lower bounds imply deterministic lower bounds: We prove that any deterministic algorithm for a natural class of problems that runs in O(1)+o(log_Δ n) rounds can be transformed to run in O(log*n −log*Δ+1) rounds. If the transformed algorithm violates a lower bound (even allowing randomization), then one can conclude that the problem requires Ω(log_Δ n) time deterministically.

3. Deterministic lower bounds imply randomized lower bounds: We prove that the randomized complexity of any natural problem on instances of size n is at least its deterministic complexity on instances of size √ log n. This shows that a deterministic Ω(log_Δ n) lower bound for any problem implies a randomized Ω(log_Δ log n) lower bound. It also illustrates that the graph shattering technique is absolutely essential to the LOCAL model.

Joint work with Tsvi Kopelowitz and Seth Pettie.  http://arxiv.org/abs/1602.08166

ThursdayJun 23, 201612:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Shamgar Gurevich Title:Small Representations of Finite Classical GroupsAbstract:opens in new windowin html    pdfopens in new window
Many properties of a finite group G can be approached using formulas involving sums over its characters. A serious obstacle in applying these formulas seemed to be lack of knowledge over the low dimensional representations of G. In fact, the "small" representations tend to contribute the largest terms to these sums, so a systematic knowledge of them might lead to proofs of some conjectures which are currently out of reach.
ThursdayJun 23, 201611:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Jonathan HermonTitle:L_2 Mixing and hypercontractivity via maximal inequalities and hitting-timesAbstract:opens in new windowin html    pdfopens in new window

There are numerous essentially equivalent characterizations of mixing in $L_1$ of a finite Markov chain. Some of these characterizations involve natural probabilistic concepts such as couplings, stopping times and hitting times. In contrast, while there are several analytic and geometric tools for bounding the $L_2$ mixing time, none of them are tight and they do not have a probabilistic interpretation.

We provide tight probabilistic characterizations in terms of hitting times distributions for mixing in $L_2$ (for normal chains) and (under reversibility) in relative entropy. This is done by assigning appropriate penalty (depending on the size of the set) to the case that the chain did not escape from a certain set.

We also prove a new extremal characterization of the log-sobolev constant in terms of a weighted version of the spectral gap (where the weight depends on the size of the support of the function).

WednesdayJun 22, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Vasily Dolgushev Title:The intricate Maze of Graph ComplexesAbstract:opens in new windowin html    pdfopens in new window
ThursdayJun 16, 201614:00
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Itay GlazerTitle:Representations of reductive groups distinguished by symmetric subgroupsAbstract:opens in new windowin html    pdfopens in new window

We will discuss representation theory of a symmetric pair (G,H), where G is a complex reductive group, and H is a real form of G. The main objects of study are the G-representations with a non trivial H-invariant functional, called the H-distinguished representations of G.


I will give a necessary condition for a G-representation to be H-distinguished and show that the multiplicity of such representations is less or equal to the number of double cosets B\G/H, where B is a Borel subgroup of G.

ThursdayJun 16, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Yair Weiss Title:Neural Networks, Graphical Models and Image RestorationAbstract:opens in new windowin html    pdfopens in new window
This is an invited talk I gave last year at a workshop on "Deep Learning for Vision". It discusses some of the history of graphical models and neural networks and speculates on the future of both fields with examples from the particular problem of image restoration.
ThursdayJun 16, 201612:00
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Eliran SubagTitle:Critical points and the Gibbs measure of pure spherical spin glassesAbstract:opens in new windowin html    pdfopens in new window
Recently, several results concerning the critical points of the energy landscape of pure $p$-spin spherical spin glasses have been obtained by means of moment computations and a proof of a certain invariance property. I will describe those and explain how they can be boosted by an investigation of the behavior around the critical points to obtain a geometric description for the Gibbs measure at low enough temperature. The talk is based on joint work with Ofer Zeitouni.
ThursdayJun 16, 201611:15
Geometric Functional Analysis and Probability SeminarRoom 290C
Speaker:Eviatar ProcacciaTitle:Can one hear the shape of a random walk?Abstract:opens in new windowin html    pdfopens in new window
We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path's boundary. We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes. Joint work with Marek Biskup.
WednesdayJun 15, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Anthony JosephTitle:A minimax theorem for trailsAbstract:opens in new windowin html    pdfopens in new window
TuesdayJun 14, 201611:30
The Chaim Leib Pekeris Memorial Lecture
Speaker:Gil KalaiTitle:The Quantum Computer PuzzleAbstract:opens in new windowin html    pdfopens in new windowDolfi and Lola Ebner Auditorium

Quantum computers are hypothetical devices, based on quantum physics, which would enable us to perform certain computations (among them some that Chaim Leib Pekeris pioneered) hundreds of orders of magnitude faster than digital computers. This feature is coined “quantum supremacy.” We start the lecture with a gentle introduction to computing - classical and quantum, with basic notions of computational complexity, and with the vision of quantum computers. 

A main reason for concern regarding the feasibility of quantum computers is that quantum systems are inherently noisy. We will explain what is "noise" and describe an optimistic hypothesis regarding quantum noise that will allow quantum computing and a pessimistic hypothesis that won’t. The remarkable progress witnessed during the past two decades in the field of experimental physics of controlled quantum systems places the decision between the pessimistic and optimistic hypotheses within reach.  On the optimistic side, one aspect or another of  quantum supremacy might be seen by experiments in the near future: by implementing quantum error-correction or by systems of free bosons or by exotic new phases of matter called anyons or by quantum annealing, or in various other ways.

In the lecture I will explain my pessimistic line of research and here is a brief summary of my view:  understanding quantum computers in the presence of noise requires consideration of behavior at different scales. In the small scale, standard models of noise from the mid-90s are suitable, and quantum evolutions and states described by them manifest a very low-level computational power. This small-scale behavior has far-reaching consequences for the behavior of noisy quantum systems at larger scales. On the one hand, it does not allow reaching the starting points for quantum fault tolerance and quantum supremacy, making them both impossible at all scales. On the other hand, it leads to novel implicit ways for modeling noise at larger scales and to various predictions on the behavior of noisy quantum systems.

We will rely on the theory of noise-sensitivity and stability developed with Benjamini and Schramm in the late 90s and on recent work with Guy Kindler related to the mysterious gap between permanents and determinants (or, in other words, between bosons and fermions).

WednesdayJun 08, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Yotam Hendel Title:Supersingular representations and the mod p LanglandsAbstract:opens in new windowin html    pdfopens in new window

Let F/Q_p be a finite extension, supersingular representations are the irreducible mod p representations of GL_n(F) which do not appear as a subquotient of a principal series representation, and similarly to the complex case, they are the building blocks of the representation theory of GL_n(F). Historically, they were first discovered by L. Barthel and R. Livne some twenty years ago and they are still not understood even for n=2.

For F=Q_p, the supersingular representations of GL_2(F) have been classified by C. Breuil, and a local mod p Langlands correspondence was established between them and certain mod p Galois representations.

When one tries to generalize this connection and move to a non-trivial extension of Q_p, Breuil's method fails; The supersingular representations in that case have complicated structure and instead of two as in the case F=Q_p we get infinitely many such representations, when there are essentially only finitely many on the Galois side.

In this talk we give an exposition of the subject and explore, using what survives from Breuil's methods, the universal modules whose quotients contain all the supersingular representations in the difficult case where F is a non-trivial extension of Q_p.

WednesdayJun 08, 201611:15
Machine Learning and Statistics SeminarRoom 290C
Speaker:Daniel SoudryTitle:No bad local minima: Data independent training error guarantees for multilayer neural networksAbstract:opens in new windowin html    pdfopens in new window
We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs with piecewise linear activation functions, quadratic loss and a single output, under mild over-parametrization. We prove that for a MNN with one hidden layer, the training error is zero at every differentiable local minimum, for almost every dataset and dropout-like noise realization. We then extend these results to the case of more than one hidden layer. Our theoretical guarantees assume essentially nothing on the training data, and are verified numerically. These results suggest why the highly non-convex loss of such MNNs can be easily optimized using local updates (e.g., stochastic gradient descent), as observed empirically.
TuesdayJun 07, 201616:00
Seminar in Geometry and TopologyRoom 290C
Speaker:Alexey Glutsyuk Title:On periodic orbits in complex planar billiardsAbstract:opens in new windowin html    pdfopens in new window
A conjecture of Victor Ivrii (1980) says that in every billiard with smooth boundary the set of periodic orbits has measure zero. This conjecture is closely related to spectral theory. Its particular case for triangular orbits was proved by M. Rychlik (1989, in two dimensions), Ya. Vorobets (1994, in any dimension) and other mathematicians. The case of quadrilateral orbits in dimension two was treated in our joint work with Yu. Kudryashov (2012). We study the complexified version of planar Ivrii's conjecture with reflections from a collection of planar holomorphic curves. We present the classification of complex counterexamples with four reflections and partial positive results. The recent one says that a billiard on one irreducible complex algebraic curve without too complicated singularities cannot have a two-dimensional family of periodic orbits of any period. The above complex results have applications to other problems on real billiards: Tabachnikov's commuting billiard problem and Plakhov's invisibility conjecture.
ThursdayJun 02, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Omri Azencot Title:Advection-based Function Matching on SurfacesAbstract:opens in new windowin html    pdfopens in new window
A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non-linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.
WednesdayJun 01, 201611:15
Machine Learning and Statistics SeminarRoom 290C
Speaker:Shalom LappinTitle:Deep Learning and Semantic Interpretation of Natural LanguageAbstract:opens in new windowin html    pdfopens in new window
Classical approaches to formal and computational semantics assign values to the terminal elements of hierarchical syntactic structures and define combinatorial operations on the semantic representations of phrases to compute the values of sentences. While these approaches offer formally elegant models of interpretation, they have not produced wide coverage systems. They do not provide for semantic learning. They have also not succeeded in integrating lexical and compositional semantics in an interesting or computationally efficient way. Recent developments in image caption generation suggest an alternative approach, which can overcome these difficulties. This work formulates the problem of matching images with descriptions as a task in machine translation. Deep neural networks use an encoder to map regions of pixels in an image to vector representations of graphic features, and a decoder to align these features with the distributional vectors of lexical and phrasal items. This approach can be generalized to deep neural networks that identify correspondences between multi-modal data structures and sentences. To the extent that this research program is successful, it will satisfy the core objective of the classical formal semantic program. It will assign truth (fulfilment) conditions to the sentences of a language, where these conditions are specified in terms of multi-modal representations of situations (scenes) in the world. These correspondences are generated not by a recursive definition of a truth predicate in a formal semantic theory, but by an extended deep neural language model.
TuesdayMay 31, 201616:00
Seminar in Geometry and TopologyRoom 290C
Speaker:Askold KhovanskiiTitle:Topological Galois theoryAbstract:opens in new windowin html    pdfopens in new window
In the topological Galois theory we consider functions representable by quadratures as multivalued analytical functions of one complex variable. It turns out that there are some topological restrictions on the way the Riemann surface of a function representable by quadratures can be positioned over the complex plan. If a function does not satisfy these restrictions, then it cannot be represented by quadratures. This approach, besides its geometrical appeal, has the following advantage. The topological obstructions are related to the character of a multivalued function. They hold not only for functions representable by quadratures, but also for a more wide class of functions. This class is obtained adding to the functions representable by quadratures all meromorphic functions and allowing the presence of such functions in all formulae. Hence the topological results on the non representability by quadratures are stronger that those of algebraic nature.
MondayMay 30, 201614:30
Foundations of Computer Science SeminarRoom 290C
Speaker:Rotem Oshman Title:Two Applications of Communication Complexity in Distributed ComputingAbstract:opens in new windowin html    pdfopens in new window

In distributed systems, communication between the participants in the computation is usually the most expensive part of the computation. Theoretical models of distributed systems usually reflect this by neglecting the cost of local computation, and charging only for messages sent between the participants; in particular, we usually assume that the computation proceeds in rounds, and in each round, each participant can send only a limited number of bits. We are interested in characterizing the number of rounds required to perform various tasks.

In this talk I will describe two sets of results. The first concerns the complexity of distributed subgraph detection: we have n servers, each representing a node in an undirected graph, and each server receives as input its adjacent edges in the graph. The goal of the computation is to determine whether the global input graph contains some fixed subgraph. I will describe upper and lower bounds for several classes of subgraphs, through a connection to Turan numbers. The general case remains open.

In the second part of the talk I will describe recent work on multi- party number-in-hand communication and information complexity, and show a tight upper and lower bound for set disjointness in the shared blackboard model.

Joint work with Mark Braverman, Andrew Drucker and Fabian Kuhn.

ThursdayMay 26, 201614:00
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Ivan Penkov Title:Ordered tensor categories of representations of Mackey Lie algebrasAbstract:opens in new windowin html    pdfopens in new window
WednesdayMay 25, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 290C
Speaker:Ivan PenkovTitle:Primitive ideals in U(sl(infinity))Abstract:opens in new windowin html    pdfopens in new window
WednesdayMay 25, 201611:15
Vision and Robotics SeminarRoom 1
Speaker:Bill Freeman Title:Visually Indicated SoundsAbstract:opens in new windowin html    pdfopens in new windowJOINT SEMINAR WITH MACHINE LEARNING & STATISTICS

Children may learn about the world by pushing, banging, and manipulating things, watching and listening as materials make their distinctive sounds-- dirt makes a thud; ceramic makes a clink. These sounds reveal physical properties of the objects, as well as the force and motion of the physical interaction.

We've explored a toy version of that learning-through-interaction by recording audio and video while we hit many things with a drumstick. We developed an algorithm the predict sounds from silent videos of the drumstick interactions. The algorithm uses a recurrent neural network to predict sound features from videos and then produces a waveform from these features with an example-based synthesis procedure. We demonstrate that the sounds generated by our model are realistic enough to fool participants in a "real or fake" psychophysical experiment, and that the task of predicting sounds allows our system to learn about material properties in the scene.

Joint work with:
Andrew Owens, Phillip Isola, Josh McDermott, Antonio Torralba, Edward H. Adelson
http://arxiv.org/abs/1512.08512

TuesdayMay 24, 201616:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Yu. Ilyashenko Title:Towards the global bifurcation theory on the planeAbstract:opens in new windowin html    pdfopens in new window
The talk provides a new perspective of the global bifurcation theory on the plane. Theory of planar bifurcations consists of three parts: local, nonlocal and global ones. It is now clear that the latter one is yet to be created. Local bifurcation theory (in what follows we will talk about the plane only) is related to transfigurations of phase portraits of differential equations near their singular points. This theory is almost completed, though recently new open problems occurred. Nonlocal theory is related to bifurcations of separatrix polygons (polycycles). Though in the last 30 years there were obtained many new results, this theory is far from being completed. Recently it was discovered that nonlocal theory contains another substantial part: a global theory. New phenomena are related with appearance of the so called sparkling saddle connections. The aim of the talk is to give an outline of the new theory and discuss numerous open problems. The main new results are: existence of an open set of structurally unstable families of planar vector fields, and of families having functional invariants (joint results with Kudryashov and Schurov). Thirty years ago Arnold stated six conjectures that outlined the future development of the global bifurcation theory in the plane. All these conjectures are now disproved. Though the theory develops in quite a different direction, this development is motivated by the Arnold's conjectures.
MondayMay 23, 201614:30
Foundations of Computer Science Seminar
Speaker:Stephen ChestnutTitle:Beating CountSketch for heavy hitters in insertion streamsAbstract:opens in new windowin html    pdfopens in new windowROOM 155

The task of finding heavy hitters is one of the best known and well studied problems in the area of data streams.  In a sense, the strongest guarantee available is the L2 guarantee, which requires finding all items that occur at least eps*||f|| times in the stream, where the i-th coordinate of the vector f is the number of occurrences of i in the stream.  The first algorithm to achieve the L2 guarantee was the CountSketch (Charikar, Chen, and Farach-Colton ICALP'02), which, for constant eps, requires O(log n) words of memory and O(log n) update time. It is known to be space-optimal if the stream includes deletions.

In this talk I will discuss recent improvements that allow us to find L2 heavy hitters in O(1) memory and O(1) update time in insertion only streams.  The improvements rely on a deeper understanding of the AMS sketch (Alon, Matias, and Szegedy STOC'96) and similar sketches and draw on the theory of Gaussian processes.  This talk is based on joint work with Vladimir Braverman, Nikita Ivkin, Jelani Nelson, Zhengyu Wang, and David P. Woodruff in arxiv:1511.00661 and arxiv:1603.00759.

WednesdayMay 18, 201611:15
Machine Learning and Statistics Seminar
Speaker:Abraham WynerTitle:Explaining the Success of AdaBoost and Random Forests as Interpolating ClassifiersAbstract:opens in new windowin html    pdfopens in new windowroom 155

There is a large literature explaining why AdaBoost is a successful classifier. The literature on AdaBoost focuses on classifier margins and boosting's interpretation as the optimization of an exponential likelihood function. These existing explanations, however, have been pointed out to be incomplete. A random forest is another popular ensemble method for which there is substantially less explanation in the literature. We introduce a novel perspective on AdaBoost and random forests that proposes that the two algorithms work for essentially similar reasons. While both classifiers achieve similar predictive accuracy, random forests cannot be conceived as a direct optimization procedure. Rather, random forests is a self-averaging, interpolating algorithm which fits training data without error but is nevertheless somewhat smooth. We show that AdaBoost has the same property. We conjecture that both AdaBoost and random forests  succeed because of this mechanism. We provide a number of examples and some theoretical justification to support this explanation. In the process, we question the conventional wisdom that suggests that boosting algorithms for classification require regularization or early stopping and should be limited to low complexity classes of learners, such as decision stumps. We conclude that boosting should be used like random forests: with large decision trees and without direct regularization or early stopping.

WednesdayMay 18, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Dimitar Granthcharov Title:Singular Gelfand-Tsetlin modulesAbstract:opens in new windowin html    pdfopens in new window
TuesdayMay 17, 201616:15
Seminar in Geometry and TopologyRoom 290C
Speaker:Boris LevitTitle:Optimal Interpolation in approximation theory, nonparametric regression and optimal designAbstract:opens in new windowin html    pdfopens in new window

For some rectangular Hardy classes of analytic functions,an optimal method of interpolation has been previously found, within the framework of Optimal Recovery. It will be shown that this method of interpolation, based on the Abel-Jacobi elliptic functions,  is also optimal, according to corresponding criteria of Nonparametric Regression and Optimal Design.

In a non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. In  these results, a pivotal role is played by an interference effect, in which both the stochastic and deterministic parts of the interpolant exhibit an oscillating behavior, with the two oscillating processes mutually subduing each other.

MondayMay 16, 201614:30
Foundations of Computer Science Seminar
Speaker:Ronitt RubinfeldTitle:Sampling CorrectorsAbstract:opens in new windowin html    pdfopens in new windowRoom 155

In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, we propose the methodology of sampling correctors. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms may then be used as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks.Warning:   This talk contains more questions than answers...

Joint work with Clement Canonne and Themis Gouleakis.

MondayMay 09, 201614:30
Foundations of Computer Science Seminar
Speaker:Ilan CohenTitle:Serving in the Dark should be done Non-UniformlyAbstract:opens in new windowin html    pdfopens in new windowRoom 155
We study the following balls and bins stochastic game between a player and an adversary: there are B bins and a sequence of ball arrival and extraction events. In an arrival event a ball is stored in an empty bin chosen by the adversary and discarded if no bin is empty. In an extraction event, an algorithm selects a bin, clears it, and gains its content.We are interested in analyzing the gain of an algorithm which serves in the dark without any feedback at all, i.e., does not see the sequence, the content of the bins, and even the content of the cleared bins (i.e. an oblivious algorithm). We compare that gain to the gain of an optimal, open eyes, strategy that gets the same online sequence. We name this gain ratio the loss of serving in the dark. The randomized algorithm that was previously analyzed is choosing a bin independently and uniformly at random, which resulted in a competitive ratio of about 1.69. We show that although no information is ever provided to the algorithm, using non-uniform probability distribution reduces the competitive ratio. Specifically, we design a 1.55-competitive algorithm and establish a lower bound of 1.5. We also prove a lower bound of 2 against any deterministic algorithm. This matches the performance of the round robin 2-competitive strategy. Finally, we present an application relating to a prompt mechanism for bounded capacity auctions.
MondayMay 09, 201614:00
Vision and Robotics SeminarRoom 1
Speaker:Nikos ParagiosTitle:Visual Perception through Hyper GraphsAbstract:opens in new windowin html    pdfopens in new windowNote the unusual day & time
Computational vision, visual computing and biomedical image analysis have made tremendous progress in the past decade. This is mostly due the development of efficient learning and inference algorithms which allow better and richer modeling of visual perception tasks. Hyper-Graph representations are among the most prominent tools to address such perception through the casting of perception as a graph optimization problem. In this talk, we briefly introduce the interest of such representations, discuss their strength and limitations, provide appropriate strategies for their inference learning and present their application to address a variety of problems of visual computing.
ThursdayMay 05, 201614:00
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Vera Serganova Title: New tensor categories related to orthogonal and symplectic groups and the strange supergroup P(infinity)Abstract:opens in new windowin html    pdfopens in new window
We study a symmetric monoidal category of tensor representations of the ind group O(infinity). This category is Koszul and its Koszul dual is the category of tensor representations of the strange supergroup P(infinity). This can be used to compute Ext groups between simple objects in both categories. The above categories are missing the duality functor. It is possible to extend these categories to certain rigid tensor categories satisfying a nice universality property. In the case of O(infinity) such extension depends on a parameter t and is closely related to the Deligne’s category Rep O(t). When t is integer, this new category is a highest weight category and the action of translation functors in this category is related to the representation of gl(infinity) in the Fock space.
ThursdayMay 05, 201611:00
Geometric Functional Analysis and Probability Seminar
Speaker:Ilya GoldsheidTitle:Recurrent Random Walks on a Strip: conditions for the CLTAbstract:opens in new windowin html    pdfopens in new window Double feature room 155
This is joint work with Dima Dolgopyat. We prove that a recurrent random walk (RW) in i.i.d. random environment (RE) on a strip which does not obey the Sinai law exhibits the Central Limit asymptotic behaviour. Moreover, there exists a collection of proper subvarieties in the space of transition probabilities such that: (a) If the RE is stationary and ergodic and the transition probabilities are concentrated on one of sub-varieties from our collection then the CLT holds; (b) If the environment is i.i.d then the above condition is also necessary for the CLT to hold. In particular, the CLT holds for the quasiperiodic environments with Diophantine frequencies in the recurrent case and complement this result by proving that in the transient case the CLT holds for all strictly ergodic environments.
ThursdayMay 05, 201611:00
Geometric Functional Analysis and Probability Seminar
Speaker:Tal OrenshteinTitle:One-dependent walks in hypergeometric-Dirichlet environmentsAbstract:opens in new windowin html    pdfopens in new windowDouble feature room 155
Dirichlet environments are one of the few examples in Random Walk in Random Environment in which some non-trivial random walk properties are fully and explicitly characterized in terms of the parameters. A key feature of the model is the so-called 'time reversal property', saying that inverting the time is resulting in the same class of models, with an explicit change of parameters. In this talk, which is based on a joint work in process with Christophe Sabot, I'll present a generalization of random walks in Dirichlet environments using hypergeometric functions having that nice feature, and discuss the question of existence of an invariant probability measure for the process on the environments from the point of view of the walker which is absolutely continuous with respect to the initial measure.
WednesdayMay 04, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Andrey Minchenko Title:Differential algebraic groups and their applicationsAbstract:opens in new windowin html    pdfopens in new window
At the most basic level, differential algebraic geometry studies solution spaces of systems of differential polynomial equations. If a matrix group is defined by a set of such equations, one arrives at the notion of a linear differential algebraic group, introduced by P. Cassidy. These groups naturally appear as Galois groups of linear differential equations with parameters. Studying linear differential algebraic groups and their representations is important for applications to finding dependencies among solutions of differential and difference equations (e.g. transcendence properties of special functions). This study makes extensive use of the representation theory of Lie algebras. Remarkably, via their Lie algebras, differential algebraic groups are related to Lie conformal algebras, defined by V. Kac. We will discuss these and other aspects of differential algebraic groups, as well as related open problems.
WednesdayMay 04, 201611:15
Machine Learning and Statistics Seminar
Speaker:Amit DanielyTitle:The Power of Initialization and a Dual View on ExpressivityAbstract:opens in new windowin html    pdfopens in new windowRoom 155
We develop a general duality between neural networks and compositional kernels. We show that initial representations generated by common random initializations are sufficiently rich to express all functions in the dual kernel space. Hence, though the training objective is hard to optimize in the worst case, the initial weights form a good starting point for optimization. Our dual view also reveals a pragmatic and aesthetic perspective of neural networks and underscores their expressive power. Joint work with Roy Frostig and Yoram Singer
TuesdayMay 03, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Victor Ivrii Title:Spectral asymptotics for fractional LaplacianAbstract:opens in new windowin html    pdfopens in new window
Consider a compact domain with the smooth boundary in the Euclidean space. Fractional Laplacian is defined on functions supported in this domain as a (non-integer) power of the positive Laplacian on the whole space restricted then to this domain. Such operators appear in the theory of stochastic processes. It turns out that the standard results about distribution of eigenvalues (including two-term asymptotics) remain true for fractional Laplacians. There are however some unsolved problems.
MondayMay 02, 201614:30
Foundations of Computer Science SeminarRoom 261
Speaker:Merav Parter Title:MST in Log-Star Rounds of Congested CliqueAbstract:opens in new windowin html    pdfopens in new windowmoved to room 155

We present a randomized algorithm that computes a Minimum Spanning Tree (MST) in O(log^* n) rounds, with high probability, in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits.

Our key technical novelty is an O(log^* n) Graph Connectivity algorithm, the heart of which is a (recursive) forest growth method, based on a combination of two ideas: a sparsity-sensitive sketching aimed at sparse graphs and a random edge sampling aimed at dense graphs.

Our result improves significantly over the $O(\log \log \log n)$ algorithm of Hegeman et al. [PODC 2015] and the $O(\log \log n)$ algorithm of Lotker et al. [SPAA 2003; SICOMP 2005].

Join work with Mohsen Ghaffari.

ThursdayApr 21, 201611:00
Geometric Functional Analysis and Probability Seminar
Speaker:Atilla YilmazTitle:Large deviations for random walk in space-time random environment: averaged vs. quenchedAbstract:opens in new windowin html    pdfopens in new windowRoom 155
I will present recent joint work with F. Rassoul-Agha (Utah) and T. Seppalainen (Madison) where we consider random walk on a hypercubic lattice of arbitrary dimension in a space-time random environment that is assumed to be temporally independent and spatially translation invariant. The large deviation principle (LDP) for the empirical velocity of the averaged walk (i.e., level-1) is simply Cramer’s theorem. We take the point of view of the particle and establish the process-level (i.e., level-3) averaged LDP for the environment Markov chain. The rate function $I_{3,a}$ is a specific relative entropy which reproduces Cramer’s rate function via the so-called contraction principle. We identify the unique minimizer of this contraction at any velocity and analyse its structure. When the environment is spatially ergodic, the level-3 quenched LDP follows from our previous work which gives a variational formula for the rate function $I_{3,q}$ involving a Donsker-Varadhan-type relative entropy $H_q$. We derive a decomposition formula for $I_{3,a}$ that expresses it as a sum of contributions from the walk (via $H_q$) and the environment. We use this formula to characterize the equality of the level-1 averaged and quenched rate functions, and conclude with several related results and open problems.
WednesdayApr 20, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Prof. Florence Fauquant-Millet Title:Adapted pairs for maximal parabolic subalgebras and polynomiality of invariantsAbstract:opens in new windowin html    pdfopens in new window
In this talk we will see how adapted pairs - introduced by A. Joseph about ten years ago, the analogue of principal s-triples for non reductive Lie algebras - may be used to prove the polynomiality of some algebras of invariants associated to a maximal parabolic subalgebra.
MondayApr 18, 201614:30
Foundations of Computer Science Seminar
Speaker:Danny HarnikTitle:Estimating the Unseen - from Theory to PracticeAbstract:opens in new windowin html    pdfopens in new windowROOM 155

Estimating the amount of distinct elements in a dataset by examining only a fraction of the data is known to be a hard problem, both theoretically and in practice.
Our work explores a breakthrough theoretical result by Valiant and Valiant from 2011 that presents a provably accurate method for doing such estimations.
Our goal is to put this theory into practice for the important task of estimating the deduplication ratio of a very large dataset. However, deploying this technique in a real world setting runs into significant obstacles.
In the talk I will describe new techniques that help bridging the gap and enable the use of this exciting approach. Our work achieves a major improvement over the current state of the art practical solutions.

The talk is for a general audience, no prior knowledge is assumed.

Based on joint work  with Dmitry Sotnikov and Ety Khaitzin that appeared at Usenix FAST 2016.

ThursdayApr 14, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Barak Zackay Title:Proper astronomical image processing - Solving the problems of image co-addition and image subtractionAbstract:opens in new windowin html    pdfopens in new window

While co-addition and subtraction of astronomical images stand at the heart of observational astronomy, the existing solutions for them lack rigorous argumentation, are not achieving maximal sensitivity and are often slow. Moreover, there is no widespread agreement on how they should be done, and often different methods are used for different scientific applications. I am going to present rigorous solutions to these problems, deriving them from the most basic statistical principles. These solutions are proved optimal, under well defined and practically acceptable assumptions, and in many cases improve substantially the performance of the most basic operations in astronomy.

For coaddition, we present a coadd image that is:
a) sufficient for any further statistical decision or measurement on the underlying constant sky, making the entire data set redundant.
b) improves both survey speed (by 5-20%) and effective spatial resolution of past and future astronomical surveys.
c) improves substantially imaging through turbulence applications.
d) much faster than many of the currently used coaddition solutions.

For subtraction,  we present a subtraction image that is:
a) optimal for transient detection under the assumption of spatially uniform noise.
b) sufficient for any further statistical decision on the differences between the images, including the identification of cosmic rays and other image artifacts.
c) Free of subtraction artifacts, allowing (for the first time) robust transient identification in real time, opening new avenues for scientific exploration.
d) orders of magnitude faster than past subtraction methods.

WednesdayApr 13, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Mark Shusterman Title:An elementary proof of Olshanskii's theorem on subgroups of a free group and its applicationsAbstract:opens in new windowin html    pdfopens in new windowplease note change in room

I will present an elementary proof of the following theorem of Alexander Olshanskii:

Let F be a free group and let A,B be finitely generated subgroups of infinite index in F. Then there exists an infinite index subgroup C of F which contains both A and a finite index subgroup of B.

The proof is carried out by introducing a 'profinite' measure on the discrete group F, and is valid also for some groups which are not free.Some applications of this result will be discussed:


1. Group Theory - Construction of locally finite faithful actions of countable groups.

2. Number Theory - Discontinuity of intersections for large algebraic extensions of local fields.

3. Ergodic Theory - Establishing cost 1 for groups boundedly generated by subgroups of infinite index and finite cost.

ThursdayApr 07, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Yoni WexlerTitle:Fast Face Recognition with Multi-BatchAbstract:opens in new windowin html    pdfopens in new window

A common approach to face recognition relies on using deep learning  for extracting a signature.  All leading work on the subject use  stupendous amounts of processing power and data. In this work we present a method for efficient and compact learning  of metric embedding.  The core idea allows a more accurate  estimation of the global gradient and hence fast and robust  convergence. In order to avoid the need for huge amounts of data we include an explicit alignment phase into the network, hence greatly reducing  the number of parameters. These insights allow us to efficiently train a compact deep learning model for face recognition in only 12 hours on a single GPU, which can  then fit a mobile device.

Joint work with: Oren Tadmor, Tal Rosenwein, Shai Shalev-Schwartz, Amnon Shashua

WednesdayApr 06, 201611:15
Machine Learning and Statistics Seminar
Speaker:Moshe KoppelTitle:Reconstructing Ancient Documents from Noisy ManuscriptsAbstract:opens in new windowin html    pdfopens in new windowRoom 155
Given multiple corrupted versions of the same text, as is common with ancient manuscripts, we wish to reconstruct the original text from which the extant corrupted versions were copied (possibly via latent intermediary versions). This is a challenge of cardinal importance in the humanities. We use a variant of EM to solve this problem and demonstrate the efficacy of the method on both synthetic and real-world data.
WednesdayApr 06, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Dmitry GourevitchTitle:Recent applications of classical theorems on D-modulesAbstract:opens in new windowin html    pdfopens in new window
MondayApr 04, 201614:30
Foundations of Computer Science Seminar
Speaker:Tali KaufmanTitle:Bounded degree high dimensional expandersAbstract:opens in new windowin html    pdfopens in new windowROOM 155

Expander graphs are widely studied, and various methods are known to obtain bounded degree expander graphs. Recently, there is a growing interest in understanding combinational expansion in higher dimensions (higher dimensional simplicial complexes). However, bounded degree combinatorial expanders (random or explicit) were not known till our work.

We present a local to global criterion on a complex that implies combinatorial expansion. We use our criterion to present explicit bounded degree high dimensional expanders. This solves in the affirmative an open question raised by Gromov, who asked whether bounded degree high dimensional expanders could at all exist.

We expect that the emerging theory of high dimensional expansion is likely to have various application in the theory of computation. Thus, one of the goals of this talk in to introduce this concept to the theory community.


Based on joint works with David Kazhdan and Alex Lubotzky, and with Shai Evra.

SundayApr 03, 201611:15
Distinguished Lecture SeriesRoom 1
Speaker:Lai-Sang Young Title:Measuring dynamical complexityAbstract:opens in new windowin html    pdfopens in new windowRefreshments after the lecture in Ziskind lobby
I will discuss, for differentiable dynamical systems, three ways to capture dynamical complexity: (A) hyperbolicity, which measures the sensitivity of dependence on initial conditions, (B) entropy, which measures the predictability of future dynamical events in the sense of information theory, and (C) the speed of correlation decay or equivalently the rate at which memory is lost. I will review these ideas in nontechnical terms, present theorems showing how they are related, and give a very brief (and somewhat personal) survey of the progress made in the last decades. For illustration, I will show how these results apply to a concrete example: shear- induced chaos in periodically kicked oscillators, a phenomenon closely related to that observed by van der Pol nearly 100 years ago.
ThursdayMar 31, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Yael Moses Title:Dynamic Scene Analysis Using CrowdCam DataAbstract:opens in new windowin html    pdfopens in new window

Dynamic events such as family gatherings, concerts or sports events are often photographed by a group of people. The set of still images obtained this way is rich in dynamic content. We consider the question of whether such a set of still images, rather than traditional video sequences, can be used for analyzing the dynamic content of the scene. This talk will describe several instances of this problem, their solutions and directions for future studies.

In particular, we will present a method to extend epipolar geometry to predict location of a moving feature in CrowdCam images. The method assumes that the temporal order of the set of images, namely photo-sequencing, is given. We will briefly describe our method to compute photo-sequencing using geometric considerations and rank aggregation.  We will also present a method for identifying the moving regions in a scene, which is a basic component in dynamic scene analysis. Finally, we will consider a new vision of developing collaborative CrowdCam, and a first step toward this goal.

This talk will be based on joint works with Tali Dekel, Adi Dafni, Mor Dar, Lior Talked, Ilan Shimshoni,  and Shai Avidan.

ThursdayMar 31, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Amir Yehudayoff Title:Geometric stability using information theoryAbstract:opens in new windowin html    pdfopens in new windowmoved to room 155

Projection inequalities bound the volume of a body in terms of a product of the volumes of lower-dimensional projections of the body. Two well-known examples are the Loomis-Whitney inequality and the more general Uniform Cover inequality. We will see how to use information theory to prove stability versions of these inequalities, showing that when they are close to being tight, the body in question is close to being a box (which is the unique case of equality). We will also see how to obtain a stability result for the edge-isoperimetric inequality in the infinite d-dimensional lattice. Namely, that a subset of Z^d with small edge-boundary must be close in symmetric difference to a d-dimensional cube.

Based on work with David Ellis, Ehud Friedgut and Guy Kindler.

WednesdayMar 30, 201611:15
Machine Learning and Statistics SeminarRoom 261
Speaker:Matan GavishTitle:Optimal thresholding of singular values and eigenvaluesAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE ROOM CHANGE

It is common practice in multivariate and matrix-valued data analysis to reduce dimensionality by performing a Singular Value Decomposition or Principal Component Analysis, and keeping only $r$ singular values or principal components, the rest being presumably associated with noise. However, the literature does not propose a disciplined criterion to determine $r$; most practitioners still look for the ``elbow in the Scree Plot'', a 50-years-old heuristic performed by eye. I'll review a line of work which develops a systematic approach to eigenvalue and singular value thresholding. This approach assumes that the signal is low-rank and that the noise is rotationally invariant. Recent results derive optimal thresholds in the presence of quite general noise distributions.

Joint work with David Donoho, Iain Johnstone and Edgar Dobriban (Stanford).

WednesdayMar 30, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Victor Abrashkin Title:p-extensions of local fields with Galois groups of nilpotent class <pAbstract:opens in new windowin html    pdfopens in new windowmoved into room 155

Let K be a complete discrete valuation field with finite residue field of characteristic p>0. Let G  be the absolute Galois group of K and for a natural M, let  G(M) be the maximal quotient of G of nilpotent class <p and period p^M. Then G(M) can be identified  with a group obtained from a Lie Z/p^M-algebra L via (truncated) Campbell-Hausdorff composition law. Under this identification the ramification subgroups in upper numbering G(M)^(v)correspond to ideals L^(v) of L. It will be explained an  explicit construction of L and the ideals L^(v). The case of fields K of characteristic p was obtained by the author in 1990's (recently refined), the case of fields K of mixed characteristic requires the assumption that K contains a primitive p^M-th root of unity (for the case M=1 cf. Number Theory Archive).

TuesdayMar 29, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Leah Edelstein-KeshetTitle:Mathematical models of molecular motors and other cellular processesAbstract:opens in new windowin html    pdfopens in new window
Transport of material inside long cells (e.g. up to meters in the case of neuronal cells) requires active processes other than simple diffusion. Molecular motors (such as kinesin and dynein) that "walk" along microtubules (long structural biopolymers) are important in such transport. In this talk I will describe some recent work on the dynamics of these proteins in simple cells: the filamentous hyphae of a fungus (Ustilago maydis). We find that quasi-steady state (QSS) reduction of the model to a Fokker-Plank equation, as well as simulations of the original model provide insight into the behavior of the system for various parameter regimes. I will conclude with a brief survey of other recent work on cellular and multi-cellular dynamics in my group.
MondayMar 28, 201611:00
Vision and Robotics SeminarRoom 141
Speaker:Dan RavivTitle:Stretchable non-rigid structuresAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL ROOM, DAY and TIME.
Geometrical understanding of bendable and stretchable structures is crucial for many applications where comparison, inference and reconstruction play an important role. Moreover, it is the first step in quantifying normal and abnormal phenomena in non-rigid domains. Moving from Euclidean (straight) distances towards intrinsic (geodesic) measures, revolutionized the way we handle bendable structures, but did not take stretching into account. Human organs, such as the heart, lungs and kidneys, are great examples for such models. In this lecture I will show that stretching can be accounted for in the atom (local) level, in a closed form using higher derivatives of the data. I further show that invariants can play a critical part in modern learning systems, used for statistical analysis of non-rigid structures, and assist in fabricating soft-models. The lecture will be self-contained and no prior knowledge is needed.
WednesdayMar 23, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Anthony JosephTitle:Two remarkable properties of the canonical S-graphs and the Kashiwara crystal Abstract:opens in new windowin html    pdfopens in new window
ThursdayMar 17, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Asaf FerberTitle:Iterated Log Law for various graph parametersAbstract:opens in new windowin html    pdfopens in new window

We show that a version of the classical Iterated Log Law of Khinchin, and independently of Kolmogorov from the 1920's, holds for various parameters in the binomial random graph model and in a random 0/1 Bernoulli matrix. In particular, for a constant p, we show that such a law holds for the number of copies of a fixed graph H in G(n,p), we show a similar statement for the number of Hamilton cycles in a random k-uniform hypergraph, provided that k\geq 4. In the graph case (that is, k=2), since the number of Hamilton cycles in G(n,p), denoted by X_n, does not converge to a normal distribution but rather tends to a log-normal distribution (as has been first proved by Janson), we show that a version of the Iterated Log Law holds for \log X_n. We also obtain similar result for the permanent of a 0/1 bernouli random matrix.

No prior knowledge is required.

Joint with Daniel Motealegre and Van Vu.

WednesdayMar 16, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Amichai PainskyTitle:Generalized Independent Component Analysis Over Finite AlphabetsAbstract:opens in new windowin html    pdfopens in new window
Independent component analysis (ICA) is a statistical method for transforming an observable multidimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear transformation with additive noise). ICA over finite fields is a special case of ICA in which both the observations and the independent components are over a finite alphabet. In this work we consider a generalization of this framework in which an observation vector is decomposed to its independent components (as much as possible) with no prior assumption on the way it was generated. This generalization is also known as Barlow's minimal redundancy representation problem [Barlow, '89] and is considered an open problem. We propose several theorems and show that this hard problem can be accurately solved with a branch and bound search tree algorithm, or tightly approximated with a series of linear problems. Moreover, we show that there exists a simple transformation (namely, order permutation) which provides a greedy yet very effective approximation of the optimal solution. We further show that while not every random vector can be efficiently decomposed into independent components, the vast majority of vectors do decompose very well (that is, with a small constant cost), as the dimension increases. The minimal redundancy representation (also known as factorial coding) has many applications, mainly in the fields of neural networks and deep learning. In this work we show that this formulation further applies to large alphabet source coding. Joint work with Prof. Saharon Rosset from the Statistics Department and Prof. Meir Feder from the EE department, Tel Aviv University
MondayMar 14, 201614:30
Foundations of Computer Science SeminarRoom 261
Speaker:Yaron Singer Title:Some limitations and possibilities of data-driven optimizationAbstract:opens in new windowin html    pdfopens in new window
As we grow highly dependent on data for making predictions, we translate these predictions into models that help us make informed decisions. But how do the guarantees we have on predictions translate to guarantees on decisions? In many cases, we learn models from sampled data and then aim to use these models to make decisions. This intuitive approach turns out to have non-trivial limitations. In some cases, despite having access to large data sets, the current frameworks we have for learnability do not suffice to guarantee desirable outcomes. In other cases, the learning techniques we have introduce estimation errors which can result in poor outcomes and stark impossibility results. In this talk we will formalize some of these ideas using convex and combinatorial optimization and discuss some possibility and impossibility results of this agenda.
ThursdayMar 10, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Mark RudelsonTitle:No-gaps delocalization for general random matricesAbstract:opens in new windowin html    pdfopens in new window

Heuristically, delocalization for a random matrix means that its normalized eigenvectors look like the vectors uniformly distributed over the unit sphere. This can be made precise in a number of different ways. We show that with high probability, any sufficiently large set of coordinates of an eigenvector carries a non-negligible portion of its Euclidean norm. Our results pertain to a large class of random matrices including matrices with independent entries, symmetric, skew-symmetric matrices, as well as more general ensembles.

Joint work with Roman Vershynin.

WednesdayMar 09, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Sebastien BubeckTitle:New Results at the Crossroads of Convexity, Learning and Information TheoryAbstract:opens in new windowin html    pdfopens in new window
I will present three new results: (i) the Cramer transform of the uniform measure on a convex body is a universal self-concordant barrier; (ii) projected gradient descent with Gaussian noise allows to sample from a log-concave measure in polynomial time; and (iii) Thompson sampling combined with a multi-scale exploration solves the Bayesian convex bandit problem. The unifying theme in these results is the interplay between concepts from convex geometry, learning and information theory. Joint work with Ronen Eldan, and for (ii) with Joseph Lehec.
ThursdayMar 03, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Alexei V. PenskoiTitle:Recent advances in geometric optimization of eigenvalues of the Laplace-Beltrami operator on closed surfacesAbstract:opens in new windowin html    pdfopens in new window
Since a metric defines the Laplace-Beltrami operator on a closed surface, the eigenvalues of the Laplace-Beltrami operator are functionals on the space of Riemannian metrics on the surface. A metric is called maximal for i-th eigenvalue if the i-th eigenvalue attends its maximum on this metric. It turns out that the question about finding maximal metrics is very deep and related to analysis, topology, algebraic and differential geometry. In this talk several recent advances in this question will be exposed.
WednesdayMar 02, 201611:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Laura Peskin Title:Mod-p representations of p-adic metaplectic groupsAbstract:opens in new windowin html    pdfopens in new window
I will discuss a classification of the mod-p representations (i.e., of representations with coefficients in an algebraic closure of F_p) of the metaplectic double cover of a p-adic symplectic group. I'll review techniques from the mod-p representation theory of p-adic reductive groups, and explain how to modify them in order to classify representations of covering groups. This is joint work with Karol Koziol.
WednesdayFeb 24, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Nicolo Cesa-BianchiTitle:Real-time bidding and regret minimizationAbstract:opens in new windowin html    pdfopens in new window
In real-time bidding (RTB), ad exchanges run second-price auctions in a few milliseconds, allowing publishers to sell ad spaces to advertisers on a per-impression basis. The fact that RTB allows the accurate tailoring of impressions to the features of each individual user, has fueled the demand for algorithmic platforms that serve the needs of either the seller or the buyer. In this talk, we focus on the problem, faced by the seller, of dynamically optimizing the reserve price in each auction with the goal of maximizing overall revenue. We cast this problem in a regret minimization setting, and describe computationally efficient algorithms achieving regret of order T^{1/2} under various assumptions both on the information available to the seller and on the mechanism generating bids. Joint work with Claudio Gentile (Varese) and Yishay Mansour (Tel-Aviv).
ThursdayFeb 18, 201611:15
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Evgeny StrahovTitle:Determinantal processes related to products of random matricesAbstract:opens in new windowin html    pdfopens in new window
I will talk about determinantal processes formed by eigenvalues and singular values of products of complex Gaussian matrices. Such determinantal processes can be understood as natural generalizations of the classical Ginibre and Laguerre ensembles of Random Matrix Theory, and the correlation kernels of these processes can be expressed in terms of special functions/double contour integrals. This enables to investigate determinantal processes for products of random matrices in different asymptotic regimes, and to compute different probabilistic quantities of interest. In particular, I will present the asymptotics for the hole probabilities, i.e. for probabilities of the events that there are no particles in a disc of radius r with its center at 0, as r goes to infinity. In addition, I will explain how the gap probabilities for squared singular values of products of random complex matrices can be described in terms of completely integrable Hamiltonian differential equations, and how to interpret these Hamiltonian differential equations as the monodromy preserving deformation equations of the Jimbo, Miwa, Mori, Ueno and Sato theory. Finally, I will discuss certain time-dependent determinantal processes related to products of random matrices.
MondayFeb 15, 201614:30
Foundations of Computer Science SeminarRoom 261
Speaker:Henry YuenTitle:Anchoring games for parallel repetitionAbstract:opens in new windowin html    pdfopens in new window

Raz's celebrated Parallel Repetition Theorem shows that the probability of simultaneously winning n independent instances of a two-player one-round game G is exponentially small in n, when the maximum success probability of G is less than 1. Though the statement is intuitive, the proof is rather nontrivial and has found important application in hardness of approximation, cryptography, and communication complexity.

There are two major open problems regarding the parallel repetition of games: does an analogue of Raz's theorem hold for (a) games with more than  two players, and (b) games with quantumly entangled players? Extending Raz’s theorem to these settings is a challenging problem for a number of reasons: techniques for attacking direct sum/direct product problems in multiparty settings are lacking, and our understanding of quantum entanglement as an information theoretic resource is quite limited.

In this work, we show to sidestep these barriers and make progress on the two open problems. We first prove exponential-decay parallel repetition theorems for a class of games we called "anchored games" in the multiplayer and entangled-player settings. Then, we show how to efficiently transform any game into an equivalent anchored game.  Together, our results provide a simple hardness-amplification technique for games in both the classical multiplayer and quantum settings.

Joint work with Mohammad Bavarian and Thomas Vidick.

ThursdayFeb 04, 201611:15
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Gaultier Lambert Title:Fluctuations of linear statistics of determinantal processesAbstract:opens in new windowin html    pdfopens in new window
Determinantal point processes arise in the description of eigenvalues of unitary invariant Hermitian random matrices, as well as in many statistical mechanics models such as random tilings, non-intersecting paths, etc. I will explain a cumulant method developed by A. Soshnikov to analyze the asymptotics distributions of linear statistics of determinantal processes and certain combinatorial identities associated with the sine process. I will present some applications to orthogonal ensembles and, if time permits, to certain biorthogonal ensembles and discuss some models which exhibit a transition from Poisson to GUE.
ThursdayJan 28, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Nathan KellerTitle:Stability Versions of Erdös-Ko-Rado Type Theorems via Isoperimetry Abstract:opens in new windowin html    pdfopens in new window

Erdös-Ko-Rado (EKR) type theorems yield upper bounds on the size of set families under various intersection requirements on the elements. Stability versions of such theorems assert that if the size of a family is close to the maximum possible then the family itself must be close (in appropriate sense) to a maximum family. In this talk we present an approach to stability versions of EKR-type theorems through isoperimetric inequalities for subsets of the hypercube. We use this approach to obtain tight stability versions of the EKR theorem itself and of the Ahlswede-Khachatrian theorem on t-intersecting families (for k < n/(t+1)), and to show that, somewhat surprisingly, both theorems hold when the "intersection" requirement is replaced by a much weaker requirement. Furthermore, we obtain stability versions of several recent EKR-type results, including Frankl's proof of the Erdös matching conjecture for n>(2s+1)k-s.

Joint work with David Ellis and Noam Lifshitz.

WednesdayJan 27, 201611:30
Machine Learning and Statistics SeminarRoom 1
Speaker:Assaf HallakTitle:Off-policy Evaluation for MDPs with Unknown StructureAbstract:opens in new windowin html    pdfopens in new windowNEW DATE
In this talk I will present my work from ICML 2015. First, I will give a general introduction to Reinforcement Learning setup and define the off-policy evaluation problem and its core difficulties. I will present the model based solution for off-policy evaluation, and explain when structure can be exploited to improve performance of such solution. This will lead us to the core of our algorithm - the much more general problem of structure learning. The paper suggests solving this problem greedily and give conditions as to when such a solution works. Finally, I will present a few empirical results demonstrating our result.
WednesdayJan 27, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Max GurevichTitle:Integrability of p-adic matrix coefficientsAbstract:opens in new windowin html    pdfopens in new window
Many works in relative p-adic harmonic analysis aim to describe which representations of a reductive group G can be embedded inside the space of smooth functions on a homogeneous space G/H. A related question is whether such an embedding can be realized in a canonical form such as an H-integral over a matrix coefficient. In a joint work with Omer Offen we treated the symmetric case, i.e., when H is the fixed point group of an involution. As part of the answer we provide a precise criterion for such integrability, which reduces in the group case to Casselman’s known square-integrability criterion.
TuesdayJan 26, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dima DolgopyatTitle:Discrepancy of multidimensional Kronicker sequencesAbstract:opens in new windowin html    pdfopens in new window

We study the discrepancy of the number of visits of a Kronicker sequence on a d dimensional torus to nice  sets. We are interested in particular in the question how the answer depends on the geometry of the set.

This is a joint work with Bassam Fayad.
(http://arxiv.org/abs/1211.4323 and http://arxiv.org/abs/1206.4853)

MondayJan 25, 201614:30
Foundations of Computer Science SeminarRoom 261
Speaker:Uri StemmerTitle:Algorithmic Stability for Adaptive Data AnalysisAbstract:opens in new windowin html    pdfopens in new window

Adaptivity is an important feature of data analysis - the choice of questions to ask about a dataset often depends on previous interactions with the same dataset.  However, statistical validity is typically studied in a nonadaptive model, where all questions are specified before the dataset is drawn.  Recent work by Dwork et al. (STOC, 2015) initiated the formal study of this problem, and gave the first upper bounds on the achievable generalization error for adaptive data analysis.

The results of Dwork et al. are based on a connection with algorithmic stability in the form of differential privacy. We extend their work by giving a quantitatively optimal, more general, and simpler proof of their main theorem that stable algorithms of the kind guaranteed by differential privacy imply low generalization error. We also show that weaker stability guarantees such as bounded KL divergence and total variation distance lead to correspondingly weaker generalization guarantees.

Joint work with Raef Bassily, Kobbi Nissim, Adam Smith, Thomas Steinke, and Jonathan Ullman.

SundayJan 24, 201612:30
Foundations of Computer Science SeminarRoom 261
Speaker:Moshe Y. VardiTitle:The SAT Revolution: Solving, Sampling, and CountingAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DAY AND TIME

For the past 40 years computer scientists generally believed that NP-complete problems are intractable. In particular, Boolean satisfiability (SAT), as a paradigmatic NP-complete problem, has been considered to be intractable. Over the past 20 years, however, there has been a quiet, but dramatic, revolution, and very large SAT instances are now being solved routinely as part of software and hardware design.

In this talk I will review this amazing development and show that we can leverage SAT solving to accomplish other Boolean reasoning tasks.  Counting the number of satisfying truth assignments of a given Boolean formula or sampling such assignments uniformly at random are fundamental computational problems in computer science with numerous applications. While the theory of these problems has been thoroughly investigated in the 1980s, approximation algorithms developed by theoreticians do not scale up to industrial-sized instances.  Algorithms used by the industry offer better scalability, but give up certain correctness guarantees to achieve scalability. We describe a novel approach, based on universal hashing and Satisfiability Modulo Theory, that scales to formulas with hundreds of thousands of variable without giving up correctness guarantees.

ThursdayJan 21, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Yoav Schechner Title:Clouds in 4DAbstract:opens in new windowin html    pdfopens in new window
The spatially varying and temporally dynamic atmosphere presents significant, exciting and fundamentally new problems for imaging and computer vision. Some problems must tackle the complexity of radiative transfer models in 3D multiply-scattering media, to achieve reconstruction based on the models. This aspect can also be used in other scattering media. Nevertheless, the huge scale of the atmosphere and its dynamics call for multiview imaging using unprecedented distributed camera systems, on the ground or in orbit. These new configurations require generalizations of traditional triangulation, radiometric calibration, background estimation, lens-flare and compression questions. This focus can narrow uncertainties in climate-change forecasts, as we explain.
WednesdayJan 20, 201611:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Amnon Yekutieli Title:Derived Categories of BimodulesAbstract:opens in new windowin html    pdfopens in new window

Homological algebra plays a major role in noncommutative ring theory. One important homological construct related to a noncommutative ring A is the dualizing complex, which is a special kind of complex of A-bimodules. When A is a ring containing a central field K, this concept is well-understood now. However, little is known about dualizing complexes when the ring A does not contain a central field (I shall refer to this as the noncommutative arithmetic setting). The main technical issue is finding the correct derived category of A-bimodules.
In this talk I will propose a promising definition of the derived category of A-bimodules in the noncommutative arithmetic setting. Here A is a (possibly) noncommutative ring, central over a commutative base ring K (e.g. K = Z). The idea is to resolve A: we choose a DG (differential graded) ring A', central and flat over K, with a DG ring quasi-isomorphism A' -> A. Such resolutions exist. The enveloping DG ring A'^{en} is the tensor product over K of A' and its opposite. Our candidate for the "derived category of A-bimodules" is the category D(A'^{en}), the derived category of DG A'^{en}-modules. A recent theorem says that the category D(A'^{en}) is independent of the resolution A', up to a canonical equivalence. This justifies our definition.
Working within D(A'^{en}), it is not hard to define dualizing complexes over A, and to prove all their expected properties (like when K is a field). We can also talk about rigid dualizing complexes in the noncommutative arithmetic setting.
What is noticeably missing is a result about existence of rigid dualizing complexes. When the K is a field, Van den Bergh had discovered a powerful existence result for rigid dualizing complexes. We are now trying to extend Van den Bergh's method to the noncommutative arithmetic setting. This is work in progress, joint with Rishi Vyas.
In this talk I will explain, in broad strokes, what are DG rings, DG modules, and the associated derived categories and derived functors. Also, I will try to go into the details of a few results and examples, to give the flavor of this material.

TuesdayJan 19, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Cy MaorTitle:Continuous distribution of dislocations -- homogenization and elastic energyAbstract:opens in new windowin html    pdfopens in new window
In homogeneous materials, discrete and continuous distributions of dislocations are often modeled by different geometric objects - typically, a body with a finite number of dislocations is modeled as a Riemannian manifold with singularities, while a body with a continuous distribution of defects is modeled as a smooth manifold with a non-Riemannian affine-connection (e.g. a metric connection with a non-zero torsion tensor). There are several approaches to how does this connection (or torsion tensor) manifests in the mechanical behavior of a body -- in some works it appears as part of the elastic energy associated with it, and in some it is related only to plastic deformations. In this talk I will present a rigorous homogenization theorem for distributed dislocations, thus bridging between the different approaches modeling them. This will be achieved by introducing a new notion of convergence of manifolds, which applies to this class of homogenization problems. Then I will present a Gamma-convergence result for elastic energies of converging elastic bodies, from which we will deduce that the torsion tensor can appear in the mechanical modeling of the body only when considering plastic deformations. Based on a joint work with Raz Kupferman.
ThursdayJan 14, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Oren Friefeld Title:From representation to inference: respecting and exploiting mathematical structures in computer vision and machine learningAbstract:opens in new windowin html    pdfopens in new window

Stochastic analysis of real-world signals consists of 3 main parts: mathematical representation; probabilistic modeling; statistical inference. For it to be effective, we need mathematically-principled and practical computational tools that take into consideration not only each of these components by itself but also their interplay. This is especially true for a large class of computer-vision and machine-learning problems that involve certain mathematical structures; the latter may be a property of the data or encoded in the representation/model to ensure mathematically-desired properties and computational tractability. For concreteness, this talk will center on structures that are geometric, hierarchical, or topological.

Structures present challenges. For example, on nonlinear spaces, most statistical tools are not directly applicable, and, moreover, computations can be expensive. As another example, in mixture models, topological constraints break statistical independence. Once we overcome the difficulties, however, structures offer many benefits. For example, respecting and exploiting the structure of Riemannian manifolds and/or Lie groups yield better probabilistic models that also support consistent synthesis. The latter is crucial for the employment of analysis-by-synthesis inference methods used within, e.g., a generative Bayesian framework. Likewise, imposing a certain structure on velocity fields yields highly-expressive diffeomorphisms that are also simple and computationally tractable; particularly, this facilitates MCMC inference, traditionally viewed as too expensive in this context.

Time permitting, throughout the talk I will also briefly touch upon related applications such as statistical shape models, transfer learning on manifolds, image warping/registration, time warping, superpixels, 3D-scene analysis, nonparametric Bayesian clustering of spherical data, multi-metric learning, and new machine-learning applications of diffeomorphisms. Lastly, we also applied the (largely model-based) ideas above to propose the first learned data augmentation scheme; as it turns out, when compared with the state-of-the-art schemes, this improves the performance of classifiers of the deep-net variety.

WednesdayJan 13, 201611:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Pavel EtingofTitle:Symmetric tensor categories in characteristic pAbstract:opens in new windowin html    pdfopens in new window
ThursdayJan 07, 201612:15
Vision and Robotics SeminarRoom 1
Speaker:Greg ShakhnarovichTitle:Rich Representations for Parsing Visual ScenesAbstract:opens in new windowin html    pdfopens in new window

I will describe recent work on building and using rich representations aimed at automatic analysis of visual scenes. In particular, I will describe methods for semantic segmentation (labeling regions of an image according to the category it belongs to), and on semantic boundary detection (recovering accurate boundaries of semantically meaningful regions, such as those corresponding to objects). We focus on feed-forward architectures for these tasks, leveraging recent advances in the art of training deep neural networks. Our approach aims to shift the burden of inducing desirable constraints from explicit structure in the model to implicit structure inherent in computing richer, context-aware representations. I will describe experiments on standard benchmark data sets that demonstrate the success of this approach.

Joint work with Mohammadreza Mostajabi, Payman Yadollahpour, and Harry Yang.

ThursdayJan 07, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Shamgar GurevitchTitle:Low Dimensional Representations of Finite Classical GroupsAbstract:opens in new windowin html    pdfopens in new window

Many questions about properties of a finite group such as random walks, spectrum of Cayley graphs, distribution of word maps etc., can be approached by using “generalized Fourier sum” formulas involving characters of the group. Numerical data show that characters of low dimensional representations of the group contribute the largest terms to these sums. However, relatively little seems to be known about these small representations so a systematic knowledge of them could lead to proofs of some of the properties. The talk will demonstrates, through concrete examples, and numerical simulations, a new method to construct and analyze those small representations, and hence hopefully to solve some of the aforementioned questions.

The talk is intended for non-experts.

This is part from a joint project with Roger Howe (Yale).

WednesdayJan 06, 201611:15
Vision and Robotics SeminarRoom 1
Speaker:Karen LivescuTitle:Segmental Sequence Models in the Neural AgeAbstract:opens in new windowin html    pdfopens in new windowJoint Vision and Machine Learning seminar note unusual day/time

Many sequence prediction tasks---such as automatic speech recognition and video analysis---benefit from long-range temporal features.  One way of utilizing long-range information is through segmental (semi-Markov) models such as segmental conditional random fields.  Such models have had some success, but have been constrained by the computational needs of considering all possible segmentations.  We have developed new segmental models with rich features based on neural segment embeddings, trained with discriminative large-margin criteria, that are efficient enough for first-pass decoding.  In our initial work with these models, we have found that they can outperform frame-based HMM/deep network baselines on two disparate tasks, phonetic recognition and sign language recognition from video.  I will present the models and their results on these tasks, as well as (time permitting) related recent work on neural segmental acoustic word embeddings.


This is joint work with Hao Tang, Weiran Wang, Herman Kamper, Taehwan Kim, and Kevin Gimpel

WednesdayJan 06, 201611:15
Algebraic Geometry and Representation Theory SeminarRoom 208
Speaker:Shamgar GurevitchTitle:Low Dimensional Representations of Finite Classical GroupsAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL ROOM

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimension tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of some of these facts. This talk will discuss a new method for systematically constructing the small representations of finite classical groups. I will explain the method with concrete examples and applications. 


This is part from a joint project with Roger Howe (Yale).

WednesdayJan 06, 201611:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Karen LivescuTitle:Segmental Sequence Models in the Neural AgeAbstract:opens in new windowin html    pdfopens in new windowJOINT Vision and Machine Learning seminar

Many sequence prediction tasks---such as automatic speech recognition and video analysis---benefit from long-range temporal features.  One way of utilizing long-range information is through segmental (semi-Markov) models such as segmental conditional random fields.  Such models have had some success, but have been constrained by the computational needs of considering all possible segmentations.  We have developed new segmental models with rich features based on neural segment embeddings, trained with discriminative large-margin criteria, that are efficient enough for first-pass decoding.  In our initial work with these models, we have found that they can outperform frame-based HMM/deep network baselines on two disparate tasks, phonetic recognition and sign language recognition from video.  I will present the models and their results on these tasks, as well as (time permitting) related recent work on neural segmental acoustic word embeddings.


This is joint work with Hao Tang, Weiran Wang, Herman Kamper, Taehwan Kim, and Kevin Gimpel

WednesdayJan 06, 201611:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Eyal Lubetzky Title:Effect of initial conditions on mixing for spin systemsAbstract:opens in new windowin html    pdfopens in new windownote unusual day

Recently, the "information percolation" framework was introduced as a way to obtain sharp estimates on mixing for spin systems at high temperatures, and in particular, to establish cutoff for the Ising model in three dimensions up to criticality from a worst starting state. I will describe how this method can be used to understand the effect of different initial states on the mixing time, both random (''warm start'') and deterministic.

Joint work with Allan Sly.

TuesdayJan 05, 201611:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Victor IvriiTitle:Eigenvalue Asymptotics for Dirichlet-to-Neumann OperatorAbstract:opens in new windowin html    pdfopens in new window

Let X  be a compact manifold with the boundary ∂ X and  (λ) be a Dirichlet-to-Neumann operator: (λ): fu|∂X  where u solves ( The Actual Formul+ λ2= 0,  u|∂X = f . We establish asymptotics as λ→ + ∞ of the number of eigenvalues of  λ-1 R (λ) between s1 and s2.

This is a joint work with Andrew Hassell, Australian National University.

MondayJan 04, 201614:30
Foundations of Computer Science SeminarRoom 261
Speaker:Noga Ron-Zewi Title:Fast Sublinear Algorithms for Error Detection and CorrectionAbstract:opens in new windowin html    pdfopens in new window

In today’s world there are huge amounts of data that need to get reliably stored or transmitted. However, some amount of noise or corruption is inevitable. An error-correcting code is a scheme for robustly representing data in the form of a codeword that allows one to detect and correct errors in transmission. Locally-testable and locally-decodable codes are special families of error-correcting codes that admit highly efficient algorithms that detect and correct errors in sublinear time with high probability, probing only a small number of entries of the corrupted codeword. While locally-testable and locally-decodable codes have been intensely studied in the past 2 decades, in recent years there has been even further incentive for their study due to their relevance for transmission and storage of massive data and the successful implementation of local codes in cloud storage systems.

In this talk, I will show an exponential improvement on the best-known running time of error detection and correction algorithms for locally-testable and locally-decodable codes.  Specifically, I will describe new families of locally-testable codes with constant rate that can detect a constant fraction of errors in time (log n)^{O(log log n)} and new families of locally-decodable codes of constant rate that can correct a constant fraction of errors in time exp(\sqrt{log n}). Prior to that, the best known running time for such codes was n^{epsilon} (for a constant epsilon) using several, quite different, constructions.

(Based on joint work with Swastik Kopparty, Or Meir and Shubhangi Saraf)

MondayJan 04, 201611:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Mattias Jonsson Title:Degenerations of Calabi-Yau manifolds and non-Archimedean analytic spacesAbstract:opens in new windowin html    pdfopens in new window
Various considerations, from mirror symmetry and elsewhere, have lead people to consider 1-parameter degenerating families of Calabi-Yau manifolds, parameterized by the punctured unit disc. A conjecture by Kontsevich-Soibelman and Gross-Wilson describe what the limiting metric space should be, under suitable hypotheses. I will present joint work with Sebastien Boucksom, in which we show a measure theoretic version of this conjecture. The precise result involves a partial compactification of the family, obtained by adding a non-Archimedean analytic space, in the sense of Berkovich, as the central fiber.
SundayJan 03, 201616:15
Foundations of Computer Science SeminarRoom A
Speaker:Ilya Razenshteyn Title:Locality-Sensitive Hashing and BeyondAbstract:opens in new windowin html    pdfopens in new windownote unusual day/room

Locality-Sensitive Hashing (LSH) is a powerful technique for the approximate nearest neighbor search (ANN) in high dimensions. In this talk I will present two recent results:

1) I will show a data structure for ANN for the Euclidean distance that provably outperforms the best possible LSH-based data structure. We proceed via designing a good *data-dependent* hash family.

2) I will show a practical and optimal LSH family for the cosine similarity (a.k.a. Euclidean distance on a sphere). It substantially outperforms the celebrated Hyperplane LSH family. Along the way, I will try to debunk two popular myths about LSH:
     * LSH-based data structures consume too much memory and are thus impractical;
     * Optimal LSH constructions are too complicated to be made practical.

The talk is based on two papers: arXiv: 1501.01062 (joint with Alexandr Andoni, STOC 2015) and arXiv: 1509.02897 (joint with Alexandr Andoni, Piotr Indyk, Thijs Laarhoven and Ludwig Schmidt, NIPS 2015).

SundayJan 03, 201612:30
Foundations of Computer Science SeminarRoom 261
Speaker:Dana Moshkovitz Title:Amplification and Derandomization Without SlowdownAbstract:opens in new windowin html    pdfopens in new windownote unusual day/time

We show techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (non-uniform) algorithms. Unlike most existing techniques that involve repetition of the randomized algorithm and hence a slowdown, our techniques produce algorithms with a similar run-time to the original randomized algorithms.
The amplification technique is related to a certain stochastic multi-armed bandit problem. The derandomization technique -- which is the main contribution of this work -- points to an intriguing connection between derandomization and sketching/sparsification.
We demonstrate the techniques by showing applications to max-cut on dense graphs, approximate clique, constraint satisfaction problems on dense bipartite graphs, and list decoding to unique decoding for Reed-Muller code.
This is joint work with Ofer Grossman.

ThursdayDec 31, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Shai Shalev-Shwartz Title:Deep Learning: The theoretical-practical gapAbstract:opens in new windowin html    pdfopens in new window
I will describe two contradicting lines of work. On one hand, a practical work on autonomous driving I was doing at Mobileye, in which deep learning is one of the key ingredients. On the other hand, recent theoretical works showing very strong hardness of learning results. Bridging this gap is a great challenge. I will describe some approaches toward a solution.
ThursdayDec 31, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Zemer KosloffTitle:Symmetric Birkhoff sums in infinite ergodic theoryAbstract:opens in new windowin html    pdfopens in new window

By a Theorem of Aaronson, normalized Birkhoff sums of positive integrable functions in infinite, ergodic systems either tend to 0 almost surely or there is a subsequence along which every further subsequence tends to infinity. This is not true for normalized symmetric Birkhoff sums where the summation is along a symmetric time interval as there are examples of infinite, ergodic systems for which the absolutely normalized symmetric Birkhoff sums of positive integrable functions may be almost surely bounded away from zero and infinity. In this talk I will start by explaining a variety of transformations (of different nature) satisfying this phenomena, discuss the case main result that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge point-wise and there even exists a universal divergence statement. Time permits I will show some examples of actions of other groups which converge and some recent (yet unwritten) results on actions by commuting skew products which are related to self intersection local times.

The contents of this talk are a combination of 3 papers, one of which is a joint work with Benjamin Weiss and Jon Aaronson and another one is work in progress with Jon Aaronson.

WednesdayDec 30, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Eran Treister Title:Efficient algorithms for large scale parameter estimationAbstract:opens in new windowin html    pdfopens in new windowJoint Mathematical Analysis and Applications & Machine Learning and Statistics seminar

Parameter estimation is performed by fitting data measurements to a model using Bayesian statistics, assuming additional prior information. The estimation requires a numerical solution of large scale optimization problem, whose objective traditionally includes data fidelity and regularization terms. In this talk I will present numerical solution methods for two such estimation problems.

In the first part of the talk I will concentrate on parameter estimation of physical models, obtained by solving optimization problems that are constrained by partial differential equations (PDEs). I will focus on my recent work on 3D Full Waveform Inversion, which arises in seismic exploration of oil and gas reservoirs, earth sub-surface mapping, ultrasound imaging and more. I will demonstrate how to computationally treat this inverse problem, and improve its solution by using travel time tomography in a joint inversion framework. This includes efficient algorithms for the solution of the Helmholtz and eikonal equations (the two associated PDEs), and a parallel software framework for applying these algorithms for the joint inversion using a Gauss Newton algorithm.

In the second part of the talk, I will consider the estimation of large scale sparse inverse covariance matrices of multivariate Gaussian distribution. Such matrices are often used to characterize and analyze data measurements in fields that range from machine learning, signal processing and computational biology. To estimate these matrices, an l1 regularized log-determinant optimization problem needs to be solved. I will present a block-coordinate descent algorithm that can efficiently solve this problem at large scales with low memory footprint, and a multilevel acceleration framework that is suitable for general sparse optimization problems. These algorithms can be used as a tool for enriching inverse problems by "learning" appropriate prior information, adopting an empirical Bayesian framework.

WednesdayDec 30, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Mikhail Borovoi Title:Real Galois cohomology of semisimple groupsAbstract:opens in new windowin html    pdfopens in new window
In a 2-page note of 1969, Victor Kac described automorphisms of finite order of simple Lie algebras over the field of complex numbers C. He used certain diagrams that were later called Kac diagrams. In this talk, based on a joint work with Dmitry Timashev, I will explain the method of Kac diagrams for calculating the Galois cohomology set H^1(R,G) for a connected semisimple algebraic group G over the field of real numbers R. I will use real forms of groups of type E_7 as examples. No prior knowledge of Galois cohomology, Kac diagrams, or groups of type E_7 will be assumed.
TuesdayDec 29, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Amit AcharyaTitle:Why gradient flows of some energies good for defect equilibria are not good for dynamics, and an improvementAbstract:opens in new windowin html    pdfopens in new window

Line defects appear in the microscopic structure of crystalline materials (e.g. metals) as well as liquid crystals, the latter an intermediate phase of matter between liquids and solids. Mathematically, their study is challenging since they correspond to topological singularities that result in blow-up of total energies of finite bodies when utilizing most commonly used classical models of energy density; as a consequence, formulating nnonlinear dynamical models (especially pde) for the representation and motion of such defects is a challenge as well. I will discuss the development and implications of a single pde model intended to describe equilibrium states and dynamics of these defects. The model alleviates the nasty singularities mentioned above and it will also be shown that incorporating a conservation law for the topological charge of line defects allows for the correct prediction of some important features of defect dynamics that would not be possible just with the knowledge of an energy function.

This is joint work with Chiqun Zhang, Dmitry Golovaty, and Noel Walkington.

MondayDec 28, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Amir AbboudTitle:Hardness in PAbstract:opens in new windowin html    pdfopens in new window

The class P attempts to capture the efficiently solvable computational tasks. It is full of practically relevant problems, with varied and fascinating combinatorial structure.
In this talk, I will give an overview of a rapidly growing body of work that seeks a better understanding of the structure within P. Inspired by NP-hardness, the main tool in this approach are combinatorial reductions. Combining these reductions with a small set of plausible conjectures, we obtain tight lower bounds on the time complexity of many of the most important problems in P.
I will present the most recent landscape of P and the conjectures on which this project is based on (e.g. the Strong Exponential Time Hypothesis). I will discuss recent attempts on identifying new conjectures: either more reliable ones, or ones that will get us closer to a full classification of the important problems in P.
Finally, I will highlight a surprising new reduction from Circuit-SAT to natural problems in P like Edit-Distance which proves that minor improvements over the quadratic running time of Edit-Distance are enough to prove major complexity separations.

ThursdayDec 24, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Shai Avidan Title:Best-Buddies Similarity for Robust Template MatchingAbstract:opens in new windowin html    pdfopens in new window
We propose a novel method for template matching in unconstrained environments. Its essence is the Best-Buddies Similarity (BBS), a useful, robust, and parameter-free similarity measure between two sets of points. BBS is based on counting the number of Best-Buddies Pairs (BBPs)- pairs of points in source and target sets, where each point is the nearest neighbor of the other. BBS has several key features that make it robust against complex geometric deformations and high levels of outliers, such as those arising from background clutter and occlusions. We study these properties, provide a statistical analysis that justifies them, and demonstrate the consistent success of BBS on a challenging real world dataset. Joint work with Tali Dekel, Shaul Oron, Miki Rubinstein and Bill Freeman
WednesdayDec 23, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Tirza RouttenbergTitle:Estimation after parameter selection: Estimation methods, performance analysis, and adaptive samplingAbstract:opens in new windowin html    pdfopens in new window

In many practical parameter estimation problems, such as medical experiments and cognitive radio communications, parameter selection is performed prior to estimation. The selection process has a major impact on subsequent estimation by introducing a selection bias and creating coupling between decoupled parameters. As a result,   classical estimation theory may be inappropriate and inaccurate and a new methodology is needed. In this study, the problem of estimating a preselected unknown deterministic parameter, chosen from a parameter set based on a predetermined data-based selection rule, \Psi, is considered.  In this talk, I present a general non-Bayesian estimation theory for estimation after parameter selection, includes estimation methods, performance analysis, and adaptive sampling strategies.  First, I use the post-selection mean-square-error (PSMSE) criterion   as a performance measure instead of the commonly used mean-square-error (MSE).  The corresponding Cramér-Rao-type bound on the PSMSE of any \Psi-unbiased estimator is derived, where the \Psi -unbiasedness is in the Lehmann-unbiasedness sense. The post-selection maximum-likelihood (PSML) estimator is presented and its \Psi–efficiency properties are demonstrated. Practical implementations of the PSML estimator are proposed as well. Finally, I discuss the concept of adaptive sampling in a two-sampling stages scheme of selection and estimation.

WednesdayDec 23, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Lenny Makar-Limanov Title:On rings stable under derivationsAbstract:opens in new windowin html    pdfopens in new window
Let z be an algebraic function of n variables and A(z) the algebra generated by all variables and all partial derivatives of z (of all orders). If z is a polynomial then A(z) is just a polynomial algebra, but when z is not a polynomial then it is not clear what is the structure of this algebra. I'll report on known cases and formulate a conjecture.
TuesdayDec 22, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Avner Peleg Title:Coupled nonlinear Schrödinger equations, Lotka-Volterra models, and control of soliton collisions in broadband optical waveguide systems. Abstract:opens in new windowin html    pdfopens in new window

Transmission rates in broadband optical waveguide systems are enhanced by launching many pulse sequences through the same waveguide. Since pulses from different sequences propagate with different group velocities, intersequence pulse collisions are frequent, and can lead to severe transmission degradation. On the other hand, the energy exchange in pulse collisions can be beneficially used for controlling the transmission.

In this work we show that collision-induced amplitude dynamics of soliton sequences of N perturbed coupled nonlinear Schrödinger (NLS) equations can be described by N-dimensional Lotka-Volterra (LV) models, where the model's form depends on the perturbation. To derive the LV models, we first carry out single-collision analysis, which is based on the method of eigenmode expansion with the eigenmodes of the linear operator describing small perturbations about the fundamental NLS soliton. We use stability and bifurcation analysis for the equilibrium points of the LV models to develop methods for achieving robust transmission stabilization and switching that work well for a variety of waveguides. Further enhancement of transmission stability is obtained in waveguides with a narrowband Ginzburg-Landau gain-loss profile. We also discuss the possibility to use the relation between NLS and LV models to realize transition to spatio-temporal chaos with NLS solitons.

ThursdayDec 17, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Amir DemboTitle:Extremal Cuts of Sparse Random GraphsAbstract:opens in new windowin html    pdfopens in new window

The Max-Cut problem seeks to determine the maximal cut size in a given graph. With no polynomial-time efficient approximation for Max-Cut (unless P=NP), its asymptotic for a typical large sparse graph is of considerable interest. We prove that for uniformly random d-regular graph of N vertices, and for the uniformly chosen Erdos-Renyi graph of M=Nd/2 edges, the leading correction to M/2 (the typical cut size), is P∗sqrt(NM/2). Here P∗ is the ground state energy of the Sherrington-Kirkpatrick model, expressed analytically via Parisi's formula.

This talk is based on a joint work with Subhabrata Sen and Andrea Montanari.

WednesdayDec 16, 201512:30
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Arkady Berenstein Title:Generalized RSKAbstract:opens in new windowin html    pdfopens in new window

The goal of my talk (based on joint work with Dima Grigoriev, Anatol Kirillov, and Gleb Koshevoy) is to generalize the celebrated Robinson-Schensted-Knuth (RSK) bijection between the set of matrices with nonnegative integer entries, and the set of the planar partitions.

Namely, for any pair of injective valuations on an integral domain we construct a canonical bijection K, which we call the generalized RSK, between the images of the valuations, i.e., between certain ordered abelian monoids.

Given a semisimple or Kac-Moody group, for each reduced word ii=(i_1,...,i_m) for a Weyl group element we produce a pair of injective valuations on C[x_1,...,x_m] and argue that the corresponding bijection K=K_ii, which maps the lattice points of the positive octant onto the lattice points of a convex polyhedral cone in R^m, is the most natural generalization of the classical RSK and, moreover, K_ii can be viewed as a bijection between Lusztig and Kashiwara parametrizations of the dual canonical basis in the corresponding quantum Schubert cell.

Generalized RSKs are abundant in "nature", for instance, any pair of polynomial maps phi,psi:C^m-->C^m with dense images determines a pair of  injective valuations on C[x_1,...,x_n] and thus defines a generalized RSK bijection K_{phi,psi} between two sub-monoids of Z_+^m.

When phi and psi are birational isomorphisms, we expect that K_{phi,psi} has a geometric "mirror image", i.e., that there is a rational function f on C^m whose poles complement the image of phi and psi so that the tropicalization of the composition psi^{-1}phi along f equals to K_{phi,psi}. We refer to such a geometric data as a (generalized) geometric RSK, and view f as a "super-potential". This fully applies to each ii-RSK situation, and we find a super-potential f=f_ii which helps to compute K_ii.

While each K_ii has a "crystal" flavor, its geometric (and mirror) counterpart f_ii emerges from the cluster twist of the relevant double Bruhat cell studied by Andrei Zelevinsky, David Kazhdan, and myself.

WednesdayDec 16, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Tomer KorenTitle:The Computational Power of Optimization in Online LearningAbstract:opens in new windowin html    pdfopens in new window

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $\sqrt{N}$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is linear in $N$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $\log{N}$.

We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $\sqrt{N}$, yielding again a quadratic improvement upon the oracle-free setting, where linear time in $N$ is known to be tight.

TuesdayDec 15, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Kushal Shah Title:Particle dynamics in periodically driven systems : Fermi Accelerators and Paul TrapsAbstract:opens in new windowin html    pdfopens in new window

Periodically driven systems are of immense interest in plasma physics both from the point of view of plasma confinement as well as plasma heating.

One of the models to explain plasma heating in capacitive RF discharges is Fermi acceleration, which consists of a particle moving in a dynamical billiard with oscillating boundaries. It is well known that the energy growth rate of an ensemble of particles in a strongly chaotic billiard with moving walls is quadratic-in-time whereas it can be exponential-in-time in billiards with multiple ergodic components. Since a real plasma device allows for an exchange of particles with the surroundings, we have now studied Fermi accelerators with a hole (small enough so as not to disturb the statistics). We find that energy gain is significantly higher in a leaky Fermi accelerators with multiple ergodic components and it can be further increased by shrinking the hole size. In the ergodic case, energy gain is found to be independent of the hole size. Work done jointly with V. Gelfreich, V. Rom-Kedar and D. Turaev [Physical Review E 91, 062920 (2015)].

Paul trap is a device used to confine electrons by using time-periodic spatially non-uniform electric fields and a Nobel Prize as awarded for its discovery in 1989. The time-averaged distribution function of plasma in such devices is usually modelled using the concept of an effective potential (ponderomotive theory). For a specific example of the electric field used in Paul traps, we had shown earlier that the exact solutions of the Vlasov equation (collisionless Boltzmann equation) do not agree with solutions obtained by the effective potential approach. Now we have been able to obtain a perturbative solution of the Vlasov equation for a much more general case and find the same discrepancy with conventional theory. These perturbative solutions represent a non-equilibrium steady state and further work needs to be done to understand their statistical evolution. Work done jointly with B. Srinivasan [arXiv:1510.03974].

MondayDec 14, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Omri WeinsteinTitle:Towards The Deterministic Communication Complexity of Approximate Nash EquilibriumAbstract:opens in new windowin html    pdfopens in new window

We study the two-party communication complexity of the geometric problem of finding an approximate Brouwer fixed-point of a composition of two Lipschitz functions g*f, where Alice knows f and Bob knows g.
We prove an essentially tight communication lower bound on this problem, using a novel adaptation of the Raz-McKenzie simulation theorem into geometric settings.
We show that a slightly stronger version of this communication problem would imply an (essentially) tight communication lower bounds on the problem of finding an approximate Nash equilibrium in 2-player (and n-player) games, where each player initially knows only his own payoff matrix. 

Joint work with Tim Roughgarden.

ThursdayDec 10, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Ohad FeldheimTitle:Double Roots of Random PolynomialsAbstract:opens in new windowin html    pdfopens in new window

We consider random polynomials of degree n whose coefficients are i.i.d. distributed over a finite set of integers, with probability at most 1/2 to take any particular value. We show that the probability that such a polynomial of degree n has a double root is dominated by the probability that 0,1 or -1 are double roots up to an error of o(n−2). Our result generalizes a similar result of Peled, Sen and Zeitouni for Littlewood polynomials.

Joint work with Ron Peled and Arnab Sen.

WednesdayDec 09, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Konstantin Ardakov Title:Non-commutative Iwasawa algebrasAbstract:opens in new windowin html    pdfopens in new window
Non-commutative Iwasawa algebras are completed group rings of compact p-adic Lie groups with mod-p, or p-adic integer, coefficients. They can also be viewed as rings of continuous p-adic distributions on the group in question. These algebras have found applications in several areas of number theory, including non-commutative Iwasawa theory and the p-adic local Langlands correspondence, but they also provide interesting examples of non-commutative Noetherian rings which are similar in certain respects to universal enveloping algebras of finite dimensional Lie algebras. After giving the basic definitions and some examples, I will advertise some open questions on the algebraic structure of these Iwasawa algebras.
ThursdayDec 03, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Ariel ShamirTitle:Creating Visual StoriesAbstract:opens in new windowin html    pdfopens in new window
Similar to text, the amount of visual data in the form of videos and images is growing enormously. One of the key challenges is to understand this data, arrange it, and create content which is semantically meaningful. In this talk I will present several such efforts to "bridge the semantic gap" using humans as "agents": capturing and utilizing eye movements, body movement or gaze direction. This enables re-editing of existing videos, tracking of sports highlights, creating one coherent video from multiple sources, and more.
ThursdayDec 03, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Ron RosenthalTitle:Eigenvalue confinement and spectral gap for random simplicial complexesAbstract:opens in new windowin html    pdfopens in new window
We consider the adjacency operator of the Linial-Meshulam model for random simplicial complexes on $n$ vertices, where each $d$-cell is added independently with probability $p$ to the complete $(d-1)$-skeleton. From the point of view of random matrix theory, the adjacency matrix is a sparse, self adjoint random matrix with dependent entries. Under the assumption $np(1-p)>> log^4 n$, we prove that the spectral gap between the $\binom{n-1}{d}$ smallest eigenvalues and the remaining $\binom{n-1}{d-1}$ eigenvalues is $np-2\sqrt{dnp(1-p)}(1+o(1))$ with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. Based on a joint work with Antti Knowles.
WednesdayDec 02, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Yuval Benjamini Title:Estimating bumps: selective inference for regions in non-stationary spatial dataAbstract:opens in new windowin html    pdfopens in new window

"Circular inference" is a pejorative coined for methods in which a hypothesis is selected after looking at the data, but the inferential procedures treat it as if it was determined in advance. Unfortunately, many throughput screening experiments in genomics or neuroimaging seek to do exactly this: identify regions (bumps) of high signal in the data and evaluate these found regions using the same data. Simple estimators that ignore the selection will be biased; when the data is non-stationary, this bias can vary dramatically between different regions. Nevertheless, methods for evaluating and comparing selected regions are crucial, because typically only a handful of regions can be further explored in tailored follow up studies. 

In this talk I describe a new conditional inference approach for characterizing these found regions by estimating their population parameters. Our method explicitly models the selection procedure, and simulates from the conditional distribution to estimate the underlying parameters. Efficient strategies for providing p-value, estimators and intervals will be discussed, as well as power versus accuracy tradeoffs. I will demonstrate the new method for estimating bumps in a comparison of DNA-methylation patterns across tissue type.

This is joint work with Jonathan Taylor and Rafael Irizarry.

WednesdayDec 02, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Oded Yacobi Title:Truncated shifted Yangians and Nakajima monomial crystalsAbstract:opens in new windowin html    pdfopens in new window
In geometric representation theory slices to Schubert varieties in the affine Grassmannian are affine varieties which arise naturally via the Satake correspondence. This talk centers on algebras called truncated shifted Yangians, which are quantizations of these slices. In particular we will describe the highest weight theory of these algebras using Nakajima's monomial crystal. This leads to conjectures about categorical ' -action (Langlands dual Lie algebra) on representation categories of truncated shifted Yangians.
TuesdayDec 01, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Konstantinos KourliourosTitle:Powers of Volume Forms on Manifolds with BoundaryAbstract:opens in new windowin html    pdfopens in new window

In this talk I will consider the problem of local analytic classification of powers of volume forms on manifolds with boundary, i.e. of ordinary volume forms multiplied by the (complex in general) power of a function f, under the action of the group of diffeomorpshims preserving both the boundary and the hypersurface defined by the zero locus of f. In the case where this function defines an isolated boundary singularity in the sense of Arnol'd, I will show how to obtain local normal forms and moduli theorems, analogous to those obtained by Arnol'd, Varchenko, Lando and others for the ordinary, without boundary case. Moreover I will show how these moduli are related to (in fact obtained by) the topological and analytic (Hodge theoretic) invariants of the boundary singularity, such as the relative Picard-Lefschetz monodromy, the relative Brieskorn lattices with their relative Gauss-Manin connection, the relative spectrum and so on, all objects generalising, in the presence of a boundary, the corresponding well known objects already defined for isolated hypersurface singularities.

MondayNov 30, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Alan RoytmanTitle:Packing Small VectorsAbstract:opens in new windowin html    pdfopens in new window

Online d-dimensional vector packing models many settings such as minimizing resources in data centers where jobs have multiple resource requirements (CPU, Memory, etc.).  However, no online d-dimensional vector packing algorithm can achieve a competitive ratio better than d.  Fortunately, in many natural applications, vectors are relatively small, and thus the lower bound does not hold.  For sufficiently small vectors, an O(log d)-competitive algorithm was known.  We improve this to a constant competitive ratio, arbitrarily close to e (where e is the base of the natural logarithm), given that vectors are sufficiently small.

We give improved results for the two dimensional case.  For arbitrarily small vectors, the First Fit algorithm for two dimensional vector packing is no better than 2-competitive.  We present a natural family of First Fit variants, and for optimized parameters get a competitive ratio of approximately 1.48 for sufficiently small vectors.

We improve upon the 1.48 competitive ratio - not via a First Fit variant - and give a competitive ratio arbitrarily close to 4/3 for packing small, two dimensional vectors.  We show that no algorithm can achieve better than a 4/3 competitive ratio for two dimensional vectors, even if one allows the algorithm to split vectors among arbitrarily many bins.

ThursdayNov 26, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Nadav Cohen Title:On the Expressive Power of Deep Learning: A Tensor AnalysisAbstract:opens in new windowin html    pdfopens in new window

It has long been conjectured that hypothesis spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical architectures than with shallow ones.  Despite the vast empirical evidence, formal arguments to date are limited and do not capture the kind of networks used in practice. Using tensor factorization, we derive a universal hypothesis space implemented by an arithmetic circuit over functions applied to local data structures (e.g. image patches). The resulting networks first pass the input through a representation layer, and then proceed with a sequence of layers comprising sum followed by product-pooling, where sum corresponds to the widely used convolution operator. The hierarchical structure of networks is born from factorizations of tensors based on the linear weights of the arithmetic circuits. We show that a shallow network corresponds to a rank-1 decomposition, whereas a deep network corresponds to a Hierarchical Tucker (HT) decomposition. Log-space computation for numerical stability transforms the networks into SimNets.

In its basic form, our main theoretical result shows that the set of polynomially sized rank-1 decomposable tensors has measure zero in the parameter space of polynomially sized HT decomposable tensors. In deep learning terminology, this amounts to saying that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require an exponential size if one wishes to implement (or approximate) them with a shallow network. Our construction and theory shed new light on various practices and ideas employed by the deep learning community, and in that sense bear a paradigmatic contribution as well.

Joint work with Or Sharir and Amnon Shashua.

ThursdayNov 26, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Yaar SolomonTitle:The Danzer problem and a solution to a problem of Gowers Abstract:opens in new windowin html    pdfopens in new window
Is there a point set Y in R^d, and C>0, such that every convex set of volume 1 contains at least one point of Y and at most C? This discrete geometry problem was posed by Gowers in 2000, and it is a special case of an open problem posed by Danzer in 1965. I will present two proofs that answers Gowers' question with a NO. The first approach is dynamical; we introduce a dynamical system and classify its minimal subsystems. This classification in particular yields the negative answer to Gowers' question. The second proof is direct and it has nice applications in combinatorics. The talk will be accessible to a general audience. [This is a joint work with Omri Solan and Barak Weiss].
WednesdayNov 25, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Andrey MinchenkoTitle:Simple Lie conformal algebrasAbstract:opens in new windowin html    pdfopens in new window

The notion of a Lie conformal algebra (LCA) comes from physics, and is related to the operator product expansion. An LCA is a module over a ring of differential operators with constant coefficients, and with a bracket which may be seen as a deformation of a Lie bracket. LCA are related to linearly compact differential Lie algebras via the so-called annihilation functor. Using this observation and the Cartan's classification of linearly compact simple Lie algebras, Bakalov, D'Andrea and Kac classified finite simple LCA in 2000. 

I will define the notion of LCA over a ring R of differential operators with not necessarily constant coefficients, extending the known one for R=K[x]. I will explain why it is natural to study such an object and will suggest an approach for the classification of finite simple LCA over arbitrary differential fields.

TuesdayNov 24, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Or AlusTitle:Statistical properties of Henon mapsAbstract:opens in new windowin html    pdfopens in new window
For most realistic Hamiltonian systems the phase space contains both chaotic and regular orbits, mixed in a complex, fractal pattern in which islands of regular motion are surrounded by a chaotic sea. The Henon map is an example of such a system. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach that is the subject of the talk. In particular transport in phase space is of great interest for dynamics, therefore the distributions of fluxes through island chains were computed. evidence for their universality was given. The relation to a model proposed by Meiss and Ott will be discussed. Also the statistics of the boundary circle winding numbers were calculated, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. In particular results that contradict conjectures that were made in the past were found.
MondayNov 23, 201517:30
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MondayNov 23, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:James R. LeeTitle:Lower bounds on the size of semi-definite programsAbstract:opens in new windowin html    pdfopens in new window

Much of the theory of mathematical programs for combinatorial optimization can be described in the following way:  A polytope of interest has exponentially many (in the dimension) facets, but can be written as the linear projection of a simpler convex body in a higher-dimensional space.  Simple might mean a polytope with a much smaller number of facets, or a spectrahedron (the intersection of an affine subspace with the PSD cone) of small dimension.  This allows one to optimize linear functionals over the base polytope by instead optimizing a lifted functional over the lifted body.

Unless P=NP, one does not expect certain polytopes--like the convex hull of indicators of traveling salesman tours in a graph--to have a small lift.  But it remained open to prove any non-trivial lower bound on the necessary dimension for a spectrahedral lift, i.e. to prove that semi-definite programs do not yield efficient optimization procedures over these polytopes.

We show that the cut, TSP, and stable set polytopes on n-vertex graphs are not the linear image of a spectrahedron of dimension less than exp(n^c) for some constant c > 0. In the process, many interesting phenomena emerge:  Factorization of operators through the PSD cone, quantum information theory, discrete Fourier analysis, and real algebraic geometry.

This is based joint work with Prasad Ragahvendra and David Steurer.

MondayNov 23, 201514:30
Algebraic Geometry and Representation Theory SeminarRoom 108
Speaker:Arkady Berenstein Title:Hecke-Hopf algebrasAbstract:opens in new windowin html    pdfopens in new window

It is well-known that Hecke algebras H_q(W) do not have interesting Hopf algebra structures because, first, the only available one would emerge only via an extremely complicated isomorphism with the group algebra of W and, second, this would  make H_q(W) into yet another cocommutative Hopf algebra.

The goal of my talk (based on joint work with D. Kazhdan) is to extend each Hecke algebra H_q(W) to a non-cocommutative Hopf algebra (we call it Hecke-Hopf algebra of W) that contains H_q(W) as a coideal.

Our Hecke-Hopf algebras have a number of applications: they generalize Bernstein presentation of Hecke algebras, provide new solutions of quantum Yang-Baxter equation and a large category of endo-functors of H_q(W)-Mod, and suggest further generalizations of Hecke algebras.

ThursdayNov 19, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Alex Bronstein Title:Learning to hashAbstract:opens in new windowin html    pdfopens in new window

In view of the recent huge interest in image classification and object recognition problems and the spectacular success of deep learning and random forests in solving these tasks, it seems astonishing that much more modest efforts are being invested into related, and often more difficult, problems of image and multimodal content-based retrieval, and, more generally, similarity assessment in large-scale databases. These problems, arising as primitives in many computer vision tasks, are becoming increasingly important in the era of exponentially increasing information. Semantic and similarity-preserving hashing methods have recently received considerable attention to address such a need, in part due to their significant memory and computational advantage over other representations.

In this talk, I will overview some of my recent attempts to construct efficient semantic hashing schemes based on deep neural networks and random forests.

Based on joint works with Qiang Qiu, Guillermo Sapiro, Michael Bronstein, and Jonathan Masci.

WednesdayNov 18, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Oren Ben-Bassat Title:Introduction to derived algebraic and analytic geometry Abstract:opens in new windowin html    pdfopens in new window

I will present a 'categorical' way of doing analytic geometry in which analytic geometry is seen as a precise analogue of algebraic geometry. Our approach works for both complex analytic geometry and p-adic analytic geometry in a uniform way. I will focus on the idea of an 'open set' as used in these various areas of math and how it is characterised categorically. In order to do this, we need to study algebras and their modules in the category of Banach spaces.  The categorical characterization that we need uses homological algebra in these 'quasi-abelian' categories which is work of Schneiders and Prosmans.  In fact, we work with the larger category of  Ind-Banach spaces for reasons I will explain. This gives us a way to establish foundations of  analytic geometry and to compare with the standard notions such as the theory of affinoid algebras, Grosse-Klonne's theory of dagger algebras (over-convergent functions), the theory of Stein domains and others.  I will explain how this extends to a formulation of derived analytic geometry following the relative algebraic geometry approach of Toen, Vaquie and Vezzosi.

This is joint work with Federico Bambozzi (Regensburg) and Kobi Kremnizer (Oxford).

TuesdayNov 17, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Shiri ArtsteinTitle:Billiard dynamics, a symplectic approachAbstract:opens in new windowin html    pdfopens in new window
We will discuss billiard dynamics in convex domains. After some background we shall describe the symplectic geometry approach using capacities, and show various results on minimal lengths of billiards (both Euclidean and the more general Minkowski billiards) and connections with other questions in geometry.
MondayNov 16, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Elette Boyle Title:Is there an Oblivious RAM Lower Bound?Abstract:opens in new windowin html    pdfopens in new window

An Oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (JACM 1996), is a (probabilistic) RAM that hides its access pattern, i.e. for every input the observed locations accessed are similarly distributed. Great progress has been made in recent years in minimizing the overhead of ORAM constructions, with the goal of obtaining the smallest overhead possible.

We revisit the lower bound on the overhead required to obliviously simulate programs, due to Goldreich and Ostrovsky.  While the lower bound is fairly general, including the offline case, when the simulator is given the reads and writes ahead of time, it does assume that the simulator behaves in a "balls and bins" fashion. That is, the simulator must act by shuffling data items around, and is not allowed to have sophisticated encoding of the data.

We prove that for the OFFLINE case, showing a lower bound without the above restriction is related to the size of the circuits for sorting. Our proof is constructive, and uses a bit-slicing approach which manipulates the bit representations of data in the simulation.  This implies that without obtaining yet unknown superlinear lower bounds on the size of such circuits, we cannot hope to get lower bounds on offline (unrestricted) ORAMs.

ThursdayNov 12, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Nathan Srebro Title:Optimization, Regularization and Generalization in Multilayer NetworksAbstract:opens in new windowin html    pdfopens in new windowJoint Machine Learning & Vision Seminar

What is it that enables learning with multi-layer networks?  What causes the network to generalize well?  What makes it possible to optimize the error, despite the problem being hard in the worst case?  In this talk I will attempt to address these questions and relate between them, highlighting the important role of optimization in deep learning.  I will then use the insight to suggest studying novel optimization methods, and will present Path-SGD, a novel optimization approach for multi-layer RELU networks that yields better optimization and better generalization.

Joint work with Behnam Neyshabur, Ryota Tomioka and Russ Salakhutdinov.

ThursdayNov 12, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Christopher JoynerTitle:Random Walk approach to spectral statistics in random Bernoulli matricesAbstract:opens in new windowin html    pdfopens in new window
Random Bernoulli matrices (in which the matrix elements are chosen independently from plus or minus 1 with equal probability) are intimately connected to the adjacency matrices of random graphs and share many spectral properties. In the limit of large matrix dimension the distribution of eigenvalues from such matrices resembles that from matrices in which the elements are chosen randomly from a Gaussian distribution - the question is why? We take a dynamical approach to this problem, which is achieved by initiating a discrete random walk process over the space of matrices. Previously we have used this idea to analyse the corresponding eigenvalue motion but I will discuss some recent developments which involve the adaptation of Stein's method to this context.
WednesdayNov 11, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Be'eri GreenfeldTitle:Gel'fand-Kirillov Dimension of Algebras: Prime Spectra, Gradations and RadicalsAbstract:opens in new windowin html    pdfopens in new window

We study properties of affine algebras with small Gel'fand-Kirillov dimension, from the points of view of the prime spectrum, gradations and radical theory.

As an application, we are able to prove that Z-graded algebras with quadratic growth, and graded domains with cubic growth have finite (and efficiently bounded) classical Krull dimension; this is motivated by Artin's conjectured geometric classification of non-commutative projective surfaces, and by opposite examples in the non-graded case.

As another application, we prove a graded version of a dichotomy question raised by Braun and Small, between primitive algebras (namely, algebras admitting faithful irreducible representations) and algebras satisfying polynomial identities.

If time permits, we discuss approximations of the well-studied Koethe problem and in particular prove a stability result for certain radicals under suitable growth conditions.

We finally propose further questions and possible directions, which already stimulated new constructions of monomial algebras.

This talk is partially based on a joint work with A. Leroy, A. Smoktunowicz and M. Ziembowski.

TuesdayNov 10, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Gilbert Weinstein Title:The Riemannian Penrose Inequality with Charge for Multiple Black HolesAbstract:opens in new windowin html    pdfopens in new window
In the 1960's, Roger Penrose noted that the Cosmic Censorship Conjecture for solutions of the Einstein equations, or more specifically the standard picture of gravitational collapse, heuristically imply lower bounds on the total energy of initial data in terms of geometric quantities such as the area of the outermost horizon. Any counter-example would strongly suggest that the conjecture fails, while proofs of the inequality, or any extensions, lend indirect support to the conjecture. The time symmetric case was established, first for a single black hole by Huisken-Ilmanen, then for multiple black holes, by Bray. In this talk, I will discuss the extension of these results to include charge and other matter models.
MondayNov 09, 201515:00
Algebraic Geometry and Representation Theory SeminarRoom 208
Speaker:Thomas BitounTitle:On p- support of an algebraic D-moduleAbstract:opens in new windowin html    pdfopens in new windowplease note unusual day, time, room
The p-support is a characteristic p variety attached to an algebraic D-module, for p large enough. It lives in the (Frobenius-twisted) cotangent space. We will discuss how it can be seen as a refined characteristic variety/singular support of the D-module. Further key words: Azumaya algebra, p-curvature.
MondayNov 09, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Tsvi Kopelowitz Title:Breaking the Variance: Approximating the Hamming Distance in 1/epsilon Time Per AlignmentAbstract:opens in new windowin html    pdfopens in new window

The algorithmic task of computing the Hamming distance between a given pattern of length m and each location in a text of length n is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence that for a given text and pattern, one cannot compute the exact Hamming distance for all locations in the text in time which is polynomially less than o(n\sqrt m). Nevertheless, Karloff showed that if one is willing to suffer a 1+-\epsilon approximation, then it is possible to solve the problem with high probability in O~(n / \epsilon^2)  time.

Due to related lower bounds for computing the Hamming distance of two strings in the one-way communication complexity model, it is strongly believed that obtaining an algorithm for solving the approximation version cannot be done much faster as a function of 1 / \epsilon. We will show that this belief is false by introducing a new O~(n / \epsilon) time algorithm that succeeds with high probability.

The main idea behind our algorithm, which is common in sparse recovery problems, is to reduce the variance of a specific randomized experiment by (approximately) separating heavy hitters from non-heavy hitters. However, while known sparse recovery techniques work very well on vectors, they do not seem to apply here, where we are dealing with mismatches between pairs of characters. We introduce two main algorithmic ingredients. The first is a new sparse recovery method that applies for pair inputs (such as in our setting). The second is a new construction of hash/projection functions, which allows to count the number of projections that induce mismatches between two characters exponentially faster than brute force. We expect that these algorithmic techniques will be of independent interest.

WednesdayNov 04, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Venkatesh Title:The fusion products of representations of current algebrasAbstract:opens in new windowin html    pdfopens in new window
The current algebra G[t] associated to a simple Lie algebra G is the Lie algebra of polynomial maps from complex plane to G. It is naturally graded with the grading defined by the degree of the polynomials. The fusion product, of Feigin and Loktev, is a graded G[t]-module, which is a refinement of the tensor product of finite dimensional cyclic G[t]-modules. More precisely, one starts with the tensor product of finite dimensional cyclic G[t]-modules, each localized at distinct points. It is again a cyclic G[t]-module generated by the tensor products of cyclic vectors. The graded module associated with the resulting cyclic module is defined to be the fusion product. Feigin and Loktev conjectured that the fusion product as a graded space is independent of the localization parameters for sufficiently well behaved modules. In this talk, we will see that this conjecture is true in most of the special cases.
TuesdayNov 03, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dmitry Turaev Title:On Bonatti-Diaz cyclesAbstract:opens in new windowin html    pdfopens in new window
We consider a partially-hyperbolic system with a heteroclinic cycle which contains a pair of saddles with different dimensions of the unstable manifold. We show that an arbitrary small perturbation of any such system creates a Bonatti-Diaz blender that leads to the emergence of persistent heterodimensional cycles. We also show that C1-generic, C2-generic, and C3- generic properties of systems in this class are different, while the higher order derivatives seem to have no effect on the generic dynamics.
MondayNov 02, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Noah Stephens-DavidowitzTitle:Solving SVP (and CVP) in 2^n Time via Discrete Gaussian Sampling