You are here

Previous Seminars

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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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 155
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
Speaker:testTitle:testAbstract:opens in new windowin html    pdfopens in new window
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 SamplingAbstract:opens in new windowin html    pdfopens in new window

We show a 2^{n+o(n)}-time algorithm for the Shortest Vector Problem on n-dimensional lattices (improving on the previous best-known algorithm of Micciancio and Voulgaris, which runs in time 4^{n+o(n)}). The algorithm uses the elementary yet powerful observation that, by properly combining samples from a Gaussian distribution over the lattice, we can produce exact samples from a narrower Gaussian distribution on the lattice. We use such a procedure repeatedly to obtain samples from an arbitrarily narrow Gaussian distribution over the lattice, allowing us to find a shortest vector.

Both the algorithm and the analysis are quite simple in hindsight. (The main technical tool is an identity on Gaussian measures with a simple geometric proof originally due to Riemann.) If time allows and interest merits, we will discuss a more technical variant of this algorithm that solves the Closest Vector Problem (a seemingly harder problem) in the same asymptotic running time.

Based on joint work with Divesh Aggarwal, Daniel Dadush, and Oded Regev. (See http://arxiv.org/abs/1412.7994 and http://arxiv.org/abs/1504.01995.)

WednesdayOct 28, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Dimitri Gurevich Title:From Quantum Groups to Noncommutative GeometryAbstract:opens in new windowin html    pdfopens in new window
Since creation theory of Quantum Groups numerous attempts to elaborate an appropriate differential calculus were undertaken. Recently, a new type of Noncommutative Geometry has been obtained on this way. Namely, we have succeeded in introducing the notions of partial derivatives on the enveloping algebras U(gl(m)) and constructing the corresponding de Rham complexes. All objects arising in our approach are deformations of their classical counterparts. In my talk I plan to introduce some basic notions of the theory of Quantum Groups and to exhibit possible applications of this type Noncommutative Geometry to quantization of certain dynamical models.
TuesdayOct 27, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Thomas GilbertTitle:Average conditional return times to rare events in billiard modelsAbstract:opens in new windowin html    pdfopens in new window
Motivated by the study of transport processes in some classes of billiard models, we wish to characterize a limiting regime of higher-dimensional billiards such that interaction between some of their degrees of freedom occurs only rarely while others mix fast. Under such conditions, the dynamics of the slow degrees of freedom can be approximated by a stochastic process with exponentially distributed waiting times. These times correspond to the times separating interactions among the slow degrees of freedom and we pro- pose to call them conditional return times. The definition extends beyond the rare interaction regime and some universal formulas apply.
MondayOct 26, 201514:30
Foundations of Computer Science SeminarRoom C
Speaker:Adi ShamirTitle:Post-Snowden CryptographyAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL ROOM
Recently, a series of unprecedented leaks by Edward Snowden had made it possible for the first time to get a glimpse into the actual capabilities and limitations of the techniques used by the NSA to eavesdrop to computers and other communication devices. In this talk, I will survey some of the things we have learned in the last couple of years, and discuss possible countermeasures against these capabilities.
ThursdayOct 22, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Michael Bronstein Title:Deep learning on geometric dataAbstract:opens in new windowin html    pdfopens in new window
The past decade in computer vision research has witnessed the re-emergence of "deep learning" and in particular, convolutional neural network techniques, allowing to learn task-specific features from examples and achieving a breakthrough in performance in a wide range of applications. However, in the geometry processing and computer graphics communities, these methods are practically unknown. One of the reasons stems from the facts that 3D shapes (typically modeled as Riemannian manifolds) are not shift-invariant spaces, hence the very notion of convolution is rather elusive. In this talk, I will show some recent works from our group trying to bridge this gap. Specifically, I will show the construction of intrinsic convolutional neural networks on meshes and point clouds, with applications such as finding dense correspondence between deformable shapes and shape retrieval.
WednesdayOct 21, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Polyxeni LamprouTitle:Catalan Numbers and Labelled GraphsAbstract:opens in new windowin html    pdfopens in new window

The Catalan numbers form a sequence of integers C_t. A collection of sets H_t with |H_t|= C_t for all t is called a Catalan set. Many examples of Catalan sets are known; the triangulations of the (t+2)-gon, the Dyck paths from (0,0) to (0, 2t) and the nilpotent ideals in the Borel subalgebra of sl_t to name but a few. In my talk I will present a new example of a Catalan set, which has a remarkable property: for all t, H_t decomposes into a (non-disjoint) union of C_{t-1} distinct subsets each of cardinality 2^{t-1}. Moreover, one may define certain interesting labelled graphs for H_t and obtain the above decomposition in a natural way. The subgraphs corresponding to the aforementioned subsets are labelled hypercubes with some edges missing. The motivation of this work was the study of the additive structure of the Kashiwara crystal B(infty).

TuesdayOct 20, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:S.V.GonchenkoTitle:Reversed mixed dynamicsAbstract:opens in new windowin html    pdfopens in new window

We say that a system possesses a mixed dynamics if
1) it has infinitely many hyperbolic periodic orbits of all possible types (stable, unstable,saddle) and
2) the closures of  the sets of orbits of different types have nonempty intersections.

Recall that Newhouse regions are open domains (from the space of smooth dynamical systems) in which systems with homoclinic tangencies are dense. Newhouse regions in which systems with mixed dynamics are generic (compose residual subsets) are called absolute Newhouse regions or Newhouse regions with mixed dynamics. Their existence was proved in the paper [1] for the case of 2d diffeomorphisms close to a diffeomorphism with a nontransversal heteroclinic cycle containing two fixed (periodic) points with the Jacobians less and greater than 1. Fundamentally, that "mixed dynamics" is the universal property of reversible chaotic systems. Moreover, in this case generic systems from absolute Newhouse regions have infinitely many stable, unstable, saddle and symmetric elliptic periodic orbits [2,3].

As well-known, reversible systems are often met in applications and they can demonstrate a chaotic orbit behavior. However, the phenomenon of mixed dynamics means that this chaos can not be associated with "strange attractor" or "conservative chaos". Attractors and repellers have here a nonempty intersection containing symmetric orbits (elliptic and saddle ones) but do not coincide, since periodic sinks (sources) do not belong to the repeller (attractor). Therefore, " mixed dynamics" should be considered as a new form of dynamical chaos posed between "strange attractor" and "conservative chaos".

These and related questions are discussed in the talk. Moreover, the main attention here is paid to the development of the concept of mixed dynamics for two-dimensional reversible maps. The main elements of this concept are presented in section below.

[1] S.V. Gonchenko, L.P. Shilnikov, D.V. Turaev. On Newhouse regions of two-dimensional diffeomorphisms close to a diffeomorphism with a nontransversal heteroclinic cycle. Proc. Steklov Inst. Math., 216 (1997), 70-118.

[2] Lamb J.S.W. and Stenkin O.V. Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits Nonlinearity, 2004, 17(4), 1217-1244.

[3] Delshams A., Gonchenko S.V., Gonchenko V.S., Lazaro J.T. and Sten'kin O.V. "Abundance of attracting, repelling and elliptic orbits in two-dimensional reversible maps".- Nonlinearity, 2013, v.26(1), 1-35.

WednesdayOct 14, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:R. VenkateshTitle:Fusion product structure of Demazure modulesAbstract:opens in new windowin html    pdfopens in new window

In this talk, we study Demazure modules which occur in a level l irreducible integrable representation of an untwisted affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie algebra. We prove that such a module is isomorphic to the fusion product of "prime" Demazure modules, where the prime factors are indexed by dominant integral weights which are either a multiple of l or take value less than l on all simple coroots. Our proof depends on a technical result which we prove in all the classical cases and G_2.  We do not need any assumption on the underlying simple Lie algebra when the last "prime" factor is too small. This is joint work with Vyjayanthi Chari, Peri Shereen and Jeffrey Wand.

WednesdayOct 07, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Elazar Goldenberg Title:Low Distortion Embedding from Edit to Hamming Distance using CouplingAbstract:opens in new windowin html    pdfopens in new window

The Hamming and the edit metrics are two common notions of measuring distances between pairs of strings x,y lying in the Boolean hypercube. The edit distance between x and y is defined as the minimum number of character insertion, deletion, and bit flips needed for converting x into y. Whereas, the Hamming distance between x and y is the number of bit flips needed for converting x to y.

In this paper we study a randomized injective embedding of the edit distance into the Hamming distance with a small distortion. This question was studied by Jowhari (ESA 2012) and is mainly motivated by two questions in communication complexity: the document exchange problem and deciding edit distance using a sketching protocol.

We show a randomized embedding with quadratic distortion. Namely, for any $x,y$ satisfying that their edit distance equals  $k$, the Hamming distance between the embedding of $x$ and $y$ is $O(k^2)$ with high probability. This improves over the distortion ratio of $O(\log n \log^* n)$ obtained by Jowhari for small values of $k$. Moreover, the embedding output size is linear in the input size and the embedding can be computed using a single pass over the input.

WednesdayOct 07, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Doron ZeilbergerTitle:The Joy of Symbol-CrunchingAbstract:opens in new windowin html    pdfopens in new window

19th century mathematicians (Gauss, Riemann, Markov, to name a few) spent a lot of their time doing tedious numerical computations. Sometimes they were assisted by (human) computers, but they still did a lot themselves. All this became unnecessary with the advent of computers, who made number-crunching million times faster (and more reliable).

20th- and 21st- century mathematicians spent (and still spend) a lot of their time doing tedious symbolic computations. Thanks to the more recent advent of Computer Algebra Systems (e.g. Maple, Mathematica, and the free system SAGE), much of their labor can be delegated to computers, who, of course, can go much faster, much further, and more reliably.

But humans are still needed! First, to teach the computer how to crunch symbols efficiently, but, just as importantly, to inspire them to formulate general conjectures, and methods of proof, for which humans are (still) crucial. I will mention several examples, most notably, a recent proof, by (the human) Guillaume Chapuy, of a conjecture made with the help of my computer Shalosh B. Ekhad (who rigorously proved many special cases), generalizing, to multi-permutations, Amitai Regev's  celebrated asymptotic formula for the number of permutations of length n avoiding an increasing subsequence of length d.

WednesdaySep 16, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Anup Rao Title:Simplified Separation of Information and CommunicationAbstract:opens in new windowin html    pdfopens in new window
Motivated by attempts to prove stronger lower bounds in communication complexity, a lot of recent work has tried to answer whether the information complexity of functions can be used to bound their communication complexity. Recently Ganor, Kol and Raz gave an example of a boolean function whose information complexity is exponentially smaller than its communication complexity. We simplify their work. I will give a black board talk highlighting the key ideas in the proof. Joint work with Makrand Sinha.
MondaySep 07, 201514:00
Special Guest LectureRoom 1
Speaker:Jasmin FisherTitle:Computing CancerAbstract:opens in new windowin html    pdfopens in new window

Cancer is a highly complex aberrant cellular state where mutations impact a multitude of signalling pathways operating in different cell types. In recent years it has become apparent that in order to understand and fight cancer, it must be viewed as a system, rather than as a set of cellular activities. This mind shift calls for new techniques that will allow us to investigate cancer as a holistic system. In this talk, I will discuss some of the  progress made towards achieving such a system-level understanding using computer modelling of biological  behaviours, also known as Executable Biology. I will concentrate on our recent attempts to better understand cancer through the following examples: 1) drug target optimization for Chronic Myeloid Leukaemia using an innovative platform called BioModelAnalyzer, which allows to prove stabilization of biological systems; 2) dynamic hybrid modelling of Glioblastoma (brain tumour) development; 3) state-based modelling of cancer signalling pathways and their analysis using model-checking; and 4) synthesis of blood stem cell programs from single-cell gene expression data. Looking forward, inspired by David Harel’s Grand Challenge proposed a decade ago, I will propose a smaller grand challenge for computing and biology that could shed new light on our ability to control cell fates during development and disease and potentially change the way we treat cancer in the future.

ThursdayAug 06, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 208
Speaker:Balázs RáthTitle:Voter model percolationAbstract:opens in new windowin html    pdfopens in new windowplease note unusual room

The voter model on $\Z^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of (extremal) stationary distributions is a family of measures $\mu_\alpha$, for $\alpha$ between 0 and 1. A configuration sampled from $\mu_\alpha$ is a strongly correlated field of 0's and 1's on $\Z^d$ in which the density of 1's is $\alpha$.

We consider such a configuration as a site percolation model on $\Z^d$. We prove that if $d \geq 5$, the probability of existence of an infinite percolation cluster of 1's exhibits a phase transition in $\alpha$. If the voter model is allowed to have sufficiently spread-out interactions, we prove the same result for $d \geq 3$.

These results partially settle a conjecture of Bricmont, Lebowitz and Maes (1987).
Joint work with Daniel Valesin (University of Groningen)

TuesdayAug 04, 201511:15
Mathematical Analysis and Applications SeminarRoom 208
Speaker:Piotr B. MuchaTitle:Two different solutions to a Burgers type systemAbstract:opens in new windowin html    pdfopens in new windowplease note change in room
I plan to talk about a construction of two different solutions to an elliptic system defined on the two dimensional torus. The system can be viewed as an elliptic regularization of the stationary Burgers 2D system. A motivation to consider the above system comes from an examination of unusual properties of a linear operator. Roughly speaking a term effects in a special stabilization of particular norms of the operator. The proof is valid for a particular large force. The main steps of the proof concern finite dimension approximation of the system and concentrate on analysis of features of large matrices, which resembles standard numerical analysis. The talk is based on the results of the paper: Jacek Cyranka, Piotr B Mucha : A construction of two different solutions to an elliptic system. arXiv:1502.03363.
ThursdayJul 30, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Eviatar ProcacciaTitle:Stationary Eden model on groupsAbstract:opens in new windowin html    pdfopens in new window

We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form $G \times Z$, where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in particular of Deijfen and Häggström in 2007.

WednesdayJul 29, 201513:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Leonid Makar-LimanovTitle:Possibly a solution of the two dimensional JC (Jacobian Conjecture).Abstract:opens in new windowin html    pdfopens in new window

Several years ago I introduced Newton polytopes related to the potential counterexamples to the JC. This approach permitted to obtain some additional information which though interesting, was not sufficient to get a contradiction. It seems that a contradiction can be obtained by comparing Newton polytopes for the left and right side of a (somewhat mysterious) equality G_x=-y_F.

WednesdayJul 29, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Jacob Greenstein Title:Double canonical basesAbstract:opens in new windowin html    pdfopens in new window
TuesdayJul 28, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Yanqiu GuoTitle:Backward Behavior of Nonlinear Parabolic and Dissipative Evolution EquationsAbstract:opens in new windowin html    pdfopens in new window

In this talk, I will discuss the backward-in-time behaviors of several nonlinear parabolic and dissipative evolution equations. This study is motivated by the investigation of the Bardos-Tartar conjecture on the 2D Navier-Stokes equations. Besides the rigorous mathematical treatment, we provide physical interpretation of the mechanism of singularity formulation, backward in time, for perturbations of the KdV equation. Finally, I will present the connection between the backward behavior and the energy spectra of the solutions.

This is a joint work with E. S. Titi.

TuesdayJul 21, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Edriss S. TitiTitle:Finite Number of Determining Parameters for the Navier-Stokes Equations with Applications into Feedback Control and Data AssimilationAbstract:opens in new windowin html    pdfopens in new window

In this talk we will implement the notion of finite number of determining parameters for the long-time dynamics of the Navier-Stokes equations (NSE), such as determining modes, nodes, volume elements, and other determining interpolants, to design finite-dimensional feedback control for stabilizing their solutions. The same approach is found to be applicable for data assimilation of weather prediction. In addition, we will show that the long-time dynamics of the NSE can be imbedded in an infinite-dimensional dynamical system that is induced by  an ordinary differential equations, named determining form, which is governed by a globally Lipschitz vector field. The NSE are used as an illustrative example, and all the above mentioned results equally hold to other dissipative evolution PDEs.

This is a joint work with A. Azouani, H. Bessaih, A. Farhat,  C. Foias, M. Jolly, R. Kravchenko, E. Lunasin and  E. Olson.

MondayJul 20, 201516:00
Geometry and Topology Seminar & Mathematical Analysis and Applications SeminarRoom 261
Speaker:Regina RotmanTitle:Quantitative homotopy theory and the lengths of geodesics on Riemannian manifoldsAbstract:opens in new windowin html    pdfopens in new window

Let M be a closed Riemannian manifold. There are numerous results that establish the existence of various minimal objects on M, such as periodic geodesics, minimal surfaces, or geodesic nets.  We will present some effective versions of these existence theorems.

For example, we will present diameter upper bounds for the lengths of three shortest simple periodic geodesics on a Riemannian 2-sphere, which can be interpreted as an effective version of the existence theorem of Lusternik and Schnirelmann. (Joint with Y. Liokumovich and A. Nabutovsky).

Finding upper bounds for the size of smallest stationary objects is closely related with construction of "optimal" homotopies.  We will show that if M is a closed surface of diameter d (with or without boundary), then any simple closed curve on M that can be contracted to a point over free loops of length less than L, can be contracted over based loops of length at most 3L+2d. (Joint with G. Chambers).

MondayJul 20, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Retsef Levi Title:Provably Near Optimal Algorithms for Dynamic Assortment Problems Abstract:opens in new windowin html    pdfopens in new window

Assortment planning is a major operational issue that arises in many industries, such as retailing, airlines and consumer electronics. Given a set of products that are differentiated by price, quality and possibly other attributes, one has to decide on the subset of products and the respective quantities that will be stocked and offered to heterogeneous customers, who exhibit substitution behavior.

The general problem can be shown to be NP-hard to approximate better than a factor linear in the number of products. In this talk we discuss how for  a range of practically interesting special cases, one could design conceptually simple policies that admit provably near-optimal solutions. The analysis reveals interesting structural properties, including hidden submodularity and decomposition properties. 


The talk is based on several papers which are Joint work with Ali Aouad, Vineet Goyal and Danny Segev

ThursdayJul 16, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 1
Speaker:Alexander FishTitle:Ergodic theorems for amenable groupsAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL ROOM

We will talk on the validity of the mean ergodic theorem along left Følner sequences in a countable amenable group G. Although the weak ergodic theorem always holds along any left Følner sequence in G, we will provide examples where the mean ergodic theorem fails in quite dramatic ways. On the other hand, if G does not admit any ICC quotients, e.g. if G is virtually nilpotent, then we will prove that the mean ergodic theorem does indeed hold along any left Følner sequence. Based on the joint work with M. Björklund (Chalmers).

WednesdayJul 15, 201513:30
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Jacob Greenstein Title:Koszul duality for semidirect productsAbstract:opens in new windowin html    pdfopens in new window
WednesdayJul 15, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Anthony JosephTitle:The Representation Theory of Invariant Subalgebras constructed from g AlgebrasAbstract:opens in new windowin html    pdfopens in new window
TuesdayJul 14, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Eitan TadmorTitle:Taking tendency into account: a new paradigm for collective dynamics Abstract:opens in new windowin html    pdfopens in new window

We discuss the collective dynamics of systems driven by the “social engagement” of agents with their local neighbors. Canonical models are based on environmental averaging, with prototype examples in opinion dynamics, flocking, self-organization of biological organisms, and rendezvous in mobile networks. The large time behavior of such systems leads to the formation of clusters, and in particular, the emergence of “consensus of opinions”.

We propose an alternative paradigm, arguing that in many relevant scenarios social interactions involve the tendency of agents “to move ahead”. We introduce a new family of models for collective dynamics with tendency. The large time behavior of these new systems leads to the emergence of “leaders”.

ThursdayJul 09, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Dan FlorentinTitle:Stability and Rate of Convergence of the Steiner SymmetrizationAbstract:opens in new windowin html    pdfopens in new window
We present a direct analytic method towards an estimate for the rate of convergence (to the Euclidean Ball) of Steiner symmetrizations. To this end we present a modified version of a known stability property of Steiner symmetrization.
MondayJul 06, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Shachar LovettTitle:Structure and Pseudo-Randomness in Coding TheoryAbstract:opens in new windowin html    pdfopens in new window

The theory of structure and pseudo-randomness has been very influential in several areas of mathematics, such as number theory, graph theory and harmonic analysis. It is also been influential in theoretical computer science, with applications in complexity theory, cryptography and property testing. At a high level, it allows to analyze arbitrary objects by decomposing them to a "structural" component and a "pseudo-random" component. The pseudo-random component behaves in many ways like random noise, while the structural component has a concise representation which makes it amenable to analysis and algorithmic manipulation.

In this talk, I will describe applications of this paradigm to coding theory. I will describe a new general approach to list decoding, which follows by decomposing an arbitrary received word to a structural received word and pseudo-random noise. This allows for a simplified analysis of the list decoding problem. In particular, I will describe how this approach leads to a resolution of a conjecture by Gopalan, Klivans and Zuckerman [STOC 2008], that the list decoding radius of Reed-Muller codes (in certain regimes) is equal to the minimal distance of the code.

Based on joint work with Abhishek Bhowmick.

ThursdayJul 02, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Kyros KutulakosTitle:Transport-Aware CamerasAbstract:opens in new windowin html    pdfopens in new window

Conventional cameras record all light falling onto their sensor regardless of the path that light followed to get there. In this talk I will present an emerging family of video cameras that can be programmed to record just a fraction of the light coming from a controllable source, based on the actual 3D path followed. Live video from these cameras offers a very unconventional view of our everyday world in which refraction and scattering can be selectively blocked or enhanced, visual structures too subtle to notice with the naked eye can become apparent, and object appearance can depend on depth.
I will discuss the unique optical properties and power efficiency of  these "transport-aware" cameras, as well as their use for 3D shape acquisition, robust time-of-flight imaging, material analysis, and scene understanding. Last but not least, I will discuss their potential to become our field's "outdoor Kinect" sensor---able to operate robustly even in direct sunlight with very low power.

Kyros Kutulakos is a Professor of Computer Science at the University of Toronto. He received his PhD degree from the University of Wisconsin-Madison in 1994 and his BS degree from the University of Crete in 1988, both in Computer Science. In addition to the University of Toronto, he has held appointments at the University of Rochester (1995-2001) and Microsoft Research Asia (2004-05 and 2011-12). He is the recipient of an Alfred P. Sloan Fellowship, an Ontario Premier's Research Excellence Award, a Marr Prize in 1999, a Marr Prize Honorable Mention in 2005, and three other paper awards (CVPR 1994, ECCV 2006, CVPR 2014). He also served as Program Co-Chair of CVPR 2003, ICCP 2010 and ICCV 2013.

ThursdayJul 02, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Dan FlorentinTitle:Stability and Rate of Convergence of the Steiner SymmetrizationAbstract:opens in new windowin html    pdfopens in new window
We present a direct analytic method towards an estimate for the rate of convergence (to the Euclidean Ball) of Steiner symmetrizations. To this end we present a modified version of a known stability property of Steiner symmetrization.
WednesdayJul 01, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Antoine DucrosTitle:Piecewise-linear and non-archimedean geometriesAbstract:opens in new windowin html    pdfopens in new window
This will be kind of a survey talk (including classical results, more recent ones, and a joint work with Amaury Thuillier which is still in progress ) about the deep links which exist between non-archimedean geometry over a valued field and piecewise linear geometry. I will mainly focus on the properties of some subsets of non-archimedean analytic spaces (in the sense of Vladimir Berkovich), called the skeleta, that inherit a canonical piecewise linear structure.
MondayJun 29, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Amir Yehudayoff Title:Learning and compressionAbstract:opens in new windowin html    pdfopens in new window

There are at least 2 aspects to learning: predicting the outcome of unseen events, and finding simple explanations of observed systems. We shall discuss 2 formal abstractions of these aspects: PAC learning and sample compression schemes. We shall start with an introduction to these notions, and then discuss the equivalence between them.

Based on a joint project with Shay Moran, Amir Shpilka and Avi Wigderson.

ThursdayJun 25, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Yinon SpinkaTitle:Long-range order in random 3-colorings of Z^dAbstract:opens in new windowin html    pdfopens in new window

Consider a random coloring of a bounded domain in Zd with the probability of each coloring F proportional to exp(−β∗N(F)), where β>0 is a parameter (representing the inverse temperature) and N(F) is the number of nearest neighboring pairs colored by the same color. This is the anti-ferromagnetic 3-state Potts model of statistical physics, used to describe magnetic interactions in a spin system. The Kotecký conjecture is that in such a model, for d≥3 and high enough β, a sampled coloring will typically exhibit long-range order, placing the same color at most of either the even or odd vertices of the domain. We give the first rigorous proof of this fact for large d. This extends previous works of Peled and of Galvin, Kahn, Randall and Sorkin, who treated the case β=∞.

The main ingredient in our proof is a new structure theorem for 3-colorings which characterizes the ways in which different "phases" may interact, putting special emphasis on the role of edges connecting vertices of the same color. We also discuss several related conjectures. No background in statistical physics will be assumed and all terms will be explained thoroughly.

Joint work with Ohad Feldheim.

WednesdayJun 24, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Yuri ZarkhinTitle:Galois groups and splitting fields of Mori trinomialsAbstract:opens in new windowin html    pdfopens in new window
We discuss a certain class of irreducible polynomials over the rationals that was introduced by Shigefumi Mori forty years ago in his Master Thesis. We prove that the Galois group of a Mori polynomial coincides with the corresponding full symmetric groups and the splitting field is "almost" unramified over its quadratic subfield.
WednesdayJun 24, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Yuri ZarkhinTitle:Galois groups and splitting fields of Mori trinomialsAbstract:opens in new windowin html    pdfopens in new window
We discuss a certain class of irreducible polynomials over the rationals that was introduced by Shigefumi Mori forty years ago in his Master Thesis. We prove that the Galois group of a Mori polynomial coincides with the corresponding full symmetric groups and the splitting field is ``almost" unramified over its quadratic subfield.
MondayJun 22, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Michael DinitzTitle:Smoothed Analysis of Dynamic NetworksAbstract:opens in new windowin html    pdfopens in new window

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models.  Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies.  Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a  precise pathological instance to enable much better performance?  Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior.  We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation.  We prove that these bounds provide a spectrum of robustness when subjected to smoothing---some are extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).

Joint work with Jeremy Fineman (Georgetown), Seth Gilbert (National University of Singapore), and Calvin Newport (Georgetown).

ThursdayJun 18, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Marc TeboulleTitle:Elementary Algorithms for High Dimensional Structured OptimizationAbstract:opens in new windowin html    pdfopens in new window

Many scientific and engineering problems are challenged by the fact they involve functions of a very large number of variables. Such problems arise naturally in signal recovery, image processing, learning theory, etc. In addition to the numerical difficulties due to the so-called curse of dimensionality, the resulting optimization problems are often nonsmooth and nonconvex.

We shall survey some of our recent results, illustrating how these difficulties may be handled in the context of well-structured optimization models, highlighting the ways in which problem structures and data information can be beneficially exploited to devise and analyze simple and efficient algorithms.

ThursdayJun 18, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Amir DemboTitle:The Atlas model, in and out of equilibriumAbstract:opens in new windowin html    pdfopens in new window

Consider a one-dimensional semi-infinite system of Brownian particles, starting at Poisson (L) point process on the positive half-line, with the left-most (Atlas) particle endowed a unit drift to the right. We show that for the equilibrium density (L=2), the asymptotic Gaussian space-time particle fluctuations are governed by the stochastic heat equation with Neumann boundary condition at zero. As a by product we resolve a conjecture of Pal and Pitman (2008) about the asympotic (random) fBM trajectory of the Atlas particle.

In a complementary work, we derive and explicitly solve the Stefan (free-boundary) equations for the limiting particle-profile when starting at out of equilibrium density (L other than 2). We thus determine the corresponding (non-random) asymptotic trajectory of the Atlas particle.

This talk is based on joint works with Li-Cheng Tsai, Manuel Cabezas, Andrey Sarantsev and Vladas Sidoravicius.

WednesdayJun 17, 201511:00
The Chaim Leib Pekeris Memorial Lecture
Speaker:Stanislav Smirnov Title:The Ising Model of a Ferromagnet from 1920 to the Present DayAbstract:opens in new windowin html    pdfopens in new windowDolfi and Lola Ebner Auditorium

The Ising model is an archetypical model of the order-disorder phase transition: though simple to formulate, it exhibits a complex behavior, much like the real-world phenomena in solid-state physics, ferromagnetism, chemistry, biology, computer science.

In 1920 the physicist Wilhelm Lenz proposed to model ferromagnetic materials by a lattice of plus-minus spins with interacting neighbors. His student Ernst Ising solved the model in dimension one four years later. The one-dimensional behavior turned out to be trivial, with no phase transition when the interaction strength changes, and for a decade people searched for other possible models. However, a ferromagnetic phase transition was established by Rudolf Peierls in higher dimensions, and in 1944 Lars Onsager famously calculated the free energy for the Ising model in two dimensions.

Since then the Ising model became widely studied, as it exhibits complicated phase transition behavior, yet allows a very detailed analysis in dimension two. We will give a historical introduction to the model, and then describe some recent results.

MondayJun 15, 201515:15
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Gerald SchwarzTitle:Oka Principles and the Linearization ProblemAbstract:opens in new windowin html    pdfopens in new windowNote the unusual day, time and place. Note that this is the second talk from the same seminar on this date.

   Let Q be a Stein space and L a complex Lie group. Then Grauert's Oka Principle states that the canonical map of the  isomorphism classes of holomorphic principle L-bundles over Q to the isomorphism classes of topological principle L-bundles over Q is an isomorphism. In particular he showed that if P, P' are holomorphic principle L-bundles and The Actual Formula a topological isomorphism, then there is a homotopy  The Actual Formula of topological isomorphisms with The Actual Formula  and The Actual Formula a holomorphic isomorphism.

   Let X and Y be Stein G-manifolds where G is a reductive complex Lie group. Then there is a  quotient Stein space  QX, and a morphism The Actual Formula  such that The Actual Formula. Similarly we haveThe Actual Formula .

   Suppose that The Actual Formula is a G-biholomorphism. Then the induced mapping The Actual Formula  has the following property: for any The Actual Formula , The Actual Formula  is G-isomorphic to  The Actual Formula (the fibers are actually affine G-varieties). We say that  The Actual Formula is admissible. Now given an admissible The Actual Formula, assume that we have a G-equivariant homeomorphism  The Actual Formula lifting The Actual Formula. Our goal is to establish an  Oka principle, saying that The Actual Formula has a deformation The Actual Formula  with The Actual Formula  and The Actual Formula biholomorphic.

   We establish this in two main cases. One case is where The Actual Formula is a diffeomorphism that restricts to  G-isomorphisms on the reduced fibers of The Actual Formula and The Actual Formula. The other case is where The Actual Formula restricts to G-isomorphisms on the fibers and X satisfies an auxiliary condition, which usually holds. Finally, we give applications to the Holomorphic Linearization Problem. Let G act holomorphically on The Actual Formula . When is there a change of coordinates such that the action of G becomes linear? We  prove that this is true, for X satisfying the same auxiliary condition as before,  if and only if the quotient QX is admissibly biholomorphic to the quotient of a G-module V.

MondayJun 15, 201514:30
Machine Learning and Statistics SeminarRoom 261
Speaker:Alex GoldenshlugerTitle:Nonparametric estimation of service time distribution in the $M/G/\infty$ queue and related estimation problemsAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY/TIME/PLACE

The subject of this talk is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from   observations of the queue--length process at the points of  the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy  over a family of target service time distributions. The original $M/G/\infty$ problem is closely related to the problem of estimating derivatives of the covariance function of a  stationary Gaussian process. We consider the latter problem and derive lower bounds on the minimax risk. The obtained results strongly suggest that the proposed estimator of the service time distribution is rate optimal.

MondayJun 15, 201514:05
Algebraic Geometry and Representation Theory SeminarRoom 1
Speaker:Aloysius Helminck Title:Orbits of parabolic subgroups on generalized symmetric spacesAbstract:opens in new windowin html    pdfopens in new windowNote the unusual day, time and place. Note that this talk will be followed by another one.

Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, The Actual Formula an involution of G defined over k, H a k-open subgroup of the fixed point group of   The Actual Formula and Gk (resp. Hk) the set of k-rational points of G (resp. H). The  homogeneous space Xk:=Gk/Hk is a generalization of a real reductive symmetric space to arbitrary fields and is called a generalized symmetric space.

Orbits of parabolic k-subgroups on these generalized symmetric spaces occur in various situations, but are especially of importance in the study of representations of Gk related to Xk. In this talk we present a number of structural results for these parabolic k-subgroups that are of importance for the study of these generalized symmetric space and their applications.

ThursdayJun 11, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Anton MalyshevTitle:Metric distortion between random finite subsets of the intervalAbstract:opens in new windowin html    pdfopens in new window

Consider a random finite metric space X given by sampling n points in the unit interval uniformly, and a deterministic finite metric space U given by placing n points in the unit interval at uniform distance. With high probability, X will contain some pairs of points at distance roughly 1/n^2, so any bijection from X to U must distort distances by a factor of roughly n. However, with high probability, two of these random spaces, X_1 and X_2, have a bijection which distorts distances by a factor of only about n^2/3. The exponent of 2/3 is optimal.

WednesdayJun 10, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Lenny Makar-Limanov Title:A description of two-generated subalgebras of a polynomial ring in one variable and a new proof of the AMS theoremAbstract:opens in new windowin html    pdfopens in new window
The famous AMS (Abhyankar-Moh-Suzuki) theorem states that if two polynomials $f$ and $g$ in one variable with coefficients in a field $F$ generate all algebra of polynomials, i.e. any polynomial $h$ in one variable can be expressed as $h = H(f, g)$ where $H$ is a polynomial in two variables, then either the degree of $f$ divides the degree of $g$, or the degree of $g$ divides the degree of $f$, or the degree of $f$ and the degree of $g$ are divisible by the characteristic of the field $F$. There were several wrong published proofs of this theorem and there are many correct published proofs of this theorem but all of them either long or not self-contained. Recently I found a (relatively) short and self-contained proof which is not published yet and which I can explain in one-two hours.
MondayJun 08, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Shai VardiTitle:Expanding the Boundaries of Local Computation AlgorithmsAbstract:opens in new windowin html    pdfopens in new window

Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Previous work on LCAs restricted its focus to graphs of bounded degree, or degree of bounded expectation that is distributed binomially.

Using a new palette of techniques, we show that it is possible to obtain LCAs for maximal independent set (MIS) and maximal matching (MM) on trees with degree bounded by $\polylog{n}$. Our result immediately extends to all graphs with degree bounded by $\polylog{n}$, as long as they do not contain short cycles (of length $\polylog{n}$).

We define a family of graphs called $d$-light graphs, and show how to convert a large class of online algorithms (including MIS and MM) to LCAs on these graphs. We then show that applying the MIS (or MM) LCA on appropriately selected $d$-light subgraphs, allows us to quickly address all of the vertices of the $\polylog{n}$-degree graph.

In addition to expanding the range of LCAs to graphs of polylogarithmic degree, our new techniques also significantly improve the running times and space requirements, expand the family of graphs, and better define the family of algorithms to which previous results apply. Furthermore our proofs are simpler and more concise than the previous proof methods.

Joint work with Omer Reingold.

ThursdayJun 04, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Rene VidalTitle:Algebraic, Sparse and Low Rank Subspace ClusteringAbstract:opens in new windowin html    pdfopens in new window
In the era of data deluge, the development of methods for discovering structure in high-dimensional data is becoming increasingly important. Traditional approaches such as PCA often assume that the data is sampled from a single low-dimensional manifold. However, in many applications in signal/image processing, machine learning and computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. In this talk, I will present methods from algebraic geometry, sparse representation theory and rank minimization for clustering and classification of data in multiple low-dimensional subspaces. I will show how these methods can be extended to handle noise, outliers as well as missing data. I will also present applications of these methods to video segmentation and face clustering.
ThursdayJun 04, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Mark RudelsonTitle:Approximation complexity of convex bodiesAbstract:opens in new windowin html    pdfopens in new window
Consider the approximation of an n-dimensional convex body by a projection of a section of an N-dimensional simplex, and call the minimal N for which such approximation exists the approximation complexity of the body. The reason for such strange definition lies in computer science. A projection of a section of a simplex is the feasible set of a linear programming problem, and so it can be efficiently generated. We will discuss how large the approximation complexity of different classes of convex bodies can be.
WednesdayJun 03, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Sasha Yomdin Title:Reciprocity laws and K-theoryAbstract:opens in new windowin html    pdfopens in new window

We associate to a full flag F in an n-dimensional variety X over a field k, a "symbol map" $\mu_F :K(F_X) \to \Sigma^n K(k)$. Here, F_X is the field of rational functions on X, and K(.) is the K-theory spectrum.

We prove a "reciprocity law" for these symbols: Given a partial flag, the sum of all symbols of full flags refining it is 0. Examining this result on the level of K-groups, we derive the following known reciprocity laws: the degree of a principal divisor is zero, the Weil reciprocity law, the residue theorem, the Contou-Carrère reciprocity law (when X is a smooth complete curve) as well as the Parshin reciprocity law and the higher residue reciprocity law (when
X is higher-dimensional).

This is a joint work with Evgeny Musicantov.

ThursdayMay 28, 201513:30
Foundations of Computer Science SeminarRoom 1
Speaker:Boaz BarakTitle:Proofs for Algorithms, Algorithms from ProofsAbstract:opens in new windowin html    pdfopens in new window

The interplay between algorithms and proofs has been one of the most fascinating and fruitful themes in theoretical  Computer Science. In this talk I will describe a different connection between these two concepts - a general methodology for algorithm design using an automatic transformation of a proof into an algorithm. This methodology yields a systematic way to design and analyze algorithms across many domains. In particular we and others have used it for problems in combinatorial optimization, machine learning, and quantum information theory, and it shows promise for making progress on important open questions such as settling Khot's Unique Games Conjecture. I will demonstrate this methodology by presenting an algorithm for the Sparse Coding / Dictionary Learning problem that handles much more general inputs than was known before, and an algorithm for the Unique Games problem that can solve all the previously known candidate hard instances.   Key to our approach is the notion of "pseudo-distributions", which are objects that are emphatically different than actual distributions but behave like them in the eyes of low degree polynomials. We use these pseudo-distributions to "lift" a proof into an algorithm via the Shor-Parrilo-Lasserre "Sum-of-Squares" semidefinite programming hierarchy. The talk will be based on several joint works with (varying subsets of) Fernando Brandao, Aram Harrow, Jonathan Kelner, David Steurer and Yuan Zhou.

ThursdayMay 28, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Gerard Ben ArousTitle:The ant in the labyrinth: recent progressAbstract:opens in new windowin html    pdfopens in new window
WednesdayMay 27, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Niv BuchbinderTitle:A Primal-Dual Approach to Online Optimization ProblemsAbstract:opens in new windowin html    pdfopens in new window
The primal-dual method is one of the fundamental design methodologies in the areas of linear programming, combinatorial optimization, and approximation algorithms. In this talk I will provide an introduction to the area of online combinatorial optimization. I will then discuss the primal-dual method as a unified framework to the design and analysis of online algorithms. Examples for which this approach is applicable include central online problems such as paging, routing, scheduling, online set cover, and graph connectivity problems. Finally, I will show some connections between online combinatorial optimization and online learning.
WednesdayMay 27, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Avner SegalTitle:A Family of New-way Integrals for the Standard L-function of Cuspidal Representations of the Exceptional Group of Type G2. Abstract:opens in new windowin html    pdfopens in new window
In a joint work with N. Gurevich we have constructed a family of Rankin-Selberg integrals representing the standard twisted L-function of a cuspidal representation of the exceptional group of type G2. This integral representations use a degenerate Eisenstein series on the family of quasi-split forms of Spin8 associated to an induction from a character on the Heisenberg parabolic subgroup. This integral representations are unusual in the sense that they unfold with a non-unique model. A priori this integral is not factorizable but using remarkable machinery proposed by I. Piatetski-Shapiro and S. Rallis we prove that in fact the integral does factor. As the local generating function of the local L-factor was unknown to us, we used the theory of C*-algebras in order to approximate it and perform the unramified computation. If time permits, I will discuss the poles of the relevant Eisenstein series and some applications to the theory of CAP representations of G2.
TuesdayMay 26, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Jair KoillerTitle:Computational anatomy and splines on manifolds Abstract:opens in new windowin html    pdfopens in new window

Computational anatomy considers spaces of shapes (e.g. medical images) endowed with a Riemannian metric (Sobolev type). The area blends  techniques from differential geometry (geometric mechanics),  analysis  and statistics. The EPDiff equation, which is basically an extension of Euler's equation,  without the incompressibility assumption, is often used to match shapes.    Time-varying images (4DCA),  one of the current research themes in the area. In longitudinal studies (say for Alzheimer's disease) snapshots at given times are interpolated/regressed.  The problem arises of comparing two such sequences for classification purposes. For some background, see the recent workshop http://www.mat.univie.ac.at/~shape2015/schedule.html . 

In this talk we discuss  finite dimensional examples using landmarks. A short process is interpreted as a tangent vector in the space of images. This leads to control problems whose state space is a tangent bundle.  Usually, cubic Riemannian splines are taken, ie., minimizing the The Actual Formula norm of the acceleration vector,  for paths connecting two tangent vectors under  a fixed time. We propose as an alternative to cubic splines the time minimal problem under bounded acceleration (morally the The Actual Formula  norm).   We suggest that both splines problems on The Actual Formulaare completely integrable in the Arnold-Liouville sense. Along the way, we present general technical results about the underlying symplectic structures of control problems whose state space has a bundle structure. 

This is joint ongoing work with Paula Balseiro, Alejandro Cabrera, and Teresa Stuchi.

ThursdayMay 21, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Lenya RyzhikTitle:The weakly random Schroedinger equation: a consumer reportAbstract:opens in new windowin html    pdfopens in new window
Consider a Schroedinger equation with a weakly random time-independent potential. When the correlation function of the potential is, roughly speaking, of the Schwartz class, it has been shown by Spohn (1977), and Erdos and Yau (2001) that the kinetic limit holds -- the expectation of the phase space energy density of the solution converges weakly (after integration against a test function, not in the probabilistic sense) to the solution of a kinetic equation. We "extend" this result to potentials whose correlation functions satisfy (in some sense) "sharp" conditions, and also prove a parallel homogenization result for slowly varying initial conditions. I will explain the quotation marks above and make some speculations on the genuinely sharp conditions on the random potential that separate various regimes. This talk is a joint work with T. Chen and T. Komorowski
WednesdayMay 20, 201513:00
Vision and Robotics SeminarRoom 1
Speaker:Thomas BroxTitle:Will ConvNets render computer vision research obsolete?Abstract:opens in new windowin html    pdfopens in new window
Deep learning based on convolutional network architectures has revolutionized the field of visual recognition in the last two years. There is hardly a classification task left, where ConvNets do not define the state-of-the-art. Outside recognition, deep learning seems to be of lesser importance, yet this could be a fallacy. In this talk I will present our recent work on convolutional networks and show that they can learn to solve computer vision problems that are not typically assigned to the field of recognition. I will present a network that has learned to be good on descriptor matching, another one can create new images of chairs, and I show two networks that have learned to estimate optical flow. I will conclude with some arguments why, despite all this, computer vision will stay a serious research field.
WednesdayMay 20, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Dan CarmonTitle:Autocorrelations of the Moebius function over function fieldsAbstract:opens in new windowin html    pdfopens in new window
In this talk we shall discuss results on autocorrelations of the arithmetic Moebius function of polynomials over finite fields, in the limit of a large base field. Special consideration will be given to base fields of characteristic 2, where both methods and results substantially differ from those applicable in odd characteristics. The methods used are mostly elementary, with a hint of algebraic geometry.
WednesdayMay 20, 201511:00
Geometric Functional Analysis and Probability SeminarRoom 108
Speaker:Kate JuschenkoTitle:Amenability of subgroups of interval exchange transformation groupAbstract:opens in new windowin html    pdfopens in new window
TuesdayMay 19, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Peter J. OlverTitle:Dispersive Quantization of Linear and Nonlinear WavesAbstract:opens in new windowin html    pdfopens in new window
The evolution, through spatially periodic linear dispersion, of rough initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. The Talbot effect, named after an optical experiment by one of the founders of photography, was first observed in optics and quantum mechanics, and leads to intriguing connections with exponential sums arising in number theory. Ramifications of these phenomena and recent progress on the analysis, numerics, and extensions to nonlinear wave models will be discussed.
MondayMay 18, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Sigal OrenTitle:Long-Range Planning with Time-Inconsistency: A Class of Computational Problems in Behavioral EconomicsAbstract:opens in new windowin html    pdfopens in new window

In many settings, people exhibit behavior that is inconsistent across time — we allocate a block of time to get work done and then procrastinate, or put effort into a project and then later fail to complete it. An active line of research in behavioral economics and related fields has developed and analyzed models for this type of time-inconsistent behavior.

Here we propose a graph-theoretic model of tasks and goals, in which dependencies among actions are represented by a directed graph, and a time-inconsistent agent constructs a path through this graph. We first show how instances of this path-finding problem on different input graphs can reconstruct a wide range of qualitative phenomena observed in the literature on time-inconsistency, including procrastination, abandonment of long-range tasks, and the benefits of reduced sets of choices. We then explore a set of analyses that quantify over the set of all graphs; among other results, we find that in any graph, there can be only polynomially many distinct forms of time-inconsistent behavior; and any graph in which a time-inconsistent agent incurs significantly more cost than an optimal agent must contain a large “procrastination” structure as a minor. Finally, we use this graph-theoretic model to explore ways in which tasks can be designed to help motivate agents to reach designated goals.

This is joint work with Jon Kleinberg.

ThursdayMay 14, 201512:15
Vision and Robotics SeminarRoom 141
Speaker:Guy Ben-YosefTitle:Full interpretation of minimal imagesAbstract:opens in new windowin html    pdfopens in new windowPlease note unusual location.

The goal in this work is to produce ‘full interpretation’ for object images, namely to identify and localize all semantic features and parts that are recognized by human observers. We develop a novel approach and tools to study this challenging task, by dividing the interpretation of the complete object to interpretation of so-called 'minimal recognizable configurations’, namely severely reduced but recognizable local regions, that are minimal in the sense that any further reduction would turn them unrecognizable. We show that for the task of full interpretation, such minimal images have unique properties, which make them particularly useful.

For modeling interpretation, we identify primitive components and relations that play a useful role in the interpretation of minimal images by humans, and incorporate them in a structured prediction algorithm. The structure elements can be point, contour, or region primitives, while relations between them range from standard unary and binary potentials based on relative location, to more complex and high dimensional relations. We show experimental results and match them to human performance. We discuss implications of ‘full’ interpretation for difficult visual tasks, such as recognizing human activities or interactions.

WednesdayMay 13, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Tamir HazanTitle:Machine Learning: Is it Artificial Intelligence, Statistics or Algorithms? Abstract:opens in new windowin html    pdfopens in new window
Machine learning originates from different fields: Artificial Intelligence (e.g, the Perceptron), Statistics (e.g., the Vapnik-Chervonenkis dimension) and Algorithms (e.g., Valiant's theory of the learnable). In this talk I will show how machine learning relates and differs from these fields while focusing on learning and inference of high-dimensional structures. Such structures arise in various AI applications, for example objects computer vision, parses in natural language processing and molecular structures in computational biology. I will present perturb-max models, which are high-dimensional probability models that measure the stability of prediction to random shifts of data measurements. These models replace the standard Gibbs distributions and allow efficient sampling, as well as generalization and regret bounds.
WednesdayMay 13, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Luc Illusie Title:Around the Thom-Sebastiani theoremAbstract:opens in new windowin html    pdfopens in new window

For germs of holomorphic functions $f : \mathbf{C}^{m+1} \to \mathbf{C}$, $g : \mathbf{C}^{n+1} \to \mathbf{C}$ having an isolated critical point at 0 with value 0, the classical Thom-Sebastiani theorem describes the vanishing cycles group $\Phi^{m+n+1}(f \oplus g)$ (and its monodromy) as a tensor product $\Phi^m(f) \otimes \Phi^n(g)$, where $(f \oplus g)(x,y) = f(x) + g(y), x = (x_0,...,x_m), y = (y_0,...,y_n)$. I will discuss algebraic variants and generalizations of this result over fields of any characteristic, where the tensor product is replaced by a certain local convolution product, as suggested by Deligne. The main theorem is a Künneth formula for $R\Psi$ in the framework of Deligne's theory of nearby cycles over general bases.

TuesdayMay 12, 201516:00
Seminar in Geometry and TopologyRoom 261
Speaker:Gal BinyaminiTitle:Counting solutions of differential equationsAbstract:opens in new windowin html    pdfopens in new window

We consider the following problem: given a set of algebraic conditions on an $n$-tuple of functions and their first $l$ derivatives, admitting finitely many solutions (in a differentiably closed field), can one give an upper bound for the number of solutions?

I will present estimates in terms of the degrees of the algebraic conditions, or more generally the volumes of their Newton polytopes (analogous to the Bezout and BKK theorems). The estimates are singly-exponential with respect to $n,l$ and have the natural asymptotic with respect to the degrees or Newton polytopes, sharpening previous doubly-exponential estimates due to Hrushovski and Pillay. I will also discuss some diophantine applications to counting transcendental lattice points on algebraic varieties.

MondayMay 11, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Aviad RubinsteinTitle:New hardness results (for Densest k-Subgraph and Nash) from "birthday repetition"Abstract:opens in new windowin html    pdfopens in new window

I will describe recent applications of "birthday repetition" that can give (conditional) quasi-polynomial time hardness results for Densest k-Subgraph and for $\epsilon$-Nash in 2-player games. (For the latter result we use a non-standard "PCP for PPAD" assumption which I will also discuss.) Both results are tight by [FS97], [LMM03], [Barman15].

Based on:
DkS- http://eccc.hpi-web.de/report/2015/074/
(joint work with Mark Braverman, Young Kun Ko, and Omri Weinstein)

Nash- http://arxiv.org/abs/1504.02411
(joint work with Yakov Babichenko and Christos Papadimitriou)

ThursdayMay 07, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Ehud FriedgutTitle:An information theoretic proof of a hypercontractive inequalityAbstract:opens in new windowin html    pdfopens in new window

In the famous KKL (Kahn-Kalai-Linial) paper of 1988 the authors "imported" to combinatorics and theoretical computer science a hypercontractive inequality known as Beckner's ineqaulity (proven first, independently, by Gross and Bonami). This inequality has since become an extremely useful and influential tool, used in tens of papers, in a wide variety of settings. In many cases there are no proofs known that do not use the inequality.

In this talk I'll try to illuminate the information theoretic nature of both the inequality and its dual, touch upon a proof of the dual version from about a decade ago, (joint with V. Rodl), and a fresh (and unrelated) information theoretic proof of the primal version.

No prior knowledge will be assumed regarding discrete Fourier analysis, Entropy, and hypercontractivity.

MondayMay 04, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Eli GafniTitle:40 Years Of Distributed-Computability on One-FootAbstract:opens in new windowin html    pdfopens in new window

Research can be viewed as a search of an accepting-state in an exponential-space. When we look in hind-sight after we find an accepting-state, can we identify a much shorter path than the one that was discovered by trial and error as the search actually proceeded?

In this talk I'll show that this is the case for Distributed-Computability: The discovery that different distributed problems have different levels of difficulty, and identifying the weakest model of distributed-computation that allows to solve a problem. I'll explain the essence of 40 years of research in an hour, by showing that if the right questions were asked at the right time, all the results could have been had in a span of time order-of-magnitude shorter.


Some of the major ideas in the talk were developed in works with Afek (TAU), and Borowsky (Akamai), Lynch (MIT), and Rajsbaum (UNAM).

ThursdayApr 30, 201516:00
Guest SeminarRoom 261
Speaker:Shmuel GurvitzTitle:Does the measurement take place when nobody observes it?Abstract:opens in new windowin html    pdfopens in new window
WednesdayApr 29, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Jonathan RosenblattTitle:On the Optimality of Averaging in Distributed Statistical LearningAbstract:opens in new windowin html    pdfopens in new window

A common approach to statistical learning on big data is to randomly split it among m machines and calculate the parameter of interest by averaging their m individual estimates.

Focusing on empirical risk minimization, or equivalently M-estimation, we study the statistical error  incurred by this strategy.
We consider two asymptotic settings: one where the number of samples per machine n->inf but the number of  parameters p is fixed, and a second high-dimensional regime where both p,n-> inf with p/n-> kappa.

Most previous works provided only moment bounds on the error incurred by splitting the data in the fixed p setting. In contrast, we present for both regimes asymptotically exact distributions for this estimation error. In the fixed-p setting, under suitable assumptions, we thus prove that to leading order, averaging is as accurate as the centralized solution. In the high-dimensional setting, we show a qualitatively different behavior: data splitting does incur a first order accuracy loss, which we quantify precisely. In addition, our asymptotic distributions allow the construction of confidence intervals and hypothesis testing on the estimated parameters. 

Our main conclusion is that in both regimes, averaging parallelized estimates is an attractive way to speedup computations and save on memory, while incurring a quantifiable and typically moderate excess error.

WednesdayApr 29, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Marko Tadic Title:Square-integrable representations of classical p-adic groups and their Jacquet modulesAbstract:opens in new windowin html    pdfopens in new window
In the talk we shall present formulas for Jacquet modules of square integrable representations of segment type, formulas for special Jacquet modules of a general square integrable representation and a new proof of the Matic’s formula for the Jacquet modules of strongly positive (square integrable) representations of classical p-adic groups.
TuesdayApr 28, 201516:00
Seminar in Geometry and TopologyRoom 261
Speaker:Marina Prokhorova Title:The index theorem for self-adjoint elliptic operators with local boundary conditionsAbstract:opens in new windowin html    pdfopens in new window

The spectral flow is a well-known invariant of a 1-parameter family of self-adjoint Fredholm operators. It is defined as the net number of operator’s eigenvalues passing through 0 with the change of parameter.

Let S be a compact surface with non-empty boundary. Consider the space Ell(S) of first order self-adjoint elliptic differential operators on S with local boundary conditions. The first part of the talk is devoted to the computing of the spectral flow along loops in Ell(S), and also along paths with conjugated ends.

After that we consider more general situation: a family of elements of Ell(S) parameterized by points of a compact space X. We define the topological index of such a family and show that it coincides with the analytical index of the family. Both indices take value in K^1(X). When X is a circle, this result turns into the formula for the spectral flow from the first part of the talk.

MondayApr 27, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Irit DinurTitle:Old and new PCP constructions Abstract:opens in new windowin html    pdfopens in new window

The PCP theorem (AS,ALMSS 1991) guarantees that every NP language has a Probabilistically Checkable Proof (PCP) system allowing a verifier to check a witness very efficiently using randomness, and allowing for small error.
Most of the talk will not assume prior knowledge, but I will also devote some time to some recent work joint with Harsha and Kindler.

In this work we make (some) progress towards proving the so-called "sliding-scale conjecture". This is a conjecture of BGLR from 1993 about the tradeoff between the number of bits read from the PCP proof and the error of the verifier.
Our work revisits older constructions and analyzes them using the more modern "modular-composition" approach.

Based on joint work with Prahladh Harsha and Guy Kindler.

WednesdayApr 22, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Andrey MinchenkoTitle:Conformal and differential Lie algebrasAbstract:opens in new windowin html    pdfopens in new window
MondayApr 20, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Nir AilonTitle:Computational Lower Bounds for the Fourier Transform Abstract:opens in new windowin html    pdfopens in new window
The Fourier Transform is one of the most important linear transformation in engineering and science with applications in a wide variety of domains spanning signal processing, pattern recognition, cryptography, polynomial multiplication, complexity theory, learning theory and more. In 1964, Cooley and Tukey discovered the Fast Fourier Transform (FFT) algorithm, which computes the transformation in time O(n log n) for a signal in n-dimensions. In spite of its importance, not much was known until recently about lower bounds. I will show that if you speed up FFT in a machine of finite precision (say, 32 or 64 bits) using linear operations only (multiplications and additions), then there exist Omega (n) orthogonal directions in input space that either overflow (exceed the machine's numerical upper limit) or underflow (exceed the machine's precision) at some point during the computation. A quantitative tradeoff between the speedup factor and the resulting numerical abuse will be presented. The talk is self-contained. Some open problems will be presented at the end.
ThursdayApr 16, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Piotr MilosTitle:Extremal individuals in branching systemsAbstract:opens in new windowin html    pdfopens in new window

Branching processes have been subject of intense and fascinating studies for a long time. In my talk I will present two problems in order to highlight their rich structure and various technical approaches in the intersection of probability and analysis.
Firstly, I will present results concerning a branching random walk with the time-inhomogeneous branching law. We consider a system of particles, which at the end of each time unit produce offspring randomly and independently. The branching law, determining the number and locations of the offspring is the same for all particles in a given generation. Until recently, a common assumption was that the branching law does not change over time. In a pioneering work, Fang and Zeitouni (2010) considered a process with two macroscopic time intervals with different branching laws. In my talk I will present the results when the branching law varies at mesoscopic and microscopic scales. In arguably the most interesting case, when the branching law is sampled randomly for every step, I will present a quenched result with detailed asymptotics of the maximal particle. Interestingly, the disorder has a slowing-down effect manifesting itself on the log level.
Secondly, I will turn to the classical branching Brownian motion. Let us assume that particles move according to a Brownian motion with drift μ and split with intensity 1. It is well-know that for μ≥2√ the system escapes to infinity, thus the overall minimum is well-defined. In order to understand it better, we modify the process such that the particles are absorbed at position 0. I will present the results concerning the law of the number of absorbed particles N. In particular I will concentrate on P(N=0) and the maximal exponential moment of N. This reveals new deep connections with the FKPP equation. Finally, I will also consider −2√<μ<2√ and Nxt the number of particles absorbed until the time t when the system starts from x. In this case I will show the convergence to the traveling wave solution of the FKPP equation for an appropriate choice of x,t−>∞.
The results were obtained jointly with B. Mallein and with J. Berestycki, E. Brunet and S. Harris respectively.

WednesdayApr 15, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Efrat Bank Title:Prime polynomial values of linear functions in short intervalsAbstract:opens in new windowin html    pdfopens in new window

In this talk I will present a function field analogue of a conjecture in number theory. This conjecture is a combination of several famous conjectures, including the Hardy-Littlewood prime tuple conjecture, conjectures on the number of primes in arithmetic progressions and in short intervals, and the Goldbach conjecture. I prove an asymptotic formula for the number of simultaneous prime values of n linear functions, in the limit of a large finite field.
A key role is played by the computation of some Galois groups.

TuesdayApr 14, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Robert Krasny Title:Lagrangian Particle Methods for Vortex DynamicsAbstract:opens in new windowin html    pdfopens in new window

This talk will describe how Lagrangian particle methods are being used to compute the dynamics of fluid vortices. In these methods the flow map is represented by moving particles that carry vorticity, the velocity is recovered by the Biot-Savart integral, and a tree code is used to reduce the computation time from The Actual Formula to The Actual Formula, where The Actual Formula is the number of particles. I'll present vortex sheet computations in 2D with reference to Kelvin-Helmholtz instability, the Moore singularity, spiral roll-up, and chaotic dynamics. Other examples include vortex rings in 3D, and vortex dynamics on a rotating sphere.

MondayApr 13, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Elette Boyle Title:Function Secret SharingAbstract:opens in new windowin html    pdfopens in new window

Motivated by the goal of securely searching and updating distributed data, we introduce the notion of function secret sharing (FSS), a form of “additive secret sharing” for {\em functions} f: {0,1}^n → G, where G is an abelian group.

An m-party FSS scheme for function class F allows one to split any function f from F into m succinctly described functions f_i, such that: (1) for every input x, f(x) is equal to the sum of evaluations \sum_i f_i(x), and (2) any strict subset of "share functions" f_i hides f. FSS provides a natural generalization of distributed point functions, as introduced by (Gilboa-Ishai Eurocrypt 2014), which coincide with the special case of two parties and the class F of point functions (which evaluate to 0 at all but one point).

We present two types of results:
- We obtain efficiency improvements and extensions of the original distributed point function construction.
- We then initiate a systematic study of general FSS, providing constructions for richer function classes, and establishing relations with other cryptographic primitives.

Joint work with Niv Gilboa and Yuval Ishai.

ThursdayApr 02, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Yonatan WexlerTitle:Machine Learning In Your PocketAbstract:opens in new windowin html    pdfopens in new window

The field of Machine Learning has been making huge strides recently. Problems such as visual recognition and classification, that were believed to be open only a few years ago, now seem solvable. The best performers use Artificial Neural Networks, in their reincarnation as "Deep Learning", where huge networks are trained over lots of data. One bottleneck in current schemes is the huge amount of required computation during both training and testing. This limits the usability of these methods when power is an issue, such as with wearable devices.

As a step towards deeper understanding of deep learning mechanisms, I will show how correct conditioning of the back-propagation training iterations results in a much improved convergence. This reduces training time, providing better results. It also allows us to train smaller models, that are harder to optimize.

In this talk I will also discuss the challenges - and describe some of the solutions - in applying Machine Learning on a mobile device that can fit your pocket. The OrCam is a wearable camera that speaks to you. It reads anything, learns and recognizes faces, and much more. It is ready to help through the day, all with a simple pointing gesture. It is already improving the lives of many blind and visually impaired people.

MondayMar 30, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Nir BitanskyTitle:On the Cryptographic Hardness of Finding a Nash Equilibrium Abstract:opens in new windowin html    pdfopens in new window
We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and injective one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which finding Nash equilibrium is known to be complete. Previous proposals for basing PPAD-hardness on program obfuscation considered a strong "virtual black-box" notion that is subject to severe limitations and is unlikely to be realizable for the programs in question. In contrast, for indistinguishability obfuscation no such limitations are known, and recently, several candidate constructions of indistinguishability obfuscation were suggested based on different hardness assumptions on multilinear maps. Our result provides further evidence of the intractability of finding a Nash equilibrium, one that is extrinsic to the evidence presented so far. Joint work with Omer Paneth and Alon Rosen (http://eccc.hpi-web.de/report/2015/001/)
ThursdayMar 26, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Lior WolfTitle:Image Annotation using Deep Learning and Fisher VectorsAbstract:opens in new windowin html    pdfopens in new window
We present a system for solving the holy grail of computer vision -- matching images and text and describing an image by an automatically generated text. Our system is based on combining deep learning tools for images and text, namely Convolutional Neural Networks, word2vec, and Recurrent Neural Networks, with a classical computer vision tool, the Fisher Vector. The Fisher Vector is modified to support hybrid distributions that are a much better fit for the text data. Our method proves to be extremely potent and we outperform by a significant margin all concurrent methods.
ThursdayMar 26, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Tom HutchcroftTitle:Hyperbolic and Parabolic Random MapsAbstract:opens in new windowin html    pdfopens in new window
We establish a sharp division of infinite random planar graphs into two types, hyperbolic and parabolic, showing that many probabilistic and geometric properties of such a graph are determined by the graph's average curvature, a local quantity which is often easy to compute. Work in progress with Omer Angel, Asaf Nachmias and Gourab Ray.
ThursdayMar 26, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Tom HutchcroftTitle:Hyperbolic and Parabolic Random MapsAbstract:opens in new windowin html    pdfopens in new window
We establish a sharp division of infinite random planar graphs into two types, hyperbolic and parabolic, showing that many probabilistic and geometric properties of such a graph are determined by the graph's average curvature, a local quantity which is often easy to compute. Work in progress with Omer Angel, Asaf Nachmias and Gourab Ray.
WednesdayMar 25, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Itai DattnerTitle:Statistical Inference for Systems of Differential EquationsAbstract:opens in new windowin html    pdfopens in new window
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by systems of differential equations. These systems describe the interrelationships between the variables involved, and depend in a complicated way on unknown quantities (e.g., initial values, constants or time dependent parameters). Most often, the researcher would like to execute important tasks such as testing the validity of a model, analyzing its qualitative behavior or predicting future states of the system. In order to execute these tasks, one usually needs to estimate the unknown quantities of the system from real data. However, in the case of differential equations, the inverse problem of parameter estimation is considered as the bottleneck in modeling dynamical systems and estimating parameters based on observed noisy state variables has a relatively sparse statistical literature. In this talk we focus on the fairly general and often applied class of systems of ordinary differential equations linear in (functions of) the parameters. For such systems we first characterize a necessary and sufficient condition for identifiability of parameters. Then we present a novel estimation approach and support it by a general statistical theory that enables the development of estimators tailored for a variety of experimental scenarios. In particular, we present estimators corresponding to some common experimental setups and discuss their statistical properties. Simulation studies and application of the method to real data will be discussed.
TuesdayMar 24, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Daniel ReemTitle:Zero-Convex Functions, Perturbation Resilience, and Subgradient Projections for Feasibility-Seeking MethodsAbstract:opens in new windowin html    pdfopens in new window

The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations instead of orthogonal projections onto the individual sets of the problem. Working in a real Hilbert space, we show that the sequential subgradient projection method is perturbation resilient. By this we mean that under appropriate conditions the sequence generated by the method converges weakly, and sometimes also strongly, to a point in the intersection of the given subsets of the feasibility problem, despite certain perturbations which are allowed in each iterative step. Unlike previous works on solving the convex feasibility problem, the involved functions, which induce the feasibility problem’s subsets, need not be convex. Instead, we allow them to belong to a wider and richer class of functions satisfying a weaker condition, that we call “zero-convexity”. This class, which is introduced and discussed here, holds a promise to solve optimization problems in various areas, especially in non-smooth and non-convex optimization. The relevance of this study to approximate minimization and to the recent superiorization methodology for constrained optimization is explained.

This is a joint work with Yair Censor.

MondayMar 23, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Gil CohenTitle:Local Correlation Breakers and Applications to Mergers and Multi-Source ExtractorsAbstract:opens in new windowin html    pdfopens in new window

We introduce and construct a pseudo-random object which we call a local correlation breaker (LCB). This is an algorithm that gets as input a sequence of (possibly correlated) random variables and an independent weak source of randomness. The output of the LCB is a sequence of random variables with the following property. If the i'th input random variable is uniform then the i'th output variable is uniform even if a bounded number of any other output variables are given. That is, an LCB uses the weak-source to "break" local correlations between random variables.

Based on LCBs we obtain improved constructions of mergers with weak-seeds and multi-source extractors. In particular, we construct a 3-source extractor for entropies delta*n, O(log n) and O(loglog n), for any constant delta. We further construct a 7-source extractor for poly-logarithmic entropy.

Joint work with Guy Rothblum.
No prior knowledge is assumed.

ThursdayMar 19, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Simon KormanTitle:Inverting RANSAC: Global Model Detection via Inlier Rate EstimationAbstract:opens in new windowin html    pdfopens in new window
This work presents a novel approach for detecting inliers in a given set of correspondences (matches). It does so without explicitly identifying any consensus set, based on a method for inlier rate estimation (IRE). Given such an estimator for the inlier rate, we also present an algorithm that detects a globally optimal transformation. We provide a theoretical analysis of the IRE method using a stochastic generative model on the continuous spaces of matches and transformations. This model allows rigorous investigation of the limits of our IRE method for the case of 2D translation, further giving bounds and insights for the more general case. Our theoretical analysis is validated empirically and is shown to hold in practice for the more general case of 2D affinities. In addition, we show that the combined framework works on challenging cases of 2D homography estimation, with very few and possibly noisy inliers, where RANSAC generally fails. Joint work with Roee Litman, Alex Bronstein and Shai Avidan.
WednesdayMar 18, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Erez LapidTitle:Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new resultsAbstract:opens in new windowin html    pdfopens in new window
Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new results - PART TWO
WednesdayMar 18, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Erez LapidTitle:Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new resultsAbstract:opens in new windowin html    pdfopens in new window
Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new results - PART TWO
ThursdayMar 12, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Toby JohnsonTitle:The frog model on treesAbstract:opens in new windowin html    pdfopens in new window

Imagine that every vertex of a graph contains a sleeping frog. At time 0, the frog at some designated vertex wakes up and begins a simple random walk. When it lands on a vertex, the sleeping frog there wakes up and begins its own simple random walk, which in turn wakes up any sleeping frogs it lands on, and so on. This process is called the frog model.

I'll talk about a question posed by Serguei Popov in 2003: On an infinite d-ary tree, is the frog model recurrent or transient? That is, is each vertex visited infinitely or finitely often by frogs? The answer is that it depends on d: there's a phase transition between recurrence and transience as d grows. Furthermore, if the system starts with Poi(m) sleeping frogs on each vertex independently, there's a phase transition as m grows. This is joint work with Christopher Hoffman and Matthew Junge.

WednesdayMar 11, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Erez LapidTitle:Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new resultsAbstract:opens in new windowin html    pdfopens in new window
Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new results - PART ONE
MondayMar 09, 201514:30
Foundations of Computer Science SeminarRoom 1
Speaker:Isaac KeslassyTitle:When Bh Sequences Meet Bloom Filters, and Hot Topics in Data CentersAbstract:opens in new windowin html    pdfopens in new window

Bloom filters and Counting Bloom Filters (CBFs) are widely used in networking device algorithms. They implement fast set representations to support membership queries with limited error. Unlike Bloom filters, CBFs also support element deletions. In the first part of the talk, I will introduce a new general method based on variable increments to improve the efficiency of CBFs and their variants. I will demonstrate that this method can always achieve a lower false positive rate and a lower overflow probability bound than CBFs in practical systems.

Next, I will present ongoing research on data center networking. In particular, I will introduce a new approach to providing network isolation, so customers can feel alone in shared clouds, without any network contention from other customers. I will also demonstrate theoretical conditions for the isolation algorithm.

WednesdayFeb 25, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Polyxeni LamprouTitle:The polyhedral structure of B(infinity): graphs, tableaux and Catalan setsAbstract:opens in new windowin html    pdfopens in new window
WednesdayFeb 18, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Bernhard KroetzTitle:On the tempered embedding theorem for real spherical spacesAbstract:opens in new windowin html    pdfopens in new window
TuesdayFeb 17, 201511:15
Mathematical Analysis and Applications SeminarRoom 261
Speaker:D. TuraevTitle:Chaotic dynamics in systems of non-holonomic mechanicsAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL ROOM
We discuss what can be main ingredients of chaotic behaviour in mechanical systems with non-holonomic constraints: attractor-repeller mergers, elliptic points and non-conservative resonances, solenoids, heterodimensional cycles, and universality.
ThursdayFeb 12, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Chaim Even ZoharTitle:Invariants of Random Knots and LinksAbstract:opens in new windowin html    pdfopens in new window
We study random knots and links in R^3 using the Petaluma model, which is based on the petal projections developed by Adams et al. (2012). In this model we obtain a formula for the distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the higher moments of the Casson invariant and the order-three knot invariant v3. These are the first precise formulas given for the distributions of invariants in any model for random knots or links. All terms above will be defined and explained. Joint work with Joel Hass, Nati Linial, and Tahl Nowik.
WednesdayFeb 11, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Vera SerganovaTitle:gl(\infty) and Deligne categoriesAbstract:opens in new windowin html    pdfopens in new window
TuesdayFeb 10, 201511:15
Mathematical Analysis and Applications SeminarRoom 261
Speaker:Vitaly MorozTitle:Grounds states of the stationary Choquard equationsAbstract:opens in new windowin html    pdfopens in new window
The Choquard equation, also known as the nonlinear Schrodinger-Newton equation is a nonlinear Schrodinger type equation where the nonlinearity is coupled with a nonlocal convolution term given by an attractive gravitational potential. We present recent results on the existence, positivity, symmetry and optimal decay properties of ground state solutions of stationary Choquard type equations under various assumptions on the decay of the external potential and the shape of the nonlinearity. This is a joint work with Jean Van Schaftingen (Louvain-la-Neuve, Belgium)
ThursdayFeb 05, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Yuval PeledTitle:On the phase transition in random simplicial complexesAbstract:opens in new windowin html    pdfopens in new window
It is well-known that the model of random graphs undergoes a dramatic change around p=1/n. It is here that the random graph is, almost surely, no longer a forest, and here it first acquires a giant connected component. Several years ago, Linial and Meshulam have introduced the X_d(n,p) model, a probability space of n-vertex d-dimensional simplicial complexes, where X_1(n,p) coincides with G(n,p). Within this model we prove a natural d-dimensional analog of these graph theoretic phenomena. Specifically, we determine the exact threshold for the nonvanishing of the real d-th homology of complexes from X_d(n,p), and show that it is strictly greater than the threshold of d-collapsibility. In addition, we compute the real Betti numbers, i.e. the dimension of the homology groups, of X_d(n,p)for p=c/n. Finally, we establish the emergence of giant shadow at this threshold. (For d=1 a giant shadow and a giant component are equivalent). Unlike the case for graphs, for d > 1 the emergence of the giant shadow is a first order phase transition. The talk will contain the necessary toplogical backgorund on simplicial complexes, and will focus on the main idea of the proof: the local weak limit of random simplicial complexes and its role in the analysis of phase transitions. Joint work with Nati Linial.
WednesdayFeb 04, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Max GurevichTitle:Ladder representations and Galois distinctionAbstract:opens in new windowin html    pdfopens in new window
The space GL_n(E)/GL_n(F), for a quadratic extension E/F of p-adic fields, serves as an approachable case for the study of harmonic analysis on p-adic symmetric spaces on one hand, while having ties with Asai L-functions on the other. It is long known that a GL_n(F)-distinguished representation of GL_n(E) must be contragredient to its own Galois conjugate. Conversely, a conjecture often attributed to Jacquet states that the last-mentioned condition is close to being sufficient for distinction. We show the conjecture is valid for the class of ladder representations which was recently explored by Lapid and Minguez. Along the way, we will suggest a reformulation of the conjecture which concerns standard modules in place of irreducible representations.
MondayFeb 02, 201515:00
Foundations of Computer Science SeminarRoom 261
Speaker:Sangxia Huang Title:Improved NP-inapproximability for 2-variable Linear EquationsAbstract:opens in new windowin html    pdfopens in new window

An instance of the E2-Lin(2) problem is a system of equations of the form "x_i + x_j = b (mod 2)". Given such a system in which it is possible to satisfy all but an epsilon fraction of the equations, we would like to find an assignment that violates as few equations as possible. In this paper, we show that it is NP-hard to satisfy all but a C*epsilon fraction of the equations, for any C< 11/8 and 0 < epsilon <= 1/8. Our result holds also for the special case of Max-Cut. The previous best NP-hardness result, standing for over 15 years, had 5/4 in place of 11/8.

Our proof is by a modified gadget reduction from a predicate that supports a pairwise independent distribution. We also show an inherent limitation to this type of gadget reduction. In particular, we show that no such reduction can establish a hardness factor C greater than ~2.54.

Joint work with Johan Hastad, Rajsekar Manokaran, Ryan O'Donnell, John Wright.

MondayFeb 02, 201514:00
Special Guest LectureRoom 1
Speaker:P. AnandanTitle:Inventing the Future: Microsoft Research in its Third DecadeAbstract:opens in new windowin html    pdfopens in new window
Microsoft Research is 23 years old and is a premiere Computer Science research organization in the world. In this talk I will look back at the work done at MSR during the recent years and explain how we are significantly contributing to progress in Science, Technology and Society.
ThursdayJan 29, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Avishay Gal-Yam and Barak ZackayTitle:New ways to look at the skyAbstract:opens in new windowin html    pdfopens in new window
We present a general review of astronomical observation, with emphasis on the ways it differs from conventional imaging or photography. We then describe emerging trends in this area driven mainly by advances in detector technology and computing power. Having set a broad context, we then describe the new multiplexed imaging technique we have developed. This method uses the sparseness of typical astronomical data in order to image large areas of target sky using a physically small detector.
ThursdayJan 29, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Gady KozmaTitle:Random walk in random environment: the operator theory approachAbstract:opens in new windowin html    pdfopens in new window

Examine random walk in a stationary, ergodic, random environment which is bistochastic i.e. the sum of probabilities to enter any fixed vertex is 1. Consider the drift as a function on the probability space on the environments, and assume it belongs to domain of definition of where D is the symmetrized generator of the walk (this is the famous  The Actual Formula condition). We show that under these conditions the walk satisfies a central limit theorem. The proof uses the "relaxed sector condition" which shows an unexpected connection to the spectral theory of unbounded operators.

All terms will be explained in the talk. This is joint work with Balint Toth.

WednesdayJan 28, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Tsachik GelanderTitle:On the asymptotic of L_2 invariants of arithmetic groups.Abstract:opens in new windowin html    pdfopens in new window
TuesdayJan 27, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Mira ShamisTitle:The standard map, and discrete Schroedinger operatorsAbstract:opens in new windowin html    pdfopens in new window
The standard map is a measure-preserving map of the torus; the dynamics generated by it is the subject of numerous conjectures. One of the approaches to the standard map leads to the study of a certain Schroedinger operator. I will start with a brief introduction to discrete Schroedinger operators, and present two results: one pertaining to a general class of discrete Schroedinger operators, and another one -- pertaining to the operator arising from the standard map. Time permitting, I will explain some of the elements of the proof. [Based on joint work with T. Spencer]
MondayJan 26, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Avinatan HassidimTitle:Random Assignment gamesAbstract:opens in new windowin html    pdfopens in new window
Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion. Joint work with Assaf Romm.
MondayJan 26, 201514:00
Vision and Robotics SeminarRoom 141
Speaker:Greg ShakhnarovichTitle:Feedforward semantic segmentation with zoom-out featuresAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL DAY/TIME/ROOM
We introduce a purely feed-forward architecture for semantic segmentation. We map small image elements (superpixels) to rich feature representations extracted from a sequence of nested regions of increasing extent. These regions are obtained by "zooming out" from the superpixel all the way to scene-level resolution. This approach exploits statistical structure in the image and in the label space without setting up explicit structured prediction mechanisms, and thus avoids complex and expensive inference. Instead superpixels are classified by a feedforward multilayer network. Our architecture achieves new state of the art performance in semantic segmentation, obtaining 64.4% average accuracy on the PASCAL VOC 2012 test set. Joint work with Mohammadreza Mostajabi and Payman Yadollahpour.
ThursdayJan 22, 201514:00
Seminar in Geometry and TopologyRoom 1
Speaker:Egor ShelukhinTitle:Autonomous Hamiltonian flows, Hofer's geometry and persistence modulesAbstract:opens in new windowin html    pdfopens in new windowNote unusual day, time and room
We describe how persistence modules, a notion originating in data sciences, can be applied to obtain new results on Hofer's geometry, related in particular to autonomous Hamiltonian flows. Joint work with Leonid Polterovich.
ThursdayJan 22, 201511:05
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Thomas LebleTitle:Large deviations for the empirical field of Coulomb and Riesz systemsAbstract:opens in new windowin html    pdfopens in new window
We study a system of $N$ particles with Coulomb/Riesz pairwise interactions under a confining potential. After rescaling we deal with a microscopic quantity, the associated empirical point process, for which we give a large deviation principle whose rate function is the sum of a relative entropy and of the "renormalized energy" defined by Sandier-Serfaty. We also present applications to point processes emerging from random matrix theory. This is joint work with S. Serfaty.
WednesdayJan 21, 201511:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Omri AbendTitle:Machine-Learning the Universal Semantics of Natural LanguagesAbstract:opens in new windowin html    pdfopens in new window
The field of Natural Language Processing (NLP) has recently been pivotal in producing important language technologies such as machine translation and question answering. Such technologies are based on elaborate structural representations of text, detected by statistical methods. However, common approaches to structural representation are language-specific or even domain-specific, limiting the applicability of NLP tools and models. How to represent both the idiosyncrasies of specific domains and languages as well as their commonalities is still an open question. In my talk I will address these questions and propose an approach for learning a level of representation shared by all languages using latent variable models for structured prediction. Under this approach, learning starts from universally-applicable coarse-grained logical structures, which is used to bootstrap the learning of more fine-grained semantic distinctions, as well as the learning of the specifics of individual languages. I will discuss the value of universal semantic structures both to the computational modeling of child language acquisition and to leading NLP applications, focusing on machine translation. Joint work with Ari Rappoport, Shay Cohen and Mark Steedman.
TuesdayJan 20, 201511:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Dmitry DolgopyatTitle:Piecewise linear Fermi-Ulam pingpongsAbstract:opens in new windowin html    pdfopens in new windowNote the new time at which the MAAA seminars begin
We consider a particle moving freely between two periodically moving infinitely heavy walls. We assume that one wall is fixed and the second one moves with piecewise linear velocities. We study the question about existence and abundance of accelerating orbits for that model. This is a joint work with Jacopo de Simoi.
MondayJan 12, 201514:00
Vision and Robotics SeminarRoom 141
Speaker:Karen LivescuTitle:Multi-view representation learning: A tutorial introduction and applications to speech and languageAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL ROOM, DAY, TIME

Many types of multi-dimensional data have a natural division into two "views", such as audio and video or images and text.
  Multi-view learning includes a variety of techniques that use multiple views
  of data to learn improved models for each of the views. The views can be multiple measurement modalities (like the examples above) but also can be different types of information extracted from the same source (words + context, document text + links) or any division of the data dimensions into subsets satisfying certain learning assumptions. Theoretical and empirical results show that multi-view  techniques can improve over single-view ones in certain settings. In many  cases multiple views help by reducing noise in some sense (what is noise in one view is not in the other). In this talk, I will focus on multi-view learning of representations (features), especially using canonical correlation analysis (CCA) and related techniques.  I will give a tutorial overview of CCA and its relationship with other techniques such as partial least squares (PLS) and linear discriminant analysis (LDA).  I will also present extensions developed by ourselves and others, such as kernel, deep, and generalized
("many-view") CCA.  Finally, I will give recent results on speech and language tasks, and demonstrate our publicly available code.

Based on joint work with Raman Arora, Weiran Wang, Jeff Bilmes, Galen Andrew, and others.

ThursdayJan 08, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Tomer MichaeliTitle:Blind deblurring and blind super-resolution using internal patch recurrenceAbstract:opens in new windowin html    pdfopens in new window

Small image patches tend to recur at multiple scales within high-quality natural images.
This fractal-like behavior has been used in the past for various tasks  including image compression, super-resolution and denoising. In this talk, I will show that this phenomenon  can also be harnessed for "blind deblurring"  and for "blind  super-resolution", that is, for removing blur or increasing resolution without a-priori knowledge of the associated blur kernel. It turns out that the cross-scale patch recurrence property is strong only in images taken under ideal imaging conditions, but significantly diminishes when the imaging conditions deviate from ideal ones. Therefore, the deviations from ideal patch recurrence actually provide information on the unknown camera blur kernel.
More specifically, we show that the correct blur kernel is the one which maximizes the  similarity between patches across scales of the image. Extensive experiments  indicate that our approach leads to state of the art results, both in deblurring and in super-resolution.

Joint work with Michal Irani.

WednesdayJan 07, 201511:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Shaul ZemelTitle:On Lattices over Valuation Rings of Arbitrary RankAbstract:opens in new windowin html    pdfopens in new window
We show how the simple property of 2-Henselianity suffices to reduce the classification of lattices over a general valuation ring in which 2 is invertible (with no restriction on the value group) to classifying quadratic spaces over the residue field. The case where 2 is not invertible is much more difficult. In this case we present the generalized Arf invariant of a unimodular rank 2 lattice, and show how in case the lattice contains a primitive vector with norm divisible by 2, a refinement of this invariant and a certain class suffice for classifying these lattices.
TuesdayJan 06, 201511:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:David DynermanTitle:Describing geometry and symmetry of cryo-EM datasets using algebraAbstract:opens in new windowin html    pdfopens in new window

Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy images. We discuss how algebra can describe two aspects of cryo-EM datasets. First, we'll describe common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are a crucial ingredient in some 2D3D reconstruction algorithms, and they can be characterized by polynomial equalities and inequalities. Second, we'll discuss how 3D symmetries of a molecule can be detected from only 2D cryo-EM images, without performing full 3D reconstruction.

MondayJan 05, 201514:30
Foundations of Computer Science SeminarRoom 261
Speaker:Dana MoshkovitzTitle:Parallel Repetition From FortificationAbstract:opens in new windowin html    pdfopens in new window
The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game in terms of the value of the base game and the number of repetitions. In this work we give a simple transformation on games -- "fortification" -- and show that for fortified games, the value of the repeated game decreases perfectly exponentially with the number of repetitions, up to an arbitrarily small additive error. Our proof is combinatorial and (very) short. As corollaries, we obtain: (1) Starting from a PCP Theorem with soundness error bounded away from 1, we get a PCP with arbitrarily small constant soundness error. In particular, starting with the combinatorial PCP of Dinur, we get a combinatorial PCP with low error. The latter can be used for hardness of approximation as in the work of Hastad. (2) Starting from the work of the author and Raz, we get a projection PCP theorem with the smallest soundness error known today. The theorem yields nearly a quadratic improvement in the size compared to previous work.
ThursdayJan 01, 201512:15
Vision and Robotics SeminarRoom 1
Speaker:Tal HassnerTitle:Towards Dense Correspondences Between Any Two ImagesAbstract:opens in new windowin html    pdfopens in new window

We present a practical method for establishing dense correspondences between two images with similar  content, but possibly different 3D scenes. One of the challenges in designing  such a system is the local scale differences of objects appearing in the two  images. Previous methods often considered only small subsets of image pixels; matching only pixels for which stable scales may be reliably estimated. More recently, others have considered dense correspondences, but with substantial costs  associated with generating, storing and matching scale invariant descriptors.
Our work here is motivated by the observation that pixels in the image have contexts -- the pixels around them -- which may be exploited in order to estimate local scales reliably and repeatably. In practice, we demonstrate that scales estimated in sparse interest points may be propagated to neighboring pixels where this information cannot be reliably determined. Doing so allows scale invariant descriptors to be extracted anywhere in the image, not just in detected interest points. As a consequence, accurate dense correspondences are obtained even between very different images, with little computational costs beyond those required by existing methods.

This is joint work with Moria Tau from the Open University of Israel

WednesdayDec 31, 201411:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Victor KacTitle:Non-commutative geometry and non-commutative integrable systemsAbstract:opens in new windowin html    pdfopens in new window
MondayDec 29, 201414:30
Foundations of Computer Science SeminarRoom 261
Speaker:Moran FeldmanTitle:Aspects of Submodular Maximization Subject to a Matroid ConstraintAbstract:opens in new windowin html    pdfopens in new window
Submodular functions form a large natural class of set functions with applications in many fields including social networks, machine learning and game theory. Optimization of submodular functions subject to various constraints attracted much attention in recent years, both from theoretical and practical points of view. This talk considers the problem of maximizing a submodular function subject to a matroid constraint, which is a central problem demonstrating many of the modern approaches and techniques used in the field of submodular maximization. Many aspects of this problem have been studied, including its polynomial time approximability, fast (almost linear time) algorithms and online models. This talk surveys some of these aspects and explores a few of the main results obtained recently
ThursdayDec 25, 201413:00
Vision and Robotics SeminarRoom 1
Speaker:Hadar ElorTitle:RingIt: Ring-ordering Casual Photos of a Dynamic EventAbstract:opens in new windowin html    pdfopens in new window
The multitude of cameras constantly present nowadays redefined the meaning of capturing an event and the meaning of sharing this event with others. The images are frequently uploaded to a common platform, and the image-navigation challenge naturally arises. In this talk I will present RingIt a novel technique to sort an unorganized set of casual photographs taken along a general ring, where the cameras capture a dynamic event in the center of the ring. We assume a nearly instantaneous event, e.g., an interesting moment in a performance captured by the digital cameras and smartphones of the surrounding crowd. The ordering method extracts the K-nearest neighbors (KNN) of each image from a rough all-pairs dissimilarity estimate. The KNN dissimilarities are refined to form a sparse Weighted Laplacian, and a spectral analysis reveals the spatial ordering of the images, allowing for a sequential display of the captured object.
WednesdayDec 24, 201411:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Jonathan BerantTitle:Scalable algorithms for translating natural language to logical formAbstract:opens in new windowin html    pdfopens in new window
Conversational interfaces and virtual assistants such as Apple's Siri, Google Now, and Facebook Graph Search, have led to a rising interest in systems that can translate natural language commands and questions to formal logical forms (like SQL queries) that can be executed against a knowledge base. A major challenge has been to scale these systems, known as semantic parsers, to large knowledge bases. In this talk, I will describe novel algorithms for large scale semantic parsing. A fundamental characteristic of semantic parsing against large knowledge bases is that the space of possible logical forms grows quickly with the length of the input sentence. Our first algorithm learns to efficiently search through this space by explicitly scoring partial logical forms, combining ideas from agenda-based parsing and reinforcement learning. Compared to previous methods, our parser is almost an order of magnitude faster, while maintaining state-of-the-art accuracy. The second algorithm addresses the problem of language variability, that is, the fact that the same logical form can be expressed in a myriad of ways in natural language. We learn to paraphrase an input question ("Where is Obama from?") to a canonical form ("What is the place of birth of Barack Obama?") that can be easily mapped to a logical form. This allows us to exploit the large amounts of free text that are available on the web, leading to a state-of-the-art semantic parser that scales to a knowledge base containing hundreds of millions of facts. This is joint work with Percy Liang.
TuesdayDec 23, 201416:00
Seminar in Geometry and TopologyRoom 261
Speaker:A. GabrielovTitle:Classification of spherical quadrilaterals (part 2)Abstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL PLACE AND TIME
A spherical quadrilateral (membrane) is a bordered surface homeomorphic to a closed disc, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in the case that at most three angles at the corners are not multiples of Pi. This is a very old problem, related to the properties of solutions of the Heun's equation (an ordinary differential equation with four regular singular points). The corresponding problem for the spherical triangles, related to the properties of solutions of the hypergeometric equation, has been solved by Klein, with some gaps in Klein's classification filled in by Eremenko in 2004. The general quadrilateral case remains open. This is joint work with V. Tarasov (IUPUI). The first part is by A. Eremenko (Purdue), 13:00-14:00, room 1. The second is by A. Gabrielov (Purdue), 16:00-17:15, room 261.
TuesdayDec 23, 201413:00
Seminar in Geometry and TopologyRoom 1
Speaker:A. EremenkoTitle:Classification of spherical quadrilaterals (part 1)Abstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL PLACE AND TIME
A spherical quadrilateral (membrane) is a bordered surface homeomorphic to a closed disc, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in the case that at most three angles at the corners are not multiples of Pi. This is a very old problem, related to the properties of solutions of the Heun's equation (an ordinary differential equation with four regular singular points). The corresponding problem for the spherical triangles, related to the properties of solutions of the hypergeometric equation, has been solved by Klein, with some gaps in Klein's classification filled in by Eremenko in 2004. The general quadrilateral case remains open. This is joint work with V. Tarasov (IUPUI). The first part is by A. Eremenko (Purdue), 13:00-14:00, room 1. The second is by A. Gabrielov (Purdue), 16:00-17:15, room 261.
TuesdayDec 23, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Sylvia SerfatyTitle:Microscopic behavior of systems with Coulomb and Riesz interactionsAbstract:opens in new windowin html    pdfopens in new window
We are interested in systems of points with Coulomb, logarithmic or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas and beta ensembles, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. We describe tools to study such systems and derive a next order (beyond mean field limit) "renormalized energy" that governs microscopic patterns of points. We present the derivation of the limiting problem and the question of its minimization and its link with the Abrikosov lattice and crystallization questions. In the statistical mechanics context, we obtain a large deviation principle on the "empirical fields." This is based on joint works with Etienne Sandier, Nicolas Rougerie, Simona Rota Nodari, Mircea Petrache, and Thomas Lebl\'{e}.
ThursdayDec 18, 201414:00
Seminar in Geometry and TopologyRoom 261
Speaker:Andrei GabrielovTitle:Lipschitz contact equivalence of functions in two variablesAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL DAY AND TIME
We consider germs at the origin in $R^2$ of continuous functions definable in a polynomially bounded o-minimal structure (e.g., semialgebraic or subanalytic). We construct a complete invariant of an equivalence class of such functions with respect to Lipschitz contact equivalence. A similar construction produces a complete bi-Lipschitz invariant for a germ of a real definable two-dimensional surface in $R^n$. This is joint work with L. Birbrair and A. Fernandes (University of Ceara, Fortaleza, Brazil)
ThursdayDec 18, 201410:30
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Alexander FishTitle:Plunnecke inequalities in countable abelian groups - general caseAbstract:opens in new windowin html    pdfopens in new windowPLEASE NOTE UNUSUAL TIME
Plunnecke inequalities for sumsets of finite sets in abelian groups are extended to measure -preserving systems (mps). For a set A in a group, and a set B of positive measure in mps, we estimate the measure of the union of translations along the set A of B. To prove the new inequalities we extend the graph-theoretic method recently developed by Petridis to "measure graphs". As an application, through Furstenberg's correspondence principle, we obtain the new Plunnecke type inequalities for lower and upper Banach density in countable abelian groups. Based on joint works with M. Bjorklund, Chalmers, and with Kamil Bulinski, Sydne
TuesdayDec 16, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Milton Lopes FilhoTitle:On the vortex-wave systemAbstract:opens in new windowin html    pdfopens in new window
The vortex-wave system is a mathematical model for two-dimensional incompressible flows with small regions of concentrated vorticity imbedded upon a continuously distributed background vorticity. The system consists of a coupleing of the 2D vorticity equation with the point-vortex system. In this talk we survey known results and recent progress on mathematical analysis of this system
ThursdayDec 11, 201412:15
Vision and Robotics SeminarRoom 1
Speaker:Boaz NadlerTitle: Edge Detection under computational constraints: a sublinear approachAbstract:opens in new windowin html    pdfopens in new window
Edge Detection is an important task in image analysis. Various applications require real-time detection of long edges in large noisy images. Motivated by such settings, in this talk we'll address the following question: How well can one detect long edges under severe computational constraints, that allow only a fraction of all image pixels to be processed ? We present fundamental lower bounds on edge detection in this setup, a sublinear algorithm for long edge detection and a theoretical analysis of the inevitable tradeoff between its detection performance and the allowed computational budget. The competitive performance of our algorithm will be illustrated on both simulated and real images. Joint work with Inbal Horev, Meirav Galun, Ronen Basri (Weizmann) and Ery Arias-Castro (UCSD).
TuesdayDec 09, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Helena Nussenzveig LopesTitle:Vortex sheets in domains with boundaryAbstract:opens in new windowin html    pdfopens in new window
Vortex sheets are idealized models for flows undergoing intense shear in a thin region. They are an ubitiquous phenomena in incompressible fluid dynamics. Mathematically, two-dimensional vortex sheets correspond to solutions of the incompressible 2D Euler equations with locally square-integrable velocity and whose vorticity is a bounded Radon measure. Existence of weak solutions with this regularity has been established when the singular part of vorticity has a distinguished sign, however there is very little qualitative information about these solutions. In this talk we examine the interaction between vortex sheets and a material boundary, namely the boundary of the fluid domain. We discuss the behavior of circulation, net force and torque across this material boundary, for vortex sheet flows.
ThursdayDec 04, 201416:30
Room 1
Speaker:Victor PrasolovTitle:TESTAbstract:opens in new windowin html    pdfopens in new window
ThursdayDec 04, 201412:00
Vision and Robotics SeminarRoom 1
Speaker:Shai AvidanTitle:Extended Lucas-Kanade TrackingAbstract:opens in new windowin html    pdfopens in new window
Lucas-Kanade (LK) is a classic tracking algorithm exploiting target structural constraints thorough template matching. Extended Lucas Kanade or ELK casts the original LK algorithm as a maximum likelihood optimization and then extends it by considering pixel object / background likelihoods in the optimization. Template matching and pixel-based object / background segregation are tied together by a unified Bayesian framework. In this framework two log-likelihood terms related to pixel object / background affiliation are introduced in addition to the standard LK template matching term. Tracking is performed using an EM algorithm, in which the E-step corresponds to pixel object/background inference, and the M-step to parameter optimization. The final algorithm, implemented using a classifier for object / background modeling and equipped with simple template update and occlusion handling logic, is evaluated on two challenging data-sets containing 50 sequences each. The first is a recently published benchmark where ELK ranks 3rd among 30 tracking methods evaluated. On the second data-set of vehicles undergoing severe view point changes ELK ranks in 1st place outperforming state-of-the-art methods. Joint work with Shaul Oron (Tel-Aviv University) and Aharon Bar-Hillel (Microsoft).
ThursdayNov 27, 201412:00
Vision and Robotics SeminarRoom 1
Speaker:Fred HamprechtTitle:Joint segmentation and tracking, and new unsolved problemsAbstract:opens in new windowin html    pdfopens in new window

On my last visit in 2012, I posed a number of open questions, including how to achieve joint segmentation and tracking, and how to obtain uncertainty estimates for a segmentation.

Some of these questions we have been able to solve [Schiegg ICCV 2013, Schiegg Bioinformatics  2014, Fiaschi CVPR 2014] and I would like to report on this progress.

Given that I will be at Weizmann for another four months, I will also pose new open questions  on image processing problems that require a combination of combinatorial  optimization and (structured) learning, as an invitation to work together.

ThursdayNov 20, 201412:00
Vision and Robotics SeminarRoom 1
Speaker:Marina AltermanTitle:Vision Through Random Refractive DistortionsAbstract:opens in new windowin html    pdfopens in new window
Random dynamic distortions naturally affect images taken through atmospheric turbulence or wavy water. We show how computer vision can function under such effects, and even exploit them, relying on physical, geometric and statistical models of refractive disturbances. We make good use of distortions created by atmospheric turbulence: distorted multi-view videos lead to tomographic reconstruction of large-scale turbulence fields, outdoors. We also demonstrate several approaches to a 'virtual periscope', to view airborne scenes from submerged cameras: (a) multiple submerged views enable stochastic localization of airborne objects in 3D; (b) the wavy water surface (and hence distortion) can be passively estimated instantly, using a special sensor, analogous to modern astronomic telescopes and (c) we show how airborne moving objects can be automatically detected, despite dynamic distortions affecting the entire scene. In all these works, exploiting physical models in new ways leads to novel imaging tasks, while the approaches we take are demonstrated in field experiments.
WednesdayNov 19, 201411:00
Algebraic Geometry and Representation Theory SeminarRoom 261
Speaker:Ary ShavivTitle:Affine generalized root systems and symmetrizable affine Kac-Moody superalgebrasAbstract:opens in new windowin html    pdfopens in new window
Correspondence between different types of Lie algebras and abstract root systems is a classical and useful tool. In the end of the 19th century E.J. Cartan and W. Killing classified real root systems and finite dimensional complex Lie algebras. They showed the correspondence between reduced root systems and these algebras. I.G. Macdonald classified affine root systems in the beginning of the 1970's. V.G. Kac later realized these systems are, in most cases, real parts of Kac-Moody algebras of affine type. V. Serganova classified generalized root systems in 1996 and showed their almost perfect correspondence to basic classical Lie superalgebras. We defined a generalization we call affine generalized root systems, and studied their correspondence to symmetrizable affine Kac-Moody superalgebras. In the talk we will define the above types of root systems, present their precise correspondences to Lie (super)algebras, and present the main points of our classification of affine generalized root systems.
TuesdayNov 18, 201416:00
Seminar in Geometry and TopologyRoom 261
Speaker:Tony Yue YuTitle:The moduli stack of non-archimedean stable mapsAbstract:opens in new windowin html    pdfopens in new window
Tropical geometry is a powerful technique to study enumerative problems in algebraic geometry. The theory of Berkovich spaces gives us a natural framework to apply tropical techniques in a much wider context. I will begin by explaining motivations from mirror symmetry. Then I will introduce a notion of Khaler structures in non-archimedean geometry. I will explain the construction of the moduli stack of non-archimedean stable maps and an analog of Gromov-Fs compactness theorem in the non-archimedean setting. They are the first steps of enumerative non-archimedean geometry. I will also discuss the tropicalization of the space of stable maps. They are based on arXiv 1401.6452 and 1407.8444. If time permits, I will discuss a related joint work with M. Porta concerning higher non-archimedean stacks and GAGA theorems.
TuesdayNov 18, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Nathan PaldonTitle:Laplace Tidal Equation over a sphere: New solutions derived from an approximate Schrodinger equationAbstract:opens in new windowin html    pdfopens in new window
Little progress was achieved in finding solutions to Laplace Tidal Equations (LTE) over a sphere since these equations were properly formulated by Jean-Pierre Laplace in 1976. For zonally propagating waves the LTE set of Partial Differential Equations was first formulated as an eigenvalue equation by Michael Selwyn Longuet-Higgins in 1968 but this formulation has not yielded explicit expressions for either the phase speeds or the latitude-dependent amplitudes of the waves. In recent years I've developed an exact Schrodinger equation formulation for wave solutions of LTE in Cartesian Coordinates and this formulation could also be applied to spherical coordinates where it yields an approximate Schrodinger eigenvalue equation in. The solutions of this approximate equation yields highly accurate explicit expressions for the zonally propagating waves solutions of LTE. The new wave solutions can be applied in various areas of Dynamical Meteorology and Physical Oceanography, including the construction of new bases for spherical global scale models and the analysis of satellite derived data on the variation of Sea Surface Height Anomalies.
TuesdayNov 18, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Nathan PaldonTitle:Laplace tidal equation over a sphere: New solutions derived from an approximate Schr\H{o}dinger equationAbstract:opens in new windowin html    pdfopens in new window
Little progress was achieved in finding solutions to Laplace Tidal Equations (LTE) over a sphere since these equations were properly formulated by Jean-Pierre Laplace in 1976. For zonally propagating waves the LTE set of Partial Differential Equations was first formulated as an eigenvalue equation by Michael Selwyn Longuet-Higgins in 1968, but this formulation has not yielded explicit expressions for either the phase speeds or the latitude-dependent amplitudes of the waves. In recent years I've developed an exact Schr\H{o}dinger equation formulation for wave solutions of LTE in Cartesian Coordinates and this formulation could also be applied to spherical coordinates where it yields an approximate Schr\H{o}dinger eigenvalue equation in. The solutions of this approximate equation yields highly accurate explicit expressions for the zonally propagating waves solutions of LTE. The new wave solutions can be applied in various areas of Dynamical Meteorology and Physical Oceanography, including the construction of new bases for spherical global scale models and the analysis of satellite derived data on the variation of Sea Surface Height Anomalies.
ThursdayNov 13, 201412:00
Vision and Robotics SeminarRoom 1
Speaker:Barak Zackay Title: Imaging through turbulence a long quest of innovative computational photography in astronomy Abstract:opens in new windowin html    pdfopens in new window

The astronomical community's largest technical challenge is coping with the earths atmosphere.  In this talk, I will present the popular methods for performing scientific measurement from the ground, coping with the time dependant distortions generated by the earths atmosphere.  We will talk about the following topics:

1) Scientific motivation for eliminating the effect of the atmosphere.

2) The statistics of turbulence - the basis for all methods is in deep understanding of the atmospheric turbulence

3) wave-front sensing + adaptive optics -  A way to correct it in hardware.

4) lucky imaging + speckle Interferometry - Ways to computationally extract scientifically valuable data despite the turbulent atmosphere.

TuesdayNov 11, 201411:00
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Prof. Matania Ben-Artzi Title: Spectral Theory And Spacetime Estimates Of Divergence-Type OperatorsAbstract:opens in new windowin html    pdfopens in new window

TuesdayNov 04, 201410:00
Vision and Robotics SeminarRoom 141
Speaker:Rob FergusTitle:Learning to Discover Efficient Mathematical IdentitiesAbstract:opens in new windowin html    pdfopens in new windowNOTE UNUSUAL TIME AND PLACE
In this talk, I will describe how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a set of grammar rules we build trees that combine different rules, looking for branches which yield compositions that are analytically equivalent to a target expression, but of lower computational complexity. However, as the size of the trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we explore two learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neural-network. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation. Joint work with Wojciech Zaremba and Karol Kurach.
TuesdaySep 16, 201416:00
Seminar in Geometry and TopologyRoom 261
Speaker:Alex IsaevTitle:Isolated hypersurface singularities and associated formsAbstract:opens in new windowin html    pdfopens in new window
In our recent articles joint with M. Eastwood and J. Alper, it was conjectured that all rational $GL_n$-invariant functions of forms of degree $d>2$ on complex space $C^n$ can be extracted, in a canonical way, from those of forms of degree $n(d-2)$ by means of assigning every form with nonvanishing discriminant the so-called associated form. While this surprising statement is interesting from the point of view of classical invariant theory, its original motivation was the reconstruction problem for isolated hypersurface singularities, which is the problem of finding a constructive proof of the well-known Mather-Yau theorem. Settling the conjecture is part of our program to solve the reconstruction problem for quasihomogeneous isolated hypersurface singularities. This amounts to showing that a certain system of invariants arising from the Milnor algebras of such singularities is complete, and the conjecture implies completeness in the homogeneous case. In my talk I will give an overview of the recent progress If time permits, I will further discuss the map that assigns a non-degenerate form its associated form. This map is rather natural and deserves attention regardless of the conjecture. For instance, it induces a natural equivariant involution on the space of elliptic curves with non-vanishing j-invariant. Surprisingly, the existence of such an involution appears to be a new fact.
ThursdayAug 28, 201411:00
Geometric Functional Analysis and Probability SeminarRoom 261
Speaker:Laurie FieldTitle:Two-sided radial SLE and length-biased chordal SLEAbstract:opens in new windowin html    pdfopens in new windowFilter test
Models in statistical physics often give measures on self-avoiding paths. We can restrict such a measure to the paths that pass through a marked point, obtaining a "pinned measure". The aggregate of the pinned measures over all possible marked points is just the original measure biased by the path's length. Does the analogous result hold for SLE curves, which appear in the scaling limits of many such models at criticality? We show that it does: the aggregate of two-sided radial SLE is length-biased chordal SLE, where the path's length is measured in the natural parametrisation.
MondayAug 25, 201413:30
Room 1
Speaker:Eviatar ProcacciaTitle:Quenched invariance principle for simple random walk on clusters in correlated percolation models.Abstract:opens in new windowin html    pdfopens in new windowPlease note change in date and room

Quenched invariance principle and heat kernel bounds for random walks on in finite percolation clusters and among i.i.d. random conductances in Zd were proved during the last two decades.The proofs of these results strongly rely on the i.i.d structure of the models and some stochastic domination with respect to super-critical Bernoulli percolation.
Many important models in probability theory and in statistical mechanics, in particular, models which come from real world phenomena, exhibit long range correlations.
In this talk I will present a new quenched invariance principle, for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Zd, d>=2, with long-range correlations. This gives new results for random interlacements in dimension d>=3 at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness (which is believed to coincide with the whole supercritical regime). An essential ingredient of the proof is a new isoperimetric inequality for correlated percolation models.