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Upcoming Seminars

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.
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.
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 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:, a website that offers provably fair solutions to everyday problems; and, 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 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.
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.

ThursdayJul 06, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Tammy Riklin-Raviv Title:TBNAbstract:opens in new windowin html    pdfopens in new window
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.