CMSA

CMSA Math-Science Literature Lecture: From Deep Learning to Deep Understanding
2020-09-28 09:00 - 12:13 (America/New_York) | Virtual
Harry Shum (Tsinghua University)
Title: From Deep Learning to Deep Understanding
Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model, and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike GPT or similar language models learnt from data, it is a multi-turn decision making system which takes user input, updates the belief state, retrieved from the database via symbolic reasoning, and decides how to complete the task with grounded response.
Talk chair: Shing-Tung Yau
Video

9/28/2020 Mathematical Physics Seminar
2020-09-28 11:00 - 12:00 | MA

CMSA Math-Science Literature Lecture: A personal story of the 4D Poincare conjecture
2020-09-28 12:30 - 14:00 | Virtual
Michael Freedman (Microsoft – Station Q)
Title: A personal story of the 4D Poincare conjecture
Abstract: The proof of PC4 involved the convergence of several historical streams. To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.
Talk Chair: Peter Kronheimer
Video

9/29/2020 Computer Science for Mathematicians
2020-09-29 11:30 - 12:30 | MA

9/30/2020 Quantum Matter Seminar
2020-09-30 10:30 - 12:00 | MA

CMSA Math-Science Literature Lecture: Immersions of manifolds and homotopy theory
2020-09-30 12:00 - 13:30 | Virtual
Ralph Cohen (Stanford University)
Title: Immersions of manifolds and homotopy theory
Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest dimension Euclidean space into which every n-manifold embeds or immerses. The embedding question is still very much unsolved, and the immersion question was solved in the 1980’s. I will discuss the homotopy theoretic techniques involved in the solution of this problem, and contributions in the 60’s, 70’s and 80’s of Massey, Brown, Peterson, and myself. I will also discuss questions regarding the best embedding and immersion dimensions of specific manifolds, such has projective spaces. Finally, I will end by discussing more modern approaches to studying spaces of embeddings due to Goodwillie, Weiss, and others. This talk will be geared toward a general mathematical audience.
Talk chair: Michael Hopkins
Video

10/1/2020 Quantum Matter seminar
2020-10-01 10:30 - 12:00 | MA

CMSA Math-Science Literature Lecture: Birational geometry
2020-10-02 10:45 - 12:15 | Virtual
Vyacheslav V. Shokurov (Johns Hopkins University)
Title: Birational geometry
Abstract: About main achievements in birational geometry during the last fifty years.
Talk chair: Caucher Birkar
Video

CMSA Math-Science Literature Lecture: Kunihiko Kodaira and complex manifolds
2020-10-05 08:00 - 09:30 | Virtual
Yujiro Kawamata (University of Tokyo)
Title: Kunihiko Kodaira and complex manifolds
Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions. After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces. Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts.
Talk chair: Baohua Fu
Video

10/05/2020 Math Physics Seminar
2020-10-05 10:30 - 12:00 | MA

4/15/2020 Quantum Matter seminar
2020-10-05 10:30 - 12:00 | MA

10/6/2020 Computer Science for Mathematicians
2020-10-06 11:30 - 12:30 | MA

10/7/2020 Quantum Matter Seminar
2020-10-07 10:30 - 12:00 | MA

10/8/2020 Quantum Matter Seminar
2020-10-08 10:30 - 12:00 | MA

Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers
2020-10-14 09:00 - 10:00 | MA
Speaker: Gil Kalai (Hebrew University and IDC Herzliya)
Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers
Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to

a) My general argument “against” quantum computers,
b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
Relevant papers:
Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.wordpress.com/2019/11/stat-quantum2.pdf
Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.wordpress.com/2020/08/laws-blog2.pdf
Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.wordpress.com/2019/09/main-pr.pdf

10/14/2020 Quantum Matter Seminar
2020-10-14 10:30 - 12:00 | MA

10/14/2020 RM&PT Seminar
2020-10-14 14:00 - 15:00 | MA

Triple Descent and a Fine-Grained Bias-Variance Decomposition
2020-10-14 15:00 - 16:00 | MA
Speaker: Jeffrey Pennington, Google Brain
Title: Triple Descent and a Fine-Grained Bias-Variance Decomposition
Abstract: Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, striking a balance between simpler models that exhibit high bias and more complex models that exhibit high variance of the predictive function. However, such a simple trade-off does not adequately describe the behavior of many modern deep learning models, which simultaneously attain low bias and low variance in the heavily overparameterized regime. Recent efforts to explain this phenomenon theoretically have focused on simple settings, such as linear regression or kernel regression with unstructured random features, which are too coarse to reveal important nuances of actual neural networks. In this talk, I will describe a precise high-dimensional asymptotic analysis of Neural Tangent Kernel regression that reveals some of these nuances, including non-monotonic behavior deep in the overparameterized regime. I will also present a novel bias-variance decomposition that unambiguously attributes these surprising observations to particular sources of randomness in the training procedure.

10/15/2020 Quantum Matter Seminar
2020-10-15 10:30 - 12:00 | Virtual

10/19/2020 Math Physics Seminar
2020-10-19 10:30 - 11:30 | MA

10/20/2020 Computer Science for Math
2020-10-20 11:30 - 12:30 | MA

10/21/2020 Quantum Matter Seminar
2020-10-21 10:30 - 12:00 | MA

10/22/2020 Quantum Matter Seminar
2020-10-22 10:30 - 12:00 | MA

10/27/2020 Computer Science for Mathematicians
2020-10-27 11:30 - 12:30 | MA

10/28/2020 Strongly Correlated Quantum Materials
2020-10-28 10:30 - 12:00 | MA

10/28/2020 RM&PT seminar
2020-10-28 14:00 - 15:00 | MA

Generalization bounds for rational self-supervised learning algorithms, or "Understanding generalizations requires rethinking deep learning"
2020-10-28 15:00 - 16:00 | MA
Speakers: Boaz Barak and Yamini Bansal, Harvard University Dept. of Computer Science
Title: Generalization bounds for rational self-supervised learning algorithms, or “Understanding generalizations requires rethinking deep learning”
Abstract: The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples. Modern deep learning algorithms typically have large generalization gaps, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous. In this talk we will see a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a complex representation of the (label free) training data, and then fitting a simple (e.g., linear) classifier to the labels. Such classifiers have become increasingly popular in recent years, as they offer several practical advantages and have been shown to approach state-of-art results. We show that (under the assumptions described below) the generalization gap of such classifiers tends to zero as long as the complexity of the simple classifier is asymptotically smaller than the number of training samples. We stress that our bound is independent of the complexity of the representation that can use an arbitrarily large number of parameters. Our bound assuming that the learning algorithm satisfies certain noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely (and sometimes provably) hold across many standard architectures. We complement this result with an empirical study, demonstrating that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and BigBiGAN. The talk will not assume any specific background in machine learning, and should be accessible to a general mathematical audience. Joint work with Gal Kaplun.

10/29/2020 Quantum Matter Seminar
2020-10-29 10:30 - 12:00 | MA

11/9/2020 Math-Physics Seminar
2020-11-02 10:30 - 11:30 | MA

11/2/2020 Math-Physics Seminar
2020-11-02 10:30 - 11:30 | MA
