Past Events

The Big Bang of Numbers: How to Build the Universe Using Only Math

Manil Suri (University of Maryland Baltimore County)

Picture yourself at a starting point before anything exists - no matter, no cosmos, not even empty space. Your task is to create the universe, but all you have to work with is, quite literally, 'nothing.' How do you proceed? 

Traditionally, you might expect physics or religion to try and answer this question, but what if you turn to mathematics instead? The resulting thought experiment gives an insightful new way of looking at mathematics - one in which you build the numbers out of nothing, and then, through a playful progression of mathematical creation, are able to arguably design everything else in the universe!

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Postcard

Poster about November 3 conference that says "How to create the universe out of nothing (Math version)"

AI Model Inspector: Towards Holistic Adversarial Robustness for Deep Learning

Industrial Problems Seminar

Pin-Yu Chen (IBM)

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In this talk, I will share my research journey toward building an AI model inspector for evaluating, improving, and exploiting adversarial robustness for deep learning. I will start by providing an overview of research topics concerning adversarial robustness and machine learning, including attacks, defenses, verification, and novel applications. For each topic, I will summarize my key research findings, such as (i) practical optimization-based attacks and their applications to explainability and scientific discovery; (ii) Plug-and-play defenses for model repairing and patching; (iii) attack-agnostic robustness assessment; and (iv) data-efficient transfer learning via model reprogramming. Finally, I will conclude my talk with my vision of preparing deep learning for the real world and the research methodology of learning with an adversary.

3-D reconstruction in macro- and micro-worlds: Challenges and Solutions

Data Science Seminar

Yunpeng Shi (Princeton University)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

In this talk I will discuss two problems of 3-D reconstruction: structure from motion (SfM) and cryo-electron microscopy (cryo-EM) imaging, which respectively solves the 3-D structure of, for example, architectures and protein molecules. My talk will be focused on two mathematical subproblems respectively in SfM and cryo-EM: robust group synchronization and image covariance estimation, and their extensions and applications. Both problems are closely related to low-rank approximations of certain matrices, but they are also challenging in very different ways.

In the first half of the talk, I will introduce the group synchronization problem given highly corrupted data, and its applications in SfM. In the meantime, a fast and accurate solution that leverages the cycle-consistency constraints will be discussed.

In the second half, I will focus on the covariance estimation problem given high-resolution images with varying contrast, and its applications in cryo-EM image restoration. Our method of covariance estimation achieves several order of magnitude speed up compared to the previous methods. Based on the fast covariance solver, I will introduce our image restoration method, called fast covariance Wiener filtering, that is completely ab-initio and unsupervised. Our method conducts a non-blind image deconvolution, image contrast estimation and image denoising in a joint way.

Navigating early career steps in industry

Industrial Problems Seminar

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

Nicole Bridgland (Fulcrum)

This talk will be about my path from PhD program to industry. My focus will be the types of jobs I’ve decided between and what I’ve learned in the process, but I’ll also talk about the types of problems I’ve worked on, and the types of preparation I found helpful. This talk will be directed at graduate students who are interested in what a non-research-oriented mathematical career might look like, either for themselves or for their students.

Does the Data Induce Capacity Control in Deep Learning?

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

Accepted statistical wisdom suggests that larger the model class, the more likely it is to overfit the training data. And yet, deep networks generalize extremely well. The larger the deep network, the better its accuracy on new data. This talk seeks to shed light upon this apparent paradox.

We will argue that deep networks are successful because of a characteristic structure in the space of learning tasks. The input correlation matrix for typical tasks has a peculiar (“sloppy”) eigenspectrum where, in addition to a few large eigenvalues (salient features), there are a large number of small eigenvalues that are distributed uniformly over exponentially large ranges. This structure in the input data is strongly mirrored in the representation learned by the network. A number of quantities such as the Hessian, the Fisher Information Matrix, as well as others activation correlations and Jacobians, are also sloppy. Even if the model class for deep networks is very large, there is an exponentially small subset of models (in the number of data) that fit such sloppy tasks. This talk will demonstrate the first analytical non-vacuous generalization bound for deep networks that does not use compression. We will also discuss an application of these concepts that develops new algorithms for semi-supervised learning.

References

  1. Does the data induce capacity control in deep learning?. Rubing Yang, Jialin Mao, and Pratik Chaudhari. [ICML '22] https://arxiv.org/abs/2110.14163
  2. Deep Reference Priors: What is the best way to pretrain a model? Yansong Gao, Rahul Ramesh, Pratik Chaudhari. [ICML '22] https://arxiv.org/abs/2202.00187

Pratik Chaudhari is an Assistant Professor in Electrical and Systems Engineering and Computer and Information Science at the University of Pennsylvania. He is a member of the GRASP Laboratory. From 2018-19, he was a Senior Applied Scientist at Amazon Web Services and a Postdoctoral Scholar in Computing and Mathematical Sciences at Caltech. Pratik received his PhD (2018) in Computer Science from UCLA, his Master's (2012) and Engineer's (2014) degrees in Aeronautics and Astronautics from MIT. He was a part of NuTonomy Inc. (now Hyundai- Aptiv Motional) from 2014—16. He received the NSF CAREER award and the Intel Rising Star Faculty Award in 2022.

Photo: https://pratikac.github.io/img/photo.jpg

Navigating a Career Path, a Case Study

Industrial Problems Seminar

Paula Dassbach (Medtronic)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

What do you want to be when you grow up? It's a question that many of us are asked from a young age. We start with dreams of being a ballerina or fireman but seldom stay on this path. This talk is to share my experience of young aspirations, educational decisions, and choices that ultimately led to a career that is immensely fulfilling. I will also share some insight into my current role and some of the projects you might work on in a medical device company. As is likely clear, I will not be presenting an industrial problem, but instead the problem that we all face and navigate. My hope is that sharing my experience can provide some tools to help you get closer to the answer of the question that many of us are still asking ourselves: 'What do I want to be when I grow up?'

Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness

Data Science Seminar

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. We will discuss the solution procedure and showcase our method on a new fair data science model for estimating fair and robust covariance matrices in the spirit of the Tyler's M-estimator (TME) model. This is joint work with Dr. Gilad Lerman and Dr. Shuzhong Zhang.

Capacity Planning for the Cloud

Industrial Problems Seminar

Alex Gutierrez (Google Inc.)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

Abstract: Cloud computing is still a young and extremely fast growing area with. In this talk I will give a high level overview of (some of!) the interesting problems that arise when planning capacity for a service that is designed to be "elastic" from a customer perspective.

Research Problems in Quantitative Finance

John Goes (GMO)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

This talk will be a high level taxonomy of quantitative research challenges in financial markets, with a particular focus on examples in fixed income (bond) markets. I will also discuss my general experience as a mathematician in the finance industry.

Multiscale analysis of manifold-valued curves

Nir Sharon (Tel Aviv University)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

A multiscale transform is a standard signal and image processing tool that enables a mathematically hierarchical analysis of objects. Customarily, the first scale corresponds to a coarse representation, and as scales increase, so is the refinement level of the entity we represent. This multiscale approach introduces a dynamic and flexible framework with many computational and approximation advantages. In this talk, we introduce a multiscale analysis that aims to represent manifold-valued curves. First, we will present the settings and our multiscale construction. Then, we will show some of the theoretical properties of our multiscale representation. Finally, we will conclude with several numerical examples illustrating how to apply our multiscale method for various data processing techniques.