Upcoming Events

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.

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?'

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

Lecture: Nicole Bridgland

Industrial Problems Seminar

Nicole Bridgland (Fulcrum)

Lecture: Yunpeng Shi

Data Science Seminar

Yunpeng Shi (Princeton University)

Lecture: Morgan Turner

Data Science Seminar

Morgan Turner (University of Minnesota, Twin Cities)

Lecture: Pin-Yu Chen 

Industrial Problems Seminar

Pin-Yu Chen (IBM)

Lecture: Stanley Osher

Data Science Seminar

Stanley Osher (University of California, Los Angeles)

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!

Register

Postcard

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

2022 Field of Dreams Conference

Register for the conference

Organizers

The Field of Dreams Conference introduces potential graduate students to graduate programs in the mathematical sciences at Alliance schools as well as professional opportunities in these fields. Scholars spend time with faculty mentors from the Alliance schools, get advice on graduate school applications, and attend seminars on graduate school preparation and expectations as well as career seminars.

Tentative list of speakers

  • Federico Ardila-Mantilla (San Francisco State University) (confirmed)
  • Kimberly Sellers (University of Pennsylvania) (confirmed)
  • Michael Young (Carnegie Mellon University) (confirmed)
Institute for Mathematics and its Applications and Math Alliance logos
Poster for Field of Dreams 2022

Poster