Colloquium

Abstract

 A century ago, breakthroughs like relativity and quantum mechanics emerged from or developed alongside rigorous mathematical theories. Today's AI revolution presents a stark contrast: progress remains predominantly empirical while mathematical theory lags significantly behind. In this talk, I will share perspectives on current efforts to establish theoretical foundations for deep learning, drawing from my personal research experiences. We will examine the strengths and limitations of various approaches---including toy models, phenomenological models, and conditional-theory approaches---and explore why certain methods succeed in capturing specific behaviors while failing to provide comprehensive understanding. The talk concludes by highlighting opportunities for the mathematics community to contribute to advancing the theoretical foundations of deep learning.

Biography

Weijie Su is an Associate Professor at the Wharton Business School and, by courtesy, in the Departments of Mathematics and Computer and Information Science at the University of Pennsylvania. He is a co-director of Penn Research in Machine Learning (PRiML) Center. Prior to joining Penn, he received his Ph.D. and bachelor’s degree from Stanford University in 2016 and Peking University in 2011, respectively. His research interests span the mathematical foundations of generative AI, privacy-preserving machine learning, optimization, mechanism design, and high-dimensional statistics. He serves as an associate editor of the Journal of Machine Learning Research, Operations Research, Journal of the American Statistical Association, Foundations and Trends in Statistics, and Journal of the Operations Research Society of China. He is a Fellow of the IMS. His work has been recognized with several awards, such as the Stanford Anderson Dissertation Award, NSF CAREER Award, Sloan Research Fellowship, IMS Peter Hall Prize, SIAM Early Career Prize in Data Science, ASA Noether Early Career Award, and the ICBS Frontiers of Science Award in Mathematics.