Invited Talk

Towards a Mathematical Theory of Machine Learning

Weinan E

2022 Invited Talk

Abstract

Given a machine learning model, what are the class of functions that can be approximated by this particular model efficiently, in the sense that the convergence rate for the approximation, estimation and optimization errors does not deteriorate as dimensionality goes up? We address this question for three classes of machine learning models: The random feature model, two-layer neural networks and the residual neural network model. During the process, we will also summarize the current status of the theoretical foundation of deep learning, and discuss some of the key open questions.

Speaker

Weinan E

Weinan E is a professor at the Center for Machine Learning Research (CMLR) and the School of Mathematical Sciences at Peking University. He is also a professor at the Department of Mathematics and Program in Applied and Computational Mathematics at Princeton University. His main research interest is numerical algorithms, machine learning and multi-scale modeling, with applications to chemistry, material sciences and fluid mechanics. Weinan E was awarded the ICIAM Collatz Prize in 2003, the SIAM Kleinman Prize in 2009 and the SIAM von Karman Prize in 2014, the SIAM-ETH Peter Henrici Prize in 2019, and the ACM Gordon-Bell Prize in 2020. He is a member of the Chinese Academy of Sciences, a fellow of SIAM, AMS and IOP. Weinan E is an invited plenary speaker at ICM 2022. He has also been an invited speaker at ICM 2002, ICIAM 2007 as well as the AMS National Meeting in 2003. In addition, he has been an invited speaker at APS, ACS, AIChe annual meetings, the World Congress of Computational Mechanics, and the American Conference of Theoretical Chemistry.

Video

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