Events

Past Event

Distinguished Colloquium Series in Interdisciplinary and Applied Mathematics

April 3, 2019
4:30 PM - 5:30 PM
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Schapiro CEPSR, 530 W. 120 St., New York, NY 10027 Davis Auditorium (Room 412, 4th Floor)
Prof. Weinan E Princeton University Title: “Mathematical Theory of Neural Network-based Machine Learning” Abstract: I will give an overview of our current understanding of the mathematical theory for neural network-based machine learning. The focus will be on the three most basic questions. (1) Why things seem to work in very high dimensions? (2) Why things seem to work in the highly over-parametrized regime where traditional machine learning theory would suggest overfitting? (3) Why simple minded gradient decent algorithms seem to work reasonable well for the seemingly very complex optimization tasks? I will discuss the representation of functions in high dimension, optimal a priori estimates of the error, and analysis of the gradient decent based algorithms. Advanced issues, such as shallow vs deep networks, GD vs SGD, will also be touched upon if time permits Biography: Weinan E received his Ph.D. from UCLA in 1989. After being a visiting member at the Courant Institute of NYU and the Institute for Advanced Study at Princeton, he joined the faculty at NYU in 1994. He is now a professor of mathematics at Princeton University, a position he has held since 1999. Weinan E’s work centers around multi-scale modeling and machine learning. Most recently he has been working on integrating machine learning and physical modeling to solve problems in traditional areas of science and engineering, such as molecular dynamics, PDEs, control theory, etc. Weinan E is the recipient of the SIAM R. E. Kleinman Prize, von Karman Prize, Peter Henrici Prize (to be awarded at ICIAM 2019), and the ICIAM Collatz Prize. He is a member of the Chinese Academy of Sciences, a fellow of the American Mathematical Society, a SIAM fellow and a fellow of the Institute of Physics.

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APAM Department
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