Speaker: Hongkai Zhao, Duke
Title: "Mathematical and Computational Understanding of Neural Networks: From Representation to Learning and From Shallow to Deep Abstract."
Abstract:
In this talk I will present some understanding of a few basic mathematical and computational questions for neural networks, as a particular form of nonlinear representation, and show how the network structure, activation function, and parameter initialization can affect its approximation properties and the learning process. In particular, we demonstrate the ill-conditioning effect for both representation and gradient based optimization. We propose structured and balanced multi-component and multi-layer neural networks (MMNN) using sine as the activation function with an initialization scaling strategy. At the end, I will discuss a few issues and challenges when using neural networks to solve partial differential equations.
Bio:
Hongkai Zhao is the Ruth F. DeVarney Distinguished Professor and Chair of the Mathematics Department at Duke University. He obtained his Ph.D in Mathematics from UCLA in 1996. His research interest includes scientific computing, numerical analysis, inverse problems and imaging, and scientific machine learning.
In person attendance at this seminar is only open to Columbia University affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.
