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BIMSA-清华机器学习和微分方程讨论班
Approximation Theory of Deep Learning from the Dynamical Systems Viewpoint
Approximation Theory of Deep Learning from the Dynamical Systems Viewpoint
演讲者
Qianxiao Li
时间
2022年12月08日 10:00 至 11:30
地点
Online
线上
Zoom 537 192 5549
(BIMSA)
摘要
In this talk, we present some recent results on the approximation theory of deep learning from the dynamical systems viewpoint. This viewpoint highlights a key new aspect of modern deep learning, namely the presence of compositional/dynamical structures. We first discuss mathematical frameworks to study the capacity of deep feed-forward architectures for function approximation. Next, we discuss approximation theories of modern architectures for sequence modelling, including recurrent neural networks, dilated convolutional networks (WaveNet), and encoder-decoder structures. These analyses reveal some interesting connections between approximation, dynamics, memory, sparsity and low rank phenomena that may guide the practical selection and design of these network architectures.
演讲者介绍
Qianxiao Li is an assistant professor in the Department of Mathematics, National University of Singapore. He graduated with a BA in mathematics from University of Cambridge and a PhD in applied mathematics from Princeton University. His research interests include the interplay of machine learning and dynamical systems, stochastic gradient algorithms and the development of data-driven methods for solving problems in the physical sciences. He is a recipient of the NRF fellowship in 2021.