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BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations
Symmetry-preserving machine learning for computer vision, scientific computing, and distribution learning
Symmetry-preserving machine learning for computer vision, scientific computing, and distribution learning
Organizers
Speaker
Wei Zhu
Time
Thursday, November 17, 2022 10:00 AM - 11:30 AM
Venue
1129B
Online
Zoom 537 192 5549
(BIMSA)
Abstract
Symmetry is ubiquitous in machine learning and scientific computing. Robust incorporation of symmetry prior into the learning process has shown to achieve significant model improvement for various learning tasks, especially in the small data regime. In the first part of the talk, I will explain a principled framework of deformation-robust symmetry-preserving machine learning. The key idea is the spectral regularization of the (group) convolutional filters, which ensures that symmetry is robustly preserved in the model even if the symmetry transformation is “contaminated” by nuisance data deformation. In the second part of the talk, I will demonstrate how to incorporate additional structural information (such as group symmetry) into generative adversarial networks (GANs) for data-efficient distribution learning. This is accomplished by developing new variational representations for divergences between probability measures with embedded structures. We study, both theoretically and empirically, the effect of structural priors in the two GAN players. The resulting structure-preserving GAN is able to achieve significantly improved sample fidelity and diversity—almost an order of magnitude measured in Fréchet Inception Distance—especially in the limited data regime.
Speaker Intro
Wei Zhu is an Assistant Professor at the Department of Mathematics and Statistics, University of Massachusetts Amherst. He received his B.S. in Mathematics from Tsinghua University in 2012, and Ph.D. in Applied Math from UCLA in 2017. Before joining UMass, he worked as a Research Assistant Professor at Duke University from 2017 to 2020. Wei is interested in developing theories and algorithms in statistical learning and applied harmonic analysis to solve problems in machine learning, inverse problems, and scientific computing. His recent research is particularly focused on exploiting and discovering the intrinsic structure and symmetry within the data to improve the interpretability, stability, reliability, and data-efficiency of deep learning models.