Symmetry-preserving machine learning for computer vision, scientific computing, and distribution learning

Applied and Computational Mathematics Seminar
Monday, March 7, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Location (note: Zoom, not Bluejeans)
Prof. Wei Zhu – UMass Amherst
Molei Tao

Please Note: Note the talk will be hosted by Zoom, not Bluejeans any more.

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.