When: Feb 01 2024 @ 1:30 PM
Where: Olin 305

Location:Olin 305

When: February 1st at 1:30 p.m.

Title: Symmetry-Preserving Machine Learning: Theory and Applications

Abstract: Symmetry is prevalent in a variety of machine learning (ML) and scientific computing tasks, including computer vision and computational modeling of physical and engineering systems. Empirical studies have demonstrated that ML models designed to integrate the intrinsic symmetry of their tasks often exhibit substantially improved performance. Despite extensive theoretical and engineering advancements in the domain of “symmetry-preserving ML”, several critical questions remain unaddressed, presenting unique challenges and opportunities for applied mathematicians.

Firstly, real-world symmetries rarely manifest perfectly and are typically subject to various deformations. Therefore, a pivotal question arises: Can we effectively quantify and enhance the robustness of models to maintain an “approximate” symmetry, even under imperfect symmetry transformations? Secondly, although empirical evidence suggests that symmetry-preserving ML models typically require fewer training data to achieve equivalent accuracy, there is a need for more precise and rigorous quantification of this reduction in sample complexity attributable to symmetry preservation. Lastly, considering the non-convex nature of optimization in modern ML, can we ascertain whether algorithms like gradient descent can guide symmetry-preserving models to indeed converge to objectively better solutions compared to their generic counterparts, and if so, to what degree?

In this talk, I will present several of my research projects addressing these intriguing questions. Surprisingly, the answers are not as straightforward as one might assume and, in some cases, are counterintuitive. If time permits, I will also discuss our recent efforts on extending these results to ML-assisted structure-preserving computational models for complex physical systems.

Bio: 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’s research focuses on the mathematical underpinnings of data science and machine learning (ML). He is particularly interested in understanding and leveraging the inherent geometric structures of the underlying systems, aiming to develop novel and efficient ML models and computational algorithms with provable guarantees. Wei is a recipient of the 2024 Air Force Young Investigator Award, and his research is supported by AFOSR, NIH, and NSF.

Zoom link: https://wse.zoom.us/j/94601022340