Academic Report of School of Mathematical Sciences [2026] No. 089

(Series Report for High-Level University Construction No. 1348)

Title：Shape Regression and Learning: Distributional Robustness and Gradient Flows

Speaker：Assistant Professor Yong Sheng Soh (National University of Singapore)

Time：16:30-17:30, Sept. 22, 2026

Location：Room 601, Huiyan Building, Yuehai Campus

Abstract: A broad range of learning problems can be abstractly viewed as performing regression of a suitably parameterized function to data.  When these functions are viewed via its level sets, these learning tasks can be equivalently viewed as instances of shape regression tasks.  In this talk, we will examine learning tasks via the perspective of shape regression tasks.  This allows us to use geometric ideas to understand phenomena that are of interest from a practitioner's perspective. We characterize the optimal level sets given the underlying data distribution in settings where the level sets are required to be convex bodies as well as star bodies.  We discuss how incorporating distributional robustness (in our learned model) affects the optimal level sets.  Finally, we discuss gradient flows over the space of shapes we learn as a means of understanding the behavior of learning algorithms.

Speaker Profile：Yong Sheng Soh is an Assistant Professor at the Department of Mathematics, National University of Singapore.  He is broadly interested in mathematical optimization, with a focus on problems arising from data analysis.  He obtained his PhD in Applied and Computational Mathematics at the California Institute of Technology.  Prior to joining NUS, he was a Research Scientist at the Institute for High Performance Computing at the Agency for Science, Technology and Research (A*STAR), Singapore.

Faculty and students are welcome to attend!

Invited by: Hu Xiaoyin

School of Mathematical Sciences

September 11, 2026