The tutorial sessions will be held in the Coordinated Science Lab on September 15, 2026.
Prof. Mikhail Belkin
School of Computing, Information, and Data Sciences, University of California San Diego
BIO:
Mikhail Belkin received his Ph.D. in 2003 from the Department of Mathematics at the University of Chicago. His research interests are in theory and applications of machine learning and data analysis. Some of his well-known work includes widely used Laplacian Eigenmaps, Graph Regularization and Manifold Regularization algorithms, which brought ideas from classical differential geometry and spectral analysis to data science. His recent work has been concerned with understanding remarkable mathematical and statistical phenomena observed in deep learning. This empirical evidence necessitated revisiting some of the basic concepts in statistics and optimization. One of his key recent findings is the “double descent” risk curve that extends the textbook U-shaped bias-variance trade-off curve beyond the point of interpolation.
Mikhail Belkin is a recipient of a NSF Career Award and a number of best paper and other awards. He has served on the editorial boards of the Journal of Machine Learning Research, IEEE Pattern Analysis and Machine Intelligence and SIAM Journal on Mathematics of Data Science.
Title: Fit without fear: on some remarkable mathematical phenomena of deep learning
Abstract: Generalization is the central topic of machine learning and data science. What patterns can be learned from observations and how can we be sure that they extend to future, not yet seen, data? In this tutorial I will outline the arc of some recent developments in current understanding (or lack thereof) of generalization in machine learning. These changes occurred largely due to empirical findings in neural networks which necessitated revisiting theoretical foundations of generalizations. The two key themes are interpolation, and its sibling, over-parameterization. Interpolation corresponds to fitting data, even noisy data, exactly. Over-parameterization enables interpolation and provides flexibility to select a right interpolating model. I will also discuss how over-parameterization leads to easy optimization through local methods such as SGD. Finally I discuss some developments in how modern systems perform supervised dimensionality reduction or feature learning.
Prof. Hoi Nguyen
Department of Mathematics, The Ohio State University
Bio:
Hoi H. Nguyen is a professor of mathematics at The Ohio State University. He received his Ph.D. from Rutgers University in 2010. His research interests include random matrix theory, probability, and combinatorics. He was a Von Neumann Fellow and a Simons Fellow, and he received an NSF career award.
Title: Random matrices: from non-asymptotic estimates to universality of spectra and cokernels
Abstract: Random matrix theory is a rich area with numerous connections and applications across mathematics and related fields. In this tutorial, I will survey several recent developments and useful techniques in the subject, focusing primarily on non-asymptotic estimates and universality phenomena for spectra and cokernels of random matrices.