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Andrea Montanari  – Stanford University

Wednesday, October 8th, 2025

Zoom opens: 10:30AM DST

Seminar begins: 10:45AM DST

 Overparameterized Systems: From Smale 17th problem to neutral networks

Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension.  Near-minima of random functions also play an important role in

high-dimensional statistics and machine learning, where minimizing an empirical risk function is the method of choice for learning a statistical model  from noisy data.

I will review some surprising empirical phenomena in modern machine learning, focusing in particular on overfitting and generalization. I will explain how tools from spin glasses and random matrix theory can be used to characterize these phenomena in simple models, and clarify them.

[Based on joint works with Kiana Asgari, Basil Saeed, Eliran Subag, Pierfrancesco Urbani]