Lecture 1 (Public lecture): The mathematics of large machine learning models
Date and Time: Monday, 11 August 2025, 16:30 to 17:30
Lecture 2: Overparametrized models: linear theory and its limits
Date and Time: Tuesday, 12 August 2025, 11:15 to 12:30
Lecture 3: Dynamical phenomena in nonlinear learning
Date and Time: Wednesday, 13 August 2025, 11:15 to 12:30
Abstract: The success of modern AI models defies classical theoretical wisdom. Classical theory recommended the use of convex optimization, and yet AI models learn by optimizing highly non-convex function. Classical theory prescribed to control model complexity and yet AI models are very complex, so complex that they often memorize the training data. Classical wisdom recommends a careful and interpretable choice of model architecture, and yet modern architectures rarely offer a parsimonious representation of a target distribution class.
The discovery that learning can take place in completely unexpected scenario poses beautiful conceptual challenges. I will try to survey recent work towards addressing them.
About the speaker: Andrea Montanari is the John D. and Sigrid Banks Professor in Statistics and Mathematics at Stanford University. He received a Laurea degree in Physics in 1997, and a Ph.D. in Physics in 2001 (both from Scuola Normale Superiore in Pisa, Italy). He has been post-doctoral fellow at Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (LPTENS), Paris, France, and the Mathematical Sciences Research Institute, Berkeley, USA. From 2002 to 2010 he was Chargé de Recherche (with Centre National de la Recherche Scientifique, CNRS) at LPTENS. He joined Stanford in 2006, and from 2006 to 2023 has been a faculty in Departments of Electrical Engineering and Statistics. From 2021 to 2023, he was the Robert and Barbara Kleist Professor in the School of Engineering.
He was awarded the CNRS bronze medal for theoretical physics in 2006, the National Science Foundation CAREER award in 2008, the Okawa Foundation Research Grant in 2013, the James L. Massey Award of the Information Theory Society in 2016, and the Le Cam Prize of the French Statistical Society in 2020. He received the ACM SIGMETRICS best paper award in 2008 and the Applied Probability Society Best Publication Award in 2015 He was elevated to IEEE Fellow in 2017 and IMS Fellow in 2020. He was an invited sectional speaker at the 2020 International Congress of Mathematicians and an IMS Medallion lecturer for the 2020 Bernoulli-IMS World Congress.
These lectures are part of the program Data Science: Probabilistic and Optimization Methods II.