ABSTRACT:

Generative models, in which one trains an algorithm to generate fake samples ‘similar’ to those of a data base, is a major new direction developed in machine learning in the recent years. In particular, generative models based on diffusion equations have become the state of the art for image generation. However, the reasons for this spectacular technological success are not well understood, and neither are its limitations. While the theory of stochastic processes asserts that a perfect guidance of the diffusion should lead back to samples of the database, this “condensation” phenomenon is avoided in practice by the “imperfection” of the algorithms used in machine learning.

After an introduction to this topic, the talk will explain how statistical physics concepts allow to analyze generative diffusion in the high-dimensional limit, where data are formed by a large number of variables.

BIO:

Marc Mezard is a Professor of Theoretical Physics. He studied physics at Ecole normale supérieure in Paris and obtained his PhD in 1984. Hired at CNRS in Paris, he was Research Director in Université Paris Sud starting in 2012. In 2022 he became Director of Ecole normale supérieure, and  then joined Bocconi University as a professor, in the newly created department of computational sciences.  His work focuses on statistical physics of disordered systems, with applications in various fields like information theory, computer science, machine learning, biophysics.

Mezard is interested in the emergent phenomena in complex systems with many interacting “atoms”, (that could be for instance agents on a market, information bits, or molecules are different or live in different environments.) The statistical physics of disordered systems that he contributes to develop finds applications in various branches of science – biology, economics and finance, information theory, computer science, statistics, signal processing. In recent years his research has focused on information processing in neural networks, machine learning and deep networks. He is particularly interested in the theoretical impact of data structure on learning strategies and generalization performance.