Mini courses

Prof. Jean Barbier

International Center for Theoretical Physics (ICTP)

Information theory and mean-field theory of high-dimensional Bayesian inference

Abstract: Mean field theory is a powerful method originally developed in statistical mechanics to study complex systems with many interacting components. Advanced mean-field techniques have been successfully applied beyond physics, particularly in inference problems in areas such as signal processing, machine learning, and information theory. This course will explore physical models related to Bayesian inference, using the language of statistical mechanics to describe them. It will illustrate how mean field theory applies to modern inference and learning problems, uch as matrix factorization/principal component analysis, regression tasks, and the perceptron neural network.

Prof. Marylou Gabrié
École Normale Supérieure (ENS)

Generative modeling and sampling using transport maps

Abstract: In this mini-course we will discuss the modeling and sampling of high-dimensional probability distributions in the current context of highly-effective generative models. We will focus in particular on generative models based on transport maps: normalizing flows, diffusion models and flow matchings.

Prof. Alessandro Ingrosso

Radboud University

Dynamics and learning in recurrent neural networks

Abstract: In this short course, we will employ a Statistical Mechanics perspective to study how deterministic and stochastic recurrent networks can be used as computational devices. After a short introduction to the theory of spin glasses and the replica method, we will study the equilibrium and dynamical properties of attractor network models. We will then move into the realm of continuous-time rate-based models, which play a key role in modern computational neuroscience. We will use dynamical mean field theory to describe their dynamical behavior in terms of chaotic transition and input-dependent chaos suppression. If time permits, we will discuss recent work analyzing the dimensionality of time-dependent trajectories, a crucial point in the ongoing endeavor of building a theory of learning in recurrent networks.

Prof. Silvia Villa

Università di Genova

Optimization methods for machine learning

Abstract: This course  focuses on convex optimization techniques fundamental to modern machine learning. It covers key optimization algorithms, including gradient descent, stochastic gradient descent, proximal methods, and acceleration techniques, with a particular emphasis on their theoretical foundations and practical applications. The course also explores the role of gradient-based optimization in training neural networks.