I work on the mathematical foundations of machine learning, especially the training dynamics of neural networks and the reliability of generative models.
Since September 2025, I have been a postdoctoral researcher at École Polytechnique Fédérale de Lausanne (EPFL), working with Lénaïc Chizat and Maria Colombo. On 1 February 2027, I will join CNRS at CY Cergy Paris Université.
I completed my PhD in December 2024 under the supervision of Julien Reygner (École des Ponts) and Philippe Moireau (École Polytechnique / Inria).
Research interests
One part of my research concerns scaling limits of residual neural networks and how architecture, network size and data influence training. I am interested in connecting mathematical descriptions from machine learning and statistical physics, and in what they can tell us about finite networks and generalisation.
I also work on score-based diffusion models and stochastic filtering, with a focus on stability and approximation guarantees for sampling algorithms. This draws on stochastic analysis, optimal transport and mean-field particle methods, including my earlier work on stochastic control and biological modelling. Numerical experiments help test the scope of the results.
E-mail: louis-pierre.chaintron-at-epfl.ch