Federated Learning (FL) is a machine learning paradigm in which each data owner keeps its data locally while collaboratively training a shared global model. This approach helps preserve data privacy and is therefore particularly appealing for sensitive domains such as healthcare. A major bottleneck in FL, however, lies in the communication cost between clients and the central server. In this paper, we introduce two algorithms that significantly reduce this cost by projecting local gradients onto a shared client–server subspace.
Gradient Projection onto Historical Descent Directions for Communication-Efficient Federated Learning, with Léonard Deroose and Jan Ramon. Submitted. 2025
keywords: Multi-agent system, Gradient compression, Optimization, Error-Feedback mechanism.
Mean-field approach : Optimizing neural networks via gradient descent updates the weights in such a way that each weight influences all the others. This evolution over time (i.e., during training) is mathematically similar to the dynamics of particles in a gas, where each particle interacts with all the others. When the number of particles (or neurons, in machine learning) becomes large, the mean-field theory replaces these individual pairwise interactions with an interaction between each particle and the average effect of all particles. This leads to a macroscopic description of the system — or, in our case, of the learning dynamics. For two-layer neural networks, we provide a rigorous derivation of this transition from the microscopic to the macroscopic description.
Law of large numbers and central limit theorem for wide two-layer neural networks: the mini-batch and noisy case, with Arnaud Guillin, Manon Michel and Boris Nectoux, Journal of Machine Learning Research, 2022. [Arxiv version]
keywords: Empirical Measure, Stochastic process, Law of large numbers, Central limit theorem, tightness.
The following two papers concern Bayesian neural networks trained with variational inference.
Law of Large Numbers for Bayesian two-layer Neural Network trained with Variational Inference, with Tom Huix, Arnaud Guillin, Manon Michel, Éric Moulines and Boris Nectoux, 36th Annual Conference on Learning Theory (COLT), 2023.
keywords: Empirical Measure, Stochastic process, Law of large numbers, tightness.
Central Limit Theorem for Bayesian Neural Network trained with Variational Inference , with Tom Huix, Arnaud Guillin, Manon Michel, Éric Moulines and Boris Nectoux, 2025. Stochastics and Partial Differential Equations: Analysis and Computations. To appear.
keywords: Empirical Measure, Stochastic process, Central limit theorem, tightness.
PhD dissertation : Vers une compréhension mathématique des réseaux neuronaux profonds par une analyse champ moyen, 2023.