Publications by Lénaïc Chizat

Doubly Regularized Entropic Wasserstein Barycenter

We study a general formulation of regularized Wasserstein barycenters that enjoy favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that minimizes the sum of ...

2025

An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Games

Lénaïc Chizat

We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired machine learning app ...

2025

Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings

Lénaïc Chizat, Tomas Vaskevicius

We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, mu, admits a density over R-d. For a semi-concave cost function bounded by cand a regularization ...

SPRINGER HEIDELBERG2025

Infinite-width limit of deep linear neural networks

Maria Colombo, Xavier Fernandez-Real Girona, Lénaïc Chizat

This paper studies the infinite-width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a ...

Hoboken2024

On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks

Michaël Unser, Sebastian Jonas Neumayer, Lénaïc Chizat

In supervised learning, the regularization path is sometimes used as a convenient theoretical proxy for the optimization path of gradient descent initialized from zero. In this paper, we study a modification of the regularization path for infinite-width 2- ...

2024

Displacement smoothness of entropic optimal transport

Lénaïc Chizat

The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schr center dot odinger map. We prove that when the cost function is Ck+1 with k is an element of N* then this map is Lip ...

Edp Sciences S A2024

On the symmetries in the dynamics of wide two-layer neural networks

Lénaïc Chizat

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023