Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics

TL;DR

This paper proves uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics, demonstrating exponential convergence and regularization effects, with applications to neural network training.

Contribution

It establishes the uniform-in-time propagation of chaos under convexity assumptions, combining hypocoercivity with regularization analysis, and applies results to neural network training.

Findings

Exponential convergence of mean field dynamics.

Uniform-in-time propagation of chaos in Wasserstein and entropic senses.

Numerical experiments validating theoretical results.

Abstract

We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show the corresponding $N$-particle system converges exponentially in a rate uniform in $N$ modulo a small error. Finally we study the short-time regularization effects of the dynamics and prove its uniform-in-time propagation of chaos property in both the Wasserstein and entropic sense. Our results can be applied to the training of two-layer neural networks with momentum and we include the numerical experiments.