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

Mean-field Langevin dynamics (MFLD) is an optimization method derived by taking the mean-field limit of noisy gradient descent for two-layer neural networks in the mean-field regime. Recently, the propagation of chaos (PoC) for MFLD has gained attention as it provides a quantitative characterization of the optimization complexity in terms of the number of particles and iterations. A remarkable progress by Chen et al. ( 2022 ) showed that the approximation error due to finite particles remains uniform in time and diminishes as the number of particles increases. In this paper, by refining the defective log-Sobolev inequalitya key result from that earlier work-under the neural network training setting, we establish an improved PoC result for MFLD, which removes the exponential dependence on the regularization coefficient from the particle approximation term of the optimization complexity. As an application, we propose a PoC-based model ensemble strategy with theoretical guarantees.