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We study the kinetic mean field Langevin dynamics under the functionalconvexity assumption of the mean field energy functional. Using hypocoercivity,we first establish the exponential convergence of the mean field dynamics andthen show the corresponding $N$-particle system converges exponentially in arate uniform in $N$ modulo a small error. Finally we study the short-timeregularization effects of the dynamics and prove its uniform-in-timepropagation of chaos property in both the Wasserstein and entropic sense. Ourresults can be applied to the training of two-layer neural networks withmomentum and we include the numerical experiments.

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