  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.
