论文标题
阻尼不足的平均场兰格文动力学的磨性性
Ergodicity of the underdamped mean-field Langevin dynamics
论文作者
论文摘要
我们研究了失水不足的平均场兰格文（MFL）方程的长时间行为，并在不同条件下提供了一般收敛以及指数收敛速率。 MFL方程的结果可以应用于研究哈密顿梯度下降算法的收敛性，以进行过度参数优化。然后，我们提供了算法的数值示例，以训练生成对抗网络（GAN）。
We study the long time behavior of an underdamped mean-field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide a numerical example of the algorithm to train a generative adversarial networks (GAN).
