# Ergodicity of the underdamped mean-field Langevin dynamics

arXiv: https://arxiv.org/abs/2007.14660 · HTML: https://mlsanity.com/paper/2007.14660/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Convex Analysis of the Mean Field Langevin Dynamics](https://mlsanity.com/paper/2201.10469/) (2022)
- [Uniform-in-time propagation of chaos for mean field Langevin dynamics](https://mlsanity.com/paper/2212.03050/) (2022)
- [Unbiased Estimation using Underdamped Langevin Dynamics](https://mlsanity.com/paper/2206.07202/) (2022)
- [Mean-field analysis for heavy ball methods: Dropout-stability, connectivity, and global convergence](https://mlsanity.com/paper/2210.06819/) (2022)
- [A Fisher-Rao gradient flow for entropic mean-field min-max games](https://mlsanity.com/paper/2405.15834/) (2024)
- [Mean Field Optimization Problem Regularized by Fisher Information](https://mlsanity.com/paper/2302.05938/) (2023)
- [Mean-field underdamped Langevin dynamics and its spacetime discretization](https://mlsanity.com/paper/2312.16360/) (2023)

## Abstract (arXiv)

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).