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

arXiv: https://arxiv.org/abs/2212.03050 · HTML: https://mlsanity.com/paper/2212.03050/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 72 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 15 of 15)

- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach](https://mlsanity.com/paper/1805.00915/) (2018)
- [A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks](https://mlsanity.com/paper/2001.11443/) (2020)
- [Mean-Field Langevin Dynamics: Exponential Convergence and Annealing](https://mlsanity.com/paper/2202.01009/) (2022)
- [Convex Analysis of the Mean Field Langevin Dynamics](https://mlsanity.com/paper/2201.10469/) (2022)
- [Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks](https://mlsanity.com/paper/1905.07769/) (2019)
- [Mean Field Analysis of Deep Neural Networks](https://mlsanity.com/paper/1903.04440/) (2019)
- [Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysis](https://mlsanity.com/paper/2012.15477/) (2020)
- [Noisy Gradient Descent Converges to Flat Minima for Nonconvex Matrix Factorization](https://mlsanity.com/paper/2102.12430/) (2021)
- [Entropic Fictitious Play for Mean Field Optimization Problem](https://mlsanity.com/paper/2202.05841/) (2022)
- [Game on Random Environment, Mean-field Langevin System and Neural Networks](https://mlsanity.com/paper/2004.02457/) (2020)
- [Ergodicity of the underdamped mean-field Langevin dynamics](https://mlsanity.com/paper/2007.14660/) (2020)
- [A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2207.09304/) (2022)

## Built on by (most cited first, 23 of 23)

- [Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape](https://mlsanity.com/paper/2402.01258/) (2024)
- [Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction](https://mlsanity.com/paper/2306.07221/) (2023)
- [Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization](https://mlsanity.com/paper/2406.08654/) (2024)
- [Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamics](https://mlsanity.com/paper/2408.07254/) (2024)
- [Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective](https://mlsanity.com/paper/2403.14917/) (2024)
- [Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior](https://mlsanity.com/paper/2406.07475/) (2024)
- [Momentum Particle Maximum Likelihood](https://mlsanity.com/paper/2312.07335/) (2023)
- [Improved Particle Approximation Error for Mean Field Neural Networks](https://mlsanity.com/paper/2405.15767/) (2024)
- [Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems](https://mlsanity.com/paper/2312.01127/) (2023)
- [Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent](https://mlsanity.com/paper/2302.07125/) (2023)
- [Sampling from the Mean-Field Stationary Distribution](https://mlsanity.com/paper/2402.07355/) (2024)
- [Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble](https://mlsanity.com/paper/2502.05784/) (2025)
- [Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems](https://mlsanity.com/paper/2303.02957/) (2023)
- [Linear convergence of proximal descent schemes on the Wasserstein space](https://mlsanity.com/paper/2411.15067/) (2024)
- [Mirror Mean-Field Langevin Dynamics](https://mlsanity.com/paper/2505.02621/) (2025)
- [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)
- [Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexity](https://mlsanity.com/paper/2501.14993/) (2025)
- [Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimization](https://mlsanity.com/paper/2503.13115/) (2025)
- [Continuous Policy and Value Iteration for Relaxed Stochastic Control Problems and Its Convergence](https://mlsanity.com/paper/2506.08121/) (2025)
- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)
- [On propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization](https://mlsanity.com/paper/2602.15094/) (2026)
- [Policy Gradient for Continuous-Time Robust Markov Decision Processes](https://mlsanity.com/paper/2606.04335/) (2026)

## Abstract (arXiv)

We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the Lp-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics. Furthermore, we prove the uniform-in-time propagation of chaos in both the L2-Wasserstein metric and relative entropy.