Exponential ergodicity of mean-field Langevin dynamics by synchronous coupling

2025/09/03 by Mohamed Alfaki Aboubacrine Assadek, Assadek, Mohamed Alfaki Aboubacrine
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #History and Overview (math.HO) #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2509.03124

openalex publication_date 2025/09/03 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the convergence property of the dynamics is of great theoretical interest. In this paper, In the continuity of [1, 2], we are interested by the long-time behavior and uniform in time propagation of chaos by synchronous coupling for mean-field Langevin dynamics (over- and under-damped).

Citations

• Quasi-Stationary Distributions of Interacting Dynamical Systems and their approximation
• On the exponential ergodicity of the McKean-Vlasov SDE depending on a polynomial interaction
• Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases
• The Kinetic Fokker-planck Equation With Mean Field Interaction
• Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks
• Couplings and quantitative contraction rates for Langevin dynamics
• Quantitative Harris type theorems for diffusions and McKean-Vlasov\n processes
• On the rate of convergence in Wasserstein distance of the empirical\n measure
• Probabilistic approach for granular media equations in the non uniformly convex case

Related

• Ergodicity of the underdamped mean-field Langevin dynamics
• Uniform-in-time propagation of chaos for mean field Langevin dynamics
• Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble
• Convex Analysis of the Mean Field Langevin Dynamics
• Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response