mlsanityData to 7 Oct 2026

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

arXiv 2212.03050 ↗First posted 6 Dec 2022math.PR stat.MLcited by 23

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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.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 15 of its 72 references that are in the map. First posted on arXiv 6 Dec 2022.

Builds on

15 of 72 references.

References · 15

  1. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
  2. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
  3. 2015Adding Gradient Noise Improves Learning for Very Deep Networkscited by 144
  4. 2018Trainability and Accuracy of Neural Networks: An Interacting Particle System Approachcited by 105
  5. 2020A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networkscited by 68
  6. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 60
  7. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 53
  8. 2019Mean-Field Langevin Dynamics and Energy Landscape of Neural Networkscited by 49
  9. 2019Mean Field Analysis of Deep Neural Networkscited by 42
  10. 2020Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysiscited by 21
  11. 2021Noisy Gradient Descent Converges to Flat Minima for Nonconvex Matrix Factorizationcited by 15
  12. 2022Entropic Fictitious Play for Mean Field Optimization Problemcited by 12
3 more
  1. 2020Game on Random Environment, Mean-field Langevin System and Neural Networkscited by 8
  2. 2020Ergodicity of the underdamped mean-field Langevin dynamicscited by 7
  3. 2022A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamicscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 9; 2025: 5; 2026: 2.

23 papers.

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  1. 2024Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscapecited by 43
  2. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 19
  3. 2024Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimizationcited by 17
  4. 2024Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamicscited by 14
  5. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  6. 2023Momentum Particle Maximum Likelihoodcited by 12
  7. 2024Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspectivecited by 12
  8. 2024Improved Particle Approximation Error for Mean Field Neural Networkscited by 12
  9. 2023Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problemscited by 11
  10. 2023Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descentcited by 7
  11. 2024Sampling from the Mean-Field Stationary Distributioncited by 7
  12. 2025Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemblecited by 5
11 more
  1. 2023Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problemscited by 4
  2. 2024Linear convergence of proximal descent schemes on the Wasserstein spacecited by 3
  3. 2025Mirror Mean-Field Langevin Dynamicscited by 3
  4. 2023Mean Field Optimization Problem Regularized by Fisher Informationcited by 2
  5. 2023Mean-field underdamped Langevin dynamics and its spacetime discretizationcited by 2
  6. 2025Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexitycited by 1
  7. 2025Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimizationcited by 1
  8. 2025Continuous Policy and Value Iteration for Relaxed Stochastic Control Problems and Its Convergencecited by 1
  9. 2024Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample sizecited by 0
  10. 2026On propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimizationcited by 0
  11. 2026Policy Gradient for Continuous-Time Robust Markov Decision Processescited by 0