mlsanityData to 7 Oct 2026

Sampling from the Mean-Field Stationary Distribution

arXiv 2402.07355 ↗First posted 12 Feb 2024math.ST cs.LG stat.MLcited by 7

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Abstract (arXiv)

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight is to decouple the two key aspects of this problem: (1) approximation of the mean-field SDE via a finite-particle system, via uniform-in-time propagation of chaos, and (2) sampling from the finite-particle stationary distribution, via standard log-concave samplers. Our approach is conceptually simpler and its flexibility allows for incorporating the state-of-the-art for both algorithms and theory. This leads to improved guarantees in numerous settings, including better guarantees for optimizing certain two-layer neural networks in the mean-field regime. A key technical contribution is to establish a new uniform-in-N log-Sobolev inequality for the stationary distribution of the mean-field Langevin dynamics.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 30 of its 83 references that are in the map. First posted on arXiv 12 Feb 2024.

Builds on

30 of 83 references.

References · 30

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  2. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
  3. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
  4. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  5. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  6. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  7. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  8. 2018Trainability and Accuracy of Neural Networks: An Interacting Particle System Approachcited by 105
  9. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  10. 2022Variational inference via Wasserstein gradient flowscited by 84
  11. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  12. 2022Improved analysis for a proximal algorithm for samplingcited by 72
18 more
  1. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 60
  2. 2020Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithmcited by 57
  3. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 53
  4. 2021Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Samplingcited by 44
  5. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  6. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  7. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  8. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  9. 2020On Linear Optimization over Wasserstein Ballscited by 23
  10. 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
  11. 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
  12. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  13. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  14. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 19
  15. 2019Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetscited by 16
  16. 2023Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximationscited by 12
  17. 2023Mean Field Optimization Problem Regularized by Fisher Informationcited by 2
  18. 2023Mean-field underdamped Langevin dynamics and its spacetime discretizationcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 2; 2026: 1.

7 papers.

  1. 2024Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamicscited by 14
  2. 2024Improved Particle Approximation Error for Mean Field Neural Networkscited by 12
  3. 2024Efficient Reinforcement Learning for Global Decision Making in the Presence of Local Agents at Scalecited by 8
  4. 2024A Particle Algorithm for Mean-Field Variational Inferencecited by 3
  5. 2025Mirror Mean-Field Langevin Dynamicscited by 3
  6. 2025Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexitycited by 1
  7. 2026Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networkscited by 1