mlsanityData to 14 Oct 2026

Mean-field underdamped Langevin dynamics and its spacetime discretization

arXiv 2312.16360 ↗First posted 26 Dec 2023stat.CO math.OC math.STcited by 2

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Abstract (arXiv)

We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 59 references that are in the map. First posted on arXiv 26 Dec 2023.

Builds on

27 of 59 references.

References · 27

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  4. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
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  11. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 78
  12. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 61
15 more
  1. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 55
  2. 2017Stochastic Particle Gradient Descent for Infinite Ensemblescited by 52
  3. 2019Mean-Field Langevin Dynamics and Energy Landscape of Neural Networkscited by 50
  4. 2019Near-Optimal Methods for Minimizing Star-Convex Functions and Beyondcited by 36
  5. 2019Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyondcited by 33
  6. 2016A Lyapunov Analysis of Momentum Methods in Optimizationcited by 28
  7. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  8. 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
  9. 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
  10. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 20
  11. 2019Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descentcited by 13
  12. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  13. 2020Ergodicity of the underdamped mean-field Langevin dynamicscited by 7
  14. 2023Accelerated Stochastic Optimization Methods under Quasar-convexitycited by 6
  15. 2023Mean Field Optimization Problem Regularized by Fisher Informationcited by 2

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Citing papers per year: 2024: 1; 2025: 1.

2 papers.

  1. 2024Sampling from the Mean-Field Stationary Distributioncited by 7
  2. 2025Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexitycited by 2