Mirror Mean-Field Langevin Dynamics
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Abstract (arXiv)
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over ℝd, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of ℝd by proposing the mirror mean-field Langevin dynamics (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 32 of its 63 references that are in the map. First posted on arXiv 5 May 2025.
Builds on
32 of 63 references.
References · 32
- 2014Convex Optimization: Algorithms and Complexitycited by 569
- 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
- 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
- 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
- 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
- 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
- 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
- 2018Mean Field Analysis of Neural Networks: A Central Limit Theoremcited by 107
- 2018Mirrored Langevin Dynamicscited by 61
- 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 60
- 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
- 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
20 more
- 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 53
- 2019Mean-Field Langevin Dynamics and Energy Landscape of Neural Networkscited by 49
- 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
- 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
- 2019Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyondcited by 33
- 2019Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetrycited by 31
- 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
- 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 29
- 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
- 2022Convergence of the Riemannian Langevin Algorithmcited by 23
- 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
- 2024Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamicscited by 14
- 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
- 2024Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspectivecited by 12
- 2024Improved Particle Approximation Error for Mean Field Neural Networkscited by 12
- 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
- 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 9
- 2024Sampling from the Mean-Field Stationary Distributioncited by 7
- 2025Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemblecited by 5
- 2024High-accuracy sampling from constrained spaces with the Metropolis-adjusted Preconditioned Langevin Algorithmcited by 4
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Citing papers per year: 2025: 1; 2026: 2.
3 papers.