[2505.02621] Mirror Mean-Field Langevin Dynamics
Abstract:The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, 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 $\mathbb{R}^d$ by proposing the \emph{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.
Mirror Mean-Field Langevin Dynamics Anming Gu∗ Juno Kim∗ University of Texas at Austin UC Berkeley anminggu@cs.utexas.edu junokim@berkeley.edu May 19, 2026 arXiv:2505.02621v2 [cs.LG] 18 May 2026…
saved by
related reading
- [2402.01258] Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscapearxiv.org
- Statistical Mechanics of Deep Learningganguli-gang.stanford.edu
- An optimization perspective on log-concave sampling and beyond | Sinho Chewichewisinho.github.io
- Modular Manifolds - Thinking Machines Labthinkingmachines.ai
- A Simplified Overview of Langevin Dynamicsfriedmanroy.github.io
- [1507.05021] Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmarxiv.org
- [2604.04891] Muon Dynamics as a Spectral Wasserstein Flowarxiv.org
- Gregory Gundersengregorygundersen.com
- Why Momentum Really Worksdistill.pub
- The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^darxiv.org
- Learning the integral of a diffusion model – Sander Dielemansander.ai
- [1605.08101] Global rates of convergence for nonconvex optimization on manifoldsarxiv.org