Uniform-in-\({N}\) Log-Sobolev Inequality for the Mean-Field Langevin Dynamics with Convex Energy

Sinho Chewi; Atsushi Nitanda; Matthew S. Zhang

doi:10.1137/24m1696068

July 23, 2026SIAM Journal on Mathematical AnalysisOpen Access

Uniform-in-\({N}\) Log-Sobolev Inequality for the Mean-Field Langevin Dynamics with Convex Energy

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Key Points

This research aims to establish a log-Sobolev inequality for mean-field Langevin dynamics' stationary distribution, independent of the number of particles.
Provided a proof based on Lipschitz transport map from Gaussian measure
Used reverse heat flow techniques developed by Kim and Milman
Demonstrated a valid log-Sobolev inequality for mean-field Langevin dynamics
Establishing the transport map confirms the connection between Gaussian measures and the dynamics involved

Implication

Establishes a log-Sobolev inequality in mean-field Langevin dynamics, suggesting broader implications for statistical mechanics.

Abstract

We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles [Formula: see text]. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman.

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Cite This Study

Chewi et al. (2026) studied this question.

synapsesocial.com/papers/6a65a2e2d3aea3239cd7625c https://doi.org/10.1137/24m1696068

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Uniform-in-\({N}\) Log-Sobolev Inequality for the Mean-Field Langevin Dynamics with Convex Energy

Key Points

Implication

Abstract

Discussion

Cite This Study

Uniform-in-\({N}\) Log-Sobolev Inequality for the Mean-Field Langevin Dynamics with Convex Energy

Key Points

Implication

Abstract

Discussion

Cite This Study

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