Nitanda, A., Lee, A., Kai, D.T.X., Sakaguchi, M. & Suzuki, T.. (2025). Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:46586-46610 Available from https://proceedings.mlr.press/v267/nitanda25a.html.
Abstract:
Mean-field Langevin dynamics (MFLD) is an optimization method derived by taking the mean-field limit of noisy gradient descent for two-layer neural networks in the mean-field regime. Recently, the propagation of chaos (PoC) for MFLD has gained attention as it provides a quantitative characterization of the optimization complexity in terms of the number of particles and iterations. A remarkable progress by Chen et al. (2022) showed that the approximation error due to finite particles remains uniform in time and diminishes as the number of particles increases. In this paper, by refining the defective log-Sobolev inequality—a key result from that earlier work—under the neural network training setting, we establish an improved PoC result for MFLD, which removes the exponential dependence on the regularization coefficient from the particle approximation term of the optimization complexity. As an application, we propose a PoC-based model ensemble strategy with theoretical guarantees.
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Funding Info:
This research / project is supported by the National Research Foundation, Singapore, and Infocomm Media Development Authority - Trust Tech Funding Initiative
Grant Reference no. : DTC-RGC-05
This research / project is supported by the Ministry of Digital Development and Information - AI Visiting Professorship Programme
Grant Reference no. : AIVP-2024-004