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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2307.02168 |
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| _version_ | 1866916118052995072 |
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| author | Chen, Fan Lin, Yiqing Ren, Zhenjie Wang, Songbo |
| author_facet | Chen, Fan Lin, Yiqing Ren, Zhenjie Wang, Songbo |
| contents | We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show the corresponding $N$-particle system converges exponentially in a rate uniform in $N$ modulo a small error. Finally we study the short-time regularization effects of the dynamics and prove its uniform-in-time propagation of chaos property in both the Wasserstein and entropic sense. Our results can be applied to the training of two-layer neural networks with momentum and we include the numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02168 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics Chen, Fan Lin, Yiqing Ren, Zhenjie Wang, Songbo Probability 60J60, 60K35 (Primary) 35B40, 35H10, 35Q83, 35Q84 (Secondary) We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show the corresponding $N$-particle system converges exponentially in a rate uniform in $N$ modulo a small error. Finally we study the short-time regularization effects of the dynamics and prove its uniform-in-time propagation of chaos property in both the Wasserstein and entropic sense. Our results can be applied to the training of two-layer neural networks with momentum and we include the numerical experiments. |
| title | Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics |
| topic | Probability 60J60, 60K35 (Primary) 35B40, 35H10, 35Q83, 35Q84 (Secondary) |
| url | https://arxiv.org/abs/2307.02168 |