Accelerating sampling via asymptotic relaxation enhancing flows
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917438915870720 |
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| author | Feng, Yuanyuan Li, Lei Liu, Jian-Guo Xu, Xiaoqian |
| author_facet | Feng, Yuanyuan Li, Lei Liu, Jian-Guo Xu, Xiaoqian |
| contents | In this paper, we accelerate Langevin Monte Carlo sampling from Gibbs measures $π\propto \exp(-U)$ by adding a large drift that preserves the invariant measure. For warm-start initial data, we characterize the sharp asymptotic decay rate of the relative entropy and introduce asymptotic relaxation enhancing flows: sequences that achieve arbitrarily fast decay. We construct such flows on the torus by scaling cellular flows and pushing them forward via diffeomorphisms, and we extend the construction to the full space using a Lyapunov function method to control behavior at infinity without periodization, obtaining explicit finite energy flows that guarantee arbitrarily fast convergence under natural growth conditions on $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accelerating sampling via asymptotic relaxation enhancing flows Feng, Yuanyuan Li, Lei Liu, Jian-Guo Xu, Xiaoqian Probability Dynamical Systems 37A25 In this paper, we accelerate Langevin Monte Carlo sampling from Gibbs measures $π\propto \exp(-U)$ by adding a large drift that preserves the invariant measure. For warm-start initial data, we characterize the sharp asymptotic decay rate of the relative entropy and introduce asymptotic relaxation enhancing flows: sequences that achieve arbitrarily fast decay. We construct such flows on the torus by scaling cellular flows and pushing them forward via diffeomorphisms, and we extend the construction to the full space using a Lyapunov function method to control behavior at infinity without periodization, obtaining explicit finite energy flows that guarantee arbitrarily fast convergence under natural growth conditions on $U$. |
| title | Accelerating sampling via asymptotic relaxation enhancing flows |
| topic | Probability Dynamical Systems 37A25 |
| url | https://arxiv.org/abs/2604.23981 |