arXiv：cs.LG· Moxian Qian·· 2 天前AI 评分35
Neural Non-Equilibrium Hamiltonian Monte Carlo（NHMC）：面向校正 Boltzmann 采样的神经非平衡 HMC
Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling
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研究者提出 Neural Non-Equilibrium Hamiltonian Monte Carlo（NHMC），将条件动量分布与可逆、保体积动力学结合，用前向—反向路径比给出的 work 统一支持训练、重要性加权、归一化常数估计与 Metropolis 校正。
正文
Abstract:Learned dynamical proposals can generate configurations without providing a tractable endpoint density. Nonequilibrium path probabilities offer a way to correct such proposals, but correction alone does not determine their ability to connect separated regions. We introduce Neural Non-Equilibrium Hamiltonian Monte Carlo (NHMC), which combines conditional momentum distributions with reversible, volume-preserving dynamics. The forward--reverse path ratio gives the work used for training, importance weighting, normalizer estimation, and Metropolis correction. We then construct a configuration-space round-trip kernel whose reverse and forward paths share an intermediate configuration. Conditional on that configuration, its path-record update is independence Metropolis--Hastings. We compare its stationary inter-region flow with the flow obtained under exact conditional matching and bound their difference by the conditional path mismatch. This separates errors in the conditional proposal from dependence between the endpoint region and the intermediate configuration. Many-well experiments test normalizers and mode probabilities; a controlled lattice $\phi^4$ experiment relates inter-sector flow to sector relaxation. Two-dimensional $U(1)$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$ experiments compare four proposal constructions sharing a structured reference, including paths with analytic and learned forces.
| Comments: | 65 pages, 30 figures, including appendices |
| Subjects: | Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Lattice (hep-lat) |
| Cite as: | arXiv:2607.15682 [cs.LG] |
| (or arXiv:2607.15682v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.15682 arXiv-issued DOI via DataCite |
Submission history
From: Moxian Qian [view email]
[v1]
Fri, 17 Jul 2026 06:50:34 UTC (1,560 KB)
[v2]
Wed, 26 Aug 2026 22:06:59 UTC (2,852 KB)
[v3]
Thu, 1 Oct 2026 06:42:49 UTC (1,275 KB)
来源：arXiv：cs.LG · arxiv.org