Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling

[2607.15682] Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2607.15682 (cs) [Submitted on 17 Jul 2026 ( v1 ), last revised 12 Oct 2026 (this version, v4)] Title: Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling Authors: Moxian Qian View PDF HTML (experimental) 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 calculations test normalizers and mode probabilities; a controlled lattice $\phi^4$ calculation compares ideal and accepted inter-sector flows and measures sector relaxation. In two dimensional $U(1)$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$ gauge theories, corrected path weight estimates reproduce finite volume Wilson loops; $U(1)$ topological susceptibilities are also compared with analytic predictions across several lattice volumes. Comments: 36 pages, 8 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:2607.15682v4 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2607.15682 Focus to learn more 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) [v4] Mon, 12 Oct 2026 05:54:37 UTC (366 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2026-07 Change to browse by: cond-mat cond-mat.stat-mech cs hep-lat References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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