提出通用状态空间的自由能估计方法，提升离散与多模态场景效率。
Free energy Estimation on Any State Space
- 用神经传输框架统一处理任意状态空间的自由能估计。
- 在离散、多模态及自回归场景中均实现高效准确估计。
- 揭示时间反演与h变换的群结构，具理论深度。
自由能估计是物理与统计中的基础挑战。传统方法依赖热力学变换，包括直接估计、准静态积分和有限时间平均。近期工作[He and Du et al., 2025]通过学习神经传输显著提升了有限时间下的效率。本文将该框架推广至任意状态空间，提出通用神经传输学习方法，实现高效估计。实验验证其在连续、离散、多模态及自回归设置下的有效性与高效性。此外，我们建立代数恒等式，揭示无穷小时间反演与广义Doob's h-变换的群论结构，表明二者复合构成广义二面体群。
原文摘要 · Abstract (English)
Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings. Beyond free energy estimation, we establish algebraic identities and reveal a group-theoretic structure linking infinitesimal time reversal and generalized Doob's $h$-transforms, showing that their compositions form a generalized dihedral group.
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