[论文] Bridging Control, Inference, Transport, and Thermodynamics: From Theor...

论文概要

研究领域: ML 作者: Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin 发布时间: 2026-09-14 arXiv: 2609.15897

中文摘要

过去十年见证了从高维数据中学习复杂结构的强大方法的发展。这些进展使物理学、应用数学和机器学习子学科之间的基本联系走到了前沿。在这篇综述中，我们将这些通常以不同语言表达的想法汇聚在一起，突出一条连接五个不同领域的概念主线：控制论、最优传输、概率推断、非平衡热力学和机器学习。共同主题是在动力学或统计约束下优化自由能类泛函。我们提供贯穿这条主线的引导式导览，并介绍在强化学习、变分推断和生成建模中的精选应用。本综述不假设读者事先熟悉这些主题，从源自物理学的原理开始。

原文摘要

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative mode...

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