连接控制、推断、输运与热力学：从理论到学习中的应用
Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
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中文总结 AI 辅助
该综述连接控制理论、最优输运、概率推断、非平衡热力学和机器学习，聚焦自由能类泛函优化，并展示在强化学习、变分推断和生成建模中的应用。
中文摘要 AI 辅助
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。这些进展凸显了物理学、应用数学和机器学习子学科之间的基本联系。在本综述中，我们汇集了这些通常以不同语言表达的思想，以突出连接五个不同领域的概念主线：控制理论、最优输运、概率推断、非平衡热力学和机器学习。一个共同主题是在动力学或统计约束下优化自由能类泛函。我们提供了一条贯穿这条主线的引导之旅，并展示了在强化学习、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，并从源自物理学的原理开始。
英文摘要
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 modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.
发表机构
- Princeton University（普林斯顿大学）
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