Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning

2026-09-14

AI Summary

本文探讨了控制理论、最优传输、概率推理、非平衡热力学和机器学习之间的联系，通过优化自由能类函数解决高维数据中的复杂结构学习问题。

Abstract

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.

Problem

• control theory
• optimal transport
• probabilistic inference
• non-equilibrium thermodynamics
• machine learning

Innovation

• control theory
• optimal transport
• probabilistic inference
• non-equilibrium thermodynamics
• machine learning