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

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

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 fu

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