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

Authors

Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin

Published in

ArXiv. Sep 14, 2026. Epub Sep 14, 2026.

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.

PMID:
42780301
Bibliographic data and abstract were imported from PubMed on 24 Sep 2026.

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