Paper Overview
- Field: Machine Learning
- Authors: Emmy Blumenthal, Nikolas Claussen, Benjamin Eysenbach, Catherine Ji, Gautam Reddy, Colin Scheibner, Benjamin Sorkin
- Published: 2026-09-14
- arXiv: 2609.15897
- Unifying framework: Free-energy-like functional optimization under dynamical or statistical constraints as the common language across five fields.
- Fields connected: Control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning.
- Applications: Reinforcement learning, variational inference, and generative modeling.
- Accessibility: Written for readers without prior background, starting from physics-first principles.
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, the authors 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.
The review offers a guided tour through this thread and presents selected applications in reinforcement learning, variational inference, and generative modeling. It does not assume readers have prior familiarity with these topics, beginning instead from principles derived from physics.
Key Themes
*Auto-collected on 2026-09-16.*