Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
cond-mat.stat-mech, cond-mat.dis-nn, cond-mat.soft, cs.LG, physics.bio-ph
Submitted: 2026-09-14
Updated: 2026-09-14
Comments: 5 Chapters, 62 pages, 16 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data.
Terminology
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.
Sources
- Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review
- Self-organized robustness in mean-field interacting systems
- A Conceptual Introduction to Hamiltonian Monte Carlo
- Proximal Policy Optimization Algorithms
- Annealed Importance Sampling
- Soft Actor-Critic Algorithms and Applications
- Implicit Bias of the JKO Scheme
- Denoising Diffusion Probabilistic Models
- Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
- Flow Matching Guide and Code
- An Introduction to Variational Autoencoders
- Flow Matching for Generative Modeling
- Blind denoising diffusion models and the blessings of dimensionality
- Score-Based Generative Modeling through Stochastic Differential Equations
- Density estimation using Real NVP
- Simple and Effective Masked Diffusion Language Models
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