Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning
Review connects control theory, optimal transport, probabilistic inference, thermodynamics, and machine learning via free-energy optimization under constraints.
The review unifies five fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. The common conceptual thread is optimization of free-energy-like functionals under dynamical or statistical constraints. Selected applications are presented in reinforcement learning, variational inference, and generative modeling. The tutorial-style text assumes no prior familiarity and begins from physics principles.
- Links control, optimal transport, inference, thermodynamics, and ML in one framework
- Common theme: free-energy-like functional optimization under constraints
- Applications span reinforcement learning, variational inference, generative modeling
- Accessible introduction starting from physics principles
Full article122 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.15897