Physics of Learning: A Lagrangian perspective to different learning paradigms

ICLR 2026 Conference Submission18398 Authors

Keywords: physics; learning; reinforcement learning; generative models; learning theory

TL;DR: A physics perspective in efficient learning

Abstract: We study the problem of building an efficient learning system. Efficient learning processes information in the least time, i.e., building a system that reaches a desired error threshold with the least number of observations. Building upon least action principles from physics, we derive classic learning algorithms, Bellman's optimality equation in reinforcement learning, and the Adam optimizer in generative models from first principles, i.e., the Learning $\textit{Lagrangian}$. We postulate that learning searches for stationary paths in the Lagrangian, and learning algorithms are derivable by seeking the stationary trajectories.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 18398