Physics of Learning: A Lagrangian perspective to different learning paradigms

• URL: http://arxiv.org/abs/2509.21049v1
• Date: Thu, 25 Sep 2025 12:00:22 GMT
• Title: Physics of Learning: A Lagrangian perspective to different learning paradigms
• Authors: Siyuan Guo, Bernhard Schölkopf,
• Abstract summary: 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.<n>We derive classic learning algorithms, Bellman's optimality equation in reinforcement learning, and the Adam in generative models from first principles.<n>We postulate that learning searches for stationary paths in the Lagrangian, and learning algorithms are derivable by seeking the stationary trajectories.
• Score: 60.75807831005178
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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