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Physics of Learning: A Lagrangian perspective to different learning paradigms (arxiv.org)
3 points by Anon84 364 days ago | hide | past | pdf | discuss on HN

In plain words: Using a physics formula that picks the path of least action, it treats learning as finding the steadiest route to a target error in the fewest observations. From that single rule it re-derives classic learning algorithms, reinforcement learning's core equation, and the Adam optimizer.

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.

Siyuan Guo, Bernhard Schölkopf
arXiv:2509.21049 · cs.LG, cs.NE · submitted Sep 25, 2025
abstract · pdf · html · Work in progress

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