Spring-block theory of feature learning in deep neural networks

2024/07/28 by Shi, Cheng, Liming Pan, Pan, Liming +2 · 1 citation
Computer Science · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2407.19353

openalex publication_date 2024/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built from microscopic neuronal dynamics. We exhibit a noise-nonlinearity phase diagram that identifies regimes where shallow or deep layers learn more effectively and propose a macroscopic mechanical theory that reproduces the diagram and links feature learning across layers to generalization.

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• Microscopic and collective signatures of feature learning in neural networks

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