A spring-block theory of feature learning in deep neural networks

• URL: http://arxiv.org/abs/2407.19353v2
• Date: Wed, 23 Oct 2024 14:11:34 GMT
• Title: A spring-block theory of feature learning in deep neural networks
• Authors: Cheng Shi, Liming Pan, Ivan Dokmanić,
• Abstract summary: Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. We show how this phenomenon emerges from collective action of nonlinearity, noise, learning rate, and other choices that shape the dynamics. We propose a macroscopic mechanical theory that reproduces the diagram, explaining why some DNNs are lazy and some active, and linking feature learning across layers to generalization.
• Score: 11.396919965037636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this phenomenon emerges from collective action of nonlinearity, noise, learning rate, and other choices that shape the dynamics, 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. We then propose a macroscopic mechanical theory that reproduces the diagram, explaining why some DNNs are lazy and some active, and linking feature learning across layers to generalization.

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