Paper ID: 2407.19353

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

Cheng Shi, Liming Pan, Ivan Dokmanić

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.

Submitted: Jul 28, 2024