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| Home > Publications database > Feature learning in deep neural networks close to criticality |
| Conference Presentation (After Call) | FZJ-2026-00967 |
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2025
Abstract: Neural networks excel due to their ability to learn features, yet its theoretical understanding continues to be a field of ongoing research. We develop a finite-width theory for deep non-linear networks, showing that their Bayesian prior is a superposition of Gaussian processes with kernel variances inversely proportional to the network width. In the proportional limit where both network width and training samples scale as N,P→∞ with P/N fixed, we derive forward-backward equations for the maximum a posteriori kernels, demonstrating how layer representations align with targets across network layers. A field-theoretic approach links finite-width corrections of the network kernels to fluctuations of the prior, bridging classical edge-of-chaos theory with feature learning and revealing key interactions between criticality, response, and network scales.
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