TY - CONF AU - Lindner, Javed AU - Fischer, Kirsten AU - Dahmen, David AU - Ringel, Zohar AU - Krämer, Michael AU - Helias, Moritz TI - Feature learning in deep neural networks close to criticality M1 - FZJ-2026-00967 PY - 2025 AB - 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. T2 - DPG Spring Meeting of the Condensed Matter Section CY - 16 Mar 2025 - 21 Mar 2025, Regensburg (Germany) Y2 - 16 Mar 2025 - 21 Mar 2025 M2 - Regensburg, Germany LB - PUB:(DE-HGF)6 UR - https://juser.fz-juelich.de/record/1052373 ER -