Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks

• URL: http://arxiv.org/abs/2602.22925v1
• Date: Thu, 26 Feb 2026 12:15:11 GMT
• Title: Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks
• Authors: Katerina Papagiannouli, Dario Trevisan, Giuseppe Pio Zitto,
• Abstract summary: Large-deviation theory provides explicit variational objectives-rate functions-on predictors.<n>We show that the posterior output rate function is obtained by a joint optimization over predictors and internal kernels.
• Score: 1.1470070927586018
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate functions-on predictors, providing an emerging notion of complexity and feature learning directly at the functional level. We show that the posterior output rate function is obtained by a joint optimization over predictors and internal kernels, in contrast with fixed-kernel (NNGP) theory. Numerical experiments demonstrate that the resulting predictions accurately describe finite-width behavior for moderately sized networks, capturing non-Gaussian tails, posterior deformation, and data-dependent kernel selection effects.

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