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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2602.22925 |
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| _version_ | 1866914353121329152 |
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| author | Papagiannouli, Katerina Trevisan, Dario Zitto, Giuseppe Pio |
| author_facet | Papagiannouli, Katerina Trevisan, Dario Zitto, Giuseppe Pio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22925 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks Papagiannouli, Katerina Trevisan, Dario Zitto, Giuseppe Pio Machine Learning G.3 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. |
| title | Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks |
| topic | Machine Learning G.3 |
| url | https://arxiv.org/abs/2602.22925 |