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SUMMARY:Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neu
 ral Networks
DTSTART:20260508T151500
DTEND:20260508T161500
DTSTAMP:20260503T225110Z
UID:ce3a892514442c973571cb59b347c3b8bbc6aef039e9d9bc47af510f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Aikaterini Papagiannouli\, University of Pisa\nBayesian neural
  networks\, in the overparameterized and infinite-width regime\, are now w
 ell understood. Under mild assumptions\, their prior converges to a Gaussi
 an process (NNGP)\, and both Bayesian inference and training dynamics can 
 be described by kernel methods. Although\, these infinite-width limits pro
 vide tractable models and sharp theoretical insights\, they also exhibit a
  fundamental rigidity: the induced feature representation becomes fixed an
 d independent of data. As a result\, feature learning disappears in the in
 finite-width limit\, and Bayesian inference reduces to kernel regression w
 ith a predetermined kernel.\n\nIn this talk\, I present a complementary la
 rge-deviation perspective on wide Bayesian neural networks. Rather than st
 udying typical Gaussian fluctuations\, we analyse exponentially rare\, but
  statistically dominant\, configurations that govern posterior concentrati
 on as width grows. At this scale\, Bayesian inference becomes variational:
  posterior mass concentrates near minimizers of an explicit functional rat
 e function defined directly on predictors.\nOur main result shows that\, i
 n contrast to the Gaussian-process limit\, the posterior large-deviation r
 ate function involves a joint optimization over predictors and internal co
 variance kernels. This nested variational structure leads to data-dependen
 t kernel selection and provides a mechanism for feature learning that pers
 ists even in the infinite-width regime. In particular\, we prove that the 
 posterior-optimal kernel generically differs from the NNGP kernel. Joint w
 ork with D. Trevisan
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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