The Impact of Likelihood Tempering on the Limiting Predictive Moments of Variational Bayesian Linear Neural Networks

תקציר מקורי באנגליתarXiv:2610.09132v1 Announce Type: cross Abstract: In wide Bayesian neural networks, Gaussian mean-field variational inference is prone to "prior dominance": the Kullback-Leibler (KL) regularization term of the ELBO outweighs the expected log-likelihood, and the variational predictive distribution collapses to the prior predictive as the width $M$ grows. Tempering the likelihood, by raising it to the power $1/T$ for a temperature $T < 1$, is equivalent to scaling the KL term by $T$. We ask in this paper how fast $T$ must decrease with $M$ to counteract this degeneracy and strike a good balance between the two terms. For single-hidden-layer linear networks with isotropic Gaussian priors, we derive the limiting predictive distribution under schedules of the form $T = \tau/M^{c}$, with constan