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

arXiv: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 0, as M o infty and compare it with the untempered neural network Gaussian process (NNGP) posterior, the infinite-width limit of the exact posterior. Our main result is that the predictive expectation and variance undergo phase transitions at different scales: the limiting expectation leaves its prior value at c = 1/2, once au falls below an explicit threshold, and equals the least-squares prediction for c > 1/2, whereas the limiting variance keeps its prior value for c 1. With suitable choices of au,c, one can recover either the NNGP posterior expectation or its variance.

Source: arXiv cs.LG | 2026-10-08