Generalization of latent–posterior alignment across uncertainty architectures

Establish whether the latent–posterior alignment behavior observed in deterministic Graph Neural Network feature extractors with mean-field Bayesian output layers also emerges under fully Bayesian architectures, correlated posterior approximations, dropout, Laplace methods, or ensembles.

Background

The paper studies Bayesian Graph Neural Networks consisting of deterministic Graph Isomorphism Network feature extractors and mean-field variational Bayesian output layers. It identifies Latent–Posterior Alignment (LPA) as a mechanism through which latent representations preferentially occupy low-variance posterior directions, thereby reducing predictive uncertainty even when the output-layer posterior variance does not contract.

The reported evidence is limited to the specified deterministic-feature-extractor and mean-field-output-layer architecture. The authors explicitly leave unresolved whether the same geometric relationship between latent representations and posterior uncertainty is a general phenomenon across alternative Bayesian and approximate-uncertainty methods, including fully Bayesian networks, correlated posterior distributions, dropout, Laplace approximations, and ensembles.