Singular Bayesian Neural Networks

ArXi:2602.00387v2 Announce Type: replace-cross Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value decay. By parameterizing weights as $W = AB^{\top}$ with $A \in \mathbb{R}^{m \times r}$, $B \in \mathbb{R}^{n \times r}$, we induce a posterior that is singular with respect to the Lebesgue measure, concentrating on the rank-$r$ manifold.