Variational Bayesian Neural Networks via Resolution of Singularities

Understand

In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs).

• To begin, using SLT, we lay to rest some of the confusion surrounding discrepancies between downstream predictive performance measured via e.g., the test log predictive density, and the variational objective.
• Next, we use the SLT-corrected asymptotic form for singular posterior distributions to inform the design of the variational family itself.
• Specifically, we build upon the idealized variational family introduced in \citet{bhattacharya_evidence_2020} which is theoretically appealing but practically intractable.