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Bayesian neural networks (BNNs) are a principled approach to modelingpredictive uncertainties in deep learning, which are important insafety-critical applications. Since exact Bayesian inference over the weightsin a BNN is intractable, various approximate inference methods exist, amongwhich sampling methods such as Hamiltonian Monte Carlo (HMC) are oftenconsidered the gold standard. While HMC provides high-quality samples, it lacksinterpretable summary statistics because its sample mean and variance ismeaningless in neural networks due to permutation symmetry. In this paper, wefirst show that the role of permutations can be meaningfully quantified by anumber of transpositions metric. We then show that the recently proposedrebasin method allows us to summarize HMC samples into a compact representationthat provides a meaningful explicit uncertainty estimate for each weight in aneural network, thus unifying sampling methods with variational inference. Weshow that this compact representation allows us to compare trained BNNsdirectly in weight space across sampling methods and variational inference, andto efficiently prune neural networks trained without explicit Bayesianframeworks by exploiting uncertainty estimates from HMC.

A Compact Representation for Bayesian Neural Networks By Removing Permutation Symmetry