  The need to avoid confident predictions on unfamiliar data has sparked
interest in out-of-distribution (OOD) detection. It is widely assumed that
Bayesian neural networks (BNN) are well suited for this task, as the endowed
epistemic uncertainty should lead to disagreement in predictions on outliers.
In this paper, we question this assumption and provide empirical evidence that
proper Bayesian inference with common neural network architectures does not
necessarily lead to good OOD detection. To circumvent the use of approximate
inference, we start by studying the infinite-width case, where Bayesian
inference can be exact considering the corresponding Gaussian process.
Strikingly, the kernels induced under common architectural choices lead to
uncertainties that do not reflect the underlying data generating process and
are therefore unsuited for OOD detection. Finally, we study finite-width
networks using HMC, and observe OOD behavior that is consistent with the
infinite-width case. Overall, our study discloses fundamental problems when
naively using BNNs for OOD detection and opens interesting avenues for future
research.
