  The question whether inputs are valid for the problem a neural network is
trying to solve has sparked interest in out-of-distribution (OOD) detection. It
is widely assumed that Bayesian neural networks (BNNs) 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 show
that proper Bayesian inference with function space priors induced by neural
networks 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 due to the correspondence with Gaussian
processes. Strikingly, the kernels derived from common architectural choices
lead to function space priors which induce predictive uncertainties that do not
reflect the underlying input data distribution and are therefore unsuited for
OOD detection. Importantly, we find the OOD behavior in this limiting case to
be consistent with the corresponding finite-width case. To overcome this
limitation, useful function space properties can also be encoded in the prior
in weight space, however, this can currently only be applied to a specified
subset of the domain and thus does not inherently extend to OOD data. Finally,
we argue that a trade-off between generalization and OOD capabilities might
render the application of BNNs for OOD detection undesirable in practice.
Overall, our study discloses fundamental problems when naively using BNNs for
OOD detection and opens interesting avenues for future research.
