  The task of out-of-distribution (OOD) detection is vital to realize safe and
reliable operation for real-world applications. After the failure of
likelihood-based detection in high dimensions had been shown, approaches based
on the \emph{typical set} have been attracting attention; however, they still
have not achieved satisfactory performance. Beginning by presenting the failure
case of the typicality-based approach, we propose a new reconstruction
error-based approach that employs normalizing flow (NF). We further introduce a
typicality-based penalty, and by incorporating it into the reconstruction error
in NF, we propose a new OOD detection method, penalized reconstruction error
(PRE). Because the PRE detects test inputs that lie off the in-distribution
manifold, it effectively detects adversarial examples as well as OOD examples.
We show the effectiveness of our method through the evaluation using natural
image datasets, CIFAR-10, TinyImageNet, and ILSVRC2012.
