  This paper presents a fast, principled approach for detecting anomalous and
out-of-distribution (OOD) samples in deep neural networks (DNN). We propose the
application of linear statistical dimensionality reduction techniques on the
semantic features produced by a DNN, in order to capture the low-dimensional
subspace truly spanned by said features. We show that the "feature
reconstruction error" (FRE), which is the $\ell_2$-norm of the difference
between the original feature in the high-dimensional space and the pre-image of
its low-dimensional reduced embedding, is highly effective for OOD and anomaly
detection. To generalize to intermediate features produced at any given layer,
we extend the methodology by applying nonlinear kernel-based methods.
Experiments using standard image datasets and DNN architectures demonstrate
that our method meets or exceeds best-in-class quality performance, but at a
fraction of the computational and memory cost required by the state of the art.
It can be trained and run very efficiently, even on a traditional CPU.
