  Detecting out-of-distribution (OOD) examples is critical in many
applications. We propose an unsupervised method to detect OOD samples using a
$k$-NN density estimate with respect to a classification model's intermediate
activations on in-distribution samples. We leverage a recent insight about
label smoothing, which we call the \emph{Label Smoothed Embedding Hypothesis},
and show that one of the implications is that the $k$-NN density estimator
performs better as an OOD detection method both theoretically and empirically
when the model is trained with label smoothing. Finally, we show that our
proposal outperforms many OOD baselines and also provide new finite-sample
high-probability statistical results for $k$-NN density estimation's ability to
detect OOD examples.
