A Theoretical Details

We begin with a useful lemma. Let X ESN(0,) and let a apple b apple 0, 0 apple c appleh d. The result for P(c apple X apple d) follows analogously. For the reader's convenience, we summarize in detail a few common techniques for defining OOD scores that measure the degree of ID-ness on the given sample. All the methods derive the score post hoc on neural networks trained with in-distribution data only.