Details

Here we derive Equation 8 for 0 and out = > 0. Since ESN(µ, 2,0) = NR(µ,), we can obtain Equation 4 for ID activation by specializing the result to =0 . We begin with a useful lemma. Let X ESN(0, 2,) and let a b 0, 0 c d. Then P(a X b)= (1+) h The result for P(c X 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.