  We show that a single softmax neural net with minimal changes can beat the
uncertainty predictions of Deep Ensembles and other more complex
single-forward-pass uncertainty approaches. Softmax neural nets cannot capture
epistemic uncertainty reliably because for OoD points they extrapolate
arbitrarily and suffer from feature collapse. This results in arbitrary softmax
entropies for OoD points which can have high entropy, low, or anything in
between. We study why, and show that with the right inductive biases, softmax
neural nets trained with maximum likelihood reliably capture epistemic
uncertainty through the feature-space density. This density is obtained using
Gaussian Discriminant Analysis, but it cannot disentangle uncertainties. We
show that it is necessary to combine this density with the softmax entropy to
disentangle aleatoric and epistemic uncertainty -- crucial e.g. for active
learning. We examine the quality of epistemic uncertainty on active learning
and OoD detection, where we obtain SOTA ~0.98 AUROC on CIFAR-10 vs SVHN.
