Deterministic Neural Networks with Inductive Biases Capture Epistemic and Aleatoric Uncertainty

Jishnu Mukhoti, Andreas Kirsch, Joost van Amersfoort, Philip H. S. Torr, Yarin Gal

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. Standard softmax neural nets suffer from feature collapse and extrapolate arbitrarily for OoD points. This results in arbitrary softmax entropies for OoD points which can have high entropy, low, or anything in between, thus cannot capture epistemic uncertainty reliably. We prove that this failure lies at the core of "why" Deep Ensemble Uncertainty works well. Instead of using softmax entropy, we show that with appropriate inductive biases softmax neural nets trained with maximum likelihood reliably capture epistemic uncertainty through their feature-space density. This density is obtained using simple Gaussian Discriminant Analysis, but it cannot represent aleatoric uncertainty reliably. We show that it is necessary to combine feature-space density with softmax entropy to disentangle uncertainties well. We evaluate the epistemic uncertainty quality on active learning and OoD detection, achieving SOTA ~98 AUROC on CIFAR-10 vs SVHN without fine-tuning on OoD data.

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