  Ensemble approaches for uncertainty estimation have recently been applied to
the tasks of misclassification detection, out-of-distribution input detection
and adversarial attack detection. Prior Networks have been proposed as an
approach to efficiently \emph{emulate} an ensemble of models for classification
by parameterising a Dirichlet prior distribution over output distributions.
These models have been shown to outperform alternative ensemble approaches,
such as Monte-Carlo Dropout, on the task of out-of-distribution input
detection. However, scaling Prior Networks to complex datasets with many
classes is difficult using the training criteria originally proposed. This
paper makes two contributions. First, we show that the appropriate training
criterion for Prior Networks is the \emph{reverse} KL-divergence between
Dirichlet distributions. This addresses issues in the nature of the training
data target distributions, enabling prior networks to be successfully trained
on classification tasks with arbitrarily many classes, as well as improving
out-of-distribution detection performance. Second, taking advantage of this new
training criterion, this paper investigates using Prior Networks to detect
adversarial attacks and proposes a generalized form of adversarial training. It
is shown that the construction of successful \emph{adaptive} whitebox attacks,
which affect the prediction and evade detection, against Prior Networks trained
on CIFAR-10 and CIFAR-100 using the proposed approach requires a greater amount
of computational effort than against networks defended using standard
adversarial training or MC-dropout.
