  It is becoming increasingly clear that many machine learning classifiers are
vulnerable to adversarial examples. In attempting to explain the origin of
adversarial examples, previous studies have typically focused on the fact that
neural networks operate on high dimensional data, they overfit, or they are too
linear. Here we argue that the origin of adversarial examples is primarily due
to an inherent uncertainty that neural networks have about their predictions.
We show that the functional form of this uncertainty is independent of
architecture, dataset, and training protocol; and depends only on the
statistics of the logit differences of the network, which do not change
significantly during training. This leads to adversarial error having a
universal scaling, as a power-law, with respect to the size of the adversarial
perturbation. We show that this universality holds for a broad range of
datasets (MNIST, CIFAR10, ImageNet, and random data), models (including
state-of-the-art deep networks, linear models, adversarially trained networks,
and networks trained on randomly shuffled labels), and attacks (FGSM, step
l.l., PGD). Motivated by these results, we study the effects of reducing
prediction entropy on adversarial robustness. Finally, we study the effect of
network architectures on adversarial sensitivity. To do this, we use neural
architecture search with reinforcement learning to find adversarially robust
architectures on CIFAR10. Our resulting architecture is more robust to white
\emph{and} black box attacks compared to previous attempts.
