    Over the last few years, the phenomenon of adversarial examples --- maliciously constructed inputs that fool trained machine learning models --- has captured the attention of the research community, especially when the adversary is restricted to making small modifications of a correctly handled input. At the same time, less surprisingly, image classifiers lack human-level performance on randomly corrupted images, such as images with additive Gaussian noise. In this work, we show that these are two manifestations of the same underlying phenomenon. We establish this connection in several ways. First, we find that adversarial examples exist at the same distance scales we would expect from a linear model with the same performance on corrupted images. Next, we show that Gaussian data augmentation during training improves robustness to small adversarial perturbations and that adversarial training improves robustness to several types of image corruptions. Finally, we present a model-independent upper bound on the distance from a corrupted image to its nearest error given test performance and show that in practice we already come close to achieving the bound, so that improving robustness further for the corrupted image distribution requires significantly reducing test error. All of this suggests that improving adversarial robustness should go hand in hand with improving performance in the presence of more general and realistic image corruptions. This yields a computationally tractable evaluation metric for defenses to consider: test error in noisy image distributions.
Small adversarial perturbations should be expected given observed error rates of models outside the natural data distribution. This paper proposes an alternative view for adversarial examples in high dimension spaces by considering the "error rate" in a Gaussian distribution centered at each test point.