The vulnerability of neural networks under adversarial attacks has raised serious concerns and motivated extensive research. It has been shown that both neural networks and adversarial attacks against them can be sensitive to input transformations such as linear translation and rotation, and that human vision, which is robust against adversarial attacks, is invariant to natural input transformations. Based on these, this paper tests the hypothesis that model robustness can be further improved when it is adversarially trained against transformed attacks and transformation-invariant attacks. Experiments on MNIST, CIFAR-10, and restricted ImageNet show that while transformations of attacks alone do not affect robustness, transformation-invariant attacks can improve model robustness by 2.5 on MNIST, 3.7 on CIFAR-10, and 1.1 on restricted ImageNet. We discuss the intuition behind this phenomenon.
Adversarial examples are perturbed inputs designed to fool machine learning models. Adversarial training injects such examples into training data to increase robustness. To scale this technique to large datasets, perturbations are crafted using fast single-step methods that maximize a linear approximation of the model's loss. We show that this form of adversarial training converges to a degenerate global minimum, wherein small curvature artifacts near the data points obfuscate a linear approximation of the loss. The model thus learns to generate weak perturbations, rather than defend against strong ones. As a result, we find that adversarial training remains vulnerable to black-box attacks, where we transfer perturbations computed on undefended models, as well as to a powerful novel single-step attack that escapes the non-smooth vicinity of the input data via a small random step. We further introduce Ensemble Adversarial Training, a technique that augments training data with perturbations transferred from other models. On ImageNet, Ensemble Adversarial Training yields models with strong robustness to black-box attacks. In particular, our most robust model won the first round of the NIPS 2017 competition on Defenses against Adversarial Attacks.