Performance-critical machine learning models should be robust to input perturbations not seen during training. Adversarial training is a method for improving a model's robustness to some perturbations by including them in the training process, but this tends to exacerbate other vulnerabilities of the model. The adversarial training framework has the effect of translating the data with respect to the cost function, while weight decay has a scaling effect. Although weight decay could be considered a crude regularization technique, it appears superior to adversarial training as it remains stable over a broader range of regimes and reduces all generalization errors. Equipped with these abstractions, we provide key baseline results and methodology for characterizing robustness. The two approaches can be combined to yield one small model that demonstrates good robustness to several white-box attacks associated with different metrics.
Deep neural networks are vulnerable to adversarial examples, even in the black-box setting, where the attacker is restricted solely to query access. Existing black-box approaches to generating adversarial examples typically require a significant number of queries, either for training a substitute network or performing gradient estimation. We introduce GenAttack, a gradient-free optimization technique that uses genetic algorithms for synthesizing adversarial examples in the black-box setting. Our experiments on different datasets (MNIST, CIFAR-10, and ImageNet) show that GenAttack can successfully generate visually imperceptible adversarial examples against state-of-the-art image recognition models with orders of magnitude fewer queries than previous approaches. Against MNIST and CIFAR-10 models, GenAttack required roughly 2,126 and 2,568 times fewer queries respectively, than ZOO, the prior state-of-the-art black-box attack. In order to scale up the attack to large-scale high-dimensional ImageNet models, we perform a series of optimizations that further improve the query efficiency of our attack leading to 237 times fewer queries against the Inception-v3 model than ZOO. Furthermore, we show that GenAttack can successfully attack some state-of-the-art ImageNet defenses, including ensemble adversarial training and non-differentiable or randomized input transformations. Our results suggest that evolutionary algorithms open up a promising area of research into effective black-box attacks. Recent work has demonstrated that neural networks are vulnerable to adversarial examples, i.e., inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much of the prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against any adversary. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest the notion of security against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models.