Adversarial training is the de facto most promising defense against adversarial examples. Yet, its passive nature inevitably prevents it from being immune to unknown attackers. To achieve a proactive defense, we need a more fundamental understanding of adversarial examples, beyond the popular bounded threat model. In this paper, we provide a causal viewpoint of adversarial vulnerability: the cause is the confounder ubiquitously existing in learning, where attackers are precisely exploiting the confounding effect. Therefore, a fundamental solution for adversarial robustness is causal intervention. As the confounder is unobserved in general, we propose to use the instrumental variable that achieves intervention without the need for confounder observation. We term our robust training method as Causal intervention by instrumental Variable (CiiV). It has a differentiable retinotopic sampling layer and a consistency loss, which is stable and guaranteed not to suffer from gradient obfuscation. Extensive experiments on a wide spectrum of attackers and settings applied in MNIST, CIFAR-10, and mini-ImageNet datasets empirically demonstrate that CiiV is robust to adaptive attacks.
Download