A Theory of Transfer-Based Black-Box Attacks: Explanation and Implications

Transfer-based attacks are a practical method of black-box adversarial attacks, in which the attacker aims to craft adversarial examples from a source (surrogate) model that is transferable to the target model. A wide range of empirical works has tried to explain the transferability of adversarial examples from different angles. However, these works only provide ad hoc explanations without quantitative analyses. The theory behind transfer-based attacks remains a mystery.This paper studies transfer-based attacks under a unified theoretical framework. We propose an explanatory model, called the manifold attack model, that formalizes popular beliefs and explains the existing empirical results. Our model explains why adversarial examples are transferable even when the source model is inaccurate. Moreover, our model implies that the existence of transferable adversarial examples depends on the “curvature” of the data manifold, which quantitatively explains why the success rates of transfer-based attacks are hard to improve. We also discuss the expressive power and the possible extensions of our model in general applications.