A wide range of defenses have been proposed to harden neural networks against adversarial attacks. However, a pattern has emerged in which the majority of adversarial defenses are quickly broken by new attacks.   Given the lack of success at generating robust defenses, we are led to ask a fundamental question:  Are adversarial attacks inevitable?
 This paper analyzes adversarial examples from a theoretical perspective, and identifies fundamental bounds on the susceptibility of a classifier to adversarial attacks.    We show that, for certain classes of problems, adversarial examples are inescapable.   Using experiments, we explore the implications of theoretical guarantees for real-world problems and discuss how factors such as dimensionality and image complexity limit a classifier's robustness against adversarial examples.


This paper identifies classes of problems for which adversarial examples are inescapable, and derives fundamental bounds on the susceptibility of any classifier to adversarial examples. 