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A wide range of defenses have been proposed to harden neural networks againstadversarial attacks. However, a pattern has emerged in which the majority ofadversarial defenses are quickly broken by new attacks. Given the lack ofsuccess at generating robust defenses, we are led to ask a fundamentalquestion: Are adversarial attacks inevitable? This paper analyzes adversarialexamples from a theoretical perspective, and identifies fundamental bounds onthe susceptibility of a classifier to adversarial attacks. We show that, forcertain classes of problems, adversarial examples are inescapable. Usingexperiments, we explore the implications of theoretical guarantees forreal-world problems and discuss how factors such as dimensionality and imagecomplexity limit a classifier's robustness against adversarial examples.

Are adversarial examples inevitable?