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The sensitivity of image classifiers to small perturbations in the input isoften viewed as a defect of their construction. We demonstrate that thissensitivity is a fundamental property of classifiers. For any arbitraryclassifier over the set of $n$-by-$n$ images, we show that for all but oneclass it is possible to change the classification of all but a tiny fraction ofthe images in that class with a perturbation of size $O(n^{1/\max{(p,1)}})$when measured in any $p$-norm for $p \geq 0$. We then discuss how thisphenomenon relates to human visual perception and the potential implicationsfor the design considerations of computer vision systems.

Image classifiers can not be made robust to small perturbations