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Daniely and Schacham recently showed that gradient descent finds adversarialexamples on random undercomplete two-layers ReLU neural networks. The term"undercomplete" refers to the fact that their proof only holds when the numberof neurons is a vanishing fraction of the ambient dimension. We extend theirresult to the overcomplete case, where the number of neurons is larger than thedimension (yet also subexponential in the dimension). In fact we prove that asingle step of gradient descent suffices. We also show this result for anysubexponential width random neural network with smooth activation function.

A single gradient step finds adversarial examples on random two-layers neural networks