Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{s}\mathbb{o}(d)$

We show that adversarial examples exist for various random convolutional networks, and furthermore, that this is a relatively simple consequence of the isoperimetric inequality on the special orthogonal group $\mathbb{s}\mathbb{o}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.