Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on SO(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 $\mathbb{SO}(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.