Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $so(d)$

Abstract

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 $so(d)$. This extends and simplifies a recent line of work which shows similar results for random fully connected networks.

Accepted to COLT 2025