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

TL;DR

This paper demonstrates that adversarial examples are prevalent in random convolutional networks, using isoperimetric inequalities on $ ext{so}(d)$ to provide a simplified and generalized proof extending prior results from fully connected networks.

Contribution

The paper introduces a novel approach leveraging isoperimetric inequalities on $ ext{so}(d)$ to show adversarial examples exist in random convolutional networks, simplifying previous proofs.

Findings

Adversarial examples exist for random convolutional networks.

Isoperimetric inequalities on $ ext{so}(d)$ underpin the proof.

Extension of results from fully connected to convolutional networks.

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