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

This provides theoretical insight into adversarial vulnerabilities in neural networks, but it is incremental as it extends known results to convolutional architectures.

The paper tackled the problem of proving the existence of adversarial examples in random convolutional networks, showing that this is a straightforward consequence of applying isoperimetric inequalities on the special orthogonal group, which extends and simplifies prior work on random fully connected networks.