Using isoperimetric inequalities on SO(d), this paper proves that random convolutional networks with odd activations or ReLU have sign-flipping adversarial examples at distance O(||x0||/sqrt(d)).
Adversarial examples in multi-layer random relu networks
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Existence of Adversarial Examples for Random Convolutional Networks via Isoperimetric Inequalities on $\mathbb{so}(d)$
Using isoperimetric inequalities on SO(d), this paper proves that random convolutional networks with odd activations or ReLU have sign-flipping adversarial examples at distance O(||x0||/sqrt(d)).