We prove, under two sufficient conditions, that idealised models can have no adversarial examples. We discuss which idealised models satisfy our conditions, and show that idealised Bayesian neural networks (BNNs) satisfy these. We continue by studying near-idealised BNNs using HMC inference, demonstrating the theoretical ideas in practice. We experiment with HMC on synthetic data derived from MNIST for which we know the ground-truth image density, showing that near-perfect epistemic uncertainty correlates to density under image manifold, and that adversarial images lie off the manifold in our setting. This suggests why MC dropout, which can be seen as performing approximate inference, has been observed to be an effective defence against adversarial examples in practice; We highlight failure-cases of non-idealised BNNs relying on dropout, suggesting a new attack for dropout models and a new defence as well. Lastly, we demonstrate the defence on a cats-vs-dogs image classification task with a VGG13 variant.
We prove that idealised Bayesian neural networks can have no adversarial examples, and give empirical evidence with real-world BNNs. The paper studies the adversarial robustness of Bayesian classifiers and state two conditions that they show are provably sufficient for "idealised models" on "idealised datasets" to not have adversarial examples Paper posit a class of discriminative BAyesian classifiers that do not have any adversarial examples.