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We prove, under two sufficient conditions, that idealised models can have noadversarial examples. We discuss which idealised models satisfy our conditions,and show that idealised Bayesian neural networks (BNNs) satisfy these. Wecontinue by studying near-idealised BNNs using HMC inference, demonstrating thetheoretical ideas in practice. We experiment with HMC on synthetic data derivedfrom MNIST for which we know the ground-truth image density, showing thatnear-perfect epistemic uncertainty correlates to density under image manifold,and that adversarial images lie off the manifold in our setting. This suggestswhy MC dropout, which can be seen as performing approximate inference, has beenobserved to be an effective defence against adversarial examples in practice;We highlight failure-cases of non-idealised BNNs relying on dropout, suggestinga new attack for dropout models and a new defence as well. Lastly, wedemonstrate the defence on a cats-vs-dogs image classification task with aVGG13 variant.

Sufficient Conditions for Idealised Models to Have No Adversarial Examples: a Theoretical and Empirical Study with Bayesian Neural Networks