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We present a new algorithm to train a robust neural network againstadversarial attacks. Our algorithm is motivated by the following two ideas.First, although recent work has demonstrated that fusing randomness can improvethe robustness of neural networks (Liu 2017), we noticed that adding noiseblindly to all the layers is not the optimal way to incorporate randomness.Instead, we model randomness under the framework of Bayesian Neural Network(BNN) to formally learn the posterior distribution of models in a scalable way.Second, we formulate the mini-max problem in BNN to learn the best modeldistribution under adversarial attacks, leading to an adversarial-trainedBayesian neural net. Experiment results demonstrate that the proposed algorithmachieves state-of-the-art performance under strong attacks. On CIFAR-10 withVGG network, our model leads to 14\% accuracy improvement compared withadversarial training (Madry 2017) and random self-ensemble (Liu 2017) under PGDattack with $0.035$ distortion, and the gap becomes even larger on a subset ofImageNet.

Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network