On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models

Sven Gowal; Krishnamurthy Dvijotham; Robert Stanforth; Rudy Bunel; Chongli Qin; Jonathan Uesato; Relja Arandjelovic; Timothy Mann; Pushmeet Kohli

arXiv · 1810.12715

On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models

Sven Gowal·Krishnamurthy Dvijotham·Robert Stanforth·Rudy Bunel·Chongli Qin·Jonathan Uesato·Relja Arandjelovic·Timothy Mann·Pushmeet Kohli

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Abstract

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

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Sven Gowal, Krishnamurthy Dvijotham, Robert Stanforth, Rudy Bunel, Chongli Qin, Jonathan Uesato, Relja Arandjelovic, Timothy Mann, Pushmeet Kohli. 2019-08-29. On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models. https://arxiv.org/abs/1810.12715

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