On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models
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.
Keywords
Cite
@article{arxiv.1810.12715,
title = {On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models},
author = {Sven Gowal and Krishnamurthy Dvijotham and Robert Stanforth and Rudy Bunel and Chongli Qin and Jonathan Uesato and Relja Arandjelovic and Timothy Mann and Pushmeet Kohli},
journal= {arXiv preprint arXiv:1810.12715},
year = {2019}
}
Comments
[v2] Best paper at NeurIPS SECML 2018 Workshop [v4] Accepted at ICCV 2019 under the title "Scalable Verified Training for Provably Robust Image Classification"