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Scaling provable adversarial defenses
Eric Wong · Frank Schmidt · Jan Hendrik Metzen · J. Zico Kolter

Tue Dec 04 07:45 AM -- 09:45 AM (PST) @ Room 517 AB #133
Recent work has developed methods for learning deep network classifiers that are \emph{provably} robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this paper, in an effort to scale these approaches to substantially larger models, we extend previous work in three main directly. First, we present a technique for extending these training procedures to much more general networks, with skip connections (such as ResNets) and general nonlinearities; the approach is fully modular, and can be implemented automatically analogously to automatic differentiation. Second, in the specific case of $\ell_\infty$ adversarial perturbations and networks with ReLU nonlinearities, we adopt a nonlinear random projection for training, which scales \emph{linearly} in the number of hidden units (previous approached scaled quadratically). Third, we show how to further improve robust error through cascade models. On both MNIST and CIFAR data sets, we train classifiers that improve substantially on the state of the art in provable robust adversarial error bounds: from 5.8% to 3.1% on MNIST (with $\ell_\infty$ perturbations of $\epsilon=0.1$), and from 80% to 36.4% on CIFAR (with $\ell_\infty$ perturbations of $\epsilon=2/255$).

Author Information

Eric Wong (Carnegie Mellon University)
Frank Schmidt (Robert Bosch GmbH)
Jan Hendrik Metzen (Robert Bosch GmbH)
J. Zico Kolter (Carnegie Mellon University / Bosch Center for AI)

Zico Kolter is an Assistant Professor in the School of Computer Science at Carnegie Mellon University, and also serves as Chief Scientist of AI Research for the Bosch Center for Artificial Intelligence. His work focuses on the intersection of machine learning and optimization, with a large focus on developing more robust, explainable, and rigorous methods in deep learning. In addition, he has worked on a number of application areas, highlighted by work on sustainability and smart energy systems. He is the recipient of the DARPA Young Faculty Award, and best paper awards at KDD, IJCAI, and PESGM.

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