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Toward Certified Robustness Against Real-World Distribution Shifts
Haoze Wu · TERUHIRO TAGOMORI · Alex Robey · Fengjun Yang · Nikolai Matni · George J. Pappas · Hamed Hassani · Corina Pasareanu · Clark Barrett

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts. To do so, we bridge the gap between hand-crafted specifications and realistic deployment settings by proposing a novel neural-symbolic verification framework, in which we train a generative model to learn perturbations from data and define specifications with respect to the output of the learned model. A unique challenge arising from this setting is that existing verifiers cannot tightly approximate sigmoid activations, which are fundamental to many state-of-the-art generative models. To address this challenge, we propose a general meta-algorithm for handling sigmoid activations which leverages classical notions of counter-example-guided abstraction refinement. The key idea is to lazily'' refine the abstraction of sigmoid functions to exclude spurious counter-examples found in the previous abstraction, thus guaranteeing progress in the verification process while keeping the state-space small. Experiments on the MNIST and CIFAR-10 datasets show that our framework significantly outperforms existing methods on a range of challenging distribution shifts.

#### Author Information

##### George J. Pappas (University of Pennsylvania)

George J. Pappas is the Joseph Moore Professor and Chair of the Department of Electrical and Systems Engineering at the University of Pennsylvania. He also holds a secondary appointment in the Departments of Computer and Information Sciences, and Mechanical Engineering and Applied Mechanics. He is member of the GRASP Lab and the PRECISE Center. He has previously served as the Deputy Dean for Research in the School of Engineering and Applied Science. His research focuses on control theory and in particular, hybrid systems, embedded systems, hierarchical and distributed control systems, with applications to unmanned aerial vehicles, distributed robotics, green buildings, and biomolecular networks. He is a Fellow of IEEE, and has received various awards such as the Antonio Ruberti Young Researcher Prize, the George S. Axelby Award, the O. Hugo Schuck Best Paper Award, the National Science Foundation PECASE, and the George H. Heilmeier Faculty Excellence Award.

##### Hamed Hassani (University of Pennsylvania)

I am an assistant professor in the Department of Electrical and Systems Engineering (as of July 2017). I hold a secondary appointment in the Department of Computer and Information Systems. I am also a faculty affiliate of the Warren Center for Network and Data Sciences. Before joining Penn, I was a research fellow at the Simons Institute, UC Berkeley (program: Foundations of Machine Learning). Prior to that, I was a post-doctoral scholar and lecturer in the Institute for Machine Learning at ETH Zürich. I received my Ph.D. degree in Computer and Communication Sciences from EPFL.