Toward Certified Robustness Against Real-World Distribution Shifts

Haoze Wu, Teruhiro Tagomori, Alexander Robey, Fengjun Yang, Nikolai Matni, Hamed Hassani, George J. Pappas, Corina Pasareanu, Clark Barrett

Keywords: certified robustness, distribution shift, generative models

TL;DR: We design algorithms for certifying the robustness of deep neural networks against real-world distribution shifts in data.

Abstract: 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 considering a neural-symbolic verification framework in which generative models are trained to learn perturbations from data and specifications are defined with respect to the output of these learned models. A pervasive challenge arising from this setting is that although S-shaped activations (e.g., sigmoid, tanh) are common in the last layer of deep generative models, existing verifiers cannot tightly approximate S-shaped activations. To address this challenge, we propose a general meta-algorithm for handling S-shaped activations which leverages classical notions of counter-example-guided abstraction refinement. The key idea is to ``lazily'' refine the abstraction of S-shaped functions to exclude spurious counter-examples found in the previous abstraction, thus guaranteeing progress in the verification process while keeping the state-space small. For networks with sigmoid activations, we show that our technique outperforms state-of-the-art verifiers on certifying robustness against both canonical adversarial perturbations and numerous real-world distribution shifts. Furthermore, experiments on the MNIST and CIFAR-10 datasets show that distribution-shift-aware algorithms have significantly higher certified robustness against distribution shifts.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2206.03669/code)