PROVEN: Verifying Robustness of Neural Networks with a Probabilistic Approach

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Lily Weng, Pin-Yu Chen, Lam Nguyen, Mark Squillante, Akhilan Boopathy, Ivan Oseledets, Luca Daniel ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6727-6736, 2019.

Abstract

We propose a novel framework PROVEN to \textbf{PRO}babilistically \textbf{VE}rify \textbf{N}eural network’s robustness with statistical guarantees. PROVEN provides probability certificates of neural network robustness when the input perturbation follow distributional characterization. Notably, PROVEN is derived from current state-of-the-art worst-case neural network robustness verification frameworks, and therefore it can provide probability certificates with little computational overhead on top of existing methods such as Fast-Lin, CROWN and CNN-Cert. Experiments on small and large MNIST and CIFAR neural network models demonstrate our probabilistic approach can tighten up robustness certificate to around $1.8 \times$ and $3.5 \times$ with at least a $99.99%$ confidence compared with the worst-case robustness certificate by CROWN and CNN-Cert.

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