Sound and Complete Verification of Polynomial Networks

Elias Abad Rocamora, Mehmet Fatih Sahin, Fanghui Liu, Grigorios G Chrysos, Volkan Cevher

Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world applications. Existing verification algorithms on ReLU neural networks (NNs) based on branch and bound (BaB) techniques cannot be trivially applied to PN verification. In this work, we devise a new bounding method, equipped with BaB for global convergence guarantees, called VPN. One key insight is that we obtain much tighter bounds than the interval bound propagation baseline. This enables sound and complete PN verification with empirical validation on MNIST, CIFAR10 and STL10 datasets. We believe our method has its own interest to NN verification.

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