Sound and Complete Verification of Polynomial Networks

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

Keywords: branch and bound, adversarial robustness, adversarial examples, certified robustness, polynomial network verification

Abstract: 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 classical 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 Verification of Polynomial Networks or VPN for short. One key insight is that we obtain much tighter bounds than the interval bound propagation (IBP) and DeepT-Fast [Bonaert et al., 2021] baselines. 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. The source code is publicly available at https://github.com/megaelius/PNVerification.

TL;DR: We propose a branch and bound algorithm for polynomial network verification.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2209.07235/code)