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.
翻译:微型网络(PNs)在面部和图像识别方面表现良好,但是,这种网络的稳健性并不明确,因此获得证书对于在现实应用中采用这种网络至关重要。基于传统分支和约束(BAB)技术的RLU神经网络(NNS)现有核查算法不能被轻描淡写地应用于PN的核查。在这项工作中,我们设计了新的捆绑方法,配有全球趋同保证的BAB,称为“多边网络核查”或“短时间”VPN。一个关键的洞察是,我们获得的界限比间隔捆绑传播(IBP)和DeepT-Fast[Bonaert等人,20211]基准要紧得多。这使我们能够在对MNIST、CIFAR10和STL10数据集进行实证的情况下进行健全和完整的PNU核查。我们认为,我们的方法本身对N的核查感兴趣。源码公布在https://github.com/meelius/PNVerization。