论文标题
多项式网络的声音和完整验证
Sound and Complete Verification of Polynomial Networks
论文作者
论文摘要
多项式网络（PNS）最近在面部和图像识别方面表现出了有希望的表现。但是，PNS的鲁棒性尚不清楚，因此获得证书对于使其在现实世界应用中的采用至关重要。基于经典分支和绑定（BAB）技术的Relu神经网络（NNS）上的现有验证算法不能微不足道地应用于PN验证。在这项工作中，我们设计了一种新的边界方法，该方法配备了BAB，以提供全球收敛保证，称为多项式网络或简称VPN的验证。一个关键的见解是，我们获得的界限比间隔结合的传播（IBP）和deept-fast [Bonaert等，2021]基准的界限。这可以通过MNIST，CIFAR10和STL10数据集进行经验验证，使声音和完整的PN验证。我们认为我们的方法对NN验证具有自身的兴趣。源代码可在https://github.com/megaelius/pnverification上公开获得。
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.
