Graph convolutional neural networks (GCNs) are powerful tools for learning graph-based knowledge representations from training data. However, they are vulnerable to small perturbations in the input graph, which makes them susceptible to input faults or adversarial attacks. This poses a significant problem for GCNs intended to be used in critical applications, which need to provide certifiably robust services even in the presence of adversarial perturbations. We propose an improved GCN robustness certification technique for node classification in the presence of node feature perturbations. We introduce a novel polyhedra-based abstract interpretation approach to tackle specific challenges of graph data and provide tight upper and lower bounds for the robustness of the GCN. Experiments show that our approach simultaneously improves the tightness of robustness bounds as well as the runtime performance of certification. Moreover, our method can be used during training to further improve the robustness of GCNs.

改进了基于图的多层感知器的鲁棒性认证技术，通过多面体抽象解释方法在节点特征扰动的情况下提供GCN鲁棒性的上下界，并在训练过程中进一步提高GCN的鲁棒性。

基于多面体抽象解释的节点扰动图卷积网络鲁棒性认证