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.
