Certifying Robustness of Graph Convolutional Networks for Node Perturbation with Polyhedra Abstract Interpretation

TL;DR

This paper introduces a novel polyhedra-based abstract interpretation method to certify the robustness of graph convolutional networks against node feature perturbations, enhancing reliability in critical applications.

Contribution

It presents an improved certification technique that provides tighter robustness bounds and better runtime performance, also applicable during training to boost GCN robustness.

Findings

Improved tightness of robustness bounds

Enhanced runtime performance of certification

Method effective during training to increase GCN robustness

Abstract

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.