Minimum Topology Attacks for Graph Neural Networks

With the great popularity of Graph Neural Networks (GNNs), their robustness to adversarial topology attacks has received significant attention. Although many attack methods have been proposed, they mainly focus on fixed-budget attacks, aiming at finding the most adversarial perturbations within a fixed budget for target node. However, considering the varied robustness of each node, there is an inevitable dilemma caused by the fixed budget, i.e., no successful perturbation is found when the budget is relatively small, while if it is too large, the yielding redundant perturbations will hurt the invisibility. To break this dilemma, we propose a new type of topology attack, named minimum-budget topology attack, aiming to adaptively find the minimum perturbation sufficient for a successful attack on each node. To this end, we propose an attack model, named MiBTack, based on a dynamic projected gradient descent algorithm, which can effectively solve the involving non-convex constraint optimization on discrete topology. Extensive results on three GNNs and four real-world datasets show that MiBTack can successfully lead all target nodes misclassified with the minimum perturbation edges. Moreover, the obtained minimum budget can be used to measure node robustness, so we can explore the relationships of robustness, topology, and uncertainty for nodes, which is beyond what the current fixed-budget topology attacks can offer.