Adversarial Immunization for Improving Certifiable Robustness on Graphs

Despite achieving strong performance in the semi-supervised node classification task, graph neural networks (GNNs) are vulnerable to adversarial attacks, similar to other deep learning models. Existing research works either focus on developing defense models or explore certifiable robustness under GNNs against adversarial attacks. However, little research attention is paid to the potential and practice of immunization to adversarial attacks on graphs. In this paper, we formulate the problem of graph adversarial immunization} as a bilevel optimization problem, i.e., vaccinating a fraction of node pairs, connected or unconnected, to improve the certifiable robustness of graph against any admissible adversarial attack. We further propose an efficient algorithm with meta-gradient in a discrete way to circumvent the computationally expensive combinatorial optimization when solving the adversarial immunization problem. Experiments are conducted on two citation networks and one social network. Experimental results demonstrate that the proposed adversarial immunization method remarkably improves the fraction of robust nodes by 14%-50%, with an affordable immune budget of only 3.2% edges.