Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attacks

Lukas Gosch, Mahalakshmi Sabanayagam, Debarghya Ghoshdastidar, Stephan Günnemann

Keywords: robustness, provable robustness, certificates, graph neural networks, neural networks, poisoning, backdoor attacks, mixed-integer linear programming, neural tangent kernel, support vector machines

TL;DR: First deterministic & white-box certificates for (Graph) Neural Networks against data poisoning & backdoors based on (i) the neural tangent kernel, and (ii) a novel reformulation of the bilevel poisoning problem as a mixed-integer linear program.

Abstract: Generalization of machine learning models can be severely compromised by data poisoning, where adversarial changes are applied to the training data. This vulnerability has led to interest in certifying (i.e., proving) that such changes up to a certain magnitude do not affect test predictions. We, for the first time, certify Graph Neural Networks (GNNs) against poisoning attacks, including backdoors, targeting the node features of a given graph. Our certificates are white-box and based upon (i) the neural tangent kernel, which characterizes the training dynamics of sufficiently wide networks; and (ii) a novel reformulation of the bilevel optimization describing poisoning as a mixed-integer linear program. We note that our framework is more general and constitutes the first approach to derive white-box poisoning certificates for NNs, which can be of independent interest beyond graph-related tasks.

Submission Number: 14