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

TL;DR

This paper introduces the first method to certify the robustness of Graph Neural Networks against data poisoning and backdoor attacks, using neural tangent kernels and a novel optimization reformulation.

Contribution

It presents a white-box certification framework for GNNs against poisoning, leveraging neural tangent kernels and a new bilevel optimization reformulation.

Findings

Certificates demonstrate robustness against poisoning attacks.

Insights into how graph structure affects GNN robustness.

Framework applicable beyond graph neural networks.

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 problem describing poisoning as a mixed-integer linear program. Consequently, we leverage our framework to provide fundamental insights into the role of graph structure and its connectivity on the worst-case robustness behavior of convolution-based and PageRank-based GNNs. 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.