Scalable and Certifiable Graph Unlearning: Overcoming the Approximation Error Barrier

Graph unlearning has emerged as a pivotal research area for ensuring privacy protection, given the widespread adoption of Graph Neural Networks (GNNs) in applications involving sensitive user data. Among existing studies, certified graph unlearning is distinguished by providing robust privacy guarantees. However, current certified graph unlearning methods are impractical for large-scale graphs because they necessitate the costly re-computation of graph propagation for each unlearning request. Although numerous scalable techniques have been developed to accelerate graph propagation for GNNs, their integration into certified graph unlearning remains uncertain as these scalable approaches introduce approximation errors into node embeddings. In contrast, certified graph unlearning demands bounded model error on exact node embeddings to maintain its certified guarantee. To address this challenge, we present ScaleGUN, the first approach to scale certified graph unlearning to billion-edge graphs. ScaleGUN integrates the approximate graph propagation technique into certified graph unlearning, offering certified guarantees for three unlearning scenarios: node feature, edge, and node unlearning. Extensive experiments on real-world datasets demonstrate the efficiency and unlearning efficacy of ScaleGUN. Remarkably, ScaleGUN accomplishes $(\epsilon,\delta)=(1,10^{-4})$ certified unlearning on the billion-edge graph ogbn-papers100M in 20 seconds for a 5,000 random edge removal request -- of which only 5 seconds are required for updating the node embeddings -- compared to 1.91 hours for retraining and 1.89 hours for re-propagation. Our code is available at https://github.com/luyi256/ScaleGUN.