Forgetting and Remembering Are Both You Need: Balanced Graph Structure Unlearning

In light of the growing emphasis on the right to be forgotten of graph data, machine unlearning has been extended to unlearn the graph structures’ knowledge from graph neural networks (GNNs), namely, structure unlearning. Whereas the complex dependencies in graph data, structure unlearning is intrinsically prone to imbalanced performance between the objectives of knowledge forgetting and model utility maintenance. Nevertheless, most existing methods fall short in addressing the two objectives in tandem and developing balanced solutions. In this paper, we propose imbalanced Structure Unlearning Mitigation using MultI-objective OpTimization (SUMMIT), which aims to develop balanced solutions regarding both knowledge forgetting and model utility maintenance effects. Corresponding to the two aspects, we first construct two tailored objectives that specifically address the challenges inherent in structure unlearning. Specifically, for the forgetting objective, we introduce a higher-order forgetting enhancement strategy aimed at mitigating the adverse effects of GNN oversmoothing on node decoupling. For the remembering objective, we adhere to the principle of ideal unlearning and propose to minimize the distributional distance between the node embeddings developed by unlearned and well-trained GNNs. Considering the potential competitive relationship between the two objectives during the optimization process, we present an adaptive two-objective balancer based on multi-objective optimization to reconcile the two objectives and strike a balance between them. We conduct comprehensive experiments to evaluate the efficacy of SUMMIT on three representative GNNs and four datasets, and compare the performance of SUMMIT with its ablation variants and a cadre of baselines. We demonstrate the superiority of SUMMIT in its ability to yield optimal and balanced solutions, addressing both the facets of knowledge forgetting and model utility maintenance.