Graph unlearning, which aims to eliminate the influence of specific nodes, edges, or attributes from a trained Graph Neural Network (GNN), is essential in applications where privacy, bias, or data obsolescence is a concern. However, existing graph unlearning techniques often necessitate additional training on the remaining data, leading to significant computational costs, particularly with large-scale graphs. To address these challenges, we propose a two-stage training-free approach, Erase then Rectify (ETR), designed for efficient and scalable graph unlearning while preserving the model utility. Specifically, we first build a theoretical foundation showing that masking parameters critical for unlearned samples enables effective unlearning. Building on this insight, the Erase stage strategically edits model parameters to eliminate the impact of unlearned samples and their propagated influence on intercorrelated nodes. To further ensure the GNN's utility, the Rectify stage devises a gradient approximation method to estimate the model's gradient on the remaining dataset, which is then used to enhance model performance. Overall, ETR achieves graph unlearning without additional training or full training data access, significantly reducing computational overhead and preserving data privacy. Extensive experiments on seven public datasets demonstrate the consistent superiority of ETR in model utility, unlearning efficiency, and unlearning effectiveness, establishing it as a promising solution for real-world graph unlearning challenges.

本研究解决了现有图学习遗忘技术需要在剩余数据上进行额外训练，导致高昂计算成本的问题。提出了一种两阶段的无训练方法“先删除再修正”（ETR），通过战略性地编辑模型参数以消除未学习样本的影响，从而有效实现图学习遗忘，并在模型性能上进行了增强。实验结果表明，ETR在模型实用性、学习遗忘效率和有效性方面都表现出色，成为解决实际图学习遗忘挑战的有前景方案。

先删除再修正：一种无需训练的参数编辑方法用于成本有效的图学习遗忘