Graph Unlearning Meets Influence-aware Negative Preference Optimization

TL;DR

This paper introduces INPO, a novel influence-aware negative preference optimization framework for graph unlearning that slows divergence and enhances robustness, outperforming existing methods in utility and forget quality.

Contribution

INPO is the first framework to incorporate influence-aware message functions and topological entropy loss for improved graph unlearning performance.

Findings

INPO achieves state-of-the-art forget quality metrics.

INPO maintains higher model utility during unlearning.

The influence-aware approach reduces impact of unlearning high-influence edges.

Abstract

Recent advancements in graph unlearning models have enhanced model utility by preserving the node representation essentially invariant, while using gradient ascent on the forget set to achieve unlearning. However, this approach causes a drastic degradation in model utility during the unlearning process due to the rapid divergence speed of gradient ascent. In this paper, we introduce \textbf{INPO}, an \textbf{I}nfluence-aware \textbf{N}egative \textbf{P}reference \textbf{O}ptimization framework that focuses on slowing the divergence speed and improving the robustness of the model utility to the unlearning process. Specifically, we first analyze that NPO has slower divergence speed and theoretically propose that unlearning high-influence edges can reduce impact of unlearning. We design an influence-aware message function to amplify the influence of unlearned edges and mitigate the tight topological coupling between the forget set and the retain set. The influence of each edge is quickly estimated by a removal-based method. Additionally, we propose a topological entropy loss from the perspective of topology to avoid excessive information loss in the local structure during unlearning. Extensive experiments conducted on five real-world datasets demonstrate that INPO-based model achieves state-of-the-art performance on all forget quality metrics while maintaining the model's utility. Codes are available at \href{https://github.com/sh-qiangchen/INPO}{https://github.com/sh-qiangchen/INPO}.