# Graph Unlearning Meets Influence-aware Negative Preference Optimization

arXiv: https://arxiv.org/abs/2510.19479 · HTML: https://mlsanity.com/paper/2510.19479/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 7 of its 10 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- LLM safety and security / [Graph unlearning](https://mlsanity.com/safety/graph-unlearning/)

## Builds on (most cited first, 7 of 7)

- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [GIF: A General Graph Unlearning Strategy via Influence Function](https://mlsanity.com/paper/2304.02835/) (2023)
- [Towards Effective and General Graph Unlearning via Mutual Evolution](https://mlsanity.com/paper/2401.11760/) (2024)
- [Unlink to Unlearn: Simplifying Edge Unlearning in GNNs](https://mlsanity.com/paper/2402.10695/) (2024)
- [Link Recommendation to Augment Influence Diffusion with Provable Guarantees](https://mlsanity.com/paper/2402.19189/) (2024)
- [Searching for Network Width with Bilaterally Coupled Network](https://mlsanity.com/paper/2203.13714/) (2022)
- [Fast Inference of Removal-Based Node Influence](https://mlsanity.com/paper/2403.08333/) (2024)

## Built on by (most cited first, 3 of 3)

- [FairGU: Fairness-aware Graph Unlearning in Social Networks](https://mlsanity.com/paper/2601.09469/) (2026)
- [Let Prompts Bridge Defense Knowledge: Transferable Graph Purification via Vulnerability-Aware GPL](https://mlsanity.com/paper/2608.29054/) (2026)
- [CUNO: Curriculum and Preference Optimization for Stable Graph Unlearning under Mass Deletion](https://mlsanity.com/paper/2609.08244/) (2026)

## Abstract (arXiv)

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 INPO, an Influence-aware Negative Preference Optimization 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 hrefhttps://github.com/sh-qiangchen/INPOhttps://github.com/sh-qiangchen/INPO.