# GIF: A General Graph Unlearning Strategy via Influence Function

arXiv: https://arxiv.org/abs/2304.02835 · HTML: https://mlsanity.com/paper/2304.02835/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Placed in Graph unlearning, one of 12 directions in LLM safety and security.
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Placed in

- LLM safety and security / [Graph unlearning](https://mlsanity.com/safety/graph-unlearning/)

## Builds on (most cited first, 30 of 30)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Recommendation Unlearning](https://mlsanity.com/paper/2201.06820/) (2022)
- [Let Invariant Rationale Discovery Inspire Graph Contrastive Learning](https://mlsanity.com/paper/2206.07869/) (2022)
- [Hard to Forget: Poisoning Attacks on Certified Machine Unlearning](https://mlsanity.com/paper/2109.08266/) (2021)
- [Poison Ink: Robust and Invisible Backdoor Attack](https://mlsanity.com/paper/2108.02488/) (2021)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [On the Effectiveness of Sampled Softmax Loss for Item Recommendation](https://mlsanity.com/paper/2201.02327/) (2022)
- [Coded Machine Unlearning](https://mlsanity.com/paper/2012.15721/) (2020)
- [Incorporating Bias-aware Margins into Contrastive Loss for Collaborative Filtering](https://mlsanity.com/paper/2210.11054/) (2022)
- [Characterizing the Influence of Graph Elements](https://mlsanity.com/paper/2210.07441/) (2022)

## Built on by (most cited first, 30 of 60)

- [Machine Unlearning: Solutions and Challenges](https://mlsanity.com/paper/2308.07061/) (2023)
- [Exploring the Landscape of Machine Unlearning: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2305.06360/) (2023)
- [Machine Unlearning Fails to Remove Data Poisoning Attacks](https://mlsanity.com/paper/2406.17216/) (2024)
- [Machine Unlearning: A Comprehensive Survey](https://mlsanity.com/paper/2405.07406/) (2024)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Towards Effective and General Graph Unlearning via Mutual Evolution](https://mlsanity.com/paper/2401.11760/) (2024)
- [Unified Parameter-Efficient Unlearning for LLMs](https://mlsanity.com/paper/2412.00383/) (2024)
- [IDEA: A Flexible Framework of Certified Unlearning for Graph Neural Networks](https://mlsanity.com/paper/2407.19398/) (2024)
- [Verification of Machine Unlearning is Fragile](https://mlsanity.com/paper/2408.00929/) (2024)
- [Graph Unlearning with Efficient Partial Retraining](https://mlsanity.com/paper/2403.07353/) (2024)
- [Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformation](https://mlsanity.com/paper/2405.14407/) (2024)
- [Scalable and Certifiable Graph Unlearning: Overcoming the Approximation Error Barrier](https://mlsanity.com/paper/2408.09212/) (2024)
- [Distill to Delete: Unlearning in Graph Networks with Knowledge Distillation](https://mlsanity.com/paper/2309.16173/) (2023)
- [A Survey of Graph Unlearning](https://mlsanity.com/paper/2310.02164/) (2023)
- [Unlink to Unlearn: Simplifying Edge Unlearning in GNNs](https://mlsanity.com/paper/2402.10695/) (2024)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [A Certified Unlearning Approach without Access to Source Data](https://mlsanity.com/paper/2506.06486/) (2025)
- [GraphGuard: Detecting and Counteracting Training Data Misuse in Graph Neural Networks](https://mlsanity.com/paper/2312.07861/) (2023)
- [OpenGU: A Comprehensive Benchmark for Graph Unlearning](https://mlsanity.com/paper/2501.02728/) (2025)
- [Deeper Understanding of Black-box Predictions via Generalized Influence Functions](https://mlsanity.com/paper/2312.05586/) (2023)
- [FUNU: Boosting Machine Unlearning Efficiency by Filtering Unnecessary Unlearning](https://mlsanity.com/paper/2501.16614/) (2025)
- [TAPE: Tailored Posterior Difference for Auditing of Machine Unlearning](https://mlsanity.com/paper/2502.19770/) (2025)
- [On the Effectiveness of Unlearning in Session-Based Recommendation](https://mlsanity.com/paper/2312.14447/) (2023)
- [Graph Memory Learning: Imitating Lifelong Remembering and Forgetting of Brain Networks](https://mlsanity.com/paper/2407.19183/) (2024)
- [FROG: Fair Removal on Graphs](https://mlsanity.com/paper/2503.18197/) (2025)
- [Unlearning Inversion Attacks for Graph Neural Networks](https://mlsanity.com/paper/2506.00808/) (2025)
- [Self-Evolving Agents as Dynamic Graph Transformation: A Survey and New Perspective](https://mlsanity.com/paper/2608.18104/) (2026)
- [Can Graph Neural Networks Expose Training Data Properties? An Efficient Risk Assessment Approach](https://mlsanity.com/paper/2411.03663/) (2024)
- [Enabling Group Fairness in Graph Unlearning via Bi-level Debiasing](https://mlsanity.com/paper/2505.09702/) (2025)
- [Influence Functions for Edge Edits in Non-Convex Graph Neural Networks](https://mlsanity.com/paper/2506.04694/) (2025)

## Abstract (arXiv)

With the greater emphasis on privacy and security in our society, the problem of graph unlearning -- revoking the influence of specific data on the trained GNN model, is drawing increasing attention. However, ranging from machine unlearning to recently emerged graph unlearning methods, existing efforts either resort to retraining paradigm, or perform approximate erasure that fails to consider the inter-dependency between connected neighbors or imposes constraints on GNN structure, therefore hard to achieve satisfying performance-complexity trade-offs. In this work, we explore the influence function tailored for graph unlearning, so as to improve the unlearning efficacy and efficiency for graph unlearning. We first present a unified problem formulation of diverse graph unlearning tasks wrt node, edge, and feature. Then, we recognize the crux to the inability of traditional influence function for graph unlearning, and devise Graph Influence Function (GIF), a model-agnostic unlearning method that can efficiently and accurately estimate parameter changes in response to a ε-mass perturbation in deleted data. The idea is to supplement the objective of the traditional influence function with an additional loss term of the influenced neighbors due to the structural dependency. Further deductions on the closed-form solution of parameter changes provide a better understanding of the unlearning mechanism. We conduct extensive experiments on four representative GNN models and three benchmark datasets to justify the superiority of GIF for diverse graph unlearning tasks in terms of unlearning efficacy, model utility, and unlearning efficiency. Our implementations are available at urlhttps://github.com/wujcan/GIF-torch/.