# Graph Unlearning via Embedding Reconstruction -- A Range-Null Space Decomposition Approach

arXiv: https://arxiv.org/abs/2508.02044 · HTML: https://mlsanity.com/paper/2508.02044/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Graph unlearning, one of 12 directions in LLM safety and security.
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (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)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [When Machine Unlearning Jeopardizes Privacy](https://mlsanity.com/paper/2005.02205/) (2020)
- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Recommendation Unlearning](https://mlsanity.com/paper/2201.06820/) (2022)
- [GIF: A General Graph Unlearning Strategy via Influence Function](https://mlsanity.com/paper/2304.02835/) (2023)
- [Poison Ink: Robust and Invisible Backdoor Attack](https://mlsanity.com/paper/2108.02488/) (2021)
- [Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning](https://mlsanity.com/paper/2401.10371/) (2024)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [GNNDelete: A General Strategy for Unlearning in Graph Neural Networks](https://mlsanity.com/paper/2302.13406/) (2023)
- [Unlearning Graph Classifiers with Limited Data Resources](https://mlsanity.com/paper/2211.03216/) (2022)
- [Inductive Graph Unlearning](https://mlsanity.com/paper/2304.03093/) (2023)
- [Towards Effective and General Graph Unlearning via Mutual Evolution](https://mlsanity.com/paper/2401.11760/) (2024)
- [IDEA: A Flexible Framework of Certified Unlearning for Graph Neural Networks](https://mlsanity.com/paper/2407.19398/) (2024)
- [Efficiently Forgetting What You Have Learned in Graph Representation Learning via Projection](https://mlsanity.com/paper/2302.08990/) (2023)
- [Graph Unlearning with Efficient Partial Retraining](https://mlsanity.com/paper/2403.07353/) (2024)
- [Writing Polishment with Simile: Task, Dataset and A Neural Approach](https://mlsanity.com/paper/2012.08117/) (2020)
- [OpenGU: A Comprehensive Benchmark for Graph Unlearning](https://mlsanity.com/paper/2501.02728/) (2025)

## Abstract (arXiv)

Graph unlearning is tailored for GNNs to handle widespread and various graph structure unlearning requests, which remain largely unexplored. The GIF (graph influence function) achieves validity under partial edge unlearning, but faces challenges in dealing with more disturbing node unlearning. To avoid the overhead of retraining and realize the model utility of unlearning, we proposed a novel node unlearning method to reverse the process of aggregation in GNN by embedding reconstruction and to adopt Range-Null Space Decomposition for the nodes' interaction learning. Experimental results on multiple representative datasets demonstrate the SOTA performance of our proposed approach.