# Efficient Knowledge Graph Unlearning with Zeroth-order Information

arXiv: https://arxiv.org/abs/2508.14013 · HTML: https://mlsanity.com/paper/2508.14013/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 38 of its 62 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Unlearn What You Want to Forget: Efficient Unlearning for LLMs](https://mlsanity.com/paper/2310.20150/) (2023)
- [When Machine Unlearning Jeopardizes Privacy](https://mlsanity.com/paper/2005.02205/) (2020)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [DeltaGrad: Rapid retraining of machine learning models](https://mlsanity.com/paper/2006.14755/) (2020)
- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Boundary Unlearning](https://mlsanity.com/paper/2303.11570/) (2023)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [KGA: A General Machine Unlearning Framework Based on Knowledge Gap Alignment](https://mlsanity.com/paper/2305.06535/) (2023)
- [Towards Adversarial Evaluations for Inexact Machine Unlearning](https://mlsanity.com/paper/2201.06640/) (2022)
- [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)
- [Spurious Forgetting in Continual Learning of Language Models](https://mlsanity.com/paper/2501.13453/) (2025)

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

- [Downgrade to Upgrade: Optimizer Simplification Enhances Robustness in LLM Unlearning](https://mlsanity.com/paper/2510.00761/) (2025)
- [Forget-It-All: Multi-Concept Machine Unlearning via Concept-Aware Neuron Masking](https://mlsanity.com/paper/2601.06163/) (2026)
- [Compositional Concepts Erasing: Disentangling Object-Style via Domain Manifold Unlearning](https://mlsanity.com/paper/2610.14514/) (2026)

## Abstract (arXiv)

Due to regulations like the Right to be Forgotten, there is growing demand for removing training data and its influence from models. Since full retraining is costly, various machine unlearning methods have been proposed. In this paper, we firstly present an efficient knowledge graph (KG) unlearning algorithm. We remark that KG unlearning is nontrivial due to the distinctive structure of KG and the semantic relations between entities. Also, unlearning by estimating the influence of removed components incurs significant computational overhead when applied to large-scale knowledge graphs. To this end, we define an influence function for KG unlearning and propose to approximate the model's sensitivity without expensive computation of first-order and second-order derivatives for parameter updates. Specifically, we use Taylor expansion to estimate the parameter changes caused by data removal. Given that the first-order gradients and second-order derivatives dominate the computational load, we use the Fisher matrices and zeroth-order optimization to approximate the inverse-Hessian vector product without constructing the computational graphs. Our experimental results demonstrate that the proposed method outperforms other state-of-the-art graph unlearning baselines significantly in terms of unlearning efficiency and unlearning quality. Our code is released at https://github.com/NKUShaw/ZOWFKGIF.