# Perturbation-Restrained Sequential Model Editing

arXiv: https://arxiv.org/abs/2405.16821 · HTML: https://mlsanity.com/paper/2405.16821/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 70 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Reading Wikipedia to Answer Open-Domain Questions](https://mlsanity.com/paper/1704.00051/) (2017)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Memory-Based Model Editing at Scale](https://mlsanity.com/paper/2206.06520/) (2022)
- [Zero-Shot Relation Extraction via Reading Comprehension](https://mlsanity.com/paper/1706.04115/) (2017)
- [Editing Large Language Models: Problems, Methods, and Opportunities](https://mlsanity.com/paper/2305.13172/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Check Your Facts and Try Again: Improving Large Language Models with External Knowledge and Automated Feedback](https://mlsanity.com/paper/2302.12813/) (2023)
- [MQuAKE: Assessing Knowledge Editing in Language Models via Multi-Hop Questions](https://mlsanity.com/paper/2305.14795/) (2023)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Aging with GRACE: Lifelong Model Editing with Discrete Key-Value Adaptors](https://mlsanity.com/paper/2211.11031/) (2022)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Evaluating the Ripple Effects of Knowledge Editing in Language Models](https://mlsanity.com/paper/2307.12976/) (2023)
- [A Comprehensive Study of Knowledge Editing for Large Language Models](https://mlsanity.com/paper/2401.01286/) (2024)
- [On Prompt-Driven Safeguarding for Large Language Models](https://mlsanity.com/paper/2401.18018/) (2024)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)

## Built on by (most cited first, 28 of 28)

- [AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models](https://mlsanity.com/paper/2410.02355/) (2024)
- [Lifelong Learning of Large Language Model based Agents: A Roadmap](https://mlsanity.com/paper/2501.07278/) (2025)
- [Reinforced Lifelong Editing for Language Models](https://mlsanity.com/paper/2502.05759/) (2025)
- [Can Editing LLMs Inject Harm?](https://mlsanity.com/paper/2407.20224/) (2024)
- [Neuron-Level Sequential Editing for Large Language Models](https://mlsanity.com/paper/2410.04045/) (2024)
- [Lifelong Knowledge Editing requires Better Regularization](https://mlsanity.com/paper/2502.01636/) (2025)
- [Is Model Editing Built on Sand? Revealing Its Illusory Success and Fragile Foundation](https://mlsanity.com/paper/2510.00625/) (2025)
- [Resolving Lexical Bias in Model Editing](https://mlsanity.com/paper/2408.10411/) (2024)
- [ThinkEval: Practical Evaluation of Knowledge Leakage in LLM Editing using Thought-based Knowledge Graphs](https://mlsanity.com/paper/2506.01386/) (2025)
- [Are We Evaluating the Edit Locality of LLM Model Editing Properly?](https://mlsanity.com/paper/2601.17343/) (2026)
- [Keys to Robust Edits: from Theoretical Insights to Practical Advances](https://mlsanity.com/paper/2410.09338/) (2024)
- [PropMEND: Hypernetworks for Knowledge Propagation in LLMs](https://mlsanity.com/paper/2506.08920/) (2025)
- [NeuralDB: Scaling Knowledge Editing in LLMs to 100,000 Facts with Neural KV Database](https://mlsanity.com/paper/2507.18028/) (2025)
- [Energy-Regularized Sequential Model Editing on Hyperspheres](https://mlsanity.com/paper/2510.01172/) (2025)
- [Reverse-Engineering Model Editing on Language Models](https://mlsanity.com/paper/2602.10134/) (2026)
- [From Backward Spreading to Forward Replay: Revisiting Target Construction in LLM Parameter Editing](https://mlsanity.com/paper/2605.00358/) (2026)
- [SUIT: Knowledge Editing with Subspace-Aware Key-Value Mappings](https://mlsanity.com/paper/2509.24502/) (2025)
- [Norm Anchors Make Model Edits Last](https://mlsanity.com/paper/2602.02543/) (2026)
- [Towards Scalable Lifelong Knowledge Editing with Selective Knowledge Suppression](https://mlsanity.com/paper/2604.19089/) (2026)
- [BetaEdit: Null-Space Constrained Sequential Model Editing](https://mlsanity.com/paper/2605.09285/) (2026)
- [RASteer: Retain-Aware Activation Steering for Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2610.01969/) (2026)
- [MetaKE: Meta-Learning for Knowledge Editing Toward a Better Accuracy-Editability Trade-off](https://mlsanity.com/paper/2603.12677/) (2026)
- [When to Write and When to Suppress: Route-Specialized Dual Adapters for Memory-Assisted Knowledge Editing](https://mlsanity.com/paper/2606.14668/) (2026)
- [Moir: Let the Model Direct Its Own Story for Robust Cross-Domain Knowledge Editing](https://mlsanity.com/paper/2607.20433/) (2026)
- [The Tokens Remember: When Tokenization Bypasses Knowledge Editing and Unlearning](https://mlsanity.com/paper/2609.29045/) (2026)
- [ManiEdit: Sequential Unstructured Knowledge Editing for Language Models from a Manifold Perspective](https://mlsanity.com/paper/2609.33534/) (2026)
- [Continual Concept Erasure in Diffusion Models by Suppressing Cross-Edit Interference](https://mlsanity.com/paper/2610.01989/) (2026)
- [Generalizable Model Editing Could Be More Than Direct Generalization](https://mlsanity.com/paper/2610.15707/) (2026)

## Abstract (arXiv)

Model editing is an emerging field that focuses on updating the knowledge embedded within large language models (LLMs) without extensive retraining. However, current model editing methods significantly compromise the general abilities of LLMs as the number of edits increases, and this trade-off poses a substantial challenge to the continual learning of LLMs. In this paper, we first theoretically analyze that the factor affecting the general abilities in sequential model editing lies in the condition number of the edited matrix. The condition number of a matrix represents its numerical sensitivity, and therefore can be used to indicate the extent to which the original knowledge associations stored in LLMs are perturbed after editing. Subsequently, statistical findings demonstrate that the value of this factor becomes larger as the number of edits increases, thereby exacerbating the deterioration of general abilities. To this end, a framework termed Perturbation Restraint on Upper bouNd for Editing (PRUNE) is proposed, which applies the condition number restraints in sequential editing. These restraints can lower the upper bound on perturbation to edited models, thus preserving the general abilities. Systematically, we conduct experiments employing three editing methods on three LLMs across four downstream tasks. The results show that PRUNE can preserve general abilities while maintaining the editing performance effectively in sequential model editing. The code are available at https://github.com/mjy1111/PRUNE.