---
title: "SpecEdit: A Spectral Approach for Multi-Round Knowledge Editing"
description: "The authors study this in locate-then-edit methods such as MEMIT and AlphaEdit. 30 references."
authors: ["Junxian Liu", "Zikun Deng", "Xin Wu", "Dazhen Deng", "Yi Cai"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.922/"
doi: "10.18653/v1/2026.findings-acl.922"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/liu-2026-specedit-spectral-approach-multi-round/"
---
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# SpecEdit: A Spectral Approach for Multi-Round Knowledge Editing

**Authors:** Junxian Liu, Zikun Deng, [Xin Wu](https://md.research.elamur.ai/free/en/authors/xin-wu/), Dazhen Deng and [Yi Cai](https://md.research.elamur.ai/free/en/authors/yi-cai/) · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.922/) · [PDF](https://aclanthology.org/2026.findings-acl.922.pdf) · [DOI 10.18653/v1/2026.findings-acl.922](https://doi.org/10.18653/v1/2026.findings-acl.922) · [OpenAlex](https://openalex.org/W7166798996)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Repeated batch editing of a large language model tends to wear down quality over time. Newly inserted facts are written less reliably, paraphrased queries generalize worse, and neighbouring knowledge gets disturbed. The authors study this in locate-then-edit methods such as MEMIT and AlphaEdit. In these methods, the closed-form update adds the second-order statistics of the model's original knowledge (K0) to those of earlier edits (Kp) and then inverts the sum.

A spectral analysis on GPT2-XL with CounterFact shows that the two sources behave very differently. Intrinsic knowledge spreads its energy over many directions, while edit history concentrates it in a few dominant ones, so simply summing them skews the resulting update.

SpecEdit addresses this in three stages:
- it isolates the editing-critical subspace (spectral decoupling);
- it restores information lost for both sources (compensation);
- it recombines the refined parts into a new closed-form solution (spectral fusion).

The module attaches to existing solvers without altering their optimization. It gives consistent improvements across several LLMs and editing methods, offering an interpretable path toward more stable lifelong editing.

## Key points
- The spectrum of Cp = KpKpᵀ shows three abrupt drops, and the position of the second drop scales with the number of edited facts (near i ≈ 500 for 500 edits). This point is used to split Cp into an editing-critical part (Cp1) and a weak tail (Cp2), and C0 is decomposed by projecting it onto the Cp1 subspace.
- SpecEdit works as a plug-and-play preprocessing and enhancement step for MEMIT and AlphaEdit, evaluated on GPT2-XL, GPT-J and LLaMA3.
- In the ablations on GPT2-XL (dim(Kp) = 6400), compensation alone lowers efficacy and generalization while helping specificity and fluency. Adding decoupling turns it into a net gain. On GPT-J, the combined gains begin to saturate, which the authors attribute to limited memory capacity.
- Stated limitations: the split point and hyperparameters may need manual tuning per model, layer or dataset, and the compensation scheme is deliberately coarse-grained.
- Code: https://github.com/MKCatch/SpecEdit

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Zhejiang University](https://md.research.elamur.ai/free/en/universities/zhejiang-university/) — University, Hangzhou, China · 172 works · 12,988 citations
- [South China University of Technology](https://md.research.elamur.ai/free/en/universities/south-china-university-of-technology/) — University, Guangzhou, China · 22 works · 1,554 citations

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## Cite

Cite as: Junxian Liu, Zikun Deng, Xin Wu, Dazhen Deng and Yi Cai. 2026. SpecEdit: A Spectral Approach for Multi-Round Knowledge Editing. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{liu2026specedit,
  title = {{SpecEdit: A Spectral Approach for Multi-Round Knowledge Editing}},
  author = {Junxian Liu, Zikun Deng, Xin Wu, Dazhen Deng and Yi Cai},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.922},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.922}
}
```

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## References

30 references, 8 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Nicola De Cao, Wilker Aziz, and Ivan Titov. 2021. Editing factual knowledge in language models. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 6491–6506. [find](https://scholar.google.com/scholar?q=Nicola+De+Cao%2C+Wilker+Aziz%2C+and+Ivan+Titov%2E+2021%2E+Editing+factual+knowledge+in+language+models%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in+Natural+Language+Processing%2C+pages+6491%E2%80%936506%2E)
2. Damai Dai, Li Dong, Yaru Hao, Zhifang Sui, Baobao Chang, and Furu Wei. 2022. Knowledge neurons in pretrained transformers. In Proceedings of the Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 8493– 8502. [find](https://scholar.google.com/scholar?q=Damai+Dai%2C+Li+Dong%2C+Yaru+Hao%2C+Zhifang+Sui%2C+Baobao+Chang%2C+and+Furu+Wei%2E+2022%2E+Knowledge+neurons+in+pretrained+transformers%2E+In+Proceedings+of+the+Annual+Meeting+of+the+Association+for+Computational+Lin)
3. Chandler Davis and W. M. Kahan. 1970. The rotation of eigenvectors by a perturbation. iii. SIAM Journal on Numerical Analysis, 7(1):1–46. [find](https://scholar.google.com/scholar?q=Chandler+Davis+and+W%2E+M%2E+Kahan%2E+1970%2E+The+rotation+of+eigenvectors+by+a+perturbation%2E+iii%2E+SIAM+Journal+on+Numerical+Analysis%2C+7%281%29%3A1%E2%80%9346%2E)
4. Junfeng Fang, Houcheng Jiang, Kun Wang, Yunshan Ma, Jie Shi, Xiang Wang, Xiangnan He, and Tat-Seng Chua. 2025. AlphaEdit: Null-space constrained knowledge editing for language models. In International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Junfeng+Fang%2C+Houcheng+Jiang%2C+Kun+Wang%2C+Yunshan+Ma%2C+Jie+Shi%2C+Xiang+Wang%2C+Xiangnan+He%2C+and+Tat%2DSeng+Chua%2E+2025%2E+AlphaEdit%3A+Null%2Dspace+constrained+knowledge+editing+for+language+models%2E+In+International)
5. Mor Geva, Roei Schuster, Jonathan Berant, and Omer Levy. 2021. Transformer feed-forward layers are key-value memories. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 5484–5495. [find](https://scholar.google.com/scholar?q=Mor+Geva%2C+Roei+Schuster%2C+Jonathan+Berant%2C+and+Omer+Levy%2E+2021%2E+Transformer+feed%2Dforward+layers+are+key%2Dvalue+memories%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in+Natural+Language+Process)
6. Jia-Chen Gu, Hao-Xiang Xu, Jun-Yu Ma, Pan Lu, Zhen-Hua Ling, Kai-Wei Chang, and Nanyun Peng. 2024. [Model editing harms general abilities of large language models: Regularization to the rescue](https://md.research.elamur.ai/free/en/papers/gu-2024-model-editing-harms-general-abilities/). In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 16801–16819.
7. Akshat Gupta, Phudish Prateepamornkul, Maochuan Lu, Ahmed Alaa, Thomas Hartvigsen, and Gopala Anumanchipalli. 2025. Lifelong knowledge editing requires better regularization. In Findings of the Association for Computational Linguistics: EMNLP. [find](https://scholar.google.com/scholar?q=Akshat+Gupta%2C+Phudish+Prateepamornkul%2C+Maochuan+Lu%2C+Ahmed+Alaa%2C+Thomas+Hartvigsen%2C+and+Gopala+Anumanchipalli%2E+2025%2E+Lifelong+knowledge+editing+requires+better+regularization%2E+In+Findings+of+the+Associ)
8. Tom Hartvigsen, Swami Sankaranarayanan, Hamid Palangi, Yoon Kim, and Marzyeh Ghassemi. 2023. Aging with GRACE: Lifelong model editing with discrete key-value adaptors. In Proceedings of Annual Conference on Neural Information Processing Systems. [find](https://scholar.google.com/scholar?q=Tom+Hartvigsen%2C+Swami+Sankaranarayanan%2C+Hamid+Palangi%2C+Yoon+Kim%2C+and+Marzyeh+Ghassemi%2E+2023%2E+Aging+with+GRACE%3A+Lifelong+model+editing+with+discrete+key%2Dvalue+adaptors%2E+In+Proceedings+of+Annual+Confere)
9. Chenhui Hu, Pengfei Cao, Yubo Chen, Kang Liu, and Jun Zhao. 2024. WilKE: Wise-layer knowledge editor for lifelong knowledge editing. In Findings of the Association for Computational Linguistics, pages 3476–3503. [find](https://scholar.google.com/scholar?q=Chenhui+Hu%2C+Pengfei+Cao%2C+Yubo+Chen%2C+Kang+Liu%2C+and+Jun+Zhao%2E+2024%2E+WilKE%3A+Wise%2Dlayer+knowledge+editor+for+lifelong+knowledge+editing%2E+In+Findings+of+the+Association+for+Computational+Linguistics%2C+pages)
10. Lei Huang, Weijiang Yu, Weitao Ma, Weihong Zhong, Zhangyin Feng, Haotian Wang, Qianglong Chen, Weihua Peng, Xiaocheng Feng, Bing Qin, and Ting Liu. 2025. [A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions](https://md.research.elamur.ai/free/en/papers/huang-2023-survey-hallucination-large-language-models/). ACM Trans. Inf. Syst., 43(2):42:1– 42:55…
11. Zeyu Huang, Yikang Shen, Xiaofeng Zhang, Jie Zhou, Wenge Rong, and Zhang Xiong. 2023. [Transformer-Patcher: One mistake worth one neuron](https://md.research.elamur.ai/free/en/papers/huang-2023-transformer-patcher-one-mistake-worth/). In Proceedings of the International Conference on Learning Representations.
12. Ziwei Ji, Tiezheng Yu, Yan Xu, Nayeon Lee, Etsuko Ishii, and Pascale Fung. 2023. [Towards mitigating LLM hallucination via self reflection](https://md.research.elamur.ai/free/en/papers/ji-2023-mitigating-llm-hallucination-self-reflection/). In Findings of the Association for Computational Linguistics: EMNLP, pages 1827–1843.
13. Houcheng Jiang, Junfeng Fang, Tianyu Zhang, Baolong Bi, An Zhang, Ruipeng Wang, Tao Liang, and Xiang Wang. 2025. [Neuron-level sequential editing for large language models](https://md.research.elamur.ai/free/en/papers/jiang-2025-neuron-level-sequential-editing-large/). In Proceedings of the Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 16678– 1670…
14. Omer Levy, Minjoon Seo, Eunsol Choi, and Luke Zettlemoyer. 2017. [Zero-shot relation extraction via reading comprehension](https://md.research.elamur.ai/free/en/papers/levy-2017-zero-shot-relation-extraction-reading/). In Proceedings of the Conference on Computational Natural Language Learning (CoNLL 2017), pages 333–342.
15. Jun-Yu Ma, Hong Wang, Hao-Xiang Xu, Zhen-Hua Ling, and Jia-Chen Gu. 2025. Perturbation-restrained sequential model editing. In Proceedings of the Thirteenth International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Jun%2DYu+Ma%2C+Hong+Wang%2C+Hao%2DXiang+Xu%2C+Zhen%2DHua+Ling%2C+and+Jia%2DChen+Gu%2E+2025%2E+Perturbation%2Drestrained+sequential+model+editing%2E+In+Proceedings+of+the+Thirteenth+International+Conference+on+Learning+Repres)
16. Aman Madaan, Niket Tandon, Peter Clark, and Yiming Yang. 2022. MemPrompt: Memory-assisted prompt editing with user feedback. In Proceedings of the Conference on Empirical Methods in Natural Language Processing. [find](https://scholar.google.com/scholar?q=Aman+Madaan%2C+Niket+Tandon%2C+Peter+Clark%2C+and+Yiming+Yang%2E+2022%2E+MemPrompt%3A+Memory%2Dassisted+prompt+editing+with+user+feedback%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in+Natural+Language+P)
17. Kevin Meng, David Bau, Alex Andonian, and Yonatan Belinkov. 2022. Locating and editing factual associations in gpt. In Advances in Neural Information Processing Systems, volume 35, pages 17359–17372. Curran Associates, Inc. [find](https://scholar.google.com/scholar?q=Kevin+Meng%2C+David+Bau%2C+Alex+Andonian%2C+and+Yonatan+Belinkov%2E+2022%2E+Locating+and+editing+factual+associations+in+gpt%2E+In+Advances+in+Neural+Information+Processing+Systems%2C+volume+35%2C+pages+17359%E2%80%9317372%2E+)
18. Kevin Meng, Arnab Sen Sharma, Alex J Andonian, Yonatan Belinkov, and David Bau. 2023. Mass-editing memory in a transformer. In The Eleventh International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Kevin+Meng%2C+Arnab+Sen+Sharma%2C+Alex+J+Andonian%2C+Yonatan+Belinkov%2C+and+David+Bau%2E+2023%2E+Mass%2Dediting+memory+in+a+transformer%2E+In+The+Eleventh+International+Conference+on+Learning+Representations%2E)
19. Eric Mitchell, Charles Lin, Antoine Bosselut, Chelsea Finn, and Christopher D Manning. 2022a. Fast model editing at scale. In International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Eric+Mitchell%2C+Charles+Lin%2C+Antoine+Bosselut%2C+Chelsea+Finn%2C+and+Christopher+D+Manning%2E+2022a%2E+Fast+model+editing+at+scale%2E+In+International+Conference+on+Learning+Representations%2E)
20. Eric Mitchell, Charles Lin, Antoine Bosselut, Christopher D. Manning, and Chelsea Finn. 2022b. Memory-based model editing at scale. In Proceedings of International Conference on Machine Learning, volume 162, pages 15817–15831. [find](https://scholar.google.com/scholar?q=Eric+Mitchell%2C+Charles+Lin%2C+Antoine+Bosselut%2C+Christopher+D%2E+Manning%2C+and+Chelsea+Finn%2E+2022b%2E+Memory%2Dbased+model+editing+at+scale%2E+In+Proceedings+of+International+Conference+on+Machine+Learning%2C+volu)
21. Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. 2017. [Attention is all you need](https://md.research.elamur.ai/free/en/papers/vaswani-2017-attention-all-need/). In Proceedings of Annual Conference on Neural Information Processing Systems, pages 5998– 6008.
22. Peng Wang, Zexi Li, Ningyu Zhang, Ziwen Xu, Yunzhi Yao, Yong Jiang, Pengjun Xie, Fei Huang, and Huajun Chen. 2024a. WISE: Rethinking the knowledge memory for lifelong model editing of large language models. In Proceedings of the Annual Conference on Neural Information Processing Systems. [find](https://scholar.google.com/scholar?q=Peng+Wang%2C+Zexi+Li%2C+Ningyu+Zhang%2C+Ziwen+Xu%2C+Yunzhi+Yao%2C+Yong+Jiang%2C+Pengjun+Xie%2C+Fei+Huang%2C+and+Huajun+Chen%2E+2024a%2E+WISE%3A+Rethinking+the+knowledge+memory+for+lifelong+model+editing+of+large+language+m)
23. Song Wang, Yaochen Zhu, Haochen Liu, Zaiyi Zheng, Chen Chen, and Jundong Li. 2024b. Knowledge editing for [large language models: A survey](https://md.research.elamur.ai/free/en/papers/minaee-2024-large-language-models-survey/). ACM Comput. Surv., 57(3).
24. Xin Wu, Yuqi Bu, Yi Cai, and Tao Wang. 2024. Updating large language models’ memories with time constraints. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 13693– 13702. [find](https://scholar.google.com/scholar?q=Xin+Wu%2C+Yuqi+Bu%2C+Yi+Cai%2C+and+Tao+Wang%2E+2024%2E+Updating+large+language+models%E2%80%99+memories+with+time+constraints%2E+In+Findings+of+the+Association+for+Computational+Linguistics%3A+EMNLP+2024%2C+pages+13693%E2%80%93+1370)
25. Haoyu Xu, Pengxiang Lan, Enneng Yang, Guibing Guo, Jianzhe Zhao, Linying Jiang, and Xingwei Wang. 2025. Knowledge decoupling via orthogonal projection for lifelong editing of large language models. In Proceedings of the Annual Meeting of the Association for Computational Linguistics (Volume 1: Long… [find](https://scholar.google.com/scholar?q=Haoyu+Xu%2C+Pengxiang+Lan%2C+Enneng+Yang%2C+Guibing+Guo%2C+Jianzhe+Zhao%2C+Linying+Jiang%2C+and+Xingwei+Wang%2E+2025%2E+Knowledge+decoupling+via+orthogonal+projection+for+lifelong+editing+of+large+language+models%2E+In)
26. Yunzhi Yao, Peng Wang, Bozhong Tian, Siyuan Cheng, Zhoubo Li, Shumin Deng, Huajun Chen, and Ningyu Zhang. 2023. Editing large language models: Problems, methods, and opportunities. pages 10222– 10240. [find](https://scholar.google.com/scholar?q=Yunzhi+Yao%2C+Peng+Wang%2C+Bozhong+Tian%2C+Siyuan+Cheng%2C+Zhoubo+Li%2C+Shumin+Deng%2C+Huajun+Chen%2C+and+Ningyu+Zhang%2E+2023%2E+Editing+large+language+models%3A+Problems%2C+methods%2C+and+opportunities%2E+pages+10222%E2%80%93+10240%2E)
27. Ningyu Zhang, Yunzhi Yao, Bozhong Tian, Peng Wang, Shumin Deng, Mengru Wang, Zekun Xi, Shengyu Mao, Jintian Zhang, Yuansheng Ni, Siyuan Cheng, Ziwen Xu, Xin Xu, Jia-Chen Gu, Yong Jiang, Pengjun Xie, Fei Huang, Lei Liang, Zhiqiang Zhang, and 3 others. 2024. A comprehensive study of knowledge editing… [find](https://scholar.google.com/scholar?q=Ningyu+Zhang%2C+Yunzhi+Yao%2C+Bozhong+Tian%2C+Peng+Wang%2C+Shumin+Deng%2C+Mengru+Wang%2C+Zekun+Xi%2C+Shengyu+Mao%2C+Jintian+Zhang%2C+Yuansheng+Ni%2C+Siyuan+Cheng%2C+Ziwen+Xu%2C+Xin+Xu%2C+Jia%2DChen+Gu%2C+Yong+Jiang%2C+Pengjun+Xie%2C+F)
28. Ce Zheng, Lei Li, Qingxiu Dong, Yuxuan Fan, Zhiyong Wu, Jingjing Xu, and Baobao Chang. 2023. Can we edit factual knowledge by in-context learning? In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 4862–4876. [find](https://scholar.google.com/scholar?q=Ce+Zheng%2C+Lei+Li%2C+Qingxiu+Dong%2C+Yuxuan+Fan%2C+Zhiyong+Wu%2C+Jingjing+Xu%2C+and+Baobao+Chang%2E+2023%2E+Can+we+edit+factual+knowledge+by+in%2Dcontext+learning%3F+In+Proceedings+of+the+Conference+on+Empirical+Methods)
29. Bihan Zhou, Haopeng Ren, Li Yuan, Yi Cai, Liuwen Cao, and Zikun Deng. 2025a. Ruleedit: Towards rule-level knowledge generalization to mitigate over-editing in large language models. In Findings of the Association for Computational Linguistics: ACL 2025, pages 3159–3175. [find](https://scholar.google.com/scholar?q=Bihan+Zhou%2C+Haopeng+Ren%2C+Li+Yuan%2C+Yi+Cai%2C+Liuwen+Cao%2C+and+Zikun+Deng%2E+2025a%2E+Ruleedit%3A+Towards+rule%2Dlevel+knowledge+generalization+to+mitigate+over%2Dediting+in+large+language+models%2E+In+Findings+of+the)
30. Wei Zhou, Wei Wei, Guibang Cao, and Fei Wang. 2025b. Editing memories through few targeted neurons. In Proceedings of the AAAI Conference on Artificial Intelligence. [find](https://scholar.google.com/scholar?q=Wei+Zhou%2C+Wei+Wei%2C+Guibang+Cao%2C+and+Fei+Wang%2E+2025b%2E+Editing+memories+through+few+targeted+neurons%2E+In+Proceedings+of+the+AAAI+Conference+on+Artificial+Intelligence%2E)

*Updated 1 November 2026*