Knowledge editing aims to efficiently modify the internal knowledge of large language models (LLMs) without compromising their other capabilities. The prevailing editing paradigm, which appends an update matrix to the original parameter matrix, has been shown by some studies to damage key numerical stability indicators (such as condition number and norm), thereby reducing editing performance and general abilities, especially in sequential editing scenario. Although subsequent methods have made some improvements, they remain within the additive framework and have not fundamentally addressed this limitation. To solve this problem, we analyze it from both statistical and mathematical perspectives and conclude that multiplying the original matrix by an orthogonal matrix does not change the numerical stability of the matrix. Inspired by this, different from the previous additive editing paradigm, a multiplicative editing paradigm termed Multiplicative Orthogonal Sequential Editing (MOSE) is proposed. Specifically, we first derive the matrix update in the multiplicative form, the new knowledge is then incorporated into an orthogonal matrix, which is multiplied by the original parameter matrix. In this way, the numerical stability of the edited matrix is unchanged, thereby maintaining editing performance and general abilities. We compared MOSE with several current knowledge editing methods, systematically evaluating their impact on both editing performance and the general abilities across three different LLMs. Experimental results show that MOSE effectively limits deviations in the edited parameter matrix and maintains its numerical stability. Compared to current methods, MOSE achieves a 12.08% improvement in sequential editing performance, while retaining 95.73% of general abilities across downstream tasks.

Hao-Xiang Xu, Chong Deng, Jiaqing Liu, Wen Wang, Qian Chen, Lujia Bao, Xiangang Li, Zhen-Hua Ling. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

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.

Model editing is a technique that edits the large language models (LLMs) with updated knowledge to alleviate hallucinations without resource-intensive retraining.While current model editing methods can effectively modify a model's behavior within a specific area of interest, they often overlook the potential unintended side effects on the general abilities of LLMs such as reasoning, natural language inference, and question answering.In this paper, we raise concerns that model editing's improvements on factuality may come at the cost of a significant degradation of the model's general abilities.We systematically analyze the side effects by evaluating four popular editing methods on three LLMs across eight representative tasks.Our extensive empirical experiments show that it is challenging for current editing methods to simultaneously improve factuality of LLMs and maintain their general abilities.Our analysis reveals that the side effects are caused by model editing altering the original model weights excessively, leading to overfitting to the edited facts.To mitigate this, a method named RECT is proposed to regularize the edit update weights by imposing constraints on their complexity based on the RElative Change in weighT.Evaluation results show that RECT can significantly mitigate the side effects of editing while still maintaining over 94% editing performance 1 .