Perturbation-Restrained Sequential Model Editing

TL;DR

This work addresses the challenge of updating knowledge in large language models through sequential edits without extensive retraining. It theorizes that the deteriorating general abilities during sequential editing are governed by the growing condition number $\kappa$ of the edited matrix, and then introduces PRUNE, a plug-and-play framework that restrains large singular values in the cumulative edit update to bound perturbations. The authors provide matrix-perturbation analysis and empirical evidence across three editing methods (MEND, ROME, MEMIT) and three LLMs, showing that PRUNE preserves general abilities while maintaining editing efficacy on factual and conceptual knowledge. The approach enables more scalable continual learning in LLMs with reduced forgetting and resource demands, though it currently focuses on single-fact edits and calls for extending to batch-edit scenarios and larger models.

Abstract

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.

Figures (16)

• Figure 1: (a) Illustration of sequential model editing. (b) The condition number of edited matrix rapidly increases as the number of edits increases. (c) Comparison of general downstream task performance before editing, after regular editing, and after restrained editing by PRUNE. (d) Comparison of editing performance after regular editing and after restrained editing by PRUNE. $f_W$, $f_{W_n}$ and $f_{\overline{W}_n}$ denote the models that are unedited, regularly edited $n$ times, and restrainedly edited by PRUNE respectively. $W$ is denoted as a matrix to be edited.
• Figure 2: The condition number, maximum singular value and minimum singular value of the edited matrix in sequential editing. Three editing methods including ROME, MEND, and MEMIT are used to edit LLaMA-2 (7B) on the CounterFactDBLP:conf/nips/MengBAB22 dataset. For editing methods that modify the parameters of multiple MLP layers, one of them is randomly selected for illustration. $W$ and $W_n$ denote the unedited and edited matrices respectively.
• Figure 3: The downstream task performance (%) of models edited by three editing methods with LLaMA-2 (7B) on the ZsRE dataset. The dashed lines refer to the results of the unrestrained editing methods. The solid lines refer to the results of the editing methods coupled with the proposed PRUNE framework. Statistical significance tests were performed to demonstrate that the improvement in PRUNE compared to baseline was statistically significant (t-test with $p$-value < $0.05$).
• Figure 4: The editing performance (%) of editing methods with LLaMA-2 (7B) on the ZsRE dataset. The dashed lines refer to the results of the unrestrained editing methods. The solid lines refer to the results of the editing methods coupled with the proposed PRUNE. Statistical significance tests were performed to demonstrate that the improvement in PRUNE compared to baseline was statistically significant (t-test with $p$-value < $0.05$).
• Figure 5: 2-dimensional PCA visualization of first 100 values. The model was edited by ROME with LLaMA-2.

Theorems & Definitions (3)

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