Perturbation-Restrained Sequential Model Editing

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 popular editing methods on three LLMs across four representative downstream tasks. Evaluation results show that PRUNE can preserve considerable general abilities while maintaining the editing performance effectively in sequential model editing. The code and data are available at https://github.com/mjy1111/PRUNE.