Beyond the Covariance Trap: Unlocking Generalization in Same-Subject Knowledge Editing for Large Language Models

Sequential knowledge editing in Large Language Models (LLMs) often leads to a degradation of general capabilities due to cumulative parameter interference. In this paper, we revisit prominent projection-based methods like AlphaEdit and reveal a surprising mismatch: their robustness is primarily driven by update regularization rather than the intended null-space projection. Based on this insight, we propose FisherEdit, a theoretically grounded method built on Fisher geometry, which replaces coarse activation-space projections with importance-aware regularization in parameter space. It penalizes changes to sensitive parameters more strongly while retaining flexibility for new facts, and admits an efficient row-wise closed-form solution. Experiments on Llama-3, Qwen2.5, and Olmo-3 across multiple benchmarks demonstrate that FisherEdit achieves state-of-the-art performance while better preserving model stability and downstream task accuracy.

Parameter-based knowledge editing updates the internal knowledge of large language models (LLMs) via localized weight modifications and has attracted significant attention. However, most existing methods overlook fundamental theoretical limitations and are rarely evaluated under realistic, practice-oriented settings. In this paper, we first present a theoretical analysis based on the dimensional Collapse Hypothesis, explaining how localized parameter edits can propagate along fragile directions in the representation space, inducing global interference and ultimately causing reasoning collapse. Building on this insight, we conduct a comprehensive empirical evaluation by systematically varying knowledge complexity, number of edits, evaluation dimensions, and baseline methods. Our results show that parameter-based editing methods consistently damage core LLM capabilities. In contrast, a simple retrieval-based baseline achieves consistently stronger performance than all parameter-editing methods across all evaluated conditions. These findings highlight that preserving the fundamental capabilities of LLMs after knowledge editing should be a central concern for future research.

Large language models (LLMs) can effectively handle outdated information through knowledge editing. However, current approaches face two key limitations: (I) Poor generalization: Most approaches rigidly inject new knowledge without ensuring that the model can use it effectively to solve practical problems. (II) Narrow scope: Current methods focus primarily on structured fact triples, overlooking the diverse unstructured forms of factual information (e.g., news, articles) prevalent in real-world contexts. To address these challenges, we propose a new paradigm: teaching LLMs to edit knowledge via Chain of Thoughts (CoTs) reasoning (CoT2Edit). We first leverage language model agents for both structured and unstructured edited data to generate CoTs, building high-quality instruction data. The model is then trained to reason over edited knowledge through supervised fine-tuning (SFT) and Group Relative Policy Optimization (GRPO). At inference time, we integrate Retrieval-Augmented Generation (RAG) to dynamically retrieve relevant edited facts for real-time knowledge editing. Experimental results demonstrate that our method achieves strong generalization across six diverse knowledge editing scenarios with just a single round of training on three open-source language models. The codes are available at https://github.com/FredJDean/CoT2Edit.