Editing Large Language Models with Geometry-Aware Regularization

Sequential editing of structured knowledge in large language models allows targeted factual updates without retraining, yet existing methods often rely on complex regularization or constraint mechanisms whose necessity remains unclear. In this work, we systematically investigate the mechanisms underlying effective and stable sequential editing. Specifically, we first analyze the empirical success of AlphaEdit and establish, via a rigorous optimization analysis, the formal equivalence between one-time and sequential editing. Building on this insight, we generalize the equivalence to a broader class of editing objectives, demonstrating that stability emerges naturally from properly accounting for accumulated editing constraints, rather than from specialized regularization or null-space operations. We empirically confirm that many commonly used regularization strategies are unnecessary for reliable sequential updates. Furthermore, we extend our framework to handle conflicting edits, ensuring robust and consistent behavior under contradictory updates. Ultimately, our work provides Ariadne's thread through the labyrinth of sequential editing, charting a path toward simpler, more interpretable, and dependable knowledge updates. Our code is available at https://github.com/Wangzzzzzzzz/OTE-SE-Alignment.

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.

Large language models (LLMs) inevitably generate some incorrect or outdated content, necessitating efficient and precise mechanisms for continual knowledge updates. However, existing model editing methods struggle to sequentially edit unstructured long-form knowledge, suffering from severe edit forgetting and degradation of general capabilities. To address these challenges, we reframe knowledge editing from a manifold perspective, viewing it as a localized displacement of an edit sub-manifold within the global knowledge manifold. Under this formulation, the problem can be decomposed into two key questions: (i) how to identify representative edit points that effectively anchor the edit sub-manifold, and (ii) how to preserve the remaining manifold structure during the sub-manifold displacement process. Based on this perspective, we propose ManiEdit, a novel manifold-aware autoregressive editing framework consisting of two core components. Pivot Localization addresses the mediocre-point dilemma by identifying high-leverage pivots to anchor the edit sub-manifold. Manifold-Aware Preservation preserves different knowledge types through an energy-weighted penalty combined with recursive null-space alignment. Experiments on two base LLMs and four unstructured editing benchmarks demonstrate that ManiEdit achieves state-of-the-art performance, outperforming the strongest baseline by up to +27.81 BERTScore and +8.50 ROUGE-L, while maintaining near-original general capabilities across six representative downstream tasks. Our code is available at: https://github.com/Areyliu/ManiEdit