A central challenge in large language model (LLM) editing is capability preservation: methods that successfully change targeted behavior can quietly game the editing proxy and corrupt general capabilities, producing degenerate behaviors reminiscent of proxy/reward hacking. We present CrispEdit, a scalable and principled second-order editing algorithm that treats capability preservation as an explicit constraint, unifying and generalizing several existing editing approaches. CrispEdit formulates editing as constrained optimization and enforces the constraint by projecting edit updates onto the low-curvature subspace of the capability-loss landscape. At the crux of CrispEdit is expressing capability constraint via Bregman divergence, whose quadratic form yields the Gauss-Newton Hessian exactly and even when the base model is not trained to convergence. We make this second-order procedure efficient at the LLM scale using Kronecker-factored approximate curvature (K-FAC) and a novel matrix-free projector that exploits Kronecker structure to avoid constructing massive projection matrices. Across standard model-editing benchmarks, CrispEdit achieves high edit success while keeping capability degradation below 1% on average across datasets, significantly improving over prior editors.

翻译：大语言模型编辑中的一个核心挑战是能力保持：成功改变目标行为的方法可能会悄然操纵编辑代理并损害通用能力，产生类似于代理/奖励破解的退化行为。本文提出CrispEdit，一种可扩展且基于原理的二阶编辑算法，将能力保持作为显式约束，统一并推广了多种现有编辑方法。CrispEdit将编辑问题构建为约束优化问题，并通过将编辑更新投影到能力损失景观的低曲率子空间来强制执行约束。CrispEdit的核心在于通过Bregman散度表达能力约束，其二次形式能精确给出高斯-牛顿海森矩阵，且即使基础模型未训练至收敛时依然成立。我们采用克罗内克分解近似曲率方法和一种新型无矩阵投影器，利用克罗内克结构避免构建大规模投影矩阵，使该二阶过程能在大语言模型规模下高效运行。在标准模型编辑基准测试中，CrispEdit在实现高编辑成功率的同时，将各数据集上的能力退化平均控制在1%以下，较现有编辑方法有显著提升。