Existing continual knowledge editing methods suffer from cognitive dissonance: after an edit, the model answers the edit prompt correctly but reverts to the old fact under complex equivalent queries. This means old and new facts coexist rather than the old being replaced. The root cause of cognitive dissonance is that existing methods fit the new fact on the target prompt without overwriting the old one. In constrained methods, static null-space projectors lock outdated representations into the protected subspace, forcing updates into orthogonal directions. To resolve cognitive dissonance, we propose P-Space (Puncturing the Null-Space to Resolve Cognitive Dissonance in Continual Knowledge Editing), which at each edit step (1) punctures the protected covariance to unprotect the outdated representation, (2) overwrites the old mapping in closed form along its original direction under the punctured projector, and (3) anchors the new fact into the covariance with adaptive scaling so that future edits preserve it. Experiments on two datasets show that P-Space outperforms existing methods while preserving general capabilities.

Knowledge editing is a promising method for updating Large Language Models efficiently. However, previous studies often suffer from poor specificity in continual editing, as they typically focus on single edits or preventing knowledge forgetting. To address this, we propose TamEdit, a trajectory-aware meta-learning method that preserves specificity for continual knowledge editing. TamEdit unifies three levels: Inner Optimization performs multi-step fast fine-tuning on the single edit; Trajectory-based Editing unifies continual edits with a growing memory; and Outer Optimization leverages meta-learning to distill cross-task strategies for preserving specificity. By capturing the relationships between different single edits within the trajectory, our method learns how to effectively avoid specificity drift. Experiments across multiple LLMs show TamEdit significantly outperforms baselines in continual editing, improving specificity by 14.81% with fast speed (requiring only 8.84% of the time cost of most baselines), while preserving general capabilities.