HebbianEdit: A Closed-Form Hebbian Memory for Knowledge Editing in LLMs

Knowledge editing aims to update specific facts in a deployed language model without retraining. Existing methods rewrite the model's internal weights, train an extra module for every edit, or keep new facts as text outside the model. However, these previous works suggest that knowledge is represented in the form of parametric memory, giving up at least one of precision, efficiency, or revocability. In this work, we rethink that knowledge editing should be interpreted as memory editing, and propose **HebbianEdit** which innovates knowledge editing as closed-form memory injection. Specifically, we write new facts as key-direction pairs into an external Hebbian memory. Then we hold the new knowledge, whose projections and readout are solved in closed form with a squared key similarity that suppresses cross-talk, implemented as a two-layer MLP. Finally, the frozen model reads the memory through hidden-state perturbation at inference time. Updating the deployed model's knowledge is thus achieved by operations on memory rather than surgery on each fact. Comprehensive experiments show that HebbianEdit scales up to ten thousand sequential edits with superior efficacy and generalization at 100% with nearly zero locality flips. More importantly, the proposed memory is built in a single closed-form pass over all edits in seconds compared to the previous methods that use 8.61-33.70 seconds per edit.