Knowledge in Superposition: Unveiling the Failures of Lifelong Knowledge Editing for Large Language Models

Abstract

Knowledge editing aims to update outdated or incorrect knowledge in large language models (LLMs). However, current knowledge editing methods have limited scalability for lifelong editing. This study explores the fundamental reason why knowledge editing fails in lifelong editing. We begin with the closed-form solution derived from linear associative memory, which underpins state-of-the-art knowledge editing methods. We extend the solution from single editing to lifelong editing, and through rigorous mathematical derivation, identify an interference term in the final solution, suggesting that editing knowledge may impact irrelevant knowledge. Further analysis of the interference term reveals a close relationship with superposition between knowledge representations. When knowledge superposition does not exist in language models, the interference term vanishes, allowing for lossless knowledge editing. Experiments across numerous language models reveal that knowledge superposition is universal, exhibiting high kurtosis, zero mean, and heavy-tailed distributions with clear scaling laws. Ultimately, by combining theory and experiments, we demonstrate that knowledge superposition is the fundamental reason for the failure of lifelong editing. Moreover, this is the first study to investigate knowledge editing from the perspective of superposition and provides a comprehensive observation of superposition across numerous real-world language models. Code available at https://github.com/ChenhuiHu/knowledge_in_superposition.