How to edit the knowledge in multi-step reasoning has become the major challenge in the knowledge editing (KE) of large language models (LLMs). The difficulty arises because the hallucinations of LLMs during multi-step reasoning often lead to incorrect use of new knowledge and incorrect answers. To address this issue, we design decoding constraints to "regulate" LLMs' reasoning, enhancing logical coherence when incorporating new knowledge. We propose a new KE framework: DEEPEDIT (Depth-first Search-based Constrained Decoding for Knowledge Editing), which enhances LLMs's ability to generate coherent reasoning chains with new knowledge through depth-first search. Our search selects the most important knowledge that satisfies our constraints as the reasoning step to efficiently increase the reasoning depth. In addition to DEEPEDIT, we propose two new KE benchmarks: MQUAKE-2002 and MQUAKE-HARD, which provide more precise and challenging assessments of KE approaches. Qualitatively, DEEPEDIT enables LLMs to produce succinct and coherent reasoning chains involving new knowledge. Quantitatively, it yields significant improvements on multiple KE benchmarks.
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