Write Facts the Way Models Read Them: Lifting the Two-Hop Curse
Zhiyun Shi
Abstract
A language model that learns a new fact by fine-tuning can repeat it but cannot reason with it: taught that a person is a citizen of a new country, it still cannot say, without chain-of-thought, who the head of state of that person's country is. This two-hop curse is widely treated as a reasoning deficit, and the strongest knowledge editors answer it with synthesized reasoning data. We show that the reasoning is intact and the writing is wrong. Fine-tuning writes a new fact as an answer to be said, whereas the second hop reads the bridge ("that person's country") as an entity, from the middle layers on: patching the model's own representation of the entity into the bridge at those layers largely restores the second hop, yet after fine-tuning the bridge there is no closer to the new entity than before the edit. We therefore propose read-equivalent writing (Legible): one loss term makes the bridge phrase, at the layer where the second hop finishes reading it, match the model's own reading of the new entity, and keeps the same relation's other subjects unchanged. Phrases and targets come from the edited model itself, and no multi-hop training data is used. Across Qwen2.5, Llama-3 and Qwen3, Legible (I) composes learned facts more often than the model composes its own knowledge, on MQuAKE's two-hop-curse questions; (II) reaches 1.8-2.6x the bridge accuracy of CaKE, whose reasoning data composes no better than plain fine-tuning, and has the best average over composition, accuracy and locality against four families of writers; and (III) lifts the curse on RippleEdits, on the benchmark of Balesni et al., who named the curse, and at 14B.