Bilinear relational structure fixes reversal curse and enables consistent model editing

ICLR 2026 Conference Submission21044 Authors

Keywords: model editing, reversal curse, language model, relational knowledge, knowledge editing

TL;DR: Language models can learn to encode relational knowledge in a bilinear relational structure, a mechanism that directly can mitigate the reversal curse and enable cosistent model editing.

Abstract: The reversal curse$-$a language model's (LM) inability to infer an unseen fact "B is A" from a learned fact "A is B"$-$ is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode knowledge. By training LMs from scratch on a synthetic dataset of relational knowledge graphs, we demonstrate that bilinear relational structure emerges in their hidden representations. This structure substantially alleviates the reversal curse, enabling LMs to infer unseen reverse facts. Crucially, we also find that this bilinear structure plays a key role in consistent model editing. When a fact is updated in a LM with this structure, the edit correctly propagates to its reverse and other logically dependent facts. In contrast, models lacking this representation not only suffer from the reversal curse but also fail to generalize edits, further introducing logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn enable LMs to behave in a logically consistent manner after editing. This implies that the success of model editing depends critically not just on editing algorithms but on the underlying representational geometry of the knowledge being modified.

Primary Area: interpretability and explainable AI

Submission Number: 21044