Recent studies have demonstrated that large language models (LLMs) store massive factual knowledge within their parameters. But existing LLMs are prone to hallucinate unintended text due to false or outdated knowledge. Since retraining LLMs is resource intensive, there has been a growing interest in the concept of model editing. Despite the emergence of benchmarks and approaches, these unidirectional editing and evaluation have failed to explore the reversal curse. Intuitively, if "The capital of France is" is edited to be a counterfact "London" within a model, then it should be able to naturally reason and recall the reverse fact, i.e., "London is the capital of" followed by "France" instead of "England". In this paper, we study bidirectional language model editing, aiming to provide rigorous model editing evaluation to assess if edited LLMs can recall the editing knowledge bidirectionally. A new evaluation metric of reversibility is introduced, and a benchmark dubbed as Bidirectional Assessment for Knowledge Editing (BAKE) is constructed to evaluate the reversibility of edited models in recalling knowledge in the reverse direction of editing. We surprisingly observe that while current editing methods and LLMs can effectively recall editing facts in the direction of editing, they suffer serious deficiencies when evaluated in the reverse direction. To mitigate the reversal curse, a method named Bidirectionally Inversible Relationship moDeling (BIRD) is proposed. A set of editing objectives that incorporate bidirectional relationships between subject and object into the updated model weights are designed. Experiments show that BIRD improves the performance of four representative LLMs of different sizes via question answering and judgement.

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