Qingyan Guo, Rui Wang, Junliang Guo, Tan Xu, Jiang Bian, Yujiu YangWhile large language models (LLMs) have achieved impressive performance across diverse tasks, recent studies showcase that causal LLMs suffer from the“reversal curse”. It is a typical example that the model knows “A’s father is B”, but is unable to reason “B’s child is A”. This limitation poses a challenge to the advancement of artificial general intelligence (AGI),as it suggests a gap in the models’ ability to comprehend and apply bidirectional reasoning. In this paper, we first conduct substantial evaluation and identify that the root cause of the reversal curse lies in the different word order between the training and inference stage, namely, the poor ability of causal language models to predict antecedent words within the training data. Accordingly, permutation on the training data is considered as a potential solution, since this can make the model predict antecedent words or tokens. However, previous permutation methods may disrupt complete phrases or entities, thereby posing challenges for the model to comprehend and learn from training data. To address this issue, we propose Semantic-aware Permutation Training (SPT), which addresses this issue by segmenting the training sentences into semantic units(i.e.,entitiesorphrases)withanassistant language model and permuting these units before feeding into the model. Extensive experiments demonstrate that SPT effectively mitigates the reversal curse since the performance on reversed questions approximates that on the forward ones, and significantly advances the performance of existing works.