Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge

• URL: http://arxiv.org/abs/2602.02470v1
• Date: Mon, 02 Feb 2026 18:50:57 GMT
• Title: Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge
• Authors: Xutao Ma, Yixiao Huang, Hanlin Zhu, Somayeh Sojoudi,
• Abstract summary: We show that even a one-layer transformer can break the reversal curse by analyzing the implicit bias of gradient descent.<n>Our work provides a novel theoretical foundation for the reversal curse and offers a principled, low-cost path to encouraging LLMs to learn higher-level rules from data.
• Score: 16.509342332774747
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Autoregressive large language models (LLMs) have achieved remarkable success in many complex tasks, yet they can still fail in very simple logical reasoning such as the "reversal curse" -- when trained on forward knowledge data of the form "$A \rightarrow B$" (e.g., Alice's husband is Bob), the model is unable to deduce the reversal knowledge "$B \leftarrow A$" (e.g., Bob's wife is Alice) during test. Extensive prior research suggests that this failure is an inherent, fundamental limit of autoregressive causal LLMs, indicating that these models tend to memorize factual-level knowledge rather than capture higher-level rules. In this paper, we challenge this view by showing that this seemingly fundamental limit can be mitigated by slightly tweaking the training data with a simple regularization data recipe called the Identity Bridge of the form "$A \to A$" (e.g., The name of Alice is Alice). Theoretically, we prove that under this recipe, even a one-layer transformer can break the reversal curse by analyzing the implicit bias of gradient descent. Empirically, we show that a 1B pretrained language model finetuned with the proposed data recipe achieves a 40% success rate on reversal tasks, in stark contrast to a near-zero success rate when trained solely on forward-knowledge data. Our work provides a novel theoretical foundation for the reversal curse and offers a principled, low-cost path to encouraging LLMs to learn higher-level rules from data.

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