Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge

Xutao Ma, Yixiao Huang, Hanlin Zhu, Somayeh Sojoudi
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:84465-84486, 2026.

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 50% 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ma26o, title = {Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge}, author = {Ma, Xutao and Huang, Yixiao and Zhu, Hanlin and Sojoudi, Somayeh}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {84465--84486}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ma26o/ma26o.pdf}, url = {https://proceedings.mlr.press/v306/ma26o.html}, 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 50% 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.} }
Endnote
%0 Conference Paper %T Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge %A Xutao Ma %A Yixiao Huang %A Hanlin Zhu %A Somayeh Sojoudi %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ma26o %I PMLR %P 84465--84486 %U https://proceedings.mlr.press/v306/ma26o.html %V 306 %X 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 50% 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.
APA
Ma, X., Huang, Y., Zhu, H. & Sojoudi, S.. (2026). Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:84465-84486 Available from https://proceedings.mlr.press/v306/ma26o.html.

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