Provable Sample Efficiency of Curriculum Post-Training for Transformer Reasoning

Dake Bu, Wei Huang, Andi Han, Atsushi Nitanda, Hau-San Wong, Qingfu Zhang, Taiji Suzuki
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:10051-10110, 2026.

Abstract

Recent curriculum techniques in the post-training stage of LLMs have been empirically observed to outperform non-curriculum approaches in improving reasoning performance, yet a principled understanding of their effectiveness and limitations remains incomplete. To bridge this gap, we develop an abstract theoretical framework and identify sufficient conditions under which curriculum post-training yields exponential improvements in sample complexity. To substantiate this framework, we model the base model’s Chain-of-Thought generation as a state-conditioned autoregressive reasoning tree, and formalize curriculum subtasks as either depth-increasing curricula that progressively extend reasoning horizons or hint-decreasing curricula that gradually remove partial hints. Our analysis shows that reinforcement learning finetuning with both curriculum strategies achieves high accuracy with polynomial sample complexity, whereas non-curriculum counterpart encounters an exponential complexity bottleneck. We further establish analogous guarantees for test-time scaling. Empirical simulations support our theoretical findings. Code is available at https://github.com/DakeBU/Curriculum-Post-training.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-bu26a, title = {Provable Sample Efficiency of Curriculum Post-Training for Transformer Reasoning}, author = {Bu, Dake and Huang, Wei and Han, Andi and Nitanda, Atsushi and Wong, Hau-San and Zhang, Qingfu and Suzuki, Taiji}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {10051--10110}, 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/bu26a/bu26a.pdf}, url = {https://proceedings.mlr.press/v306/bu26a.html}, abstract = {Recent curriculum techniques in the post-training stage of LLMs have been empirically observed to outperform non-curriculum approaches in improving reasoning performance, yet a principled understanding of their effectiveness and limitations remains incomplete. To bridge this gap, we develop an abstract theoretical framework and identify sufficient conditions under which curriculum post-training yields exponential improvements in sample complexity. To substantiate this framework, we model the base model’s Chain-of-Thought generation as a state-conditioned autoregressive reasoning tree, and formalize curriculum subtasks as either depth-increasing curricula that progressively extend reasoning horizons or hint-decreasing curricula that gradually remove partial hints. Our analysis shows that reinforcement learning finetuning with both curriculum strategies achieves high accuracy with polynomial sample complexity, whereas non-curriculum counterpart encounters an exponential complexity bottleneck. We further establish analogous guarantees for test-time scaling. Empirical simulations support our theoretical findings. Code is available at https://github.com/DakeBU/Curriculum-Post-training.} }
Endnote
%0 Conference Paper %T Provable Sample Efficiency of Curriculum Post-Training for Transformer Reasoning %A Dake Bu %A Wei Huang %A Andi Han %A Atsushi Nitanda %A Hau-San Wong %A Qingfu Zhang %A Taiji Suzuki %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-bu26a %I PMLR %P 10051--10110 %U https://proceedings.mlr.press/v306/bu26a.html %V 306 %X Recent curriculum techniques in the post-training stage of LLMs have been empirically observed to outperform non-curriculum approaches in improving reasoning performance, yet a principled understanding of their effectiveness and limitations remains incomplete. To bridge this gap, we develop an abstract theoretical framework and identify sufficient conditions under which curriculum post-training yields exponential improvements in sample complexity. To substantiate this framework, we model the base model’s Chain-of-Thought generation as a state-conditioned autoregressive reasoning tree, and formalize curriculum subtasks as either depth-increasing curricula that progressively extend reasoning horizons or hint-decreasing curricula that gradually remove partial hints. Our analysis shows that reinforcement learning finetuning with both curriculum strategies achieves high accuracy with polynomial sample complexity, whereas non-curriculum counterpart encounters an exponential complexity bottleneck. We further establish analogous guarantees for test-time scaling. Empirical simulations support our theoretical findings. Code is available at https://github.com/DakeBU/Curriculum-Post-training.
APA
Bu, D., Huang, W., Han, A., Nitanda, A., Wong, H., Zhang, Q. & Suzuki, T.. (2026). Provable Sample Efficiency of Curriculum Post-Training for Transformer Reasoning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:10051-10110 Available from https://proceedings.mlr.press/v306/bu26a.html.

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