Elamur Research⌕
☰
home / papers / 2026 / StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason

StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason

Paper · 2026 · Kaiyi Zhang, Ang Lv, Jinpeng Li et al.

Summary

Reinforcement learning with verifiable rewards (RLVR) improves LLM reasoning, but it has two weaknesses. The first is the near-miss reward problem: one early slip ruins an otherwise sound solution, so the rollout earns no reward. The second is exploration stagnation: the policy keeps sampling familiar solutions instead of finding better ones. StepHint addresses both by using reasoning chains from stronger models as partial guidance. Each chain is cut into reasoning steps with an adaptive method. Candidate boundaries are positions where the model's estimated probability of emitting the end-of-reasoning token (</think>) is higher than at the following position. Endpoints are then sampled from these candidates under a minimum-length constraint. The policy then receives hints of several levels, each containing a different number of opening steps, and completes the rest itself. This narrows the search space while leaving room for independent exploration. Training on math problems drawn from DAPO and DeepMath, StepHint beats competitive RLVR enhancements on six math benchmarks and two out-of-domain benchmarks. This suggests that stepwise hinting is a practical way to make RL training of reasoners more efficient and better at generalizing.

Key points

  • The method works with any policy optimizer (e.g., PPO, GRPO). It provides multiple hint levels per problem so that at least one level suits the model's current ability, which keeps changing during training.
  • It shows notable pass@k gains on the hard AIME24 and AIME25 benchmarks. It also achieves the best scores on non-math, out-of-domain tasks.
  • In the partitioning ablation, the </think>-probability split outperforms random/length-based splitting and newline-based splitting in every reported column. For example, the final column gives 60.35 versus 58.90 (newline) and 57.43 (random).
  • The training data is derived from DAPO and DeepMath problems, with chains generated by advanced models. Compute was 8 × A100 GPUs. Code is available at github.com/Cardinalere/StepHint.
  • Limitation: hint quality depends on, and is capped by, the teacher model. The authors plan self-generated hints as future work.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Peking UniversityBeijing · China244 works · 39,359 citations🎓Wuhan UniversityWuhan · China35 works · 1,127 citations🏢Ant GroupHangzhou · China42 works · 1,131 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,426 works

Cite

Cite as Kaiyi Zhang, Ang Lv, Jinpeng Li, Yongbo Wang, Feng Wang, Haoyuan hu and Rui Yan. 2026. StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.acl-long.1755

@inproceedings{zhang2026stephint,
  title = {{StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason}},
  author = {Kaiyi Zhang, Ang Lv, Jinpeng Li, Yongbo Wang, Feng Wang, Haoyuan hu and Rui Yan},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.1755},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1755}
}

References

49 references, 22 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde De Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, and 1 others. 2021. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374.
  2. Daixuan Cheng, Shaohan Huang, Xuekai Zhu, Bo Dai, Wayne Xin Zhao, Zhenliang Zhang, and Furu Wei. 2025. Reasoning with exploration: An entropy perspective. arXiv preprint arXiv:2506.14758. find
  3. Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. 2018. Think you have solved question answering? try arc, the ai2 reasoning challenge. arXiv preprint arXiv:1803.05457.
  4. Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, and 1 others. 2024. The llama 3 herd of models. arXiv e-prints, pages arXiv–2407.
  5. Leo Gao, John Schulman, and Jacob Hilton. 2023. Scaling laws for reward model overoptimization. In International Conference on Machine Learning, pages 10835–10866. PMLR.
  6. Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, and 1 others. 2025. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948.
  7. Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, and 1 others. 2024. Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems. arXiv preprint arXiv:2402.14008.
  8. Zhiwei He, Tian Liang, Jiahao Xu, Qiuzhi Liu, Xingyu Chen, Yue Wang, Linfeng Song, Dian Yu, Zhenwen Liang, Wenxuan Wang, and 1 others. 2025. Deepmath-103k: A large-scale, challenging, decontaminated, and verifiable mathematical dataset for advancing reasoning. arXiv preprint arXiv:2504.11456. find
  9. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021. Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874.
  10. Jingcheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, Xiangyu Zhang, and Heung-Yeung Shum. 2025. Open-reasoner-zero: An open source approach to scaling up reinforcement learning on the base model. arXiv preprint arXiv:2503.24290.
  11. Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, and 1 others. 2024. Openai o1 system card. arXiv preprint arXiv:2412.16720.
  12. Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, and 1 others. 2022. Solving quantitative reasoning problems with language models. Advances in Neural Information Processing Systems, 35:3843–3857…
  13. Jia Li, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Huang, Kashif Rasul, Longhui Yu, Albert Q Jiang, Ziju Shen, and 1 others. 2024. Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions. Hugging Face repository, 13:9. find
  14. Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. 2025. Understanding r1-zero-like training: A critical perspective. arXiv preprint arXiv:2503.20783.
  15. Zichen Liu, Changyu Chen, Xinyi Wan, Chao Du, Wee Sun Lee, and Min Lin. 2024. Oat: A research-friendly framework for llm online alignment. https://github.com/sail-sg/oat. ↗
  16. Ang Lv, Yuhan Chen, Kaiyi Zhang, Yulong Wang, Lifeng Liu, Ji-Rong Wen, Jian Xie, and Rui Yan. 2024. Interpreting key mechanisms of factual recall in transformer-based language models. Preprint, arXiv:2403.19521. — [arXiv:2403.19521](https://arxiv.org/abs/2403.19521) find
  17. Ang Lv, Jinpeng Li, Yuhan Chen, Gao Xing, Ji Zhang, and Rui Yan. 2023a. DialoGPS: Dialogue path sampling in continuous semantic space for data augmentation in multi-turn conversations. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers),… find
  18. Ang Lv, Jinpeng Li, Shufang Xie, and Rui Yan. 2023b. Envisioning future from the past: Hierarchical duality learning for multi-turn dialogue generation. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 7382–7394, Toronto, Canad… find
  19. Ang Lv, Jin Ma, Yiyuan Ma, and Siyuan Qiao. 2026. Coupling experts and routers in mixture-of-experts via an auxiliary loss. In The Fourteenth International Conference on Learning Representations. find
  20. Zengzhi Wang, Rui Xia, and Pengfei Liu. 2023. Generative ai for math: Part i–mathpile: A billion-token-scale pretraining corpus for math. arXiv preprint arXiv:2312.17120. find
  21. Ang Lv, Ruobing Xie, Yining Qian, Songhao Wu, Xingwu Sun, Zhanhui Kang, Di Wang, and Rui Yan. 2025a. Autonomy-of-experts models. In Forty-second International Conference on Machine Learning. find
  22. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, and 1 others. 2022. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824– 24837.
  23. Ang Lv, Ruobing Xie, Xingwu Sun, Zhanhui Kang, and Rui Yan. 2025b. The climb carves wisdom deeper than the summit: On the noisy rewards in learning to reason. Preprint, arXiv:2505.22653. — [arXiv:2505.22653](https://arxiv.org/abs/2505.22653) find
  24. David JC MacKay. 2003. Information theory, inference and learning algorithms. Cambridge university press. find
  25. Arindam Mitra, Hamed Khanpour, Corby Rosset, and Ahmed Awadallah. 2024. Orca-math: Unlocking the potential of slms in grade school math. arXiv preprint arXiv:2402.14830.
  26. Marie-Francine Moens. 2017. Argumentation mining: How can a machine acquire common sense and world knowledge? Argument & Computation, 9:1 – 14. find
  27. Yury Polyanskiy and Yihong Wu. 2025. Information theory: From coding to learning. Cambridge university press. find
  28. David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R Bowman. 2024. Gpqa: A graduate-level google-proof q&a benchmark. In First Conference on Language Modeling.
  29. John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347. find
  30. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, and 1 others. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300.
  31. Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. 2024. Hybridflow: A flexible and efficient rlhf framework. arXiv preprint arXiv: 2409.19256.
  32. Jinyang Wu, Mingkuan Feng, Shuai Zhang, Feihu Che, Zengqi Wen, Chonghua Liao, and Jianhua Tao. 2024. Beyond examples: High-level automated reasoning paradigm in in-context learning via mcts. arXiv preprint arXiv:2411.18478. — [arXiv:2411.18478](https://arxiv.org/abs/2411.18478) find
  33. Songhao Wu, Ang Lv, Ruobing Xie, Xingwu Sun, Di Wang, Rui Yan, and Yankai Lin. 2025. Union-of-experts: Experts in mixture-of-experts are secretly routers. find
  34. Shufang Xie, Ang Lv, Yingce Xia, Lijun Wu, Tao Qin, Tie-Yan Liu, and Rui Yan. 2022. Target-side input augmentation for sequence to sequence generation. In International Conference on Learning Representations. find
  35. Jianhao Yan, Yafu Li, Zican Hu, Zhi Wang, Ganqu Cui, Xiaoye Qu, Yu Cheng, and Yue Zhang. 2025. Learning to reason under off-policy guidance. arXiv preprint arXiv:2504.14945. find
  36. An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Haoran Wei, Huan Lin, Jialong Tang, Jialin Wang, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Ma, and 40 others. 2024a. Qwen2 technical report. arXiv preprint arX… find
  37. An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, and Zhenru Zhang. 2024b. Qwen2.5-math technical report: Toward mathematical expert model via self-improvement.…
  38. Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. 2025. Limo: Less is more for reasoning. arXiv preprint arXiv:2502.03387.
  39. Qwen Team. 2025. Qwq-32b: Embracing the power of reinforcement learning. find
  40. Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, and 1 others. 2025. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476.
  41. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2022. Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171.
  42. Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Shiji Song, and Gao Huang. 2025. Does reinforcement learning really incentivize reasoning capacity in llms beyond the base model? arXiv preprint arXiv:2504.13837.
  43. Qwen Team. 2024. Qwen2.5: A party of foundation models. find
  44. Weihao Zeng, Yuzhen Huang, Qian Liu, Wei Liu, Keqing He, Zejun Ma, and Junxian He. 2025. Simplerl-zoo: Investigating and taming zero reinforcement learning for open base models in the wild. arXiv preprint arXiv:2503.18892. conditional mutual information between two random variables, R and T k , give…
  45. I(R; T k \|S k−1 ) = H(R\|S k−1 ) − H(R\|S k−1 , T k ) find
  46. Xiaoqing Zhang, Huabin Zheng, Ang Lv, Yuhan Liu, Zirui Song, Xiuying Chen, Rui Yan, and Flood Sung. 2025a. Divide-fuse-conquer: Eliciting "aha moments" in multi-scenario games. Preprint, arXiv:2505.16401. — [arXiv:2505.16401](https://arxiv.org/abs/2505.16401) find
  47. Xuechen Zhang, Zijian Huang, Yingcong Li, Chenshun Ni, Jiasi Chen, and Samet Oymak. 2025b. Bread: Branched rollouts from expert anchors bridge sft & rl for reasoning. arXiv preprint arXiv:2506.17211. — [arXiv:2506.17211](https://arxiv.org/abs/2506.17211) find
  48. A fundamental property of mutual information is that it is always non-negative (MacKay, 2003; Polyanskiy and Wu, 2025): I(R; T k \|S k−1 ) ≥ 0 find
  49. From this, it directly follows that: Xueliang Zhao, Wei Wu, Jian Guan, and Lingpeng Kong. 2025. Promptcot: Synthesizing olympiad-level problems for mathematical reasoning in large language models. arXiv preprint arXiv:2503.02324. find

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/zhang-2026-stephint-multi-level-stepwise-hints/