Elamur Research
☰
home / papers / 2025 / Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs

Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs

Written for the Research library (claude-opus-5-5) from the paper text. Original — arxiv.org/pdf/2503.01307

Summary

Why do some base language models gain a lot from reinforcement learning on verifiable tasks while others stall? The authors observe that Qwen-2.5-3B improves sharply on the Countdown arithmetic puzzle under a given RL setup, while Llama-3.2-3B, trained the same way, barely moves. They attribute this to four problem-solving habits seen in human experts: verification, backtracking, subgoal setting and backward chaining. They then measure how often each habit appears in model outputs. Before any training, Qwen already shows these habits, and Llama mostly does not. The authors test two interventions on Llama. The first is a short fine-tuning on synthetic Countdown traces that display chosen behaviors. The second is continued pretraining on OpenWebMath material that was selected and rewritten to contain many such behaviors. Both let Llama follow or exceed Qwen's RL trajectory. Traces with wrong final answers work about as well as correct ones, as long as the reasoning patterns are present. The study suggests that a model's ability to benefit from extra test-time compute depends on behaviors it has before RL, and that data curation can shape this ability.

Key points

  • Testbed and models: Countdown (combine given numbers with +, −, ×, ÷ to reach a target) is used to compare Qwen-2.5-3B and Llama-3.2-3B. Base Qwen mainly shows verification and backtracking.
  • Which behaviors matter: Priming with backtracking proved especially important. During RL, the primed Llama increased backtracking and verification, while backward chaining and subgoal setting declined.
  • Correctness vs. behavior: Llama primed on incorrect solutions that still contain the target reasoning patterns improves about as much as Llama primed on correct solutions.
  • Curated pretraining:
    • Qwen-2.5-32B labeled OpenWebMath documents for the behaviors and rewrote them into a question–thought–answer format.
    • This produced a behavior-rich set and a control set with few behaviors, each 8.3 million tokens.
    • After RL, the behavior-rich Llama matched Qwen, while the control stayed close to base Llama.
  • Resources: The authors also counted behavior frequencies in 200,000 sampled documents from OpenWebMath and FineMath. Code is at github.com/kanishkg/cognitive-behaviors.

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

Fields: Other

Cited by

110 papers of our library cite it (of the 140673 whose bibliographies we read); 3 of them have a page here, 107 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2503.01307 · arXiv 2503.01307

@misc{gandhi2025cognitive,
  title = {{Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs}},
  author = {Gandhi, Kanishk and Chakravarthy, Ayush and Singh, Anikait and Lile, Nathan and Goodman, Noah D.},
  year = {2025},
  doi = {10.48550/arxiv.2503.01307},
  eprint = {2503.01307},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2503.01307}
}

References

48 references, 17 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Arash Ahmadian, Chris Cremer, Matthias Gallé, Marzieh Fadaee, Julia Kreutzer, Olivier Pietquin, Ahmet Üstün, and Sara Hooker. Back to basics: Revisiting reinforce style optimization for learning from human feedback in llms. arXiv preprint arXiv:2402.14740, 2024. find
  2. Loubna Ben Allal, Anton Lozhkov, Elie Bakouch, Gabriel Martín Blázquez, Guilherme Penedo, Lewis Tunstall, Andrés Marafioti, Hynek Kydlíček, Agustín Piqueres Lajarín, Vaibhav Srivastav, Joshua Lochner, Caleb Fahlgren, Xuan-Son Nguyen, Clémentine Fourrier, Ben Burtenshaw, Hugo Larcher, Haojun Zhao, C… find our card
  3. Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V. Le, Christopher Ré, and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling, 2024. URL https://arxiv.org/abs/2407.21787. ↗ our card
  4. Countdown. Countdown (game show). Online, 2024. URL https://en.wikipedia.org/ wiki/Countdown\_(game\_show). [Accessed 29-March-2024]. ↗
  5. Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, et al. Process reinforcement through implicit rewards. arXiv preprint arXiv:2502.01456, 2025. find our card
  6. Kanishk Gandhi, Dorsa Sadigh, and Noah D Goodman. Strategic reasoning with language models. arXiv preprint arXiv:2305.19165, 2023. find
  7. Kanishk Gandhi, Denise HJ Lee, Gabriel Grand, Muxin Liu, Winson Cheng, Archit Sharma, and Noah Goodman. Stream of search (sos): Learning to search in language. In First Conference on Language Modeling, 2024. find
  8. Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, Archie Sravankumar, Artem Korenev, Arthur Hinsvark, Arun Rao,… find
  9. Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948, 2025. find our card
  10. Alex Havrilla, Yuqing Du, Sharath Chandra Raparthy, Christoforos Nalmpantis, Jane Dwivedi-Yu, Maksym Zhuravinskyi, Eric Hambro, Sainbayar Sukhbaatar, and Roberta Raileanu. Teaching large language models to reason with reinforcement learning. arXiv preprint arXiv:2403.04642, 2024. find
  11. Matthew Douglas Hoffman, Du Phan, David Dohan, Sholto Douglas, Tuan Anh Le, Aaron Parisi, Pavel Sountsov, Charles Sutton, Sharad Vikram, and Rif A Saurous. Training chain-of-thought via latent-variable inference. In NeurIPS, 2023. find
  12. Jian Hu. Reinforce++: A simple and efficient approach for aligning large language models, 2025. URL https://arxiv.org/abs/2501.03262. ↗
  13. Hyeonbin Hwang, Doyoung Kim, Seungone Kim, Seonghyeon Ye, and Minjoon Seo. Self-explore: Enhancing mathematical reasoning in language models with fine-grained rewards. arXiv preprint arXiv:2404.10346, 2024. find
  14. Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai o1 system card. arXiv preprint arXiv:2412.16720, 2024. find our card
  15. Andy L Jones. Scaling scaling laws with board games. arXiv preprint arXiv:2104.03113, 2021. — [arXiv:2104.03113](https://arxiv.org/abs/2104.03113) find
  16. Amirhossein Kazemnejad, Milad Aghajohari, Eva Portelance, Alessandro Sordoni, Siva Reddy, Aaron Courville, and Nicolas Le Roux. Vineppo: Unlocking rl potential for llm reasoning through refined credit assignment. arXiv preprint arXiv:2410.01679, 2024. find
  17. Aviral Kumar, Vincent Zhuang, Rishabh Agarwal, Yi Su, John D Co-Reyes, Avi Singh, Kate Baumli, Shariq Iqbal, Colton Bishop, Rebecca Roelofs, et al. Training language models to self-correct via reinforcement learning. arXiv preprint arXiv:2409.12917, 2024. find our card
  18. Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention. In Proceedings of the ACM SIGOPS 29th Symposium on Operating Systems Principles, 2023. find
  19. Lucas Lehnert, Sainbayar Sukhbaatar, DiJia Su, Qinqing Zheng, Paul Mcvay, Michael Rabbat, and Yuandong Tian. Beyond a*: Better planning with transformers via search dynamics bootstrapping. arXiv preprint arXiv:2402.14083, 2024. find
  20. Chen Li, Weiqi Wang, Jingcheng Hu, Yixuan Wei, Nanning Zheng, Han Hu, Zheng Zhang, and Houwen Peng. Common 7b language models already possess strong math capabilities. arXiv preprint arXiv:2403.04706, 2024. find
  21. Dacheng Li, Shiyi Cao, Tyler Griggs, Shu Liu, Xiangxi Mo, Shishir G Patil, Matei Zaharia, Joseph E Gonzalez, and Ion Stoica. Llms can easily learn to reason from demonstrations structure, not content, is what matters! arXiv preprint arXiv:2502.07374, 2025. find
  22. Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. In The Twelfth International Conference on Learning Representations, 2023. find our card
  23. Zichen Liu, Changyu Chen, Wenjun Li, Tianyu Pang, Chao Du, and Min Lin. There may not be aha moment in r1-zero-like training — a pilot study. https://oatllm.notion.site/ oat-zero, 2025. Notion Blog. ↗
  24. Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization, 2019. URL https://arxiv.org/abs/1711.05101. ↗
  25. Liangchen Luo, Yinxiao Liu, Rosanne Liu, Samrat Phatale, Harsh Lara, Yunxuan Li, Lei Shu, Yun Zhu, Lei Meng, Jiao Sun, et al. Improve mathematical reasoning in language models by automated process supervision. arXiv preprint arXiv:2406.06592, 2, 2024. find our card
  26. Janet Metcalfe. Feeling of knowing in memory and problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12(2):288, 1986. find
  27. Melanie Mitchell. Abstraction and analogy-making in artificial intelligence. Annals of the New York Academy of Sciences, 1505(1):79–101, 2021. find
  28. Jiayi Pan, Junjie Zhang, Xingyao Wang, Lifan Yuan, Hao Peng, and Alane Suhr. Tinyzero. https://github.com/Jiayi-Pan/TinyZero, 2025. Accessed: 2025-01-24. ↗
  29. Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba. Openwebmath: An open dataset of high-quality mathematical web text, 2023. find our card
  30. Yuxiao Qu, Tianjun Zhang, Naman Garg, and Aviral Kumar. Recursive introspection: Teaching language model agents how to self-improve. Advances in Neural Information Processing Systems, 37:55249–55285, 2025. find
  31. Qwen, :, An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng… find
  32. David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R Bowman. Gpqa: A graduate-level google-proof q&a benchmark. In First Conference on Language Modeling, 2024. find our card
  33. John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms, 2017. URL https://arxiv.org/abs/1707.06347. ↗
  34. John Schultz, Jakub Adamek, Matej Jusup, Marc Lanctot, Michael Kaisers, Sarah Perrin, Daniel Hennes, Jeremy Shar, Cannada Lewis, Anian Ruoss, et al. Mastering board games by external and internal planning with language models. arXiv preprint arXiv:2412.12119, 2024. find
  35. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, and Daya Guo. Deepseekmath: Pushing the limits of mathematical reasoning in open language models, 2024. URL https://arxiv.org/abs/ 2402.03300. ↗ our card
  36. Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. Hybridflow: A flexible and efficient rlhf framework. arXiv preprint arXiv: 2409.19256, 2024. find our card
  37. Herbert A Simon and Allen Newell. Human problem solving: The state of the theory in 1970. American psychologist, 26(2):145, 1971. find
  38. Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling llm test-time compute optimally can be more effective than scaling model parameters. arXiv preprint arXiv:2408.03314, 2024. find our card
  39. Peiyi Wang, Lei Li, Zhihong Shao, RX Xu, Damai Dai, Yifei Li, Deli Chen, Yu Wu, and Zhifang Sui. Math-shepherd: Verify and reinforce llms step-by-step without human annotations. arXiv preprint arXiv:2312.08935, 2023. find our card
  40. Ronald J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn., 8(3–4):229–256, May 1992. ISSN 0885-6125. doi: 10.1007/BF00992696. URL https://doi.org/10.1007/BF00992696. ↗
  41. Siwei Wu, Zhongyuan Peng, Xinrun Du, Tuney Zheng, Minghao Liu, Jialong Wu, Jiachen Ma, Yizhi Li, Jian Yang, Wangchunshu Zhou, et al. A comparative study on reasoning patterns of openai’s o1 model. arXiv preprint arXiv:2410.13639, 2024. — [arXiv:2410.13639](https://arxiv.org/abs/2410.13639) find
  42. Violet Xiang, Charlie Snell, Kanishk Gandhi, Alon Albalak, Anikait Singh, Chase Blagden, Duy Phung, Rafael Rafailov, Nathan Lile, Dakota Mahan, et al. Towards system 2 reasoning in llms: Learning how to think with meta chain-of-though. arXiv preprint arXiv:2501.04682, 2025. find
  43. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Advances in neural information processing systems, 36:11809–11822, 2023. find
  44. Guanghao Ye, Khiem Duc Pham, Xinzhi Zhang, Sivakanth Gopi, Baolin Peng, Beibin Li, Janardhan Kulkarni, and Huseyin A Inan. On the emergence of thinking in llms i: Searching for the right intuition. arXiv preprint arXiv:2502.06773, 2025. — [arXiv:2502.06773](https://arxiv.org/abs/2502.06773) find
  45. Tian Ye, Zicheng Xu, Yuanzhi Li, and Zeyuan Allen-Zhu. Physics of language models: Part 2.2, how to learn from mistakes on grade-school math problems. arXiv preprint arXiv:2408.16293, 2024. find
  46. Edward Yeo, Yuxuan Tong, Morry Niu, Graham Neubig, and Xiang Yue. Demystifying long chain-of-thought reasoning in llms, 2025. URL https://arxiv.org/abs/2502.03373. ↗ our card
  47. Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. Star: Bootstrapping reasoning with reasoning. Advances in Neural Information Processing Systems, 35:15476–15488, 2022. find our card
  48. Eric Zelikman, Georges Raif Harik, Yijia Shao, Varuna Jayasiri, Nick Haber, and Noah Goodman. Quiet-star: Language models can teach themselves to think before speaking. In First Conference on Language Modeling, 2024. *Figure 9: Scores of the priming datasets generated with Claude. Analyzing the aver… find our card