---
title: "Towards Thinking-Optimal Scaling of Test-Time Compute for"
description: "From this they build TOPS (Thinking-OPtimal Scaling). 52 references, cited by 42 papers here."
authors: ["Wenkai Yang", "Shuming Ma", "Yankai Lin", "Furu Wei"]
year: 2025
venue: "arXiv:2502.18080"
source: "https://arxiv.org/abs/2502.18080"
doi: "10.48550/arxiv.2502.18080"
arxiv: "2502.18080"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/yang-2025-towards-thinking-optimal-scaling-test/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/yang-2025-towards-thinking-optimal-scaling-test/)

[home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2025](https://md.research.elamur.ai/free/en/papers/2025/page/3/) / Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning

# Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning

**Authors:** [Wenkai Yang](https://md.research.elamur.ai/free/en/authors/wenkai-yang/), [Shuming Ma](https://md.research.elamur.ai/free/en/authors/shuming-ma/), [Yankai Lin](https://md.research.elamur.ai/free/en/authors/yankai-lin/) and [Furu Wei](https://md.research.elamur.ai/free/en/authors/furu-wei/) · **Year:** 2025 · **Venue:** [arXiv:2502.18080](https://md.research.elamur.ai/free/en/venues/neural-information-processing-systems/) ([NeurIPS 2025](https://md.research.elamur.ai/free/en/venues/neural-information-processing-systems/2025/)) · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2502.18080) · [PDF](https://arxiv.org/pdf/2502.18080) · [DOI 10.48550/arxiv.2502.18080](https://doi.org/10.48550/arxiv.2502.18080) · [arXiv 2502.18080](https://arxiv.org/abs/2502.18080) · [OpenAlex](https://openalex.org/W4414851194)

**Citations:** 1 citations (OpenAlex, 2026-10-14) · [42](https://md.research.elamur.ai/free/en/papers/yang-2025-towards-thinking-optimal-scaling-test/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper asks whether making LLMs reason with ever-longer Chains of Thought can actually *hurt* accuracy, beyond simply wasting compute. The authors first compare o1-like models with their System-1 counterparts on MATH500 and AIME2024, counting all tokens with the Qwen2.5 tokenizer. Models such as QwQ-32B-Preview produce far more tokens for modest gains. In a controlled study, they fine-tune LLaMA3.1-8B-Instruct and Qwen2.5-32B-Instruct on QwQ-32B-Preview traces of short, medium and long length. Training on longer traces often lowers accuracy, especially on easier tasks, and the best length differs by difficulty. Longer traces also tend to contain more faulty steps. From this they build TOPS (Thinking-OPtimal Scaling). A small seed set teaches a "tag" model to reason at several effort levels. That model then solves many new problems, and only its shortest correct answer per problem is kept for self-improvement. The resulting Qwen2.5-32B-TOPS beats other distillation-based 32B o1-like models and, after iteration, roughly matches QwQ-32B-Preview. This matters because it shows reasoning length should adapt to the problem rather than simply grow.

## Key points
- **Seed data:** about 1.3K problems (1256 for LLaMA3.1-8B-Tag, 1312 for Qwen2.5-32B-Tag). Average response lengths per effort level for the Qwen tag model are roughly 1.6K tokens (low), 2.5K (medium) and 3.8K (high).
- **Benchmarks:** GSM8K, MATH500 and AIME2024, with a 16,384-token generation cap. Qwen2.5-32B-TOPS spends fewer tokens on easy GSM8K and more on hard AIME2024.
- **Iterative self-improvement:** the authors drew 4,500 unused MATH problems plus AIME 1983–2023 and sampled 8 responses each. Additional SFT mostly shortened outputs without clear accuracy gains. DPO, with long incorrect answers (and overly short wrong ones) as rejected responses, improved both accuracy and efficiency.
- **LLaMA3.1-8B results:** TOPS-SFT outperforms Random-SFT while using fewer tokens:
  - GSM8K: 88.54 vs 87.94, with about 571 vs 1051 tokens;
  - MATH500: 61.28 vs 60.52;
  - AIME2024: 8.00 vs 4.67.
- **Scope and availability:** the study covers only math and the SFT setting. Code, data and models are released at github.com/RUCBM/TOPS.

*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 University](https://md.research.elamur.ai/free/en/universities/peking-university/) — University, Beijing, China · 315 works · 43,267 citations
- [Microsoft Research Asia](https://md.research.elamur.ai/free/en/companies/microsoft-research-asia/) — Company, Beijing, China · 82 works · 61,484 citations
- [Renmin University of China](https://md.research.elamur.ai/free/en/universities/renmin-university-of-china/) — University, Beijing, China · 139 works · 17,752 citations

📚 Shelves (5): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 18,614 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 17,965 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 17,450 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 17,296 works · [👁️ Computer Vision and Pattern Recognition](https://md.research.elamur.ai/free/en/shelves/computer-science/computer-vision-and-pattern-recognition/) · 3,486 works

🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 3,894 works · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,685 works

## Cite

Cite as: Wenkai Yang, Shuming Ma, Yankai Lin and Furu Wei. 2025. Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning. arXiv:2502.18080.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{yang2025thinking,
  title = {{Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning}},
  author = {Wenkai Yang, Shuming Ma, Yankai Lin and Furu Wei},
  year = {2025},
  doi = {10.48550/arxiv.2502.18080},
  eprint = {2502.18080},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2502.18080}
}
```

- [← previous General-Reasoner: Advancing LLM Reasoning Across All Domains](https://md.research.elamur.ai/free/en/papers/ma-2025-general-reasoner-advancing-llm-reasoning/)
- [next → BIG5-CHAT: Shaping LLM Personalities Through Training on Human-Grounded Data](https://md.research.elamur.ai/free/en/papers/li-2025-big5-chat-shaping-llm-personalities/)
- [↑ back to papers of 2025](https://md.research.elamur.ai/free/en/papers/2025/page/3/)

## References

52 references, 30 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. 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](https://md.research.elamur.ai/free/en/papers/brown-2024-large-language-monkeys-scaling-inference/). arXiv preprint arXiv:2407.21787, 2024.
2. Lingjiao Chen, Jared Quincy Davis, Boris Hanin, Peter Bailis, Ion Stoica, Matei Zaharia, and James Zou. Are more LLM calls all you need? towards the scaling properties of compound AI systems. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openrevie… [find](https://scholar.google.com/scholar?q=Lingjiao+Chen%2C+Jared+Quincy+Davis%2C+Boris+Hanin%2C+Peter+Bailis%2C+Ion+Stoica%2C+Matei+Zaharia%2C+and+James+Zou%2E+Are+more+LLM+calls+all+you+need%3F+towards+the+scaling+properties+of+compound+AI+systems%2E+In+The+T)
3. Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, et al. Do not think that much for 2+ 3=? on the overthinking of o1-like llms. arXiv preprint arXiv:2412.[21187, 2024](https://md.research.elamur.ai/free/en/papers/chen-2024-think-that-much-2-3/).
4. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. [Training verifiers to solve math word problems](https://md.research.elamur.ai/free/en/papers/cobbe-2021-training-verifiers-solve-math-word/). arXiv preprint arXiv:2110.14168, 2021.
5. Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, Jiarui Yuan, Huayu Chen, Kaiyan Zhang, Xingtai Lv, Shuo Wang, Yuan Yao, Hao Peng, Yu Cheng, Zhiyuan Liu, Maosong Sun, Bowen Zhou, and Ning Ding. Process reinforcement through implicit… — [Process Reinforcement through Implicit Rewards](https://md.research.elamur.ai/free/en/papers/cui-2025-process-reinforcement-through-implicit-rewards/)
6. DeepSeek. [Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning](https://md.research.elamur.ai/free/en/papers/deepseek-ai-2025-deepseek-r1-incentivizing-reasoning-capability/), 1 2025. URL [https://github.com/deepseek-ai/DeepSeek-R1/blob/main/DeepSeek_](https://github.com/deepseek-ai/DeepSeek-R1/blob/main/DeepSeek_) R1.pdf. [↗](https://github.com/deepseek-ai/DeepSeek-R1/blob/main/DeepSeek_)
7. Kanishk Gandhi, Denise Lee, Gabriel Grand, Muxin Liu, Winson Cheng, Archit Sharma, and Noah D Goodman. Stream of search (sos): Learning to search in language. arXiv preprint arXiv:2404.03683, 2024. [find](https://scholar.google.com/scholar?q=Kanishk+Gandhi%2C+Denise+Lee%2C+Gabriel+Grand%2C+Muxin+Liu%2C+Winson+Cheng%2C+Archit+Sharma%2C+and+Noah+D+Goodman%2E+Stream+of+search+%28sos%29%3A+Learning+to+search+in+language%2E+arXiv+preprint+arXiv%3A2404%2E03683%2C+2024%2E)
8. Bofei Gao, Feifan Song, Zhe Yang, Zefan Cai, Yibo Miao, Qingxiu Dong, Lei Li, Chenghao Ma, Liang Chen, Runxin Xu, et al. [Omni-math: A universal olympiad level mathematic benchmark for large language models](https://md.research.elamur.ai/free/en/papers/gao-2024-omni-math-universal-olympiad-level/). arXiv preprint arXiv:2410.07985, 2024.
9. Elliot Glazer, Ege Erdil, Tamay Besiroglu, Diego Chicharro, Evan Chen, Alex Gunning, Caroline Falkman Olsson, Jean-Stanislas Denain, Anson Ho, Emily de Oliveira Santos, et al. [Frontiermath: A benchmark for evaluating advanced mathematical reasoning in ai](https://md.research.elamur.ai/free/en/papers/glazer-2024-frontiermath-benchmark-evaluating-advanced-mathematical/). arXiv preprint arXiv:2411.04872, 2024.
10. Google. Gemini 2.0 flash experimental, 2024. technologies/gemini/flash/. URL [https://deepmind.google/](https://deepmind.google/) [↗](https://deepmind.google/)
11. Google. Gemini 2.0 flash thinking mode, 2024. gemini-api/docs/thinking-mode. URL [https://ai.google.dev/](https://ai.google.dev/) [↗](https://ai.google.dev/)
12. Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang. [rstar-math: Small llms can master math reasoning with self-evolved deep thinking](https://md.research.elamur.ai/free/en/papers/guan-2025-rstar-math-small-llms-can/). arXiv preprint arXiv:2501.04519, 2025.
13. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. [Measuring mathematical problem solving with the MATH dataset](https://md.research.elamur.ai/free/en/papers/hendrycks-2021-measuring-mathematical-problem-solving-math/). In Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2), 2021. URL ht…
14. Zhen Huang, Haoyang Zou, Xuefeng Li, Yixiu Liu, Yuxiang Zheng, Ethan Chern, Shijie Xia, Yiwei Qin, Weizhe Yuan, and Pengfei Liu. O1 replication journey–part 2: Surpassing o1-preview through simple distillation, big progress or bitter lesson? arXiv preprint arXiv:2411.16489, 2024. [find](https://scholar.google.com/scholar?q=Zhen+Huang%2C+Haoyang+Zou%2C+Xuefeng+Li%2C+Yixiu+Liu%2C+Yuxiang+Zheng%2C+Ethan+Chern%2C+Shijie+Xia%2C+Yiwei+Qin%2C+Weizhe+Yuan%2C+and+Pengfei+Liu%2E+O1+replication+journey%E2%80%93part+2%3A+Surpassing+o1%2Dpreview+through+simple+dis)
15. Kimi Team. [Kimi k1.5: Scaling reinforcement learning with llms](https://md.research.elamur.ai/free/en/papers/kimi-team-2025-kimi-k1-5-scaling-reinforcement/), 1 2025. URL [https://github.com/MoonshotAI/Kimi-k1.5/blob/main/Kimi_k1.5.pdf](https://github.com/MoonshotAI/Kimi-k1.5/blob/main/Kimi_k1.5.pdf). [↗](https://github.com/MoonshotAI/Kimi-k1.5/blob/main/Kimi_k1.5.pdf)
16. Xin Lai, Zhuotao Tian, Yukang Chen, Senqiao Yang, Xiangru Peng, and Jiaya Jia. [Step-dpo: Step-wise preference optimization for long-chain reasoning of llms](https://md.research.elamur.ai/free/en/papers/lai-2024-step-dpo-step-wise-preference/). arXiv preprint arXiv:2406.18629, 2024.
17. Jia Li, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Huang, Kashif Rasul, Longhui Yu, Albert Q Jiang, Ziju Shen, et al. Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions. Hugging Face repository, 13, 2024. [find](https://scholar.google.com/scholar?q=Jia+Li%2C+Edward+Beeching%2C+Lewis+Tunstall%2C+Ben+Lipkin%2C+Roman+Soletskyi%2C+Shengyi+Huang%2C+Kashif+Rasul%2C+Longhui+Yu%2C+Albert+Q+Jiang%2C+Ziju+Shen%2C+et+al%2E+Numinamath%3A+The+largest+public+dataset+in+ai4maths+with)
18. Yifei Li, Zeqi Lin, Shizhuo Zhang, Qiang Fu, Bei Chen, Jian-Guang Lou, and Weizhu Chen. [Making language models better reasoners with step-aware verifier](https://md.research.elamur.ai/free/en/papers/li-2023-making-language-models-better-reasoners/). In Anna Rogers, Jordan Boyd-Graber, and Naoaki Okazaki, editors, Proceedings of the 61st Annual Meeting of the Association for Computational Lingu…
19. Zongzhao Li, Zongyang Ma, Mingze Li, Songyou Li, Yu Rong, Tingyang Xu, Ziqi Zhang, Deli Zhao, and Wenbing Huang. Star-r1: Spatial transformation reasoning by reinforcing multimodal llms. arXiv preprint arXiv:2505.15804, 2025. — [arXiv:2505.15804](https://arxiv.org/abs/2505.15804) [find](https://scholar.google.com/scholar?q=Zongzhao+Li%2C+Zongyang+Ma%2C+Mingze+Li%2C+Songyou+Li%2C+Yu+Rong%2C+Tingyang+Xu%2C+Ziqi+Zhang%2C+Deli+Zhao%2C+and+Wenbing+Huang%2E+Star%2Dr1%3A+Spatial+transformation+reasoning+by+reinforcing+multimodal+llms%2E+arXiv+preprin)
20. Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. arXiv preprint arXiv:2305.[20050, 2023](https://md.research.elamur.ai/free/en/papers/lightman-2023-let-s-verify-step-step/).
21. Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al. Deepseek-v3 technical report. arXiv preprint arXiv:2412.19437, 2024. [find](https://scholar.google.com/scholar?q=Aixin+Liu%2C+Bei+Feng%2C+Bing+Xue%2C+Bingxuan+Wang%2C+Bochao+Wu%2C+Chengda+Lu%2C+Chenggang+Zhao%2C+Chengqi+Deng%2C+Chenyu+Zhang%2C+Chong+Ruan%2C+et+al%2E+Deepseek%2Dv3+technical+report%2E+arXiv+preprint+arXiv%3A2412%2E19437%2C+2024%2E)
22. Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning. arXiv preprint arXiv:2501.12570, 2025. [find](https://scholar.google.com/scholar?q=Haotian+Luo%2C+Li+Shen%2C+Haiying+He%2C+Yibo+Wang%2C+Shiwei+Liu%2C+Wei+Li%2C+Naiqiang+Tan%2C+Xiaochun+Cao%2C+and+Dacheng+Tao%2E+O1%2Dpruner%3A+Length%2Dharmonizing+fine%2Dtuning+for+o1%2Dlike+reasoning+pruning%2E+arXiv+preprint+ar)
23. Xueguang Ma, Qian Liu, Dongfu Jiang, Ge Zhang, Zejun Ma, and Wenhu Chen. [General-reasoner: Advancing llm reasoning across all domains](https://md.research.elamur.ai/free/en/papers/ma-2025-general-reasoner-advancing-llm-reasoning/). arXiv preprint arXiv:2505.14652, 2025.
24. MetaAI. Introducing llama 3.1: Our most capable models to date. [https://ai.meta.com/](https://ai.meta.com/) blog/meta-llama-3-1/, 2024. [↗](https://ai.meta.com/)
25. Yingqian Min, Zhipeng Chen, Jinhao Jiang, Jie Chen, Jia Deng, Yiwen Hu, Yiru Tang, Jiapeng Wang, Xiaoxue Cheng, Huatong Song, et al. [Imitate, explore, and self-improve: A reproduction report on slow-thinking reasoning systems](https://md.research.elamur.ai/free/en/papers/min-2024-imitate-explore-self-improve-reproduction/). arXiv preprint arXiv:2412.09413, 2024.
26. NovaSky Team. Sky-t1: Train your own o1 preview model within $450. [https://novasky-ai.github.io/posts/sky-t1](https://novasky-ai.github.io/posts/sky-t1), 2025. Accessed: 2025-01-09. [↗](https://novasky-ai.github.io/posts/sky-t1)
27. OpenAI. Hello gpt-4o, 2024. URL [https://openai.com/index/hello-gpt-4o](https://openai.com/index/hello-gpt-4o). [↗](https://openai.com/index/hello-gpt-4o)
28. OpenAI. Learning to reason with llms, 2024. learning-to-reason-with-llms. URL [https://openai.com/index/](https://openai.com/index/) [↗](https://openai.com/index/)
29. Qwen Team. Qwen2. 5: A party of foundation models. Qwen (Sept. 2024). url: [https://qwenlm.github](https://qwenlm.github). io/blog/qwen2, 5, 2024. [↗](https://qwenlm.github)
30. Qwen Team. Qwq: Reflect deeply on the boundaries of the unknown, November 2024. URL [https://qwenlm.github.io/blog/qwq-32b-preview/](https://qwenlm.github.io/blog/qwq-32b-preview/). [↗](https://qwenlm.github.io/blog/qwq-32b-preview/)
31. Qwen Team. Qwq-32b: Embracing the power of reinforcement learning, November 2025. URL [https://qwenlm.github.io/blog/qwq-32b/](https://qwenlm.github.io/blog/qwq-32b/). [↗](https://qwenlm.github.io/blog/qwq-32b/)
32. Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. [Direct preference optimization: Your language model is secretly a reward model](https://md.research.elamur.ai/free/en/papers/rafailov-2023-direct-preference-optimization-language-model/). Advances in Neural Information Processing Systems, 36, 2024.
33. 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](https://md.research.elamur.ai/free/en/papers/rein-2023-gpqa-graduate-level-google-proof/). arXiv preprint arXiv:2311.12022, 2023.
34. Baptiste Roziere, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Romain Sauvestre, Tal Remez, et al. [Code llama: Open foundation models for code](https://md.research.elamur.ai/free/en/papers/roziere-2024-code-llama-open-foundation-models/). arXiv preprint arXiv:2308.12950, 2023.
35. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. [Deepseekmath: Pushing the limits of mathematical reasoning in open language models](https://md.research.elamur.ai/free/en/papers/shao-2024-deepseekmath-pushing-limits-mathematical-reasoning/). arXiv preprint arXiv:2402.03300, 2024.
36. Skywork-o1. Skywork-o1 open series. [https://huggingface.co/Skywork](https://huggingface.co/Skywork), November 2024. URL https://huggingface.co/Skywork. [↗](https://huggingface.co/Skywork)
37. Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. [Scaling llm test-time compute optimally can be more effective than scaling model parameters](https://md.research.elamur.ai/free/en/papers/snell-2024-scaling-llm-test-time-compute/). arXiv preprint arXiv:2408.03314, 2024.
38. Lin Sun, Guangxiang Zhao, Xiaoqi Jian, Yuhan Wu, Weihong Lin, Yongfu Zhu, Linglin Zhang, Jinzhu Wu, Junfeng Ran, Sai-er Hu, et al. [Tinyr1-32b-preview: Boosting accuracy with branch-merge distillation](https://md.research.elamur.ai/free/en/papers/sun-2025-tinyr1-32b-preview-boosting-accuracy/). arXiv preprint arXiv:2503.04872, 2025.
39. Peiyi Wang, Lei Li, Zhihong Shao, Runxin Xu, Damai Dai, Yifei Li, Deli Chen, Yu Wu, and Zhifang Sui. [Math-shepherd: Verify and reinforce llms step-by-step without human annotations](https://md.research.elamur.ai/free/en/papers/wang-2024-math-shepherd-verify-reinforce-llms/). In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pa…
40. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. [Self-consistency improves chain of thought reasoning in language models](https://md.research.elamur.ai/free/en/papers/wang-2022-self-consistency-improves-chain-thought/). In The Eleventh International Conference on Learning Representations, 2023. URL [https://openreview.net/forum?id=…](https://openreview.net/forum?id=…) [↗](https://openreview.net/forum?id=…)
41. Yubo Wang, Xueguang Ma, Ge Zhang, Yuansheng Ni, Abhranil Chandra, Shiguang Guo, Weiming Ren, Aaran Arulraj, Xuan He, Ziyan Jiang, et al. [Mmlu-pro: A more robust and challenging multi-task language understanding benchmark](https://md.research.elamur.ai/free/en/papers/wang-2024-mmlu-pro-more-robust-challenging/). Advances in Neural Information Processing Systems, 37:95266–95290, 2024.
42. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. [Chain-of-thought prompting elicits reasoning in large language models](https://md.research.elamur.ai/free/en/papers/wei-2022-chain-thought-prompting-elicits-reasoning/). Advances in neural information processing systems, 35:24824–24837, 2022.
43. Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. An empirical analysis of compute-optimal inference for problem-solving with language models. 2024. [find](https://scholar.google.com/scholar?q=Yangzhen+Wu%2C+Zhiqing+Sun%2C+Shanda+Li%2C+Sean+Welleck%2C+and+Yiming+Yang%2E+An+empirical+analysis+of+compute%2Doptimal+inference+for+problem%2Dsolving+with+language+models%2E+2024%2E)
44. 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](https://scholar.google.com/scholar?q=Violet+Xiang%2C+Charlie+Snell%2C+Kanishk+Gandhi%2C+Alon+Albalak%2C+Anikait+Singh%2C+Chase+Blagden%2C+Duy+Phung%2C+Rafael+Rafailov%2C+Nathan+Lile%2C+Dakota+Mahan%2C+et+al%2E+Towards+system+2+reasoning+in+llms%3A+Learning+how+)
45. An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, et al. Qwen2. 5-math technical report: Toward mathematical expert model via self-improvement. arXiv preprint arXiv:2409.[12122, 2024](https://md.research.elamur.ai/free/en/papers/yang-2024-qwen2-5-math-technical-report/).
46. Wenkai Yang, Jingwen Chen, Yankai Lin, and Ji-Rong Wen. Deepcritic: Deliberate critique with large language models. arXiv preprint arXiv:2505.00662, 2025. — [arXiv:2505.00662](https://arxiv.org/abs/2505.00662) [find](https://scholar.google.com/scholar?q=Wenkai+Yang%2C+Jingwen+Chen%2C+Yankai+Lin%2C+and+Ji%2DRong+Wen%2E+Deepcritic%3A+Deliberate+critique+with+large+language+models%2E+arXiv+preprint+arXiv%3A2505%2E00662%2C+2025%2E+%E2%80%94+%5BarXiv%3A2505%2E00662%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F25)
47. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik R Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL [https://openreview.net/forum?id=5Xc1ecx…](https://openreview.net/forum?id=5Xc1ecx…) [↗](https://openreview.net/forum?id=5Xc1ecx…)
48. Longhui Yu, Weisen Jiang, Han Shi, Jincheng YU, Zhengying Liu, Yu Zhang, James Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. [Metamath: Bootstrap your own mathematical questions for large language models](https://md.research.elamur.ai/free/en/papers/yu-2023-metamath-bootstrap-your-own-mathematical/). In The Twelfth International Conference on Learning Representations, 2024. URL https://openr…
49. Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. [Star: Bootstrapping reasoning with reasoning](https://md.research.elamur.ai/free/en/papers/zelikman-2022-star-bootstrapping-reasoning-reasoning/). Advances in Neural Information Processing Systems, 35:15476–15488, 2022.
50. Di Zhang, Xiaoshui Huang, Dongzhan Zhou, Yuqiang Li, and Wanli Ouyang. Accessing gpt-4 level mathematical olympiad solutions via monte carlo tree self-refine with llama-3 8b. arXiv preprint arXiv:2406.07394, 2024. [find](https://scholar.google.com/scholar?q=Di+Zhang%2C+Xiaoshui+Huang%2C+Dongzhan+Zhou%2C+Yuqiang+Li%2C+and+Wanli+Ouyang%2E+Accessing+gpt%2D4+level+mathematical+olympiad+solutions+via+monte+carlo+tree+self%2Drefine+with+llama%2D3+8b%2E+arXiv+preprint+arXiv%3A2406)
51. Zhuosheng Zhang, Aston Zhang, Mu Li, and Alex Smola. [Automatic chain of thought prompting in large language models](https://md.research.elamur.ai/free/en/papers/zhang-2022-automatic-chain-thought-prompting-large/). In The Eleventh International Conference on Learning Representations, 2023. URL [https://openreview.net/forum?id=5NTt8GFjUHkr](https://openreview.net/forum?id=5NTt8GFjUHkr). [↗](https://openreview.net/forum?id=5NTt8GFjUHkr)
52. Yu Zhao, Huifeng Yin, Bo Zeng, Hao Wang, Tianqi Shi, Chenyang Lyu, Longyue Wang, Weihua Luo, and Kaifu Zhang. [Marco-o1: Towards open reasoning models for open-ended solutions](https://md.research.elamur.ai/free/en/papers/zhao-2024-marco-o1-towards-open-reasoning/). arXiv preprint arXiv:2411.14405, 2024. *Table 5: CoT token count returned from o1-mini API and estimated by Qwen2.5 tokenize…

*Updated 2 November 2026*