---
title: "When More is Less — paper by Wu et al. (2025)"
description: "The authors argue that it does not. 45 references, cited by 68 papers here. Among them: 5."
authors: ["Yuyang Wu", "Yifei Wang", "Ziyu Ye", "Tianqi Du", "Stefanie Jegelka", "Yisen Wang"]
year: 2025
venue: "arXiv:2502.07266"
source: "https://arxiv.org/abs/2502.07266"
doi: "10.48550/arxiv.2502.07266"
arxiv: "2502.07266"
licence: "CC BY-NC-SA 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by-nc-sa/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/wu-2025-more-less-understanding-chain-thought/"
---
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# When More is Less: Understanding Chain-of-Thought Length in LLMs

**Authors:** [Yuyang Wu](https://md.research.elamur.ai/free/en/authors/yuyang-wu/), [Yifei Wang](https://md.research.elamur.ai/free/en/authors/yifei-wang/), Ziyu Ye, Tianqi Du, [Stefanie Jegelka](https://md.research.elamur.ai/free/en/authors/stefanie-jegelka/) and [Yisen Wang](https://md.research.elamur.ai/free/en/authors/yisen-wang/) · **Year:** 2025 · **Venue:** arXiv:2502.07266 · **Licence:** [CC BY-NC-SA 4.0 (arXiv)](http://creativecommons.org/licenses/by-nc-sa/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2502.07266) · [PDF](https://arxiv.org/pdf/2502.07266) · [DOI 10.48550/arxiv.2502.07266](https://doi.org/10.48550/arxiv.2502.07266) · [arXiv 2502.07266](https://arxiv.org/abs/2502.07266) · [OpenAlex](https://openalex.org/W4407424296)

**Citations:** 5 citations (OpenAlex, 2026-10-14) · [68](https://md.research.elamur.ai/free/en/papers/wu-2025-more-less-understanding-chain-thought/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper asks whether longer Chain-of-Thought (CoT) reasoning always helps LLMs. The authors argue that it does not. They combine three lines of evidence: measurements on public models, controlled experiments, and a formal model. Public models include the Qwen2.5 Instruct series on MATH Level 5, plus RL runs. The controlled experiments train a small GPT2 on synthetic addition-only arithmetic.

Across these settings, accuracy rises and then falls as the number of reasoning steps grows. More steps make each sub-step easier, but errors compound along the chain. The best-performing length shifts in two directions:

- **Harder problems** need longer chains.
- **Stronger models** do best with shorter ones.

The authors call this second trend a simplicity bias. It also shows up during RL training, where responses get shorter as accuracy improves. The theory formally derives these trends.

Practically, the work explains "overthinking." It shows that training on CoTs of suitable length helps. It also proposes an inference-time vote that weights answers by CoT length.

## Key points
- **Model size:** On MATH Level 5 (60 sampled solutions per question), the optimal CoT length drops from about 14 steps for Qwen2.5-1.5B-Instruct to about 4 steps for the 72B model.
- **Task difficulty:** Measured as 1 minus accuracy, difficulty correlates positively with optimal length (r = 0.57, p ≈ 1.9e-8 on 100 questions). For the 72B model, the longest CoTs score up to roughly 40% lower than optimal-length ones.
- **RL training:** GRPO training of Qwen2.5-7B-Instruct on LeetCode-2K gradually shortens the average response as reward improves.
- **Controlled study:** In synthetic addition tasks, difficulty is the operator count T and CoT length is about T divided by the step size t. A 6-layer GPT2 reproduces the inverted U-shaped curves.
- **Length-aware voting:** The method (also called "Length-Filtered Vote") bins sampled answers by CoT length (bin size 2). It then runs a majority vote over only the 3 bins with the lowest answer entropy. On 100 GPQA questions, it consistently beats plain self-consistency.

*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

- [Massachusetts Institute of Technology](https://md.research.elamur.ai/free/en/universities/massachusetts-institute-of-technology/) — University, Cambridge, United States · 243 works · 76,506 citations
- [Peking University](https://md.research.elamur.ai/free/en/universities/peking-university/) — University, Beijing, China · 315 works · 43,267 citations
- [University of Chicago](https://md.research.elamur.ai/free/en/universities/university-of-chicago/) — University, Chicago, United States · 52 works · 50,893 citations
- [Munich Center for Machine Learning](https://md.research.elamur.ai/free/en/universities/munich-center-for-machine-learning/) — University, Munich, Germany · 62 works · 1,167 citations

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🧭 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: Yuyang Wu, Yifei Wang, Ziyu Ye, Tianqi Du, Stefanie Jegelka and Yisen Wang. 2025. When More is Less: Understanding Chain-of-Thought Length in LLMs. arXiv:2502.07266.

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

```bibtex
@misc{wu2025when,
  title = {{When More is Less: Understanding Chain-of-Thought Length in LLMs}},
  author = {Yuyang Wu, Yifei Wang, Ziyu Ye, Tianqi Du, Stefanie Jegelka and Yisen Wang},
  year = {2025},
  doi = {10.48550/arxiv.2502.07266},
  eprint = {2502.07266},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2502.07266}
}
```

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## References

45 references, 25 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Devansh Arpit, Stanisław Jastrz˛ebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. A closer look at memorization in deep networks. In International conference on machine learning, pages 233–242. PMLR, 2017. [find](https://scholar.google.com/scholar?q=Devansh+Arpit%2C+Stanis%C5%82aw+Jastrz%CB%9Bebski%2C+Nicolas+Ballas%2C+David+Krueger%2C+Emmanuel+Bengio%2C+Maxinder+S+Kanwal%2C+Tegan+Maharaj%2C+Asja+Fischer%2C+Aaron+Courville%2C+Yoshua+Bengio%2C+et+al%2E+A+closer+look+at+memorizat)
2. 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/), 2024. URL https://arxiv.org/abs/2407.21787. [↗](https://arxiv.org/abs/2407.21787)
3. Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chri… — [Language Models are Few-Shot Learners](https://md.research.elamur.ai/free/en/papers/brown-2020-language-models-few-shot-learners/)
4. Lijie Chen, Binghui Peng, and Hongxun Wu. Theoretical limitations of multi-layer transformer, 2024. URL https://arxiv.org/abs/2412.02975. — [arXiv:2412.02975](https://arxiv.org/abs/2412.02975) [↗](https://arxiv.org/abs/2412.02975)
5. Qiguang Chen, Libo Qin, Jiaqi WANG, Jingxuan Zhou, and Wanxiang Che. Unlocking the capabilities of thought: A reasoning boundary framework to quantify and optimize chain-of-thought. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL [https://openreview.net/foru…](https://openreview.net/foru…) [↗](https://openreview.net/foru…)
6. Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, and Dong Yu. [Do not think that much for 2+3=? on the overthinking of o1-like llms](https://md.research.elamur.ai/free/en/papers/chen-2024-think-that-much-2-3/), 2024. URL https://arxiv.org/abs/2412.21187. [↗](https://arxiv.org/abs/2412.21187)
7. Yanxi Chen, Xuchen Pan, Yaliang Li, Bolin Ding, and Jingren Zhou. A simple and provable scaling law for the test-time compute of large language models, 2024. URL https://arxiv.org/abs/2411.19477. — [arXiv:2411.19477](https://arxiv.org/abs/2411.19477) [↗](https://arxiv.org/abs/2411.19477)
8. Yilong Chen, Junyuan Shang, Zhenyu Zhang, Yanxi Xie, Jiawei Sheng, Tingwen Liu, Shuohuan Wang, Yu Sun, Hua Wu, and Haifeng Wang. [Inner thinking transformer: Leveraging dynamic depth scaling to foster adaptive internal thinking](https://md.research.elamur.ai/free/en/papers/chen-2025-inner-thinking-transformer-leveraging-dynamic/), 2025. URL https://arxiv.org/abs/2502.13842. [↗](https://arxiv.org/abs/2502.13842)
9. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. [Training verifiers to solve math word problems](https://md.research.elamur.ai/free/en/papers/cobbe-2021-training-verifiers-solve-math-word/), 2021. URL https://arxiv.org/abs/2110.14168. [↗](https://arxiv.org/abs/2110.14168)
10. Yingqian Cui, Pengfei He, Xianfeng Tang, Qi He, Chen Luo, Jiliang Tang, and Yue Xing. A theoretical understanding of chain-of-thought: Coherent reasoning and error-aware demonstration, 2024. URL https://arxiv.org/abs/2410.16540. — [arXiv:2410.16540](https://arxiv.org/abs/2410.16540) [↗](https://arxiv.org/abs/2410.16540)
11. Guhao Feng, Bohang Zhang, Yuntian Gu, Haotian Ye, Di He, and Liwei Wang. Towards revealing the mystery behind chain of thought: A theoretical perspective. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL [https://openreview.net/forum?id=qHrADgAdYu](https://openreview.net/forum?id=qHrADgAdYu). [↗](https://openreview.net/forum?id=qHrADgAdYu)
12. Yao Fu, Hao Peng, Ashish Sabharwal, Peter Clark, and Tushar Khot. [Complexity-based prompting for multi-step reasoning](https://md.research.elamur.ai/free/en/papers/fu-2022-complexity-based-prompting-multi-step/), 2023. URL https://arxiv.org/abs/2210.00720. [↗](https://arxiv.org/abs/2210.00720)
13. Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D. Goodman. [Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars](https://md.research.elamur.ai/free/en/papers/gandhi-2025-cognitive-behaviors-that-enable-self/), 2025. URL https://arxiv.org/abs/2503.01307. [↗](https://arxiv.org/abs/2503.01307)
14. Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, and Tom Goldstein. Scaling up test-time compute with latent reasoning: A recurrent depth approach. arXiv preprint arXiv:2502.05171, 2025. [find](https://scholar.google.com/scholar?q=Jonas+Geiping%2C+Sean+McLeish%2C+Neel+Jain%2C+John+Kirchenbauer%2C+Siddharth+Singh%2C+Brian+R+Bartoldson%2C+Bhavya+Kailkhura%2C+Abhinav+Bhatele%2C+and+Tom+Goldstein%2E+Scaling+up+test%2Dtime+compute+with+latent+reasoning)
15. 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](https://md.research.elamur.ai/free/en/papers/deepseek-ai-2025-deepseek-r1-incentivizing-reasoning-capability/). arXiv preprint arXiv:2501.12948, 2025.
16. Tingxu Han, Zhenting Wang, Chunrong Fang, Shiyu Zhao, Shiqing Ma, and Zhenyu Chen. [Token-budget-aware llm reasoning](https://md.research.elamur.ai/free/en/papers/han-2024-token-budget-aware-llm-reasoning/). arXiv preprint arXiv:2412.18547, 2024.
17. Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. [Measuring massive multitask language understanding](https://md.research.elamur.ai/free/en/papers/hendrycks-2020-measuring-massive-multitask-language-understanding/). In International Conference on Learning Representations, 2021. URL [https://openreview.net/forum?id=d7KBjmI3GmQ](https://openreview.net/forum?id=d7KBjmI3GmQ). [↗](https://openreview.net/forum?id=d7KBjmI3GmQ)
18. 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/), 2021. URL https://arxiv.org/abs/2103.03874. [↗](https://arxiv.org/abs/2103.03874)
19. Minyoung Huh, Hossein Mobahi, Richard Zhang, Brian Cheung, Pulkit Agrawal, and Phillip Isola. The low-rank simplicity bias in deep networks. arXiv preprint arXiv:2103.10427, 2021. — [arXiv:2103.10427](https://arxiv.org/abs/2103.10427) [find](https://scholar.google.com/scholar?q=Minyoung+Huh%2C+Hossein+Mobahi%2C+Richard+Zhang%2C+Brian+Cheung%2C+Pulkit+Agrawal%2C+and+Phillip+Isola%2E+The+low%2Drank+simplicity+bias+in+deep+networks%2E+arXiv+preprint+arXiv%3A2103%2E10427%2C+2021%2E+%E2%80%94+%5BarXiv%3A2103%2E10427%5D)
20. Mingyu Jin, Qinkai Yu, Dong Shu, Haiyan Zhao, Wenyue Hua, Yanda Meng, Yongfeng Zhang, and Mengnan Du. [The impact of reasoning step length on large language models](https://md.research.elamur.ai/free/en/papers/jin-2024-impact-reasoning-step-length-large/). In Annual Meeting of the Association for Computational Linguistics, 2024. URL [https://api.semanticscholar.org/CorpusID:266902900](https://api.semanticscholar.org/CorpusID:266902900). [↗](https://api.semanticscholar.org/CorpusID:266902900)
21. Ming Li, Yanhong Li, and Tianyi Zhou. [What happened in llms layers when trained for fast vs. slow thinking: A gradient perspective](https://md.research.elamur.ai/free/en/papers/li-2025-what-happened-llms-layers-when/), 2024. URL https://arxiv.org/abs/2410.23743. [↗](https://arxiv.org/abs/2410.23743)
22. Zhiyuan Li, Hong Liu, Denny Zhou, and Tengyu Ma. Chain of thought empowers transformers to solve inherently serial problems, 2024. URL https://arxiv.org/abs/2402.12875. [↗](https://arxiv.org/abs/2402.12875)
23. 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)
24. Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang, and Xinchao Wang. [Cot-valve: Length-compressible chain-of-thought tuning](https://md.research.elamur.ai/free/en/papers/ma-2025-cot-valve-length-compressible-chain/). arXiv preprint arXiv:2502.09601, 2025.
25. Zijie Meng, Yan Zhang, Zhaopeng Feng, and Zuozhu Liu. Dcr: Divide-and-conquer reasoning for multi-choice question answering with llms, 2024. URL https://arxiv.org/abs/2401.05190. — [arXiv:2401.05190](https://arxiv.org/abs/2401.05190) [↗](https://arxiv.org/abs/2401.05190)
26. Sania Nayab, Giulio Rossolini, Giorgio Buttazzo, Nicolamaria Manes, and Fabrizio Giacomelli. Concise thoughts: Impact of output length on llm reasoning and cost, 2024. URL https://arxiv.org/abs/2407.19825. — [arXiv:2407.19825](https://arxiv.org/abs/2407.19825) [↗](https://arxiv.org/abs/2407.19825)
27. 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](https://scholar.google.com/scholar?q=Qwen%2C+%3A%2C+An+Yang%2C+Baosong+Yang%2C+Beichen+Zhang%2C+Binyuan+Hui%2C+Bo+Zheng%2C+Bowen+Yu%2C+Chengyuan+Li%2C+Dayiheng+Liu%2C+Fei+Huang%2C+Haoran+Wei%2C+Huan+Lin%2C+Jian+Yang%2C+Jianhong+Tu%2C+Jianwei+Zhang%2C+Jianxin+Yang%2C+Jiaxi+)
28. Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019. [find](https://scholar.google.com/scholar?q=Alec+Radford%2C+Jeffrey+Wu%2C+Rewon+Child%2C+David+Luan%2C+Dario+Amodei%2C+Ilya+Sutskever%2C+et+al%2E+Language+models+are+unsupervised+multitask+learners%2E+OpenAI+blog%2C+1%288%29%3A9%2C+2019%2E)
29. 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/), 2023. URL https://arxiv.org/abs/2311.12022. [↗](https://arxiv.org/abs/2311.12022)
30. John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms, 2017. URL https://arxiv.org/abs/1707.06347. [↗](https://arxiv.org/abs/1707.06347)
31. 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](https://md.research.elamur.ai/free/en/papers/shao-2024-deepseekmath-pushing-limits-mathematical-reasoning/), 2024. URL https://arxiv.org/abs/2402.03300. [↗](https://arxiv.org/abs/2402.03300)
32. 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](https://md.research.elamur.ai/free/en/papers/sheng-2024-hybridflow-flexible-efficient-rlhf-framework/). In Proceedings of the Twentieth European Conference on Computer Systems, EuroSys ’25, page 1279–1297. ACM, March 2025. doi: 10.1145/…
33. 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/), 2024. URL https://arxiv.org/abs/2408.03314. [↗](https://arxiv.org/abs/2408.03314)
34. Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Shaochen Zhong, Hanjie Chen, et al. [Stop overthinking: A survey on efficient reasoning for large language models](https://md.research.elamur.ai/free/en/papers/sui-2025-stop-overthinking-survey-efficient-reasoning/). arXiv preprint arXiv:2503.16419, 2025.
35. Jean-Francois Ton, Muhammad Faaiz Taufiq, and Yang Liu. [Understanding chain-of-thought in llms through information theory](https://md.research.elamur.ai/free/en/papers/ton-2024-understanding-chain-thought-llms-through/), 2024. URL https://arxiv.org/abs/2411.11984. [↗](https://arxiv.org/abs/2411.11984)
36. Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, et al. [Llama: Open and efficient foundation language models](https://md.research.elamur.ai/free/en/papers/touvron-2023-llama-open-efficient-foundation-language/). arXiv preprint arXiv:2302.13971, 2023.
37. 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=…)
38. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian ichter, Fei Xia, Ed Chi, Quoc V Le, and Denny Zhou. [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/). In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Proce…
39. Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. Scaling inference computation: Compute-optimal inference for problem-solving with language models. In The 4th Workshop on Mathematical Reasoning and AI at NeurIPS’24, 2024. URL [https://openreview.net/forum?id=j7DZWSc8qu](https://openreview.net/forum?id=j7DZWSc8qu). [↗](https://openreview.net/forum?id=j7DZWSc8qu)
40. Yunhui Xia, Wei Shen, Yan Wang, Jason Klein Liu, Huifeng Sun, Siyue Wu, Jian Hu, and Xiaolong Xu. Leetcodedataset: A temporal dataset for robust evaluation and efficient training of code llms, 2025. URL https://arxiv.org/abs/2504.14655. — [arXiv:2504.14655](https://arxiv.org/abs/2504.14655) [↗](https://arxiv.org/abs/2504.14655)
41. Keyulu Xu, Jingling Li, Mozhi Zhang, Simon S Du, Ken-ichi Kawarabayashi, and Stefanie Jegelka. What can neural networks reason about? arXiv preprint arXiv:1905.13211, 2019. [find](https://scholar.google.com/scholar?q=Keyulu+Xu%2C+Jingling+Li%2C+Mozhi+Zhang%2C+Simon+S+Du%2C+Ken%2Dichi+Kawarabayashi%2C+and+Stefanie+Jegelka%2E+What+can+neural+networks+reason+about%3F+arXiv+preprint+arXiv%3A1905%2E13211%2C+2019%2E)
42. 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…)
43. Tian Ye, Zicheng Xu, Yuanzhi Li, and Zeyuan Allen-Zhu. [Physics of language models: Part 2.1, grade-school math and the hidden reasoning process](https://md.research.elamur.ai/free/en/papers/ye-2024-physics-language-models-part-2/), 2024. URL https://arxiv.org/abs/2407.20311. [↗](https://arxiv.org/abs/2407.20311)
44. Yizhou Zhang, Lun Du, Defu Cao, Qiang Fu, and Yan Liu. An examination on the effectiveness of divide-and-conquer prompting in large language models, 2024. URL https://arxiv.org/abs/2402.05359. — [arXiv:2402.05359](https://arxiv.org/abs/2402.05359) [↗](https://arxiv.org/abs/2402.05359)
45. Denny Zhou, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, Quoc V Le, and Ed H. Chi. [Least-to-most prompting enables complex reasoning in large language models](https://md.research.elamur.ai/free/en/papers/al-2022-least-most-prompting-enables-complex/). In The Eleventh International Conference on Learning Representations, 202…

*Updated 2 November 2026*