---
title: "What Characterizes Effective Reasoning? Revisiting Length,"
description: "This paper tests those claims across ten LRMs on HARP (math) and GPQA-Diamond (science), both… 39 references, cited by 4 papers here."
authors: ["Yunzhen Feng", "Julia Kempe", "Cheng Zhang", "Parag Jain", "Anthony Hartshorn"]
year: 2025
venue: "arXiv:2509.19284"
source: "https://arxiv.org/abs/2509.19284"
doi: "10.48550/arxiv.2509.19284"
arxiv: "2509.19284"
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/feng-2025-characterizes-effective-reasoning-revisiting-length/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/feng-2025-characterizes-effective-reasoning-revisiting-length/)

[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/14/) / What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT

# What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT

**Authors:** Yunzhen Feng, [Julia Kempe](https://md.research.elamur.ai/free/en/authors/julia-kempe/), [Cheng Zhang](https://md.research.elamur.ai/free/en/authors/cheng-zhang/), [Parag Jain](https://md.research.elamur.ai/free/en/authors/parag-jain/) and [Anthony Hartshorn](https://md.research.elamur.ai/free/en/authors/anthony-hartshorn/) · **Year:** 2025 · **Venue:** arXiv:2509.19284 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2509.19284) · [PDF](https://arxiv.org/pdf/2509.19284) · [DOI 10.48550/arxiv.2509.19284](https://doi.org/10.48550/arxiv.2509.19284) · [arXiv 2509.19284](https://arxiv.org/abs/2509.19284) · [OpenAlex](https://openalex.org/W4415251619)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · 4 in our library, of the 149,439 papers whose bibliographies we read

## Summary
Large reasoning models often spend large amounts of test-time compute on very long chains of thought. Earlier work, starting with S1's appended "wait" tokens, claimed that longer traces and more self-review help, but later studies disagreed. This paper tests those claims across ten LRMs on HARP (math) and GPQA-Diamond (science), both of which carry human-labeled difficulty levels.

The authors compare traces generated for the same question. Within a question, longer CoTs and a higher Review Ratio are linked to lower accuracy, and the effect is stronger on harder problems. They then have a model convert each CoT into a reasoning graph written in Graphviz. From this graph they compute the Failed-Step Fraction (FSF), the share of steps that sit in abandoned branches. FSF predicts correctness better and more consistently than length or review behavior, for every model studied.

Two interventions support a causal role for FSF:
- **Reranking:** selecting among sampled CoTs by FSF gives the largest accuracy gains.
- **Editing:** deleting failed branches from incorrect traces raises the chance of eventually reaching the right answer.

The results favor structure-aware test-time scaling over simply generating more tokens.

## Key points
- **Correlation study:** ten reasoning models were evaluated on HARP and GPQA-Diamond. Within a question, shorter traces and lower Review Ratio go with higher accuracy, and the link is stronger for difficult questions.
- **FSF as a predictor:** FSF was significantly correlated with correctness for all 10 models on both datasets. It held across difficulty strata and beat both Length and Review Ratio.
- **Test-time reranking:** 64 samples were drawn per problem on AIME-25 and GPQA-Diamond. Choosing the top sample by FSF gave the best pass@1, with gains of up to 10% on AIME.
- **CoT editing:** this was done on incorrect HARP traces, using 11,520 continuations in total (8 per edited CoT). Cutting the failed branch improved accuracy by roughly 8–14 points. For DeepSeek R1 (last failed branch), accuracy rose from 9.72% to 23.75%. For GPT oss 120B (first failed branch), it rose from 28.05% to 36.41%. Replacing the branch with a summary helped less than removing it.
- **Interpretation:** models keep being steered by earlier mistakes even after backtracking. The authors therefore suggest pruning or summarizing failed branches in the context.

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

📚 Shelves (5): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 17,959 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 17,789 works · [👁️ Computer Vision and Pattern Recognition](https://md.research.elamur.ai/free/en/shelves/computer-science/computer-vision-and-pattern-recognition/) · 3,621 works

🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,948 works

## Cite

Cite as: Yunzhen Feng, Julia Kempe, Cheng Zhang, Parag Jain and Anthony Hartshorn. 2025. What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT. arXiv:2509.19284.

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

```bibtex
@misc{feng2025what,
  title = {{What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoT}},
  author = {Yunzhen Feng, Julia Kempe, Cheng Zhang, Parag Jain and Anthony Hartshorn},
  year = {2025},
  doi = {10.48550/arxiv.2509.19284},
  eprint = {2509.19284},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2509.19284}
}
```

- [← previous UD-English-CHILDES: A Collected Resource of Gold and Silver Universal Dependencies Trees for Child Language Interactions](https://md.research.elamur.ai/free/en/papers/yang-2025-ud-english-childes-collected-resource/)
- [next → WikiQA-IS: Assisted Benchmark Generation and Automated Evaluation of Icelandic Cultural Knowledge in LLMs](https://md.research.elamur.ai/free/en/papers/arnardottir-2025-wikiqa-is-assisted-benchmark-generation/)
- [↑ back to papers of 2025](https://md.research.elamur.ai/free/en/papers/2025/page/14/)

## References

39 references, 19 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Sandhini Agarwal et al. [gpt-oss-120b & gpt-oss-20b model card](https://md.research.elamur.ai/free/en/papers/agarwal-2025-gpt-oss-120b-gpt-oss/), 2025. https://arxiv.org/abs/2508.10925. [↗](https://arxiv.org/abs/2508.10925)
2. Sohyun An, Ruochen Wang, Tianyi Zhou, and Cho-Jui Hsieh. Don’t think longer, think wisely: Optimizing thinking dynamics for large reasoning models. arXiv preprint arXiv:2505.21765, 2025. — [arXiv:2505.21765](https://arxiv.org/abs/2505.21765) [find](https://scholar.google.com/scholar?q=Sohyun+An%2C+Ruochen+Wang%2C+Tianyi+Zhou%2C+and+Cho%2DJui+Hsieh%2E+Don%E2%80%99t+think+longer%2C+think+wisely%3A+Optimizing+thinking+dynamics+for+large+reasoning+models%2E+arXiv+preprint+arXiv%3A2505%2E21765%2C+2025%2E+%E2%80%94+%5BarXiv%3A2505)
3. Anthropic. Claude 3.7 sonnet and claude code. [https://www.anthropic.com/news/claude-3-7-sonnet](https://www.anthropic.com/news/claude-3-7-sonnet), February 2025. Describes Claude 3.7 Sonnet and its thinking mode. [↗](https://www.anthropic.com/news/claude-3-7-sonnet)
4. Zhenni Bi, Kai Han, Chuanjian Liu, Yehui Tang, and Yunhe Wang. [Forest-of-thought: Scaling test-time compute for enhancing llm reasoning](https://md.research.elamur.ai/free/en/papers/bi-2024-forest-thought-scaling-test-time/). arXiv preprint arXiv:2412.09078, 2024.
5. 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/).
6. Yanda Chen, Joe Benton, Ansh Radhakrishnan, Jonathan Uesato, Carson Denison, John Schulman, Arushi Somani, Peter Hase, Misha Wagner, Fabien Roger, et al. Reasoning models don’t always say what they think. arXiv preprint arXiv:2505.[05410, 2025](https://md.research.elamur.ai/free/en/papers/chen-2025-reasoning-models-don-t-always/).
7. Peter A Facione. Critical thinking: A statement of expert consensus for purposes of educational assessment and instruction. research findings and recommendations. 1990. [find](https://scholar.google.com/scholar?q=Peter+A+Facione%2E+Critical+thinking%3A+A+statement+of+expert+consensus+for+purposes+of+educational+assessment+and+instruction%2E+research+findings+and+recommendations%2E+1990%2E)
8. 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/). arXiv preprint arXiv:2503.01307, 2025.
9. Emden R Gansner. Drawing graphs with graphviz. Technical report, AT&T Bell Laboratories, Murray, Tech. Rep, Tech. Rep., 2009. [find](https://scholar.google.com/scholar?q=Emden+R+Gansner%2E+Drawing+graphs+with+graphviz%2E+Technical+report%2C+AT%26T+Bell+Laboratories%2C+Murray%2C+Tech%2E+Rep%2C+Tech%2E+Rep%2E%2C+2009%2E)
10. Jiaxuan Gao, Shu Yan, Qixin Tan, Lu Yang, Shusheng Xu, Wei Fu, Zhiyu Mei, Kaifeng Lyu, and Yi Wu. How far are we from optimal reasoning efficiency? arXiv preprint arXiv:2506.07104, 2025. — [arXiv:2506.07104](https://arxiv.org/abs/2506.07104) [find](https://scholar.google.com/scholar?q=Jiaxuan+Gao%2C+Shu+Yan%2C+Qixin+Tan%2C+Lu+Yang%2C+Shusheng+Xu%2C+Wei+Fu%2C+Zhiyu+Mei%2C+Kaifeng+Lyu%2C+and+Yi+Wu%2E+How+far+are+we+from+optimal+reasoning+efficiency%3F+arXiv+preprint+arXiv%3A2506%2E07104%2C+2025%2E+%E2%80%94+%5BarXiv%3A2506)
11. Soumya Suvra Ghosal, Souradip Chakraborty, Avinash Reddy, Yifu Lu, Mengdi Wang, Dinesh Manocha, Furong Huang, Mohammad Ghavamzadeh, and Amrit Singh Bedi. Does thinking more always help? understanding test-time scaling in reasoning models. arXiv preprint arXiv:2506.04210, 2025. — [arXiv:2506.04210](https://arxiv.org/abs/2506.04210) [find](https://scholar.google.com/scholar?q=Soumya+Suvra+Ghosal%2C+Souradip+Chakraborty%2C+Avinash+Reddy%2C+Yifu+Lu%2C+Mengdi+Wang%2C+Dinesh+Manocha%2C+Furong+Huang%2C+Mohammad+Ghavamzadeh%2C+and+Amrit+Singh+Bedi%2E+Does+thinking+more+always+help%3F+understanding+)
12. Olga Golovneva, Moya Peng Chen, Spencer Poff, Martin Corredor, Luke Zettlemoyer, Maryam Fazel-Zarandi, and Asli Celikyilmaz. [Roscoe: A suite of metrics for scoring step-by-step reasoning](https://md.research.elamur.ai/free/en/papers/golovneva-2022-roscoe-suite-metrics-scoring-step/). In The Eleventh International Conference on Learning Representations, 2023.
13. 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.
14. Qianyue Hao, Sibo Li, Jian Yuan, and Yong Li. Rl of thoughts: Navigating llm reasoning with inference-time reinforcement learning. arXiv preprint arXiv:2505.14140, 2025. — [arXiv:2505.14140](https://arxiv.org/abs/2505.14140) [find](https://scholar.google.com/scholar?q=Qianyue+Hao%2C+Sibo+Li%2C+Jian+Yuan%2C+and+Yong+Li%2E+Rl+of+thoughts%3A+Navigating+llm+reasoning+with+inference%2Dtime+reinforcement+learning%2E+arXiv+preprint+arXiv%3A2505%2E14140%2C+2025%2E+%E2%80%94+%5BarXiv%3A2505%2E14140%5D%28https%3A%2F%2Fa)
15. Michael Hassid, Gabriel Synnaeve, Yossi Adi, and Roy Schwartz. Don’t overthink it. preferring shorter thinking chains for improved llm reasoning. arXiv preprint arXiv:2505.17813, 2025. — [arXiv:2505.17813](https://arxiv.org/abs/2505.17813) [find](https://scholar.google.com/scholar?q=Michael+Hassid%2C+Gabriel+Synnaeve%2C+Yossi+Adi%2C+and+Roy+Schwartz%2E+Don%E2%80%99t+overthink+it%2E+preferring+shorter+thinking+chains+for+improved+llm+reasoning%2E+arXiv+preprint+arXiv%3A2505%2E17813%2C+2025%2E+%E2%80%94+%5BarXiv%3A2505%2E1)
16. Zhiyuan Hu, Yibo Wang, Hanze Dong, Yuhui Xu, Amrita Saha, Caiming Xiong, Bryan Hooi, and Junnan Li. Beyond’aha!’: Toward systematic meta-abilities alignment in large reasoning models. arXiv preprint arXiv:2505.10554, 2025. — [arXiv:2505.10554](https://arxiv.org/abs/2505.10554) [find](https://scholar.google.com/scholar?q=Zhiyuan+Hu%2C+Yibo+Wang%2C+Hanze+Dong%2C+Yuhui+Xu%2C+Amrita+Saha%2C+Caiming+Xiong%2C+Bryan+Hooi%2C+and+Junnan+Li%2E+Beyond%E2%80%99aha%21%E2%80%99%3A+Toward+systematic+meta%2Dabilities+alignment+in+large+reasoning+models%2E+arXiv+preprint+a)
17. 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](https://md.research.elamur.ai/free/en/papers/openai-2024-openai-o1-system-card/). arXiv preprint arXiv:2412.16720, 2024.
18. Gangwei Jiang, Yahui Liu, Zhaoyi Li, Qi Wang, Fuzheng Zhang, Linqi Song, Ying Wei, and Defu Lian. [What makes a good reasoning chain? uncovering structural patterns in long chain-of-thought reasoning](https://md.research.elamur.ai/free/en/papers/jiang-2025-what-makes-good-reasoning-chain/). arXiv preprint arXiv:2505.22148, 2025.
19. William Jurayj, Jeffrey Cheng, and Benjamin Van Durme. [Is that your final answer? test-time scaling improves selective question answering](https://md.research.elamur.ai/free/en/papers/jurayj-2025-is-that-your-final-answer/). arXiv preprint arXiv:2502.13962, 2025.
20. Hynek Kydlíček. Math-Verify: Math Verification Library, 2025. [https://github.com/huggingface/math-verify](https://github.com/huggingface/math-verify). [↗](https://github.com/huggingface/math-verify)
21. Tamera Lanham, Anna Chen, Ansh Radhakrishnan, Benoit Steiner, Carson Denison, Danny Hernandez, Dustin Li, Esin Durmus, Evan Hubinger, Jackson Kernion, et al. [Measuring faithfulness in chain-of-thought reasoning](https://md.research.elamur.ai/free/en/papers/lanham-2023-measuring-faithfulness-chain-thought-reasoning/). arXiv preprint arXiv:2307.13702, 2023.
22. Baohao Liao, Hanze Dong, Yuhui Xu, Doyen Sahoo, Christof Monz, Junnan Li, and Caiming Xiong. Fractured chain-of-thought reasoning. arXiv preprint arXiv:2505.12992, 2025. — [arXiv:2505.12992](https://arxiv.org/abs/2505.12992) [find](https://scholar.google.com/scholar?q=Baohao+Liao%2C+Hanze+Dong%2C+Yuhui+Xu%2C+Doyen+Sahoo%2C+Christof+Monz%2C+Junnan+Li%2C+and+Caiming+Xiong%2E+Fractured+chain%2Dof%2Dthought+reasoning%2E+arXiv+preprint+arXiv%3A2505%2E12992%2C+2025%2E+%E2%80%94+%5BarXiv%3A2505%2E12992%5D%28https%3A%2F%2Fa)
23. Sara Vera Marjanović, Arkil Patel, Vaibhav Adlakha, Milad Aghajohari, Parishad BehnamGhader, Mehar Bhatia, Aditi Khandelwal, Austin Kraft, Benno Krojer, Xing Han Lù, et al. Deepseek-r1 thoughtology: Let’s think about llm reasoning. arXiv preprint arXiv:2504.[07128, 2025](https://md.research.elamur.ai/free/en/papers/marjanovic-2025-deepseek-r1-thoughtology-let-s/).
24. AI Meta. The llama 4 herd: The beginning of a new era of natively multimodal ai innovation. [https://ai.meta](https://ai.meta). com/blog/llama-4-multimodal-intelligence/, checked on, 4(7):2025, 2025. [↗](https://ai.meta)
25. Gouki Minegishi, Hiroki Furuta, Takeshi Kojima, Yusuke Iwasawa, and Yutaka Matsuo. Topology of reasoning: Understanding large reasoning models through reasoning graph properties. arXiv preprint arXiv:2506.05744, 2025. — [arXiv:2506.05744](https://arxiv.org/abs/2506.05744) [find](https://scholar.google.com/scholar?q=Gouki+Minegishi%2C+Hiroki+Furuta%2C+Takeshi+Kojima%2C+Yusuke+Iwasawa%2C+and+Yutaka+Matsuo%2E+Topology+of+reasoning%3A+Understanding+large+reasoning+models+through+reasoning+graph+properties%2E+arXiv+preprint+arXiv%3A)
26. Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, and Tatsunori Hashimoto. [s1: Simple test-time scaling](https://md.research.elamur.ai/free/en/papers/muennighoff-2025-s1-simple-test-time-scaling/). arXiv preprint arXiv:2501.19393, 2025.
27. Abhinav Rastogi, Albert Q Jiang, Andy Lo, Gabrielle Berrada, Guillaume Lample, Jason Rute, Joep Barmentlo, Karmesh Yadav, Kartik Khandelwal, Khyathi Raghavi Chandu, et al. Magistral. arXiv preprint arXiv:2506.10910, 2025. [find](https://scholar.google.com/scholar?q=Abhinav+Rastogi%2C+Albert+Q+Jiang%2C+Andy+Lo%2C+Gabrielle+Berrada%2C+Guillaume+Lample%2C+Jason+Rute%2C+Joep+Barmentlo%2C+Karmesh+Yadav%2C+Kartik+Khandelwal%2C+Khyathi+Raghavi+Chandu%2C+et+al%2E+Magistral%2E+arXiv+preprint+ar)
28. 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/). In First Conference on Language Modeling, 2024.
29. Liran Ringel, Elad Tolochinsky, and Yaniv Romano. Learning a continue-thinking token for enhanced test-time scaling. arXiv preprint arXiv:2506.11274, 2025. [find](https://scholar.google.com/scholar?q=Liran+Ringel%2C+Elad+Tolochinsky%2C+and+Yaniv+Romano%2E+Learning+a+continue%2Dthinking+token+for+enhanced+test%2Dtime+scaling%2E+arXiv+preprint+arXiv%3A2506%2E11274%2C+2025%2E)
30. 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.
31. Kimi Team, Yifan Bai, Yiping Bao, Guanduo Chen, Jiahao Chen, Ningxin Chen, Ruijue Chen, Yanru Chen, Yuankun Chen, Yutian Chen, et al. [Kimi k2: Open agentic intelligence](https://md.research.elamur.ai/free/en/papers/kimi-team-2025-kimi-k2-open-agentic/). arXiv preprint arXiv:2507.20534, 2025.
32. Chenlong Wang, Yuanning Feng, Dongping Chen, Zhaoyang Chu, Ranjay Krishna, and Tianyi Zhou. Wait, we don’t need to" wait"! removing thinking tokens improves reasoning efficiency. arXiv preprint arXiv:2506.08343, 2025. [find](https://scholar.google.com/scholar?q=Chenlong+Wang%2C+Yuanning+Feng%2C+Dongping+Chen%2C+Zhaoyang+Chu%2C+Ranjay+Krishna%2C+and+Tianyi+Zhou%2E+Wait%2C+we+don%E2%80%99t+need+to%22+wait%22%21+removing+thinking+tokens+improves+reasoning+efficiency%2E+arXiv+preprint+arXiv%3A)
33. Guojun Wu. It’s not that simple. an analysis of simple test-time scaling. arXiv preprint arXiv:2507.14419, 2025. — [arXiv:2507.14419](https://arxiv.org/abs/2507.14419) [find](https://scholar.google.com/scholar?q=Guojun+Wu%2E+It%E2%80%99s+not+that+simple%2E+an+analysis+of+simple+test%2Dtime+scaling%2E+arXiv+preprint+arXiv%3A2507%2E14419%2C+2025%2E+%E2%80%94+%5BarXiv%3A2507%2E14419%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2507%2E14419%29)
34. Juncheng Wu, Sheng Liu, Haoqin Tu, Hang Yu, Xiaoke Huang, James Zou, Cihang Xie, and Yuyin Zhou. Knowledge or reasoning? a close look at how llms think across domains. arXiv preprint arXiv:2506.02126, 2025a. [find](https://scholar.google.com/scholar?q=Juncheng+Wu%2C+Sheng+Liu%2C+Haoqin+Tu%2C+Hang+Yu%2C+Xiaoke+Huang%2C+James+Zou%2C+Cihang+Xie%2C+and+Yuyin+Zhou%2E+Knowledge+or+reasoning%3F+a+close+look+at+how+llms+think+across+domains%2E+arXiv+preprint+arXiv%3A2506%2E02126%2C)
35. Yuyang Wu, Yifei Wang, Ziyu Ye, Tianqi Du, Stefanie Jegelka, and Yisen Wang. [When more is less: Understanding chain-of-thought length in llms](https://md.research.elamur.ai/free/en/papers/wu-2025-more-less-understanding-chain-thought/). arXiv preprint arXiv:2502.07266, 2025b. xAI. Grok 3 mini. [https://docs.x.ai/docs/models/grok-3-mini](https://docs.x.ai/docs/models/grok-3-mini), 2025. Model documentation. [↗](https://docs.x.ai/docs/models/grok-3-mini)
36. An Yang, Anfeng Li, et al. [Qwen3 technical report](https://md.research.elamur.ai/free/en/papers/yang-2025-qwen3-technical-report/), 2025. https://arxiv.org/abs/2505.09388. [↗](https://arxiv.org/abs/2505.09388)
37. 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](https://scholar.google.com/scholar?q=Shunyu+Yao%2C+Dian+Yu%2C+Jeffrey+Zhao%2C+Izhak+Shafran%2C+Tom+Griffiths%2C+Yuan+Cao%2C+and+Karthik+Narasimhan%2E+Tree+of+thoughts%3A+Deliberate+problem+solving+with+large+language+models%2E+Advances+in+neural+informati)
38. Albert S Yue, Lovish Madaan, Ted Moskovitz, DJ Strouse, and Aaditya K Singh. Harp: A challenging human-annotated math reasoning benchmark. arXiv preprint arXiv:2412.08819, 2024. — [arXiv:2412.08819](https://arxiv.org/abs/2412.08819) [find](https://scholar.google.com/scholar?q=Albert+S+Yue%2C+Lovish+Madaan%2C+Ted+Moskovitz%2C+DJ+Strouse%2C+and+Aaditya+K+Singh%2E+Harp%3A+A+challenging+human%2Dannotated+math+reasoning+benchmark%2E+arXiv+preprint+arXiv%3A2412%2E08819%2C+2024%2E+%E2%80%94+%5BarXiv%3A2412%2E08819%5D%28h)
39. Anqi Zhang, Yulin Chen, Jane Pan, Chen Zhao, Aurojit Panda, Jinyang Li, and He He. Reasoning models know when they’re right: Probing hidden states for self-verification. arXiv preprint arXiv:2504.[05419, 2025](https://md.research.elamur.ai/free/en/papers/zhang-2025-reasoning-models-know-they-re/).

*Updated 3 November 2026*