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home / papers / 2026 / ConMA : Confidence-Guided Kernel Sampling with Multi-Stage Aggregation for LLM Reasoning

ConMA : Confidence-Guided Kernel Sampling with Multi-Stage Aggregation for LLM Reasoning

Paper · 2026 · Yinuo Wang, Qingjie Li, Wenyao Cui et al.

Summary

Test-time scaling improves LLM reasoning by generating many solution attempts and combining them. However, common setups spend the entire budget in a single batch and often depend on a trained verifier or reward model. ConMA is a training-free, verifier-free alternative that divides a fixed maximum budget into small rounds.

Each round has three steps:

  • Confidence-Guided Kernel Sampling (CKS) clusters trajectories by final answer. It scores each cluster by mixing vote share with the model's own token-probability confidence, computed over the full trace and its final tokens. Only a compact top-scoring "kernel" is kept.
  • Diversity-Seeking Exploration (DSE) asks the model for new trajectories that reason differently from kernel representatives.
  • Multi-Stage Aggregation (MSA) has the model repeatedly choose one answer in a multiple-choice format. The chosen trajectories seed the next round, and consensus triggers early stopping.

On mathematical and scientific reasoning benchmarks, ConMA raises Qwen3-4B to 80% on AIME25 while drawing far fewer samples than the cap. The results suggest that how candidates are managed across rounds matters more than how many are drawn.

Key points

  • With a maximum budget of N = 64, Qwen3-4B reaches 80.0% on AIME25. On average it uses about 18 samples on AIME25 and 19.62 on AIME 2024, which the authors report as a cost reduction of over 70%.
  • Early stopping is reliable: every AIME 2025 problem resolved in Stage 1 was correct (15/15). About 86.7% of AIME 2025 problems converged within the first two stages.
  • In an ablation on AIME 2025 (N = 64), accuracy dropped by 7.9 points without CKS, 6.6 points without MSA, and 4.8 points without diversity-oriented exploration.
  • The iterative rounds recovered initially misjudged answers in 19.7% of GPQA-Diamond questions and 16.7% of AIME 2025 questions.
  • The authors note two limitations. The method depends on the base model being well calibrated and able to discriminate between answers. It also targets tasks with verifiable answers and does not yet extend to open-ended generation.

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

🎓Beijing Institute of TechnologyBeijing · China34 works · 3,652 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 2Research subjects and languages the work is about.Language models & pretraining · 3,320 worksReasoning · 1,426 works

Cite

Cite as Yinuo Wang, Qingjie Li, Wenyao Cui, Qiuchi Li and Zhang Huaping. 2026. ConMA : Confidence-Guided Kernel Sampling with Multi-Stage Aggregation for LLM Reasoning. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-acl.1475

@inproceedings{wang2026conma,
  title = {{ConMA : Confidence-Guided Kernel Sampling with Multi-Stage Aggregation for LLM Reasoning}},
  author = {Yinuo Wang, Qingjie Li, Wenyao Cui, Qiuchi Li and Zhang Huaping},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1475},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1475}
}

References

31 references, 16 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. 2024. Large language monkeys: Scaling inference compute with repeated sampling. Preprint, arXiv:2407.21787.
  2. Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, and 1 others. 2020. Language models are few-shot learners. Advances in Neural Information Processing Systems (NeurIPS), 33:1877–1901.
  3. Chengkun Cai, Xu Zhao, Haoliang Liu, Zhongyu Jiang, Tianfang Zhang, Zongkai Wu, Jenq-Neng Hwang, and Lei Li. 2025. The Role of Deductive and Inductive Reasoning in Large Language Models. In Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL).
  4. Songlin Chen, Weicheng Wang, Xiaoliang Chen, Peng Lu, Zaiyan Yang, and Yajun Du. 2024. Llama-lora neural prompt engineering: A deep tuning framework for automatically generating chinese text logical reasoning thinking chains. DATA INTELLIGENCE, 6(2):375–408. find
  5. 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. 2021. Training verifiers to solve math word problems. Preprint, arXiv:2110.14168.
  6. Colin Hong, Xu Guo, Anand Chaanan Singh, Esha Choukse, and Dmitrii Ustiugov. 2025. Slim-SC: Thought pruning for efficient scaling with self-consistency. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 34500–34517, Suzhou, China. Association for Comput… find
  7. Zhewei Kang, Xuandong Zhao, and Dawn Song. 2025. Scalable best-of-n selection for large language models via self-certainty. Preprint, arXiv:2502.18581. find
  8. Takeshi Kojima, Shixiang Shane Gu, Dennis Reidsma, Yutaka Matsuo, and Yusuke Iwasawa. 2022. Large language models are zero-shot reasoners. Advances in Neural Information Processing Systems (NeurIPS), 35:22199–22213.
  9. Yifei Li, Zeqi Lin, Shizhuo Zhang, Qiang Fu, Bei Chen, Jian-Guang Lou, and Weizhu Chen. 2023. Making language models better reasoners with step-aware verifier. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 5315–5333, Toronto…
  10. Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. 2024. Let’s verify step by step. In The Twelfth International Conference on Learning Representations.
  11. Chris Yuhao Liu, Liang Zeng, Yuzhen Xiao, Jujie He, Jiacai Liu, Chaojie Wang, Rui Yan, Wei Shen, Fuxiang Zhang, Jiacheng Xu, Yang Liu, and Yahui Zhou. 2025a. Skywork-reward-v2: Scaling preference data curation via human-ai synergy. Preprint, arXiv:2507.01352.
  12. Runze Liu, Junqi Gao, Jian Zhao, Kaiyan Zhang, Xiu Li, Biqing Qi, Wanli Ouyang, and Bowen Zhou. 2025b. Can 1b llm surpass 405b llm? rethinking compute-optimal test-time scaling. Preprint, arXiv:2502.06703.
  13. Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye, Yiming Yang, Shashank Gupta, Bodhisattwa Prasad Majumder, Katherine Hermann, Sean Welleck, Amir Yazdanbakhsh, and Peter Clark. 2023. Self-refine: Iterative refinement with… find
  14. OpenAI, Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, Red Avila, Igor Babuschkin, Suchir Balaji, Valerie Balcom, Paul Baltescu, Haiming Bao, Mohammad Bavarian, Jeff Belgum, and 262 others.… — GPT-4 Technical Report
  15. David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman. 2023. Gpqa: A graduate-level google-proof qa benchmark. Preprint, arXiv:2311.12022.
  16. Jingzhe Shi, Qinwei Ma, Hongyi Liu, Hang Zhao, Jenq-Neng Hwang, and Lei Li. 2026. Intrinsic entropy of context length scaling in llms. In The Fourteenth International Conference on Learning Representations. find
  17. Noah Shinn, Federico Cassano, Edward Berman, Ashwin Gopinath, Karthik Narasimhan, and Shunyu Yao. 2023. Reflexion: Language agents with verbal reinforcement learning. Preprint, arXiv:2303.11366.
  18. Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. 2025. Scaling llm test-time compute optimally can be more effective than scaling parameters for reasoning. International Conference on Learning Representations (ICLR). find
  19. Peiyi Wang, Lei Li, Zhihong Shao, RX Xu, Damai Dai, Deli Li, Yunjie anduz, Zhifang Wu, and W Liu. 2024. Math-shepherd: Verify and reinforce llms step-by-step without human annotations.
  20. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023. Self-consistency improves chain of thought reasoning in language models. International Conference on Learning Representations (ICLR).
  21. Zeng Xingshan Liu Weiwen Wang Yufei Li Liangyou Wang Yasheng Shang Lifeng Jiang Xin Liu Qun Wong Kam-Fai Wang, Zezhong. 2025. Stepwise reasoning checkpoint analysis: A test time scaling method to enhance llms’ reasoning. find
  22. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Ed Chi, Quoc Le, and Denny Zhou. 2022. Chain-of-thought prompting elicits reasoning in large language models. Advances in Neural Information Processing Systems (NeurIPS), 35:24824–24837.
  23. An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, Chujie Zheng, Dayiheng Liu, Fan Zhou, Fei Huang, Feng Hu, Hao Ge, Haoran Wei, Huan Lin, Jialong Tang, and 41 others. 2025. Qwen3 technical report. Preprint, arXiv:2505.09388.
  24. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L Griffiths, Yuan Cao, and Karthik Narasimhan. 2024. Tree of thoughts: Deliberate problem solving with large language models. Advances in Neural Information Processing Systems (NeurIPS), 36. find
  25. Yuandong Tian Jiawei Zhao Yichao Fu, Xuewei Wang. 2026. Deep think with confidence. arxiv. find
  26. Yifan Zhang and Team Math-AI. 2023. American mathematics competition 2023. find
  27. Yifan Zhang and Team Math-AI. 2024. American invitational mathematics examination (aime) 2024. find
  28. Yifan Zhang and Team Math-AI. 2025. American invitational mathematics examination (aime) 2025. find
  29. Jiahang Xu Li Lyna Zhang Fan Yang Mao Yang Zhenting Qi, Mingyuan MA. 2025. Mutual reasoning makes smaller llms stronger problem-solver. find
  30. Qwen Team. 2025. Qwq-32b: Embracing the power of reinforcement learning. find
  31. Jonathan Uesato, Nate Kushman, Ramana Kumar, H. Francis Song, Noah Yamamoto Siegel, Lisa Wang, Antonia Creswell, Geoffrey Irving, and Irina Higgins. 2023. Solving math word problems with process-based and outcome-based feedback. find

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