---
title: "CoTEvol — paper by Wang et al. (2026) — summary and ideas"
description: "Training LLMs for math reasoning depends on high-quality Chain-of-Thought (CoT) data, which is expensive to annotate. 40 references."
authors: ["Zhuo Wang", "Zhuo Zhang", "Yafu Li", "Yu Cheng", "Lizhen Qu", "Zenglin Xu"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.1903/"
doi: "10.18653/v1/2026.findings-acl.1903"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/wang-2026-cotevol-self-evolving-chain-thoughts/"
---
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# CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning

**Authors:** Zhuo Wang, Zhuo Zhang, [Yafu Li](https://md.research.elamur.ai/free/en/authors/yafu-li/), [Yu Cheng](https://md.research.elamur.ai/free/en/authors/yu-cheng/), [Lizhen Qu](https://md.research.elamur.ai/free/en/authors/lizhen-qu/) and [Zenglin Xu](https://md.research.elamur.ai/free/en/authors/zenglin-xu/) · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.1903/) · [PDF](https://aclanthology.org/2026.findings-acl.1903.pdf) · [DOI 10.18653/v1/2026.findings-acl.1903](https://doi.org/10.18653/v1/2026.findings-acl.1903) · [OpenAlex](https://openalex.org/W7166858177)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Training LLMs for math reasoning depends on high-quality Chain-of-Thought (CoT) data, which is expensive to annotate. Existing workarounds have drawbacks. Distilling from frontier models gives shrinking returns and can inherit teacher bias. Test-time search methods such as Best-of-N and Self-Refine run largely independent attempts and waste compute. CoTEvol treats CoT synthesis as a genetic-algorithm search over a population of reasoning trajectories produced by the model itself. Its operators are:
- **Reflective global crossover:** recombines complementary solutions using feedback built from successes and failures.
- **Uncertainty-guided local mutation:** uses entropy to find unstable steps and resamples them at a higher temperature.

Cheap rule-based fitness functions steer the search, and the best-scoring trajectory per problem is kept for supervised fine-tuning. On the S1K and LIMO training sets, the method raises the rate of correct synthesized CoTs by over 30%, reaching above 80%, while using fewer FLOPs. Models fine-tuned on the evolved data gain 6.6% on average across eight math benchmarks, beating distillation and self-synthesis baselines. This points to a cheaper, scalable way to build reasoning data.

## Key points
- **Fitness function:** combines three rule-based verifiers.
  - Answer correctness: 1 for correct, 0.5 for numeric but wrong, 0 otherwise.
  - Format: 0.5 when the answer appears in `\boxed{}`.
  - Length: a cosine-scaled reward that differs for correct and incorrect answers.
- **Compute cost:** synthesis with Qwen2.5-7B-Instruct costs 453.83×10¹² FLOPs, versus 733.95 for Self-Refine and 1689.53 for Best-of-N (which uses Qwen2.5-Math-RM-72B). CoTEvol saves compute by starting from 4 solutions and evolving only the top 2.
- **Iterations and λ:** three evolution rounds yield gains of 6.8 (S1K) and 6.3 (LIMO) points, with the first round contributing most. The mutation temperature hyperparameter works best at λ = 5.
- **Inference-time search (Pass@10):** CoTEvol reaches 86.2 on MATH500 and 87.5 on AMC23, outperforming Best-of-N and Self-Refine.
- **Failed problems and limitations:** for problems that fail to evolve, patching with distilled D-CoT traces works best. Training on multiple evolved trajectories per problem did not beat the best-only setup.

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

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- [Shanghai Innovation Institute](https://md.research.elamur.ai/free/en/universities/shanghai-innovation-institute/) — University, Shanghai, China · 24 works · 262 citations

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## Cite

Cite as: Zhuo Wang, Zhuo Zhang, Yafu Li, Yu Cheng, Lizhen Qu and Zenglin Xu. 2026. CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical 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.

```bibtex
@inproceedings{wang2026cotevol,
  title = {{CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning}},
  author = {Zhuo Wang, Zhuo Zhang, Yafu Li, Yu Cheng, Lizhen Qu and Zenglin Xu},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1903},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1903}
}
```

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*Updated 1 November 2026*