---
title: "Chain-of-Reasoning — paper by Yu et al. (2025)"
description: "The authors propose Chain-of-Reasoning (CoR), a framework in which one model works… 41.0 points. 55 references, cited by 18 papers here."
authors: ["Yiyao Yu", "Yuxiang Zhang", "Dongdong Zhang", "Xiao Liang", "Hengyuan Zhang", "Xingxing Zhang", "Mahmoud Khademi", "Hany Hassan Awadalla", "Junjie Wang", "Yujiu Yang", "Furu Wei"]
year: 2025
venue: "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2025.acl-long.1213/"
doi: "10.18653/v1/2025.acl-long.1213"
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/yu-2025-chain-reasoning-unified-mathematical-reasoning/"
---
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# Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective

**Authors:** [Yiyao Yu](https://md.research.elamur.ai/free/en/authors/yiyao-yu/), [Yuxiang Zhang](https://md.research.elamur.ai/free/en/authors/yuxiang-zhang/), [Dongdong Zhang](https://md.research.elamur.ai/free/en/authors/dongdong-zhang/), [Xiao Liang](https://md.research.elamur.ai/free/en/authors/xiao-liang/), [Hengyuan Zhang](https://md.research.elamur.ai/free/en/authors/hengyuan-zhang/), [Xingxing Zhang](https://md.research.elamur.ai/free/en/authors/xingxing-zhang/), [Mahmoud Khademi](https://md.research.elamur.ai/free/en/authors/mahmoud-khademi/), [Hany Hassan Awadalla](https://md.research.elamur.ai/free/en/authors/hany-awadalla/), [Junjie Wang](https://md.research.elamur.ai/free/en/authors/junjie-wang/), [Yujiu Yang](https://md.research.elamur.ai/free/en/authors/yujiu-yang/) and [Furu Wei](https://md.research.elamur.ai/free/en/authors/furu-wei/) · **Year:** 2025 · **Venue:** [Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2025](https://md.research.elamur.ai/free/en/venues/acl/2025/)) · **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/2025.acl-long.1213/) · [PDF](https://aclanthology.org/2025.acl-long.1213.pdf) · [DOI 10.18653/v1/2025.acl-long.1213](https://doi.org/10.18653/v1/2025.acl-long.1213) · [OpenAlex](https://openalex.org/W4412889980)

**Citations:** 5 citations (OpenAlex, 2026-10-14) · [18](https://md.research.elamur.ai/free/en/papers/yu-2025-chain-reasoning-unified-mathematical-reasoning/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary

Current LLM math solvers are usually tuned for a single reasoning style. Some use natural-language chains of thought, others use executable code, and others use formal proofs. As a result, a model strong at arithmetic word problems often fails at theorem proving, and the reverse. The authors propose Chain-of-Reasoning (CoR), a framework in which one model works through a problem sequentially, first with Natural Language Reasoning (NLR), next with Algorithmic Reasoning (AR), and finally with Symbolic Reasoning (SR), before combining the candidate answers into a final solution. Prompts control how many paradigms are used. To train such a model, they built the Multi-Paradigm Mathematical (MPM) dataset and designed Progressive Paradigm Training (PPT), which adds paradigms stage by stage. The result is CoR-Math-7B. Across five benchmarks covering computation and formal proving, it beats strong baselines in a zero-shot setting while needing comparatively little fine-tuning data. This suggests that combining paradigms, rather than searching extensively within one, is an efficient path to general mathematical reasoning.

## Key points

- **Data and code:** The MPM dataset contains 167k multi-paradigm reasoning paths. The code is released at github.com/microsoft/CoR.
- **Headline results:** On theorem proving (miniF2F), CoR-Math-7B scores 41.0 points above GPT-4o in a zero-shot setting, reaching 66.0%. On MATH it gains 24.2 points over GPT-4 and about 15 points over RL-based methods.
- **Multi- vs. single-paradigm ablation:** All runs fine-tune DeepSeekMath-7B-Base with 10,000 samples per paradigm. Compared with the best single-paradigm model, CoR gains 12.9 points on GSM8K, 29.1 on MATH and 8.6 on miniF2F. It also solves 20 more problems on AMC2023 and 11 more on AIME2024.
- **Order of paradigms matters:** Placing SR before AR gives 66.7% on MATH, compared with 49.9% when AR comes first.
- **Scaling:** CoR improves with model size on Qwen2.5-Math (1.5B → 7B) and Llama-3.1 (8B → 70B).

*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

- [Microsoft](https://md.research.elamur.ai/free/en/companies/microsoft/) — Company, Redmond, United States · 378 works · 161,630 citations
- [Tsinghua University](https://md.research.elamur.ai/free/en/universities/tsinghua-university/) — University, Beijing, China · 415 works · 94,028 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: Yiyao Yu, Yuxiang Zhang, Dongdong Zhang, Xiao Liang, Hengyuan Zhang, Xingxing Zhang, Mahmoud Khademi, Hany Hassan Awadalla, Junjie Wang, Yujiu Yang and Furu Wei. 2025. Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

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

```bibtex
@inproceedings{yu2025chain,
  title = {{Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective}},
  author = {Yiyao Yu, Yuxiang Zhang, Dongdong Zhang, Xiao Liang, Hengyuan Zhang, Xingxing Zhang, Mahmoud Khademi, Hany Hassan Awadalla, Junjie Wang, Yujiu Yang and Furu Wei},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.1213},
  url = {https://doi.org/10.18653/v1/2025.acl-long.1213}
}
```

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*Updated 2 November 2026*