@inproceedings{yu-etal-2025-chain,
title = "Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective",
author = "Yu, Yiyao and
Zhang, Yuxiang and
Zhang, Dongdong and
Liang, Xiao and
Zhang, Hengyuan and
Zhang, Xingxing and
Khademi, Mahmoud and
Awadalla, Hany Hassan and
Wang, Junjie and
Yang, Yujiu and
Wei, Furu",
editor = "Che, Wanxiang and
Nabende, Joyce and
Shutova, Ekaterina and
Pilehvar, Mohammad Taher",
booktitle = "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
month = jul,
year = "2025",
address = "Vienna, Austria",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.acl-long.1213/",
doi = "10.18653/v1/2025.acl-long.1213",
pages = "24914--24937",
ISBN = "979-8-89176-251-0",
abstract = "Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms {---} Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR) {---} to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of at CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0{\%} absolute improvement over GPT-4o in theorem proving tasks and a 15{\%} improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehensive ability of our model, enabling zero-shot generalization across tasks.The code is available at https://github.com/microsoft/CoR."
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<abstract>Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms — Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR) — to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of at CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4o in theorem proving tasks and a 15% improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehensive ability of our model, enabling zero-shot generalization across tasks.The code is available at https://github.com/microsoft/CoR.</abstract>
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%0 Conference Proceedings
%T Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective
%A Yu, Yiyao
%A Zhang, Yuxiang
%A Zhang, Dongdong
%A Liang, Xiao
%A Zhang, Hengyuan
%A Zhang, Xingxing
%A Khademi, Mahmoud
%A Awadalla, Hany Hassan
%A Wang, Junjie
%A Yang, Yujiu
%A Wei, Furu
%Y Che, Wanxiang
%Y Nabende, Joyce
%Y Shutova, Ekaterina
%Y Pilehvar, Mohammad Taher
%S Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2025
%8 July
%I Association for Computational Linguistics
%C Vienna, Austria
%@ 979-8-89176-251-0
%F yu-etal-2025-chain
%X Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms — Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR) — to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of at CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4o in theorem proving tasks and a 15% improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehensive ability of our model, enabling zero-shot generalization across tasks.The code is available at https://github.com/microsoft/CoR.
%R 10.18653/v1/2025.acl-long.1213
%U https://aclanthology.org/2025.acl-long.1213/
%U https://doi.org/10.18653/v1/2025.acl-long.1213
%P 24914-24937
Markdown (Informal)
[Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://aclanthology.org/2025.acl-long.1213/) (Yu et al., ACL 2025)
ACL
- 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. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 24914–24937, Vienna, Austria. Association for Computational Linguistics.