Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective

• URL: http://arxiv.org/abs/2501.11110v2
• Date: Mon, 12 May 2025 13:04:44 GMT
• Title: Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective
• Authors: Yiyao Yu, Yuxiang Zhang, Dongdong Zhang, Xiao Liang, Hengyuan Zhang, Xingxing Zhang, Mahmoud Khademi, Hany Awadalla, Junjie Wang, Yujiu Yang, Furu Wei,
• Abstract summary: Chain-of-Reasoning (CoR) is a novel unified framework integrating multiple reasoning paradigms.<n>CoR generates multiple potential answers via different reasoning paradigms and synthesizes them into a coherent final solution.<n> Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models.
• Score: 82.9413277326097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet often rely on single-paradigm reasoning, limiting their effectiveness across diverse tasks. We introduce Chain-of-Reasoning (CoR), a novel unified framework integrating multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers via different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy for models to progressively master these paradigms, leading to 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 and a 15.0% improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehension ability of our model, enabling zero-shot generalization across tasks.

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