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

• URL: http://arxiv.org/abs/2501.11110v1
• Date: Sun, 19 Jan 2025 16:53:26 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, Ziyi Yang, Mahmoud Khademi, Hany Awadalla, Junjie Wang, Yujiu Yang, Furu Wei,
• Abstract summary: Chain-of-Reasoning (CoR) is a novel unified framework that integrates multiple reasoning paradigms. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models.
• Score: 90.86370957353911
• License:
• 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 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-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

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