Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective - Yu, Yiyao; Zhang, Yuxiang; Zhang, Dongdong; Liang, Xiao; Zhang, Hengyuan; Zhang, Xingxing; Khademi, Mahmoud; Awadalla, Hany; Wang, Junjie; Yang, Yujiu; Wei, Furu (Meeting of the Association for Computational Linguistics, 2025)
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.