融合多种推理方式，让大模型更懂数学题
Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective
- 用自然语言、算法和符号三种推理协同解题
- 在定理证明上比GPT-4o高41%，算术任务超强化学习方法15%
- 适合需要跨领域数学推理的科研与教育场景
大型语言模型在数学推理方面取得显著进展，但通常依赖单一推理范式，限制了其在多样化任务中的表现。本文提出链式推理（CoR）框架，融合自然语言推理（NLR）、算法推理（AR）和符号推理（SR）三种范式，实现协同工作。CoR通过不同范式生成多个候选答案，并整合为一致的最终解答。我们设计渐进式范式训练（PPT）策略，使模型逐步掌握各推理范式，构建出CoR-Math-7B模型。实验表明，CoR-Math-7B显著优于现有最先进模型：在定理证明任务中较GPT-4o绝对提升41.0%，在MATH基准算术任务上较基于强化学习的方法提升15.0%。结果验证了该模型在数学理解上的增强能力，支持零样本跨任务泛化。
原文摘要 · Abstract (English)
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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