MetaLadder：通过类比问题推理迁移提升数学解题质量

MetaLadder: Ascending Mathematical Solution Quality via Analogical-Problem Reasoning Transfer

March 19, 2025

作者: Honglin Lin, Zhuoshi Pan, Yu Li, Qizhi Pei, Xin Gao, Mengzhang Cai, Conghui He, Lijun Wu

cs.AI

摘要

大型语言模型（LLMs）在解决数学推理任务中展现了显著潜力，其中思维链（CoT）数据作为引导答案生成的关键要素。现有范式通常直接针对给定问题生成CoT和答案，这与人类解决问题的策略存在一定差异。人类在解题时，常会回忆类似案例并借鉴其解决方案来推理当前任务。受此认知过程启发，我们提出了MetaLadder这一新颖框架，它明确提示LLMs在解决目标问题前，先回忆并反思元问题——那些在结构或语义上相似的问题及其CoT解决方案。此外，我们引入了一种问题重述机制，通过重新表述原问题来增强模型对目标问题的理解，从而进一步提升推理准确性。因此，模型能够实现从类比问题中的推理迁移，模拟人类“从示例中学习”及泛化能力。在数学基准测试上的大量实验表明，我们的MetaLadder显著提升了LLMs的解题准确率，大幅超越了基于标准CoT的方法（准确率提升10.3%）及其他方法。我们的代码与数据已发布于https://github.com/LHL3341/MetaLadder。

English

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.