arXiv:2503.14891cs.CLcs.AI2025-03EMNLP被引 8

让大模型像人一样通过类比旧题解新题,准确率提升10.3%。

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

  • 先回忆相似题目及其解题思路,再解决当前问题。
  • 在数学基准上比传统方法高10.3%准确率。
  • 适合想提升模型推理能力的研究者和开发者。

大型语言模型(LLMs)在数学推理任务中展现出良好潜力,通常依赖思维链(CoT)数据来引导答案生成。现有方法直接为给定问题生成CoT和答案,与人类解题方式存在一定差异。人类常通过回忆类似案例并借鉴其解法来推理当前问题。受此认知过程启发,我们提出 extbf{MetaLadder},一种新框架:显式提示模型在解决目标问题前,回顾结构或语义相似的元问题及其CoT解法,并进行反思。此外,引入问题重述机制,通过重新生成原问题来增强模型理解,进一步提升推理准确性。该方法实现了从类比问题到目标问题的推理迁移,模拟人类“举一反三”的学习能力。在多个数学基准上的实验表明,MetaLadder显著提升模型求解准确率,大幅优于标准CoT方法(准确率提升10.3%)及其他对比方法。代码与数据已开源于https://github.com/LHL3341/MetaLadder。

原文摘要 · Abstract (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 \textbf{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 (\textbf{10.3\%} accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

数学推理类比学习思维链大模型

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