MetaLadder：通過類比問題推理遷移提升數學解題質量

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

大型語言模型（LLMs）在解決數學推理任務方面展現了顯著的潛力，其中思維鏈（Chain-of-Thought, CoT）數據作為引導答案生成的關鍵要素。現有範式通常直接為給定問題生成CoT和答案，這在某種程度上偏離了人類解決問題的策略。人類在解決問題時，往往會回憶起類似的案例，並利用其解決方案來推理當前任務。受這一認知過程的啟發，我們提出了MetaLadder，這是一個新穎的框架，它明確提示LLMs在處理目標問題之前，回憶並反思那些在結構或語義上相似的元問題及其CoT解決方案。此外，我們引入了一種問題重述機制，通過重新生成原始問題來增強模型對目標問題的理解，從而進一步提高推理的準確性。因此，模型能夠實現從類比問題中的推理轉移，模仿人類“從例子中學習”和泛化的能力。在數學基準上的大量實驗表明，我們的MetaLadder顯著提升了LLMs解決問題的準確性，大幅超越了基於標準CoT的方法（10.3%的準確率提升）及其他方法。我們的代碼和數據已發佈於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.