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

• URL: http://arxiv.org/abs/2503.14891v1
• Date: Wed, 19 Mar 2025 04:36:35 GMT
• Title: MetaLadder: Ascending Mathematical Solution Quality via Analogical-Problem Reasoning Transfer
• Authors: Honglin Lin, Zhuoshi Pan, Yu Li, Qizhi Pei, Xin Gao, Mengzhang Cai, Conghui He, Lijun Wu,
• Abstract summary: Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks.<n>We propose textbfMetaLadder, a framework that explicitly prompts LLMs to recall and reflect on meta-problems.<n>Our experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy.
• Score: 37.81465564673498
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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