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

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

TL;DR

MetaLadder addresses how humans solve hard math problems by recalling analogous cases. It introduces an analogy-based data sequence $QSQ'C'QC$ and a problem-restating step, enabling transfer of reasoning across similar tasks and self-evolution of training data. Across GSM8K, MATH, and out-of-domain benchmarks, MetaLadder substantially surpasses standard CoT and prior augmentation methods, with notable gains and improved generalization. The approach demonstrates that structured analogical reasoning and proactive problem comprehension materially enhance LLMs' mathematical problem-solving capabilities.

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.

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

TL;DR

MetaLadder addresses how humans solve hard math problems by recalling analogous cases. It introduces an analogy-based data sequence and a problem-restating step, enabling transfer of reasoning across similar tasks and self-evolution of training data. Across GSM8K, MATH, and out-of-domain benchmarks, MetaLadder substantially surpasses standard CoT and prior augmentation methods, with notable gains and improved generalization. The approach demonstrates that structured analogical reasoning and proactive problem comprehension materially enhance LLMs' mathematical problem-solving capabilities.

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.

Paper Structure

This paper contains 27 sections, 14 equations, 3 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Data Synthesis for Math Reasoning
  4. RAG for Problem Solving
  5. MetaLadder
  6. Overview
  7. Reflective Data Generation
  8. Analogical Reasoning Activation
  9. Analogical Self-evolution
  10. Shortcut Inference
  11. Experiments
  12. Experimental Setup
  13. Main Results
  14. Ablation on Components
  15. Analysis
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Compare our MetaLadder with other methods (Standard CoT, Question & Answer Augmentation, Reflective Augmentation) on training data construction.
  • Figure 2: Overview of the MetaLadder framework for generating reflective data. The process starts with the original problem $Q$, followed by the problem type and solution method $S$, and the generation of analogous problems $Q'$ and solutions $C'$. Afterward, the original problem $Q$ is reintroduced to prompt the model to restate the problem. These components are then combined with the solution $C$ of the original problem $Q$ to form the training data.
  • Figure 3: Left: Performance of enhancing different amounts of original data. Middle: Results of 3 rounds of evolution on LLaMA and DeepSeek. Right: Combination of MetaLadder with AugCoT method.