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.

Related papers

• Syzygy of Thoughts: Improving LLM CoT with the Minimal Free Resolution [59.39066657300045]
  Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps. We propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving.
  arXiv  Detail & Related papers  (2025-04-13T13:35:41Z)
• Benchmarking Systematic Relational Reasoning with Large Language and Reasoning Models [15.56445409535547]
  Large Language Models (LLMs) have been found to struggle with systematic reasoning. This paper focuses on tasks that require systematic reasoning about relational compositions. We find that the considered LLMs and LRMs overall perform poorly overall, albeit better than random chance.
  arXiv  Detail & Related papers  (2025-03-30T15:41:55Z)
• SRA-MCTS: Self-driven Reasoning Augmentation with Monte Carlo Tree Search for Code Generation [14.786100203787194]
  Large language models demonstrate exceptional performance in simple code generation tasks but face challenges in tackling complex problems. We propose a reasoning-augmented data generation process, SRA-MCTS, which guides the model to autonomously generate high-quality intermediate reasoning paths. Our method operates entirely through the model itself without requiring additional supervision.
  arXiv  Detail & Related papers  (2024-11-17T12:31:04Z)
• MathCAMPS: Fine-grained Synthesis of Mathematical Problems From Human Curricula [33.5782208232163]
  We propose Math CAMPS: a method to synthesize high-quality mathematical problems at scale. We encode each standard in a formal grammar, allowing us to sample diverse symbolic problems and their answers. We derive follow-up questions from symbolic structures and convert them into follow-up word problems.
  arXiv  Detail & Related papers  (2024-07-01T01:56:28Z)
• MindStar: Enhancing Math Reasoning in Pre-trained LLMs at Inference Time [51.5039731721706]
  MindStar is a purely inference-based searching method for large language models. It formulates reasoning tasks as searching problems and proposes two search ideas to identify the optimal reasoning paths. It significantly enhances the reasoning abilities of open-source models, such as Llama-2-13B and Mistral-7B, and achieves comparable performance to GPT-3.5 and Grok-1.
  arXiv  Detail & Related papers  (2024-05-25T15:07:33Z)
• Distilling Algorithmic Reasoning from LLMs via Explaining Solution Programs [2.3020018305241337]
  Distilling explicit chain-of-thought reasoning paths has emerged as an effective method for improving the reasoning abilities of large language models. We propose a novel approach to distill reasoning abilities from LLMs by leveraging their capacity to explain solutions. Our experiments demonstrate that learning from explanations enables the Reasoner to more effectively guide program implementation by a Coder.
  arXiv  Detail & Related papers  (2024-04-11T22:19:50Z)
• Thought Propagation: An Analogical Approach to Complex Reasoning with Large Language Models [62.96551299003463]
  We propose textbftextitThought Propagation (TP) to enhance the complex reasoning ability of Large Language Models. TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch.
  arXiv  Detail & Related papers  (2023-10-06T01:40:09Z)
• Faith and Fate: Limits of Transformers on Compositionality [109.79516190693415]
  We investigate the limits of transformer large language models across three representative compositional tasks. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. Our empirical findings suggest that transformer LLMs solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching.
  arXiv  Detail & Related papers  (2023-05-29T23:24:14Z)
• Meta Cyclical Annealing Schedule: A Simple Approach to Avoiding Meta-Amortization Error [50.83356836818667]
  We develop a novel meta-regularization objective using it cyclical annealing schedule and it maximum mean discrepancy (MMD) criterion. The experimental results show that our approach substantially outperforms standard meta-learning algorithms.
  arXiv  Detail & Related papers  (2020-03-04T04:43:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.