M eta L adder: Ascending Mathematical Solution Quality via Analogical-Problem Reasoning Transfer (2025)

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 MetaLadder , a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogical 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.

## introduction large language models (llms) have achieved remarkable success in mathematical reasoning tasks by leveraging chain-of-thought (cot) data, which explicitly guides models to decompose problems into intermediate reasoning steps before producing final answers @xcite @xcite . pioneering works such as @xcite demonstrated that training llms on cotstyle solutions significantly improves their ability * corresponding author. to solve complex problems, with subsequent studies @xcite further refining this paradigm. for instance, models like minerva and gpt-4 @xcite have showcased near-human performance by distilling high-quality cot trajectories from expert demonstrations. these methods typically follow a straightforward template: given a problem, the model generates a cot explanation step-by-step, which then leads to the correct answer. while effective, such approaches align only partially with the nuanced cognitive processes @xcite humans employ during problem-solving. despite their success, existing cot-based finetuning methods rely on a rigid "@xmath0, which diverges from how humans approach challenging mathematical tasks. when solving problems, humans rarely generate solutions in isolation; instead, they actively recall analogous problems and their solutions, especially for difficult or unfamiliar questions @xcite . for example, encountering a combinatorics problem, a student might recall similar problems involving permutations or recursive strategies, using their structures to guide the current solution. this ability to leverage prior analogical experiences is critical for generalizing knowledge and tackling novel challenges. however, current llm training paradigms largely overlook this aspect, treating each problem as an independent instance without encouraging cross-problem reasoning. this limitation constrains models' capacity to transfer learned reasoning patterns, particularly for problems requiring abstract structural or semantic similarities to prior examples. to bridge this gap, we propose metaladder, a framework inspired by human-like analogical reasoning and problem comprehension. metaladder explicitly guides llms to recall and reflect on meta-problems-structurally or semantically analogous problems with known cot solutions-before generating answers for the target problem. these meta-problems and their cot trajectories serve as scaffolding to derive the current solution, mirroring how humans "stand on the shoulders" of past experiences. additionally, we introduce a problem-restating mechanism: before reasoning, the model regenerates the original question in its own words, enhancing its comprehension of the problem's core components and constraints. this dual mechanism-analogical recall and active restatement-enables the model to decompose complex problems into familiar reasoning patterns, effectively mimicking the human ability to "learn from examples" and generalize solutions across analogous contexts. by integrating these steps, metaladder successfully transforms the traditional linear cot process into a dynamic, context-aware reasoning ladder, where each rung represents a retrieved meta-problem or a refined understanding of the target task. extensive experiments validate metaladder's effectiveness. on mathematical benchmarks like gsm8k and math, models trained with metaladder achieve significant improvements over standard cot fine-tuning baselines, with accuracy gains of 12.4% and 11.3%, respectively, surpassing recent advanced methods. further analysis reveals that metaladder-trained models exhibit stronger generalization to structurally novel problems, solving 9.3% more "out-of-distribution" test cases than vanilla cot models. qualitative examples demonstrate that the model not only retrieves relevant meta-problems but also adapts their solutions creatively. these results collectively highlight that emulating human-like analogical reasoning and ac-tive comprehension is a powerful yet underexplored direction for advancing llms' mathematical reasoning capabilities. ## metaladder we first introduce the overall metaladder framework for enhancing mathematical problem-solving (section 3.1). then we present each our method in detail by explaining the generation of reflective data to guide the model's reasoning process (section 3.2), describing the composition of training data to activate the model's analogical reasoning (section 3.3). besides, we also add a selfevolve process in our framework to enable the model's ability to autonomously generate data for self-improvement (section 3.4). finally, we also incorporate a shortcut inference mechanism for fast and effective generation (section 3.5). ## conclusion in this paper, we introduce metaladder, a novel framework that enhances the mathematical problem-solving abilities of llms. by explicitly prompting the model to reflect on analogical problems and their solutions, metaladder enables it to transfer reasoning across similar tasks, mimicking human learning. additionally, our problem-restating mechanism further enhances the model's reasoning accuracy. experimental results across multiple mathematical benchmarks demonstrate that metaladder significantly improves llm performance, surpassing both standard chain-of-thought (cot) methods and other state-of-the-art approaches. our work highlights the importance of integrating analogical reasoning and meta-cognitive strategies into llms for complex reasoning tasks.