WarriorMath: Enhancing the Mathematical Ability of Large Language Models with a Defect-aware Framework

TL;DR

WarriorMath is a novel framework that enhances large language models' mathematical skills by generating defect-aware training data through expert collaboration and progressive fine-tuning, leading to state-of-the-art performance.

Contribution

It introduces a defect-aware data synthesis process and progressive training strategy that specifically target LLM weaknesses, improving mathematical problem-solving capabilities.

Findings

Outperforms baselines by 12.57% on average across six benchmarks.

Produces high-quality, defect-aware training data through expert collaboration.

Sets new state-of-the-art in mathematical problem solving for LLMs.

Abstract

Large Language Models (LLMs) excel in solving mathematical problems, yet their performance is often limited by the availability of high-quality, diverse training data. Existing methods focus on augmenting datasets through rephrasing or difficulty progression but overlook the specific failure modes of LLMs. This results in synthetic questions that the model can already solve, providing minimal performance gains. To address this, we propose WarriorMath, a defect-aware framework for mathematical problem solving that integrates both targeted data synthesis and progressive training. In the synthesis stage, we employ multiple expert LLMs in a collaborative process to generate, critique, and refine problems. Questions that base LLMs fail to solve are identified and iteratively improved through expert-level feedback, producing high-quality, defect-aware training data. In the training stage, we introduce a progressive learning framework that iteratively fine-tunes the model using increasingly challenging data tailored to its weaknesses. Experiments on six mathematical benchmarks show that WarriorMath outperforms strong baselines by 12.57% on average, setting a new state-of-the-art. Our results demonstrate the effectiveness of a defect-aware, multi-expert framework for improving mathematical ability.