具有细粒度难度指导的自进化多角色协作框架用于创新数学问题生成
A self-evolving multi-role collaborative framework with fine-grained difficulty guidance for innovative mathematical problem generation
AI总结：
本文提出一种自进化多角色协作框架，通过细粒度难度指导提升创新数学问题生成的正确率与创新性。
摘要：
数学问题生成（MPG）是智能教育领域的重要研究方向。近年来，大语言模型（LLMs）的快速发展为问题生成任务带来了新的技术方法。尽管现有LLMs能够实现较高的正确率，但通常缺乏创新性且表现不佳。在本文中，我们提出了创新数学问题生成（IMPG）任务。为解决IMPG任务，本文提出了一种具有细粒度难度指导的自进化、多角色协作框架。首先，构建了一个由采样器、生成器、评估器、状态机和记忆组成的多角色协作机制，通过自我评估和外部反馈的迭代优化确保生成问题的正确性。其次，我们引入了改进的难度模型以量化难度并提供细粒度指导。我们采用数据驱动的关联引导路径采样（DAPS）算法来增强采样编码的语义合理性。第三，我们构建了HSM3K-CN数据集，该数据集包含高质量的高中数学问题。采用多阶段训练流水线，包括持续预训练（CPT）、监督微调（SFT）和组相对策略优化（GRPO），以增强基础模型的生成和评估能力。最后，通过知识蒸馏将专家模型的评估能力转移到学徒模型中，实现系统的自进化。实验表明，与基线模型相比，我们提出的方法显著提高了生成问题的创新性，同时保持了较高的正确率。
英文摘要：
Mathematical problem generation (MPG) is a significant research direction in the field of intelligent education. In recent years, the rapid development of large language models (LLMs) has enabled new technological approaches to problem-generation tasks. Although existing LLMs can achieve high correctness rates, they generally lack innovation and exhibit poor discrimination. In this paper, we propose the task of innovative math problem generation (IMPG). To solve the IMPG task, this paper proposes a self-evolving, multi-role collaborative framework with fine-grained difficulty guidance. First, a multi-role collaborative mechanism comprising a sampler, generator, evaluator, state machine, and memory is constructed, ensuring the correctness of generated problems through iterative optimization informed by self-assessment and external feedback. Second, we introduce an improved difficulty model to quantify difficulty and provide fine-grained guidance. We adopt the data-driven association-guided path sampling (DAPS) algorithm to enhance the semantic rationality of sampled encodings. Third, we construct the HSM3K-CN dataset, which comprises high-quality high school math problems. A multi-stage training pipeline is adopted, incorporating continual pre-training (CPT), supervised fine-tuning (SFT), and group relative policy optimization (GRPO), to enhance the generation and evaluation capabilities of the base model. Finally, system self-evolution is achieved by transferring evaluation capabilities from the expert model to the apprentice model via distillation. Experiments show that, compared to baseline models, our proposed method significantly improves the innovation of the generated problems while maintaining a high correctness rate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
