A self-evolving multi-role collaborative framework with fine-grained difficulty guidance for innovative mathematical problem generation

TL;DR

This paper introduces a self-evolving, multi-role framework for generating innovative mathematical problems with fine-grained difficulty guidance, leveraging large language models and a new dataset to improve correctness and creativity.

Contribution

It proposes a novel collaborative framework with multiple roles, an improved difficulty model, and a new dataset, advancing the quality and innovation in mathematical problem generation.

Findings

Significantly improves problem innovation over baselines.

Maintains high correctness rate in generated problems.

Enhances problem generation through self-evolution and fine-grained guidance.

Abstract

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.