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

arXiv: https://arxiv.org/abs/2601.11792 · HTML: https://mlsanity.com/paper/2601.11792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

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## Abstract (arXiv)

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.