MathSmith-HC-Problem-Synthesizer-Qwen3-8B

MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy

Overview

MathSmith is a framework for synthesizing challenging mathematical problems to enhance LLM reasoning. This model is a reinforced policy-based synthesizer optimized to generate novel, Olympiad-level mathematical problems from scratch.

The model generates <rationale>–<problem> pairs, where:

• <rationale>: structured reasoning describing concept integration and difficulty design strategies.
• <problem>: a single Olympiad-level mathematical question that admits a verifiable numeric or symbolic answer.

MathSmith-HC (High Consistency) combines complexity and consistency as difficulty rewards during reinforcement learning, producing more stable problems than the version optimized solely for complexity.

---

MathSmith Pipeline

The MathSmith framework consists of four main stages:

1. Concept Collection: Randomly sample concept–explanation pairs from PlanetMath to ensure data independence and avoid benchmark contamination.
2. Supervised Fine-tuning (SFT): Train the model on collected concept–explanation pairs to establish foundational understanding of problem generation.
3. Reinforcement Learning (RL): Optimize the model using GRPO with rewards based on structural validity, reasoning complexity (trace length), and answer consistency.
4. Weakness-Focused Self-Improvement: Iteratively identify and address model weaknesses by generating targeted problem variants for specific mathematical concepts.

Dependence

• Transformers 4.52.4
• Pytorch 2.7.0+cu126
• Datasets 3.6.0
• Tokenizers 0.21.1

Citation

If you find this work useful, please cite:

@article{zhan2025mathsmith,
  title={MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy},
  author={Zhan, Shaoxiong and Lai, Yanlin and Lu, Ziyu and Lin, Dahua and Yang, Ziqing and Tan, Fei},
  journal={arXiv preprint arXiv:2508.05592},
  year={2025}
}