# Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement

**Authors:** An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, Zhenru Zhang  
**arXiv:** [2409.12122](https://arxiv.org/abs/2409.12122)  
**Date:** 2024-09-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2409.12122v1/

## Key points

- Authors led by An Yang present math-specific large language models integrating self-improvement philosophy
- Pre-training phase leverages model to generate high-quality mathematical data
- Post-training phase involves developing a reward model (RM) through extensive sampling from
- RM applied in supervised fine-tuning (SFT) for iterative training and updating
- Advanced model created through iterative rounds of SFT guided by RM
- RM crucial in guiding sampling during the inference stage to optimize performance
- Models exhibit advanced mathematical reasoning capabilities such as Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR)
- Evaluation spans across 10 mathematics datasets in English and Chinese, covering various difficulty levels
- Collaborative efforts of authors have significantly advanced mathematical expertise through innovative language models

## Summary

In this technical report, a team of authors led by An Yang presents a series of math-specific large language models  and . These models integrate self-improvement philosophy throughout the entire pipeline, from pre-training to post-training and inference stages. During pre-training, the authors leverage the  model to generate large-scale, high-quality mathematical data. In the post-training phase, they develop a reward model (RM) through extensive sampling from , which is then applied in supervised fine-tuning (SFT). This allows for iterative training and updating of the RM to guide subsequent rounds of SFT data iteration, ultimately leading to the creation of the advanced  model. Moreover, during the inference stage, the RM plays a crucial role in guiding sampling to optimize the performance of the model. Notably, exhibits advanced mathematical reasoning capabilities such as Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR), supporting both Chinese and English languages. The evaluation of these models spans across 10 mathematics datasets in English and Chinese,< kd>GSM8K,MATH,GaoKao ,AMC23,and AIME24 </ kd>, covering various difficulty levels from grade school to math competition problems. The collaborative efforts of authors Beichen Zhang,Binyuan Hui,Bofei Gao,Bowen Yu,Chengpeng Li,Dayiheng Liu,Jianhong Tu,Jingren Zhou,< kd>Junyang Lin,Keming Lu,Mingfeng Xue,Runji Lin,Tianyu Liu,Xingzhang Ren,and Zhenru Zhang </kd> have contributed significantly to advancing mathematical expertise through innovative language models like .