# DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

**Authors:** Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, Daya Guo  
**arXiv:** [2402.03300](https://arxiv.org/abs/2402.03300)  
**Date:** 2024-02-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2402.03300v3/

## Key points

- DeepSeekMath 7B developed by a team of researchers led by Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu and Daya Guo
- Incorporates 120 billion math-related tokens from Common Crawl alongside natural language and code data
- Achieved remarkable performance on the MATH benchmark with a score of 51.7%
- Demonstrated prowess without relying on external toolkits or voting techniques
- Approaches the performance levels of established models such as Gemini-Ultra and GPT-4
- Achieved an even higher score of 60.9% on MATH when tested for self-consistency over 64 samples
- Success attributed to leveraging publicly available web data through a meticulously engineered data selection pipeline and introducing Group Relative Policy Optimization (GRPO)
- GRPO played a crucial role in enhancing mathematical reasoning abilities while optimizing memory usage concurrently

## Summary

In the realm of language models, mathematical reasoning presents a formidable challenge due to its intricate and organized nature. To address this challenge, a team of researchers led by Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu and Daya Guo have developed DeepSeekMath 7B. This model builds upon the pre-training of DeepSeek-Coder-Base-v1.5 7B by incorporating 120 billion math-related tokens sourced from Common Crawl alongside natural language and code data. The groundbreaking achievement of DeepSeekMath 7B is evident in its remarkable performance on the competition-level MATH benchmark. With an impressive score of 51.7%, this model has demonstrated its prowess without relying on external toolkits or voting techniques. In fact, it approaches the performance levels of established models such as Gemini-Ultra and GPT-4. Furthermore, when tested for self-consistency over 64 samples from DeepSeekMath 7B , an even higher score of 60.9% on MATH was achieved. The success of DeepSeekMath can be attributed to two key factors that set it apart from other models in the field. Firstly,the researchers leveraged the vast potential of publicly available web data through a meticulously engineered data selection pipeline.This strategic approach allowed them to enrich the model's understanding and application of mathematical concepts significantly. Secondly,the introduction of Group Relative Policy Optimization (GRPO),a variant of Proximal Policy Optimization (PPO), played a crucial role in enhancing DeepSeekMath's mathematical reasoning abilities while optimizing memory usage concurrently.This innovative technique not only improved the model's performance but also streamlined its computational efficiency. In summary, DeepSeekMath represents a significant advancement in open language models' ability to tackle complex mathematical reasoning tasks effectively. By pushing the limits of what is achievable in this domain through strategic data selection and optimization techniques like GRPO, this research paves the way for further advancements in artificial intelligence and natural language processing technologies.