DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
<|reference_start|>DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models: Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.<|reference_end|>
@article{shao2024deepseekmath:,
    title={DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open
  Language Models},
    author={Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi,
  Haowei Zhang, Mingchuan Zhang, Y.K. Li, Y. Wu, Daya Guo},
    journal={arXiv preprint arXiv:2402.03300},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03300},
    primaryClass={cs.CL cs.AI cs.LG}
}