title: DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open
    Language Models
summary: 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.
paper_authors._id: 65c19a1f55c4f06fa9692c52
paper_authors.name: Zhihong Shao
paper_authors.status: claimed_verified
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paper_authors.fullname: Zhihong Shao
paper_authors.type: user
paper_authors.user: ZhihongShao
paper_authors._id: 65c19a1f55c4f06fa9692c53
paper_authors.name: Peiyi Wang
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paper_authors.fullname: PEIYI, WANG
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paper_authors.user: peiyiwang89
paper_authors._id: 65c19a1f55c4f06fa9692c54
paper_authors.name: Qihao Zhu
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paper_authors.fullname: zhuqihao
paper_authors.type: user
paper_authors.user: zqh11
paper_authors._id: 65c19a1f55c4f06fa9692c55
paper_authors.name: Runxin Xu
paper_authors._id: 65c19a1f55c4f06fa9692c56
paper_authors.name: Junxiao Song
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-02-13T08:13:39.870Z
paper_authors._id: 6565a2dd131d13ccc5d8cb12
paper_authors.avatarUrl: /avatars/f5c5441ba74791b64c9740911f952bac.svg
paper_authors.fullname: Junxiao Song
paper_authors.type: user
paper_authors.user: haha-point
paper_authors._id: 65c19a1f55c4f06fa9692c57
paper_authors.name: Mingchuan Zhang
paper_authors._id: 65c19a1f55c4f06fa9692c58
paper_authors.name: Y. K. Li
paper_authors._id: 65c19a1f55c4f06fa9692c59
paper_authors.name: Y. Wu
paper_authors._id: 65c19a1f55c4f06fa9692c5a
paper_authors.name: Daya Guo
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-02-13T08:14:02.332Z
paper_authors._id: 653df20eaa1f487614da4db1
paper_authors.avatarUrl: /avatars/12b27ce2c59f53b7e464039deab36a5d.svg
paper_authors.fullname: Daya Guo
paper_authors.type: user
paper_authors.user: guoday
paper_title: DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open
    Language Models
paper_summary: 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.
paper_ai_keywords: DeepSeekMath 7B DeepSeek-Coder-Base-v1.5 7B math-related tokens Common Crawl MATH benchmark Gemini-Ultra GPT-4 self-consistency Group Relative Policy Optimization (GRPO) Proximal Policy Optimization (PPO)