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

5 Feb 2024  ·  Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, Y. K. Li, Y. Wu, Daya Guo ·

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.

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Results from the Paper


Ranked #9 on Math Word Problem Solving on MATH (using extra training data)

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Task Dataset Model Metric Name Metric Value Global Rank Uses Extra
Training Data
Benchmark
Arithmetic Reasoning GSM8K DeepSeekMATH-RL-7B Accuracy 88.2 # 23
Parameters (Billion) 7 # 4
Math Word Problem Solving MATH DeepSeekMATH-RL-7B (w/ code, greedy decoding) Accuracy 58.8 # 9
Parameters (Billions) 7 # 47
Math Word Problem Solving MATH DeepSeekMATH-RL-7B (greedy decoding) Accuracy 51.7 # 21
Parameters (Billions) 7 # 47

Methods