arXiv:2402.03300 · 中英对照阅读

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

Zhihong Shao1,2∗†, Peiyi Wang1,3∗†, Qihao Zhu1,3∗†, Runxin Xu1, Junxiao Song1 Xiao Bi1, Haowei Zhang1, Mingchuan Zhang1, Y.K. Li1, Y. Wu1, Daya Guo1∗ 1DeepSeek-AI, 2Tsinghua University, 3Peking University {zhihongshao,wangpeiyi,zhuqh,guoday}@deepseek.com https://github.com/deepseek-ai/DeepSeek-Math

摘要

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.

原文 arXiv:2402.03300