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

1 Introduction

1. What is DeepSeekMath 7B, and what did it achieve?
   DeepSeek-Coder-Base-v1.5 7B further pretrained on 120B math tokens from Common Crawl plus text and code, then instruction-tuned and trained with RL. It reached 51.7% on competition-level MATH without tools or voting (60.9% with self-consistency over 64 samples), approaching GPT-4 and Gemini Ultra.
   • Shao et al., 2024, DeepSeekMath (arXiv preprint arXiv:2402.03300), §1
2. To which two factors do Shao et al. attribute DeepSeekMath’s mathematical ability?
   A carefully engineered pipeline for selecting math data from public web pages, and Group Relative Policy Optimization (GRPO), a variant of PPO that improves reasoning while using less memory.
   • Shao et al., 2024, DeepSeekMath (arXiv preprint arXiv:2402.03300), §1
3. What did DeepSeekMath show about model size and data quality?
   DeepSeekMath-Base 7B matched Minerva 540B on math benchmarks: parameter count isn’t the only key factor; a small model pretrained on high-quality data can be strong.
   • Shao et al., 2024, DeepSeekMath (arXiv preprint arXiv:2402.03300), §1