Emerging Reasoning with Reinforcement Learning Is Both Effective and Efficient

They replicate the DeepSeek-R1-Zero and DeepSeek-R1 training on small models with limited data. We show that long Chain-of-Thought (CoT) and self-reflection can emerge on a 7B model with only 8K MATH examples, and they achieve surprisingly strong results on complex mathematical reasoning. They fully open-source their training code and details to the community to inspire more works on reasoning.