Study Reveals Scaling Laws for LLM Reinforcement Learning in Mathematical Reasoning

An empirical study systematically investigates the behavior of large language models (LLMs) after reinforcement learning, focusing on mathematical reasoning. This research analyzes the scaling characteristics of the Qwen2.5 dense model series, which ranges from 0.5B to 72B parameters. Four significant findings arise from the study: larger models exhibit greater learning efficiency regarding compute and data metrics, a strong predictive power-law relationship among test loss, compute, and data is observed in both base and instruction-tuned models, and while larger models are more efficient, their analytical learning efficiency trends need further investigation. The interaction of model size, data quantity, and computational resources is characterized to influence performance. This research fills a gap in understanding scaling laws for LLMs during post-training reinforcement learning, which has received less attention than pre-training. The paper is cataloged as arXiv:2509.25300v4 and classified as a replace-cross announcement.