Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement

Qwen2.5-Math is a series of math-specialized large language models (1.5B, 7B, and 72B parameters) developed by the Qwen team (Alibaba Group). The core innovation is a self-improvement pipeline spanning pre-training, post-training, and inference. During pre-training, Qwen2-Math-Instruct generates large-scale high-quality mathematical data. In post-training, a reward model (RM) is trained via massive sampling from Qwen2-Math-Instruct and used for iterative evolution of supervised fine-tuning (SFT) data; the final SFT model undergoes reinforcement learning with the ultimate RM. At inference, the RM guides sampling. Qwen2.5-Math-Instruct supports both Chinese and English and possesses advanced mathematical reasoning capabilities including Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR). The models are evaluated on 10 mathematics datasets in English and Chinese, covering grade school to competition problems (e.g., GSM8K, MATH, GaoKao, AMC23, AIME24). The technical report details the methodology and results.