Qwen2.5-Math: Advanced Open-Source Mathematical LLM Series Released

The Qwen team has released Qwen2.5-Math, an upgrade to their previous Qwen2-Math series, open-sourcing base models (1.5B, 7B, 72B), instruct models (1.5B, 7B, 72B), and a reward model (RM-72B). Unlike Qwen2-Math, which only handled English with CoT, Qwen2.5-Math supports both CoT and TIR for Chinese and English problems. The base models were trained on an expanded corpus (Qwen Math Corpus v2 with over 1T tokens) and improved via synthesized data and better initialization. The instruct models, trained with a reward model and GRPO, show significant gains over the previous series, with Qwen2.5-Math-72B-Instruct achieving 92.9 on MATH under TIR with RM@8, and solving 12 out of 30 AIME 2024 problems, while competitors like GPT-4 Turbo solved only 1-2. Notably, the 7B instruct model matches Qwen2-Math-72B-Instruct, and even the 1.5B model scores around 80 on MATH with a Python interpreter. The team implemented rigorous decontamination measures, including n-gram matching and longest common subsequence ratio, and provided demos for TIR and multimodal math reasoning.