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

By An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jingren Zhou, Junyang Lin, Keming Lu and 5 more. arXiv.org, 2024

1,049 citations recorded by the source corpus.

In this report, we present a series of math-specific large language models: Qwen2.5-Math and Qwen2.5-Math-Instruct-1.5B/7B/72B. The core innovation of the Qwen2.5 series lies in integrating the philosophy of self-improvement throughout the entire pipeline, from pre-training and post-training to inference: (1) During the pre-training phase, Qwen2-Math-Instruct is utilized to generate large-scale, high-quality mathematical data. (2) In the post-training phase, we develop a reward model (RM) by conducting massive sampling from Qwen2-Math-Instruct. This RM is then applied to the iterative evolution of data in supervised fine-tuning (SFT). With a stronger SFT model, it's possible to iteratively train and update the RM, which in turn guides the next round of SFT data iteration. On the final SFT model, we employ the ultimate RM for reinforcement learning, resulting in the Qwen2.5-Math-Instruct. (3) Furthermore, during the inference stage, the RM is used to guide sampling, optimizing the model's performance. Qwen2.5-Math-Instruct supports both Chinese and English, and possess advanced mathematical reasoning capabilities, including Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR). We evaluate our models on 10 mathematics datasets in both English and Chinese, such as GSM8K, MATH, GaoKao, AMC23, and AIME24, covering a range of difficulties from grade school level to math competition problems.

Subfields: Artificial Intelligence, Control and Systems Engineering, Information Systems

View Paper: https://www.semanticscholar.org/paper/9fb201282f53a4ce89f28cbe5026af78912aa8c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Maosong Sun
2. Ning Ding
3. Yuhang Cao
4. Yuan Yao
5. Yuhang Zang
6. Min Lin
7. Dahua Lin
8. Tianyu Pang

In Control and Systems Engineering

1. Yuan Yao
2. Min Lin
3. Dahua Lin
4. Zi-Yan Liu
5. Wee Sun Lee
6. Francesco Orabona

In Information Systems

1. Maosong Sun
2. Weize Chen
3. Ganqu Cui

Citations in the corpus

• ReTool: Reinforcement Learning for Strategic Tool Use in LLMs (2025, neutral): “Our method outperforms Qwen-Math-72B-TIR [30] and o1-preview [11] significantly on AIME2024 and AIME2025.”
• Qwen3 Technical Report (2025, neutral): “5-Math (Yang et al., 2024c) for mathematical content and Qwen2.”
• LIMO: Less is More for Reasoning (2025, neutral): “Two key developments have created conditions for reimagining reasoning in LLMs: (1) Knowledge foundation revolution : Modern foundation models now incorporate unprecedented amounts of mathematical content during pre-training (Qwen et al., 2025; Yang et al., 2024; Wang et al., 2024).”
• SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild (2025, neutral): “We build our evaluation script based on Yang et al. (2024b), using a temperature of 1.0 and a maximum generation length of 16K tokens.”
• rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking (2025, neutral): “Recent studies have demonstrated that large language models (LLMs) are capable of tackling mathematical problems [Team, 2024a, Yang et al., 2024, OpenAI, 2024, Liu et al., 2024].”
• Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model (2025, neutral): “Answer: [Yes] Justification: Our main results are evaluated using the avg@16 metric, which aggregates performance across multiple runs.”
• Visual-RFT: Visual Reinforcement Fine-Tuning (2025, positive): “Studies have explored improving LLMs’ performance in reasoning tasks such as solving mathematical problems [2, 22, 33, 43, 45] and coding [6, 8, 51, 54].”
• Understanding R1-Zero-Like Training: A Critical Perspective (2025, positive): “5-Math (Yang et al., 2024b) uses chat model’s data (question-answer pairs) during the pretraining stage, we hypothesize that they might pretrain on the concatenated text to maximize log p θ ( q ; o ) directly.”
• WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct (2023, neutral): “…Series (Touvron et al., 2023a;b; Dubey et al., 2024; Taylor et al., 2022), DeepSeek (Bi et al., 2024; Shao et al., 2024), Qwen (Bai et al., 2023; Yang et al., 2024) etc. Notably, Llama serves as a foundational model for supervised fine-tuning, leading to the development of models like Alpaca,…”
• The Lessons of Developing Process Reward Models in Mathematical Reasoning (2025, neutral): “…and follow the scoring method for responses in (Lightman et al., 2023), it can be found that regardless of whether we employ the minimum score or the product of scores to evaluate the full solution, the lowest step score acts as the key limiting factor that affects the selection criteria of PRMs.”
• Process Reinforcement through Implicit Rewards (2025, positive): “5-Math-7B-Base ( Yang et al., 2024b) with PRIME after a lightweight SFT warmup stage.”