mlsanityData to 7 Oct 2026

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

arXiv 2409.12122 ↗First posted 18 Sep 2024cs.CL cs.AI cs.LGcited by 1,057

On the map: Synthetic data and self-improvement for LLMs → Synthetic reasoning data and bootstrapping

Abstract (arXiv)

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.

Key facts. Cited by 1,057 papers in the map (data through 7 Oct 2026). Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs. Builds on 23 of its 27 references that are in the map. First posted on arXiv 18 Sep 2024.

Builds on

23 of 27 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models23 May
  2. 2023Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models11 Dec

Other references · 21

  1. 2022Training language models to follow instructions with human feedbackcited by 15,712
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  3. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  4. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
  5. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  6. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  7. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,359
  8. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,099
  9. 2023AGIEval: A Human-Centric Benchmark for Evaluating Foundation Modelscited by 701
  10. 2023Scaling Relationship on Learning Mathematical Reasoning with Large Language Modelscited by 417
  11. 2023Llemma: An Open Language Model For Mathematicscited by 385
  12. 2024DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligencecited by 325
9 more
  1. 2023Evaluating the Performance of Large Language Models on GAOKAO Benchmarkcited by 182
  2. 2024MathScale: Scaling Instruction Tuning for Mathematical Reasoningcited by 144
  3. 2024MAmmoTH2: Scaling Instructions from the Webcited by 143
  4. 2024InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoningcited by 117
  5. 2023CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?cited by 89
  6. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipelinecited by 81
  7. 2023MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoningcited by 45
  8. 2024Towards Scalable Automated Alignment of LLMs: A Surveycited by 33
  9. 2024DotaMath: Decomposition of Thought with Code Assistance and Self-correction for Mathematical Reasoningcited by 19

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 46; 2025: 591; 2026: 420.

1,057 papers.

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  1. 2025Qwen3 Technical Reportcited by 8,195
  2. 2024Qwen2.5 Technical Reportcited by 4,713
  3. 2025Understanding R1-Zero-Like Training: A Critical Perspectivecited by 1,276
  4. 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wildcited by 505
  5. 2025Visual-RFT: Visual Reinforcement Fine-Tuningcited by 501
  6. 2025LIMO: Less is More for Reasoningcited by 488
  7. 2025Process Reinforcement through Implicit Rewardscited by 478
  8. 2025Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Modelcited by 450
  9. 2025The Lessons of Developing Process Reward Models in Mathematical Reasoningcited by 402
  10. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 381
  11. 2025ReTool: Reinforcement Learning for Strategic Tool Use in LLMscited by 377
  12. 2025Absolute Zero: Reinforced Self-play Reasoning with Zero Datacited by 323
38 more
  1. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 308
  2. 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 288
  3. 2024Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Modelscited by 277
  4. 2024ProcessBench: Identifying Process Errors in Mathematical Reasoningcited by 277
  5. 2025Reasoning with Exploration: An Entropy Perspectivecited by 277
  6. 2025Learning to Reason under Off-Policy Guidancecited by 266
  7. 2025AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoningcited by 234
  8. 2025Spurious Rewards: Rethinking Training Signals in RLVRcited by 199
  9. 2025The Landscape of Agentic Reinforcement Learning for LLMs: A Surveycited by 195
  10. 2025A Survey of Reinforcement Learning for Large Reasoning Modelscited by 175
  11. 2025ToRL: Scaling Tool-Integrated RLcited by 166
  12. 2025The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoningcited by 160
  13. 2025Qwen2.5-1M Technical Reportcited by 158
  14. 2025The Surprising Effectiveness of Negative Reinforcement in LLM Reasoningcited by 158
  15. 2025LIMR: Less is More for RL Scalingcited by 136
  16. 2025Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scalingcited by 135
  17. 2025Can MLLMs Reason in Multimodality? EMMA: An Enhanced MultiModal ReAsoning Benchmarkcited by 132
  18. 2025General-Reasoner: Advancing LLM Reasoning Across All Domainscited by 132
  19. 2025AbstentionBench: Reasoning LLMs Fail on Unanswerable Questionscited by 129
  20. 2025Qwen3Guard Technical Reportcited by 125
  21. 2025Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivizationcited by 124
  22. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoningcited by 118
  23. 2025KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Codingcited by 115
  24. 2025OctoThinker: Mid-training Incentivizes Reinforcement Learning Scalingcited by 110
  25. 2025Small Models Struggle to Learn from Strong Reasonerscited by 109
  26. 2025A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systemscited by 108
  27. 2025Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rolloutscited by 108
  28. 2025Geometric-Mean Policy Optimizationcited by 107
  29. 2025Reward-Guided Speculative Decoding for Efficient LLM Reasoningcited by 106
  30. 2025Online Difficulty Filtering for Reasoning Oriented Reinforcement Learningcited by 100
  31. 2025PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Modelscited by 98
  32. 2025Self-Training Elicits Concise Reasoning in Large Language Modelscited by 97
  33. 2025Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questionscited by 95
  34. 2025Audio-Reasoner: Improving Reasoning Capability in Large Audio Language Modelscited by 94
  35. 2025GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoningcited by 94
  36. 2025Q-Insight: Understanding Image Quality via Visual Reinforcement Learningcited by 93
  37. 2024OpenR: An Open Source Framework for Advanced Reasoning with Large Language Modelscited by 92
  38. 2024LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoningcited by 90

50 most cited of 1,057 All 1,057 (JSON)

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  1. 2026Question Begets Question: Self-Evolving Curriculum for Reinforcement Fine-Tuning on Competition Mathematics
  2. 2025Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models
  3. 2024Self-Explore: Enhancing Mathematical Reasoning in Language Models with Fine-grained Rewards
  4. 2025Reinforcement learning fine-tuning of language model for instruction following and math reasoning
  5. 2023Qwen Technical Report
  6. 2025Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning
  7. 2025On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification
  8. 2025Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning