NuminaMath-QwQ-CoT-5M

# INTELLECT-MATH: Frontier Mathematical Reasoning through Better Initializations for Reinforcement Learning

INTELLECT-MATH is a 7B parameter model optimized for mathematical reasoning. It was trained in two stages, an SFT stage, in which the model was fine-tuned on verified QwQ outputs, and an RL stage, in which the model was trained using the [PRIME-RL](https://github.com/PRIME-RL/PRIME) recipe.

We demonstrate that the quality of our SFT data can impact the performance and training speed of the RL stage: Due to its better synthetic SFT dataset that encourages the model to imitate the reasoning behavior of a strong teacher model, INTELLECT-MATH outperforms Eurus-2-PRIME, the previous state-of-the-art trained with PRIME-RL, and matches its performance with 10x faster training.

| | Intellect-Math (Step 255) | Intellect-Math (Step 47) | Eurus-2-Prime (Step 592) | Intellect-Math-SFT | Eurus-2-SFT | Qwen-2.5-Math |
|----------------|---------------------------:|--------------------------:|--------------------------:|--------------------:|------------:|-------------:|
| **MATH-500** | 82.0 | 81.6 | 79.2 | 72.8 | 65.1 | 79.8 |
| **OLYMPIADBENCH** | 49.5 | 46.7 | 42.1 | 39.1 | 29.8 | 40.7 |
| **AIME 2024** | 26.7 | 26.7 | 26.7 | 16.6 | 3.3 | 13.3 |
| **AMC** | 60.2 | 57.8 | 57.8 | 45.8 | 30.1 | 50.6 |
| **MINERVA MATH** | 39.7 | 37.8 | 38.6 | 33.8 | 32.7 | 34.6 |
| **AVG** | 51.6 | 50.1 | 48.9 | 41.6 | 32.2 | 43.8 |

### Links

- 📜 [Blog Post](https://www.primeintellect.ai/blog/intellect-math)
- 🔗 [Github](https://github.com/PrimeIntellect-ai/INTELLECT-MATH)
- 🤗 [Hugging Face Collection](https://huggingface.co/collections/PrimeIntellect/intellect-math-678a2a25d7c5d74b37b16581)

# INTELLECT-MATH：依托强化学习更佳初始化策略实现前沿数学推理

INTELLECT-MATH是一款专为数学推理优化的70亿参数模型。该模型采用两阶段训练流程：第一阶段为监督微调（Supervised Fine-Tuning，SFT）阶段，基于经过验证的QwQ输出对模型进行微调；第二阶段为强化学习（Reinforcement Learning，RL）阶段，采用[PRIME-RL](https://github.com/PRIME-RL/PRIME)训练范式完成训练。

研究表明，SFT数据的质量会对RL阶段的训练性能与训练速度产生显著影响：得益于更优质的合成SFT数据集，该模型能够模仿顶尖教师模型的推理行为，因此INTELLECT-MATH的表现优于此前基于PRIME-RL训练的前沿模型Eurus-2-PRIME，且仅需原训练时长的1/10即可达到与之相当的性能。

| | INTELLECT-MATH（迭代步数255） | INTELLECT-MATH（迭代步数47） | Eurus-2-PRIME（迭代步数592） | INTELLECT-MATH-SFT | Eurus-2-SFT | Qwen-2.5-Math |
|----------------|---------------------------:|--------------------------:|--------------------------:|--------------------:|------------:|-------------:|
| **MATH-500** | 82.0 | 81.6 | 79.2 | 72.8 | 65.1 | 79.8 |
| **OLYMPIADBENCH** | 49.5 | 46.7 | 42.1 | 39.1 | 29.8 | 40.7 |
| **2024年美国数学邀请赛（AIME 2024）** | 26.7 | 26.7 | 26.7 | 16.6 | 3.3 | 13.3 |
| **美国数学竞赛（AMC）** | 60.2 | 57.8 | 57.8 | 45.8 | 30.1 | 50.6 |
| **MINERVA MATH** | 39.7 | 37.8 | 38.6 | 33.8 | 32.7 | 34.6 |
| **平均（AVG）** | 51.6 | 50.1 | 48.9 | 41.6 | 32.2 | 43.8 |

### 相关链接
- 📜 [官方博客](https://www.primeintellect.ai/blog/intellect-math)
- 🔗 [GitHub仓库](https://github.com/PrimeIntellect-ai/INTELLECT-MATH)
- 🤗 [Hugging Face数据集合集](https://huggingface.co/collections/PrimeIntellect/intellect-math-678a2a25d7c5d74b37b16581)