INTELLECT-MATH-SFT-Data

# 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：通过强化学习的更佳初始化实现前沿数学推理

INTELLECT-MATH是一款参数量为70亿的数学推理优化模型。其训练分为两个阶段：第一阶段为监督微调（Supervised Fine-Tuning, SFT）阶段，模型在经过验证的QwQ输出数据上完成微调；第二阶段为强化学习（Reinforcement Learning, RL）阶段，采用[PRIME-RL](https://github.com/PRIME-RL/PRIME)训练配方开展训练。

研究表明，监督微调数据集的质量会对强化学习阶段的训练性能与训练速度产生显著影响。得益于用于引导模型模仿顶尖教师模型推理行为的高质量合成监督微调数据集，INTELLECT-MATH的性能超越了此前基于PRIME-RL训练的当前最优模型Eurus-2-PRIME，且仅需前者1/10的训练时长即可达到与之相当的性能水平。

| 评测基准 | Intellect-Math（第255步训练） | Intellect-Math（第47步训练） | Eurus-2-Prime（第592步训练） | 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 |
| **AMC（美国数学竞赛）** | 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 |

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

搜集汇总

背景与挑战

背景概述

INTELLECT-MATH-SFT-Data是一个用于数学推理模型监督微调(SFT)的高质量数据集，包含经过验证的QwQ输出，其特点是能显著提升后续强化学习阶段的训练效率和模型性能，在MATH-500等多个数学推理基准测试中表现优异。