OmniAI-ZJU/NuminaMath-Cot-Distillation-100K

# NuminaMath-Cot-Distillation-100K: A Distilled Reasoning Dataset for Group Fine-Tuning

## 💡 Dataset Summary
**NuminaMath-Cot-Distillation-100K** is a high-quality instruction-tuning dataset specifically designed for mathematical reasoning tasks. It is the official dataset released for the paper **"GFT: From Imitation to Reward Fine-Tuning with Unbiased Group Advantages and Dynamic Coefficient Rectification,"** which has been accepted to **ACL 2026 Findings**.

This dataset is engineered to address the "single-path dependency" and "entropy collapse" issues inherent in standard Supervised Fine-Tuning (SFT) by providing diverse reasoning trajectories for each mathematical problem.It serves as the foundational data for training models within the **Group Fine-Tuning (GFT)** framework.

## 📚 Dataset Lineage
This dataset is a secondary development and enhancement of the open-source [NuminaMath-CoT](https://huggingface.co/datasets/AI-MO/NuminaMath-CoT) dataset.NuminaMath-CoT provides a wide range of mathematical challenges, from high school exercises to international olympiad-level problems.

## 🛠️ Construction Method
Following the methodology described in the GFT paper, we applied the following modifications to create this 100K version:

* **Data Sampling**: We randomly sampled **100,000 (100K)** unique mathematical problems from the original NuminaMath-CoT corpus.
* **Expert Trace Preservation**: For each problem, we retained the original chain-of-thought (CoT) reasoning path to serve as the "Expert Demonstration" ($y_{exp}$).
* **Multi-Path Teacher Distillation**:
* **Teacher Model**: We utilized **Qwen-2.5-Math-72B** as the powerful teacher model to introduce diverse reasoning paradigms.
* **Response Generation**: For every problem in the 100K subset, we generated **8 distilled responses** using the teacher model.
* **Rationale**: These diverse teacher outputs ($y_{demo}$) are integrated into a hybrid response group to break single-path dependency and provide comparative signals for advantage-based learning.

## 🚀 Usage & Purpose
This dataset is optimized for:
* **GFT Training**: Supporting the construction of hybrid response groups to perform Group Advantage Learning (GAL) and Dynamic Coefficient Rectification (DCR).
* **RL Alignment**: Providing a superior cold-start initialization for subsequent reinforcement learning (e.g., GRPO), raising the attainable performance ceiling.
* **Diversity Analysis**: Enabling researchers to analyze solution coverage and solution variety in mathematical reasoning.

## 📖 Citation
If you use this dataset in your research, please cite our ACL paper:

```bibtex
@article{gan2026gft,
title={GFT: From Imitation to Reward Fine-Tuning with Unbiased Group Advantages and Dynamic Coefficient Rectification},
author={Gan, Wangjie and Pan, Miao and Xi, Linbo and Zhang, Wenqi and Chen, Jintao and Yin, Jianwei and Zhang, Xuhong},
journal={arXiv preprint arXiv:2604.14258},
year={2026}
}

# NuminaMath-Cot-Distillation-100K：面向群体微调的蒸馏推理数据集

## 💡 数据集概述
**NuminaMath-Cot-Distillation-100K** 是专为数学推理任务设计的高质量指令微调数据集，同时也是已被ACL 2026 Findings收录的论文**“GFT：基于无偏群体优势与动态系数修正的从模仿到奖励微调”**的官方配套数据集。

本数据集旨在解决标准监督微调（Supervised Fine-Tuning, SFT）中固有的“单路径依赖”与“熵坍缩”问题，为每道数学题提供多样化的推理轨迹。它是**群体微调（Group Fine-Tuning, GFT）**框架下模型训练的基础数据集。

## 📚 数据集溯源
本数据集是对开源数据集[NuminaMath-CoT](https://huggingface.co/datasets/AI-MO/NuminaMath-CoT)的二次开发与优化。NuminaMath-CoT涵盖了从高中习题到国际奥赛级别的各类数学挑战题目。

## 🛠️ 构建方法
遵循GFT论文中阐述的方法论，我们通过以下步骤构建了这一10万条数据的版本：
* **数据采样**：从原始NuminaMath-CoT语料库中随机抽取100,000（100K）道独特的数学题目。
* **专家轨迹保留**：针对每道题目，保留原始的思维链（chain-of-thought, CoT）推理路径作为“专家演示”（$y_{exp}$）。
* **多路径教师蒸馏**：
* **教师模型**：采用**Qwen-2.5-Math-72B**作为高性能教师模型，以引入多样化的推理范式。
* **响应生成**：针对100K子集内的每道题目，使用教师模型生成8条蒸馏后的响应。
* **设计逻辑**：将这些多样化的教师模型输出（$y_{demo}$）整合为混合响应组，以打破单路径依赖，并为基于优势的学习提供对比信号。

## 🚀 用途与价值
本数据集的优化适配场景包括：
* **群体微调训练**：支持构建混合响应组，以开展群体优势学习（Group Advantage Learning, GAL）与动态系数修正（Dynamic Coefficient Rectification, DCR）。
* **强化学习对齐**：为后续的强化学习（Reinforcement Learning, RL，如GRPO）提供优质的冷启动初始化方案，提升模型可达到的性能上限。
* **多样性分析**：助力研究者分析数学推理中的解法覆盖度与解法多样性。

## 📖 引用说明
若您在研究中使用本数据集，请引用我们的ACL论文：
bibtex
@article{gan2026gft,
title={GFT: 基于无偏群体优势与动态系数修正的从模仿到奖励微调},
author={Gan, Wangjie and Pan, Miao and Xi, Linbo and Zhang, Wenqi and Chen, Jintao and Yin, Jianwei and Zhang, Xuhong},
journal={arXiv preprint arXiv:2604.14258},
year={2026}
}