gretel-math-gsm8k-v0

# gretelai/gsm8k-synthetic-diverse-405b

This dataset is a synthetically generated version inspired by the GSM8K `https://huggingface.co/datasets/openai/gsm8k` dataset, created entirely using **Gretel Navigator with meta-llama/Meta-Llama-3.1-405B** as the agent LLM. It contains ~1500 Grade School-level math word problems with step-by-step solutions, focusing on age group, difficulty, and domain diversity.

## Key Features:
- Synthetically Generated: Math problems created using Gretel Navigator, employing evolutionary techniques, LLM-as-a-judge, and verification of annotated calculations via the `sympy` library.
- Stratified Test Set: 300 examples for test, remaining for training, stratified by topic and difficulty.
- Diverse Contexts and Names: Problems feature a wide range of real-world contexts and include diverse names and ethnicities.
- Age Group Labeling: Each problem is tagged with an appropriate age group (grades 2 through 6).
- Difficulty Categorization: Problems are categorized as easy, medium, or hard.
- Expanded Domains: Covers a wide range of topics including basic algebra, geometry, and more.
- Step-by-Step Solutions: Clear reasoning with annotated arithmetic operations.

## Dataset Statistics and Distribution


## Gretel Navigator (selected model: meta-llama/Meta-Llama-3.1-405B) Dataset - Distribution Analysis

### Topic Distribution

| topic | Train | Test |
|:-------------------------|--------:|-------:|
| algebra | 25 | 20 |
| arithmetic | 31 | 25 |
| compound interest | 26 | 21 |
| data interpretation | 27 | 20 |
| exponential growth/decay | 25 | 21 |
| fractions | 29 | 24 |
| geometry | 35 | 29 |
| optimization | 23 | 19 |
| percentages | 37 | 29 |
| polynomials | 21 | 18 |
| probability | 20 | 17 |
| proportions | 30 | 24 |
| ratios | 41 | 33 |

### Difficulty Distribution

| difficulty | Train | Test |
|:-------------|--------:|-------:|
| easy | 93 | 75 |
| hard | 82 | 67 |
| medium | 101 | 83 |
| very hard | 94 | 75 |

## Citation and Usage

If you use this dataset in your research or applications, please cite it as:

```
@dataset{gretelai_gsm8k_synthetic,
author = {Gretel AI},
title = {Synthetically Generated Math Word Problems Dataset (gsm8k) with enhanced diversity using Gretel Navigator and meta-llama/Meta-Llama-3.1-405B},
year = {2024},
month = {9},
publisher = {Gretel},
howpublished = {https://huggingface.co/gretelai/gsm8k-synthetic-diverse-405b},
}
```

For questions, issues, or additional information, please visit the dataset repository on Hugging Face or contact Gretel AI.

# gretelai/gsm8k-synthetic-diverse-405b

本数据集是受GSM8K（https://huggingface.co/datasets/openai/gsm8k）数据集启发而合成生成的版本，完全通过**Gretel Navigator结合大语言模型（Large Language Model, LLM）meta-llama/Meta-Llama-3.1-405B**作为AI智能体（AI Agent）构建而成。该数据集包含约1500道小学年级数学应用题及分步解题过程，聚焦于年龄段、难度与领域的多样性。

## 核心特性
- 合成生成：本数据集的数学题目由Gretel Navigator生成，采用进化技术、大语言模型作为评判者（LLM-as-a-judge），并通过`sympy`库（sympy）对标注的计算过程进行验证。
- 分层测试集：包含300条测试样本，剩余样本用于训练，且按主题与难度进行分层采样。
- 多样化语境与命名：题目涵盖广泛的真实世界语境，并包含多元的姓名与族裔特征。
- 年龄段标注：每道题目均标注了适配的年龄段（2至6年级）。
- 难度分级：题目被划分为简单、中等、困难三个等级。
- 扩展领域：覆盖包括基础代数、几何在内的广泛主题。
- 分步解题过程：提供清晰的推理过程与标注化的算术运算步骤。

## 数据集统计与分布


## Gretel Navigator（所选模型：meta-llama/Meta-Llama-3.1-405B）数据集——分布分析

### 主题分布

| 主题 | 训练集样本数 | 测试集样本数 |
|:-------------------------|--------:|-------:|
| 代数（algebra） | 25 | 20 |
| 算术（arithmetic） | 31 | 25 |
| 复利（compound interest） | 26 | 21 |
| 数据解读（data interpretation） | 27 | 20 |
| 指数增长/衰减（exponential growth/decay） | 25 | 21 |
| 分数（fractions） | 29 | 24 |
| 几何（geometry） | 35 | 29 |
| 优化（optimization） | 23 | 19 |
| 百分比（percentages） | 37 | 29 |
| 多项式（polynomials） | 21 | 18 |
| 概率（probability） | 20 | 17 |
| 比例（proportions） | 30 | 24 |
| 比率（ratios） | 41 | 33 |

### 难度分布

| 难度等级 | 训练集样本数 | 测试集样本数 |
|:-------------|--------:|-------:|
| 简单（easy） | 93 | 75 |
| 困难（hard） | 82 | 67 |
| 中等（medium） | 101 | 83 |
| 极难（very hard） | 94 | 75 |

## 引用与使用说明

如果您在研究或应用中使用本数据集，请按如下格式引用：

@dataset{gretelai_gsm8k_synthetic,
author = {Gretel AI},
title = {使用Gretel Navigator与meta-llama/Meta-Llama-3.1-405B构建的多样化合成数学应用题数据集（gsm8k)},
year = {2024},
month = {9},
publisher = {Gretel},
howpublished = {https://huggingface.co/gretelai/gsm8k-synthetic-diverse-405b},
}

如需咨询、反馈或获取更多信息，请访问Hugging Face上的数据集仓库，或联系Gretel AI。