naimulislam/reasoning-math-advanced-1m

---
license: mit
task_categories:
- text-generation
- question-answering
language:
- en
tags:
- reasoning
- chain-of-thought
- synthetic
- math
- logic
- cot
size_categories:
- 1M<n<10M
pretty_name: Reasoning Math Advanced 1M
---

# 🧠 Reasoning Math Advanced 1M

## 📖 Dataset Summary
Reasoning Math Advanced 1M is a large-scale, synthetic dataset designed to enhance the reasoning capabilities of Large Language Models (LLMs). Comprising 1,000,000 unique samples, this dataset focuses on Math, Logic, and Common Sense reasoning tasks.

A unique feature of this dataset is its adaptive reasoning structure, where the presence of Chain-of-Thought (CoT) reasoning scales with difficulty. All reasoning traces are encapsulated within specific `<thinking>` tags to facilitate distinct internal monologue training.

## ⚙️ Dataset Structure
Each data point contains the following fields:

| Field | Type | Description |
| :--- | :--- | :--- |
| `serial_number` | int | Unique identifier for the sample. |
| `difficulty` | str | The complexity level: Easy, Medium, or Hard. |
| `question` | str | The input query or problem statement. |
| `reasoning` | str | The internal thought process (CoT). Wrapped in `<thinking>...</thinking>`. |
| `final_answer` | str | The concise final conclusion or solution. |

### Data Instance Example
```json
{
"serial_number": 4052,
"difficulty": "Hard",
"question": "Solve for x and y: 1) 3x + 2y = 12, 2) 5x - y = 7",
"reasoning": "<thinking>Step 1: Multiply Eq 2 by 2 to align y coefficients: 10x - 2y = 14.\nStep 2: Add modified Eq 2 to Eq 1: (3x + 10x) + (2y - 2y) = 12 + 14 -> 13x = 26.\nStep 3: Solve for x: x = 2.\nStep 4: Substitute x back into Eq 2: 5(2) - y = 7 -> 10 - 7 = y -> y = 3.</thinking>",
"final_answer": "x=2, y=3"
}
```

## 🧠 Difficulty & Reasoning Logic
The dataset is engineered to teach models when to think, not just how to think. The reasoning field behavior is strictly determined by the difficulty classification:

| Difficulty | Reasoning Presence | Description |
| :--- | :--- | :--- |
| **Easy** | 0% (Empty) | Direct Q&A. The model learns to answer simple queries immediately without over-thinking. |
| **Medium** | 50% | Mixed behavior. The model learns that intermediate difficulty sometimes requires thought, sometimes does not. |
| **Hard** | 100% | Full CoT. The reasoning field is always populated and wrapped in `<thinking>` tags. |

## 💻 How to Use
You can load this dataset directly using the Hugging Face datasets library:

```python
from datasets import load_dataset

# Replace with your actual repo name
dataset = load_dataset("naimulislam/reasoning-math-advanced-1m")

# Inspect a sample
print(dataset['train'][0])
```

## Training Prompt Format
To utilize the `<thinking>` tags effectively during fine-tuning, we recommend a prompt format that encourages the model to generate the opening tag.

**Input Template:**
```text
Question: {question}
Answer:
```

**Target Output (Hard):**
```text
<thinking>
...reasoning steps...
</thinking>
{final_answer}
```

## 🛠️ Dataset Creation
This dataset was synthetically generated using a specialized logic engine that creates diverse problem sets across:
* **Linear Algebra** (Systems of equations)
* **Polynomial Expansion** (FOIL method)
* **Logic Puzzles** (Transitive properties, Truth tables)
* **Arithmetic Sequences**
* **Probability Theory**

## 📜 License
This dataset is released under the MIT License.

## 🤝 Citation
If you use this dataset in your research, please credit:
```bibtex
@dataset{massive_reasoning_1m,
author = Naimul Islam Nahid,
title = Reasoning Math Advanced 1M,
year = 2025,
publisher = Hugging Face,
journal = naimulislam/reasoning-math-advanced-1m,
}
```

---
license: MIT许可证
task_categories:
- 文本生成
- 问答
language:
- 英语
tags:
- 推理
- 思维链（Chain-of-Thought，CoT）
- 合成
- 数学
- 逻辑
- CoT
size_categories:
- 100万<样本数<1000万
pretty_name: Reasoning Math Advanced 1M
---

## 🧠 推理数学进阶1M

## 📖 数据集概述
推理数学进阶1M是一款大规模合成数据集，旨在提升大语言模型（Large Language Model，LLM）的推理能力。该数据集包含100万个独特样本，专注于数学、逻辑与常识推理任务。

本数据集的独特之处在于其自适应推理结构：思维链（Chain-of-Thought，CoT）推理的出现比例随样本难度动态调整。所有推理轨迹均被包裹在专用的`<thinking>`标签中，以便开展差异化的内部独白训练。

## ⚙️ 数据集结构
每个数据点包含以下字段：

| 字段名 | 数据类型 | 字段说明 |
| :--- | :--- | :--- |
| `serial_number` | int | 样本唯一标识符。 |
| `difficulty` | str | 复杂度等级，分为简单（Easy）、中等（Medium）与困难（Hard）三级。 |
| `question` | str | 输入查询或问题描述。 |
| `reasoning` | str | 内部思维过程（即思维链推理），被包裹在`<thinking>...</thinking>`标签内。 |
| `final_answer` | str | 简洁的最终结论或解决方案。 |

### 数据实例示例
json
{
"serial_number": 4052,
"difficulty": "Hard",
"question": "Solve for x and y: 1) 3x + 2y = 12, 2) 5x - y = 7",
"reasoning": "<thinking>Step 1: Multiply Eq 2 by 2 to align y coefficients: 10x - 2y = 14.
Step 2: Add modified Eq 2 to Eq 1: (3x + 10x) + (2y - 2y) = 12 + 14 -> 13x = 26.
Step 3: Solve for x: x = 2.
Step 4: Substitute x back into Eq 2: 5(2) - y = 7 -> 10 - 7 = y -> y = 3.</thinking>",
"final_answer": "x=2, y=3"
}

## 🧠 难度与推理逻辑
本数据集的设计目标是教会模型“何时进行推理”，而非仅掌握“如何推理”。推理字段的内容严格由样本的难度等级决定：

| 难度等级 | 推理内容占比 | 字段说明 |
| :--- | :--- | :--- |
| **简单（Easy）** | 0%（空内容） | 直接问答模式，模型可无需过度思考即可直接回答简单查询。 |
| **中等（Medium）** | 50% | 混合模式，模型将学习到中等难度的问题有时需要推理，有时则无需。 |
| **困难（Hard）** | 100% | 完整思维链模式，推理字段始终包含被`<thinking>`标签包裹的完整推理过程。 |

## 💻 使用方法
您可直接通过Hugging Face数据集库加载该数据集：

python
from datasets import load_dataset

# Replace with your actual repo name
dataset = load_dataset("naimulislam/reasoning-math-advanced-1m")

# Inspect a sample
print(dataset['train'][0])

## 训练提示模板
为在微调阶段有效利用`<thinking>`标签，我们推荐采用可引导模型生成该起始标签的提示模板。

**输入模板：**
text
Question: {question}
Answer:

**目标输出（困难样本）：**
text
<thinking>
...reasoning steps...
</thinking>
{final_answer}

## 🛠️ 数据集构建
本数据集通过专用逻辑引擎合成生成，涵盖以下多样题型：
* **线性代数（Linear Algebra）**（方程组求解）
* **多项式展开（Polynomial Expansion）**（FOIL法则）
* **逻辑谜题（Logic Puzzles）**（传递性属性、真值表）
* **算术序列（Arithmetic Sequences）**
* **概率论（Probability Theory）**

## 📜 许可证
本数据集采用MIT许可证发布。

## 🤝 引用格式
若您在研究中使用该数据集，请引用以下文献：
bibtex
@dataset{massive_reasoning_1m,
author = Naimul Islam Nahid,
title = Reasoning Math Advanced 1M,
year = 2025,
publisher = Hugging Face,
journal = naimulislam/reasoning-math-advanced-1m,
}