Datasets:
Tasks:
Text Generation
Modalities:
Text
Formats:
json
Languages:
English
Size:
10M - 100M
ArXiv:
Tags:
math
License:
Commit ·
2da6a6b
0
Parent(s):
Duplicate from tokyotech-llm/swallow-math-v2
Browse filesCo-authored-by: Kazuki Fujii <kazukifujii@users.noreply.huggingface.co>
This view is limited to 50 files because it contains too many changes. See raw diff
- .gitattributes +938 -0
- README.md +232 -0
- rewriting-method.png +3 -0
- stage1-length-filter/train-00000-of-00128.jsonl +3 -0
- stage1-length-filter/train-00001-of-00128.jsonl +3 -0
- stage1-length-filter/train-00002-of-00128.jsonl +3 -0
- stage1-length-filter/train-00003-of-00128.jsonl +3 -0
- stage1-length-filter/train-00004-of-00128.jsonl +3 -0
- stage1-length-filter/train-00005-of-00128.jsonl +3 -0
- stage1-length-filter/train-00006-of-00128.jsonl +3 -0
- stage1-length-filter/train-00007-of-00128.jsonl +3 -0
- stage1-length-filter/train-00008-of-00128.jsonl +3 -0
- stage1-length-filter/train-00009-of-00128.jsonl +3 -0
- stage1-length-filter/train-00010-of-00128.jsonl +3 -0
- stage1-length-filter/train-00011-of-00128.jsonl +3 -0
- stage1-length-filter/train-00012-of-00128.jsonl +3 -0
- stage1-length-filter/train-00013-of-00128.jsonl +3 -0
- stage1-length-filter/train-00014-of-00128.jsonl +3 -0
- stage1-length-filter/train-00015-of-00128.jsonl +3 -0
- stage1-length-filter/train-00016-of-00128.jsonl +3 -0
- stage1-length-filter/train-00017-of-00128.jsonl +3 -0
- stage1-length-filter/train-00018-of-00128.jsonl +3 -0
- stage1-length-filter/train-00019-of-00128.jsonl +3 -0
- stage1-length-filter/train-00020-of-00128.jsonl +3 -0
- stage1-length-filter/train-00021-of-00128.jsonl +3 -0
- stage1-length-filter/train-00022-of-00128.jsonl +3 -0
- stage1-length-filter/train-00023-of-00128.jsonl +3 -0
- stage1-length-filter/train-00024-of-00128.jsonl +3 -0
- stage1-length-filter/train-00025-of-00128.jsonl +3 -0
- stage1-length-filter/train-00026-of-00128.jsonl +3 -0
- stage1-length-filter/train-00027-of-00128.jsonl +3 -0
- stage1-length-filter/train-00028-of-00128.jsonl +3 -0
- stage1-length-filter/train-00029-of-00128.jsonl +3 -0
- stage1-length-filter/train-00030-of-00128.jsonl +3 -0
- stage1-length-filter/train-00031-of-00128.jsonl +3 -0
- stage1-length-filter/train-00032-of-00128.jsonl +3 -0
- stage1-length-filter/train-00033-of-00128.jsonl +3 -0
- stage1-length-filter/train-00034-of-00128.jsonl +3 -0
- stage1-length-filter/train-00035-of-00128.jsonl +3 -0
- stage1-length-filter/train-00036-of-00128.jsonl +3 -0
- stage1-length-filter/train-00037-of-00128.jsonl +3 -0
- stage1-length-filter/train-00038-of-00128.jsonl +3 -0
- stage1-length-filter/train-00039-of-00128.jsonl +3 -0
- stage1-length-filter/train-00040-of-00128.jsonl +3 -0
- stage1-length-filter/train-00041-of-00128.jsonl +3 -0
- stage1-length-filter/train-00042-of-00128.jsonl +3 -0
- stage1-length-filter/train-00043-of-00128.jsonl +3 -0
- stage1-length-filter/train-00044-of-00128.jsonl +3 -0
- stage1-length-filter/train-00045-of-00128.jsonl +3 -0
- stage1-length-filter/train-00046-of-00128.jsonl +3 -0
.gitattributes
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|
| 1 |
+
---
|
| 2 |
+
license: apache-2.0
|
| 3 |
+
task_categories:
|
| 4 |
+
- text-generation
|
| 5 |
+
language:
|
| 6 |
+
- en
|
| 7 |
+
tags:
|
| 8 |
+
- math
|
| 9 |
+
pretty_name: swallowmath2
|
| 10 |
+
size_categories:
|
| 11 |
+
- 10M<n<100M
|
| 12 |
+
modalities:
|
| 13 |
+
- Text
|
| 14 |
+
formats:
|
| 15 |
+
- json
|
| 16 |
+
configs:
|
| 17 |
+
- config_name: swallow-math-v2-qa
|
| 18 |
+
data_files:
|
| 19 |
+
- split: train
|
| 20 |
+
path: stage3-qa/train*
|
| 21 |
+
- config_name: swallow-math-v2-textbook
|
| 22 |
+
data_files:
|
| 23 |
+
- split: train
|
| 24 |
+
path: stage3-textbook/train*
|
| 25 |
+
---
|
| 26 |
+
|
| 27 |
+
# SwallowMath-v2
|
| 28 |
+
|
| 29 |
+
<img src="https://huggingface.co/datasets/tokyotech-llm/swallow-math/resolve/main/figures/swallow-code-math-log.png" alt="SwallowMath-v2 Icon" width="500">
|
| 30 |
+
|
| 31 |
+
### Resources
|
| 32 |
+
|
| 33 |
+
- 📑 **arXiv**: Read our paper for detailed methodology at [arXiv:2505.02881](https://arxiv.org/abs/2505.02881).
|
| 34 |
+
- 🤗 **Sister Dataset**: Discover [SwallowCode2](https://huggingface.co/datasets/tokyotech-llm/swallow-code-v2), our companion dataset for code generation.
|
| 35 |
+
|
| 36 |
+
## 🧮 What is it?
|
| 37 |
+
|
| 38 |
+
[SwallowMath-v2](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2) is a large-scale mathematical dataset containing **32 billion tokens**, developed as the successor to [SwallowMath-v1](https://huggingface.co/datasets/tokyotech-llm/swallow-math).
|
| 39 |
+
Building on the success of v1, this release aims to construct a **larger-scale and more permissively licensed** corpus to support open and reproducible research on mathematical reasoning for large language models (LLMs).
|
| 40 |
+
As in our previous dataset SwallowMath-v1, SwallowMath-v2 employs an **LLM-driven rewriting approach**—removing boilerplate, restoring missing context, and reformatting solutions into clear, step-by-step explanations.
|
| 41 |
+
Additionally, we explored multiple rewriting styles and adopted the two most effective ones—Textbook and Q&A—in the final synthesis stage, yielding higher consistency and reasoning quality.
|
| 42 |
+
|
| 43 |
+
Empirical evaluations demonstrate that models trained with SwallowMath-v2 achieve stronger performance on **GSM-Plus** and **BBH**, surpassing other open mathematical datasets.<br>
|
| 44 |
+
<sub>† On the MATH benchmark, the SwallowMath-v2 (Q&A) variant performs slightly below Nemotron-CC-Math-v1-4+.
|
| 45 |
+
However, SwallowMath-v2 offers a significantly more permissive Apache-2.0 license, providing clearer usage rights for both research and commercial applications.</sub>
|
| 46 |
+
|
| 47 |
+
<img src="./swallow_math-v2.jpg" width="800"/>
|
| 48 |
+
|
| 49 |
+
## 📊 Dataset Comparison
|
| 50 |
+
|
| 51 |
+
| Dataset | Token Count (Llama-3 Tokenizer) | License |
|
| 52 |
+
| :-------------------------------- | :-----------------------------: | :--------------------------------- |
|
| 53 |
+
| **[Nemotron-CC-Math-v1 4+](https://huggingface.co/datasets/nvidia/Nemotron-CC-Math-v1)** | 51.4 B tokens | [NVIDIA Open Data License Agreement](https://huggingface.co/datasets/nvidia/Nemotron-Pretraining-Dataset-sample/raw/main/LICENSE.md) |
|
| 54 |
+
| [MegaMathWeb-Pro](https://huggingface.co/datasets/LLM360/MegaMath) | 13.0B tokens | Open Data Commons License Attribution family |
|
| 55 |
+
| **SwallowMath-v1 (our previous)** | 3.6 B tokens | Llama-3.3 Community License |
|
| 56 |
+
| **SwallowMath-v2 (this work)** | 32.0 B tokens | **Apache 2.0 License** |
|
| 57 |
+
|
| 58 |
+
|
| 59 |
+
## 📦 What is being released?
|
| 60 |
+
|
| 61 |
+
**SwallowMath-v2**: Approximately **32** billion tokens, derived from FineMath-3+, containing rewritten mathematical content with concise, step-by-step explanations formatted in Markdown and LaTeX.
|
| 62 |
+
All data is publicly available under the **Apache 2.0** license.
|
| 63 |
+
|
| 64 |
+
### 🗂️ Dataset structure
|
| 65 |
+
|
| 66 |
+
- [stage1-length-filter](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2/tree/main/stage1-length-filter): Filtered subset of finemath-3+ by text length
|
| 67 |
+
- [stage2-extract-math-text](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2/tree/main/stage2-extract-math-text): Refined version with LLM-based extraction of stage-1
|
| 68 |
+
- [stage3-ablations](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2/tree/main/stage3-ablations): Datasets for rewriting-style ablation experiments
|
| 69 |
+
- [stage3-qa](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2/tree/main/stage3-qa): SwallowMath-v2 (Q&A) dataset (12,635,739 samples, **13.6B** tokens)
|
| 70 |
+
- [stage3-textbook](https://huggingface.co/datasets/tokyotech-llm/swallow-math-v2/tree/main/stage3-textbook): SwallowMath-v2 (textbook) (13,302,336 samples, **18.3B** tokens)
|
| 71 |
+
|
| 72 |
+
## 🧩 Dataset curation
|
| 73 |
+
|
| 74 |
+
SwallowMath-v2 builds on FineMath-3+, a high-quality subset of mathematical content filtered from CommonCrawl.
|
| 75 |
+
We enhance it through an **LLM-driven rewriting pipeline** tailored for mathematical reasoning, addressing key limitations such as boilerplate, missing context, and verbose explanations.
|
| 76 |
+
|
| 77 |
+
### ⚙️ Rewriting Pipeline
|
| 78 |
+
Using [Qwen3-235B-A22B-2507-Instruct](https://huggingface.co/Qwen/Qwen3-235B-A22B-Instruct-2507), the pipeline proceeded as follows:
|
| 79 |
+
|
| 80 |
+
1. **Stage 1 - Length Filtering**: Remove over-long samples from FineMath-3+ to saty with model context limits.
|
| 81 |
+
2. **Stage 2 - Math Extraction**: Extract mathmatical text segments from stage1 using LLM(= [Qwen3-32B](https://huggingface.co/Qwen/Qwen3-32B))
|
| 82 |
+
3. **Stage 3 - Rewriting**: Rewrite Stage 2 samples into Q&A and textbook styles.
|
| 83 |
+
|
| 84 |
+
### 🧪 Rewriting style ablation experiments
|
| 85 |
+
|
| 86 |
+
We designed and compared five rewriting styles:
|
| 87 |
+
1. Textbook — Structured presentation of definitions, worked examples, and solution procedures
|
| 88 |
+
2. Q&A — Single/Multi-turn question–answer format
|
| 89 |
+
3. Planning — Explicit plan description followed by step-wise reasoning
|
| 90 |
+
4. Socratic — Teacher–student dialogue, solving the problem interactively
|
| 91 |
+
5. Multiple Solution — Generation of multiple candidate solutions with justification for the optimal one
|
| 92 |
+
|
| 93 |
+
|
| 94 |
+
As shown in the figure below, the **Q&A** style yields the highest performance on *GSM8K* and *GSM-Plus*, the **Textbook** style performs best on BBH, and both are effective on MATH.
|
| 95 |
+
These findings motivated the adoption of the Textbook and Q&A styles in the final SwallowMath-v2 dataset.
|
| 96 |
+
<img src="rewriting-method.png" width="800"/>
|
| 97 |
+
|
| 98 |
+
### Q&A style example
|
| 99 |
+
|
| 100 |
+
Here is an example of a Q&A-style rewritten dataset.
|
| 101 |
+
|
| 102 |
+
```json
|
| 103 |
+
**Question 1**:
|
| 104 |
+
What is the length of the line segment connecting the points $(-2, 4)$ and $(-1, 1)$?
|
| 105 |
+
|
| 106 |
+
**Answer 1**:
|
| 107 |
+
The length of a line segment between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the distance formula:
|
| 108 |
+
$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
|
| 109 |
+
For the points $(-2, 4)$ and $(-1, 1)$:
|
| 110 |
+
$$\sqrt{(-1 - (-2))^2 + (1 - 4)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}$$
|
| 111 |
+
|
| 112 |
+
**Code Implementation 1**:
|
| 113 |
+
```python
|
| 114 |
+
import math
|
| 115 |
+
|
| 116 |
+
# Calculate distance between (-2, 4) and (-1, 1)
|
| 117 |
+
x1, y1 = -2, 4
|
| 118 |
+
x2, y2 = -1, 1
|
| 119 |
+
|
| 120 |
+
distance = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
|
| 121 |
+
print(f"Distance = {distance:.4f} (exact value: √10 ≈ {math.sqrt(10):.4f})")
|
| 122 |
+
# Output: Distance = 3.1623 (exact value: √10 ≈ 3.1623)
|
| 123 |
+
```
|
| 124 |
+
|
| 125 |
+
### textbook style example
|
| 126 |
+
|
| 127 |
+
Here is an example of a textbook-style rewritten dataset.
|
| 128 |
+
|
| 129 |
+
```json
|
| 130 |
+
## Background:
|
| 131 |
+
Arc length is a fundamental concept in calculus that measures the distance along a curved path. Unlike straight-line distances (which use the Pythagorean theorem), curved paths require integration because their slope continuously changes. The formula for arc length derives from approximating a curve with infinitesimally small straight-line segments and summing their lengths—a technique formalized in the 17th century with the development of calculus. This concept is essential in physics (e.g., calculating the path of a moving object), engineering (e.g., designing roads or bridges), and computer graphics (e.g., rendering smooth curves).
|
| 132 |
+
|
| 133 |
+
## Detailed Explanation:
|
| 134 |
+
The text explains the mathematical framework for computing the arc length of a curve defined by $y = f(x)$, using both general theory and a specific example. Below is a breakdown of each component, preserving all original formulas and data.
|
| 135 |
+
|
| 136 |
+
### General Formula
|
| 137 |
+
The arc length of a curve $y = f(x)$ is given by the integral:
|
| 138 |
+
$$
|
| 139 |
+
\int \sqrt{1 + \left(f'(x)\right)^2} \, dx
|
| 140 |
+
$$
|
| 141 |
+
This formula arises from the Pythagorean theorem applied to infinitesimal segments. For a tiny segment of the curve, the horizontal change is $dx$ and the vertical change is $dy = f'(x) \, dx$. The length of this segment is $\sqrt{(dx)^2 + (dy)^2} = \sqrt{(dx)^2 + (f'(x) \, dx)^2} = \sqrt{1 + (f'(x))^2} \, dx$. Summing these infinitesimal lengths via integration gives the total arc length.
|
| 142 |
+
|
| 143 |
+
### Example: Parabola $y = x^2$
|
| 144 |
+
For the parabola $y = x^2$ between $x = -2$ and $x = 2$, the arc length is computed as:
|
| 145 |
+
$$
|
| 146 |
+
\int_{-2}^{2} \sqrt{1 + (2x)^2} \, dx = \int_{-2}^{2} \sqrt{1 + 4x^2} \, dx
|
| 147 |
+
$$
|
| 148 |
+
**Derivation**:
|
| 149 |
+
- The derivative of $y = x^2$ is $f'(x) = 2x$.
|
| 150 |
+
- Substituting into the general formula gives $\sqrt{1 + (2x)^2} = \sqrt{1 + 4x^2}$.
|
| 151 |
+
- The limits $x = -2$ to $x = 2$ define the interval of integration.
|
| 152 |
+
This integral evaluates to approximately $9.7$ (as noted later in the text), though the exact value requires trigonometric substitution or numerical methods.
|
| 153 |
+
|
| 154 |
+
### Concept Check: Line Segment Length
|
| 155 |
+
The text verifies understanding with a simpler case: the straight-line distance between $(-2, 4)$ and $(-1, 1)$. The calculation is:
|
| 156 |
+
$$
|
| 157 |
+
\sqrt{(-1 - (-2))^2 + (1 - 4)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{10}
|
| 158 |
+
$$
|
| 159 |
+
**Why this matters**:
|
| 160 |
+
- This is the discrete analog of the arc length formula. For a straight line, the derivative $f'(x)$ is constant, so the integral simplifies to the distance formula.
|
| 161 |
+
- Here, $\Delta x = 1$ and $\Delta y = -3$, matching the Pythagorean theorem $\sqrt{(\Delta x)^2 + (\Delta y)^2}$.
|
| 162 |
+
|
| 163 |
+
### Key Takeaways
|
| 164 |
+
1. **Approximation via line segments**:
|
| 165 |
+
The arc length is approximated by summing tiny line segments:
|
| 166 |
+
$$
|
| 167 |
+
\sum \sqrt{(\Delta x)^2 + (\Delta y)^2}
|
| 168 |
+
$$
|
| 169 |
+
As $\Delta x \to 0$, this sum becomes the integral $\int \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$. This is the foundation of the formula.
|
| 170 |
+
|
| 171 |
+
2. **Derivative's role**:
|
| 172 |
+
The term $\frac{dy}{dx}$ (or $f'(x)$) accounts for the curve's slope. Steeper slopes increase the integrand, reflecting longer path lengths for the same horizontal distance.
|
| 173 |
+
|
| 174 |
+
3. **Specific application to $y = x^2$**:
|
| 175 |
+
For $y = x^2$, $\frac{dy}{dx} = 2x$, so the integrand becomes $\sqrt{1 + (2x)^2} = \sqrt{1 + 4x^2}$. This shows how the derivative directly shapes the integral.
|
| 176 |
+
|
| 177 |
+
### Units of Arc Length
|
| 178 |
+
The text clarifies that **the unit of arc length matches the unit of the coordinate axes**. For example:
|
| 179 |
+
- If $x$ and $y$ are measured in inches, the arc length $\int_{-2}^{2} \sqrt{1 + 4x^2} \, dx \approx 9.7$ is also in inches.
|
| 180 |
+
- This holds because both $dx$ and $dy$ inherit the axis units, and the square root operation preserves dimensional consistency.
|
| 181 |
+
This principle ensures physical meaningfulness in real-world applications (e.g., calculating the length of a wire bent into a parabolic shape).
|
| 182 |
+
```
|
| 183 |
+
|
| 184 |
+
### 📈 Rewriting model scalability
|
| 185 |
+
|
| 186 |
+
We investigated whether **the scale of the rewriting model** influences the quality of the generated data.
|
| 187 |
+
Using identical prompts, we compared generations from **Qwen3-30B-A3B** and **Qwen3-235B-A22B**, observing the effect of model size on output quality.
|
| 188 |
+
Results (see figure below) indicate no significant improvement in downstream performance with larger rewriting models—suggesting that dataset quality is primarily governed by prompt design and rewriting style rather than model scale.<br>
|
| 189 |
+
<sub>† SwallowMath-v1, our previous dataset, was generated from FineMath-4+ using Llama-3.3-70B-Instruct.
|
| 190 |
+
It is therefore **not directly related** to the model scalability experiments presented here.
|
| 191 |
+
The dataset is relatively small—about 3.6 billion tokens, roughly one-tenth the size of SwallowMath-v2—and is shown only for reference.</sub>
|
| 192 |
+
|
| 193 |
+
<img src="swallow_math-v2-model-size.jpg" size="800"/>
|
| 194 |
+
|
| 195 |
+
## 📝 Considerations for Using the Data
|
| 196 |
+
|
| 197 |
+
### Social Impact of the Dataset
|
| 198 |
+
|
| 199 |
+
SwallowMath-v2 aims to democratize access to high-quality mathematical training data, fostering advancements in LLM mathematical reasoning.
|
| 200 |
+
By releasing an openly licensed dataset, we enhance transparency in the dataset improvement pipeline, and lower barriers for training mathematically proficient models.
|
| 201 |
+
|
| 202 |
+
### Discussion of Biases
|
| 203 |
+
The dataset may inherit biases from FineMath-3+, including:
|
| 204 |
+
|
| 205 |
+
- Focus on English-language content.
|
| 206 |
+
- Potential over-representation of certain problem types (e.g., algebra vs. geometry).
|
| 207 |
+
|
| 208 |
+
## ⚖️ Licensing Information
|
| 209 |
+
|
| 210 |
+
SwallowMath-v2 is released under the **Apache-2.0** license.
|
| 211 |
+
|
| 212 |
+
## 👥 Contributors
|
| 213 |
+
|
| 214 |
+
The dataset was primarily developed by the following contributors:
|
| 215 |
+
|
| 216 |
+
- [Kazuki Fujii](https://www.linkedin.com/in/kazuki-fujii/) — Designed the experiments, implemented the data pipeline, and conducted the experiments.
|
| 217 |
+
- [Yukito Tajima](https://www.linkedin.com/in/yukito-tajima-51bbb2299/) — Implemented the data pipeline and optimized the inference pipeline. (vLLM, TensorRT-LLM)
|
| 218 |
+
- [Masaki Kawamura](https://www.linkedin.com/in/masaki-kawamura-0806a7361/) — Co-designed the experiments, evaluated the models, and performed visualization and analysis.
|
| 219 |
+
|
| 220 |
+
## 📖 Citation
|
| 221 |
+
|
| 222 |
+
```
|
| 223 |
+
@misc{fujii2025rewritingpretrainingdataboosts,
|
| 224 |
+
title={Rewriting Pre-Training Data Boosts LLM Performance in Math and Code},
|
| 225 |
+
author={Kazuki Fujii and Yukito Tajima and Sakae Mizuki and Hinari Shimada and Taihei Shiotani and Koshiro Saito and Masanari Ohi and Masaki Kawamura and Taishi Nakamura and Takumi Okamoto and Shigeki Ishida and Kakeru Hattori and Youmi Ma and Hiroya Takamura and Rio Yokota and Naoaki Okazaki},
|
| 226 |
+
year={2025},
|
| 227 |
+
eprint={2505.02881},
|
| 228 |
+
archivePrefix={arXiv},
|
| 229 |
+
primaryClass={cs.LG},
|
| 230 |
+
url={https://arxiv.org/abs/2505.02881},
|
| 231 |
+
}
|
| 232 |
+
```
|
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