---
license: cc-by-4.0
language:
- zh
- en
tags:
- multimodal-mathematical-reasoning
- geometry
- tikz
- latex
- image-to-tikz
- benchmark
size_categories:
- 10K<n<100K
task_categories:
- image-to-text
- visual-question-answering
- text-generation
pretty_name: TriGeoBench
---

# TriGeoBench

TriGeoBench is a geometry-centric multimodal mathematics benchmark designed for evaluating mathematical reasoning with visual diagrams and image-to-TikZ generation. The dataset contains mathematical problems, solutions, diagram images, and corresponding TikZ annotations.

This repository is anonymized for peer review. Author and institution information will be added upon acceptance.

## Dataset Files

The dataset contains four Parquet files:

```text
TriGeoBench
├── README.md
├── image2tikz/
│   ├── train.parquet
│   └── test.parquet
└── question/
    ├── train.parquet
    └── test.parquet
````

The dataset supports two tasks:

1. **Image-to-TikZ generation**: generating TikZ code from a geometric diagram image.
2. **Multimodal mathematical reasoning**: solving math problems with textual questions, solutions, and associated figures.

## Image-to-TikZ Data

Files:

```text
image2tikz/train.parquet
image2tikz/test.parquet
```

Each row corresponds to one diagram image and its ground-truth TikZ code.

### Fields

| Field        | Description                                                  |
| ------------ | ------------------------------------------------------------ |
| `key`        | Unique figure identifier. It is composed of `<problem_id>_<position>_<figure_index>`, where `position` indicates whether the figure appears in the question or the solution. This key can be linked to the corresponding problem in the question-level data. |
| `image`      | Base64-encoded image.                                        |
| `latex_gt`   | Ground-truth TikZ code corresponding to the image.           |
| `difficulty` | Figure complexity level. Possible values are `容易`, `中等`, and `困难`. |

## Question-Level Data

Files:

```text
question/train.parquet
question/test.parquet
```

Each row corresponds to one mathematical problem, including the problem text, solution, metadata, and associated figures.

### Fields

| Field             | Description                                                  |
| ----------------- | ------------------------------------------------------------ |
| `sample_id`       | Unique problem identifier. It can be linked to the `key` field in the image-to-TikZ data. |
| `difficulty`      | Problem difficulty level. Possible values are `容易`, `中等`, and `困难`. |
| `question_type`   | Problem type. Possible values include `选择题`, `填空题`, `解答题`, and `证明题`. |
| `knowledge_point` | Main mathematical knowledge area. Possible values include `向量`, `函数`, `平面几何`, `立体几何`, and `解析几何`. |
| `question`        | Problem statement in LaTeX format.                           |
| `solution`        | Solution or answer in LaTeX format.                          |
| `q_figX`          | Base64-encoded image of the X-th figure appearing in the question. |
| `q_figX_latex_gt` | Ground-truth TikZ code of the X-th question figure.          |
| `s_figY`          | Base64-encoded image of the Y-th figure appearing in the solution. |
| `s_figY_latex_gt` | Ground-truth TikZ code of the Y-th solution figure.          |

Here, `X` and `Y` denote figure indices. A problem may contain different numbers of question-side and solution-side figures.

## Data Splits

The dataset is split into training and test sets for both tasks:

| Task                   | Train File                 | Test File                 |
| ---------------------- | -------------------------- | ------------------------- |
| Image-to-TikZ          | `image2tikz_train.parquet` | `image2tikz_test.parquet` |
| Mathematical Reasoning | `question_train.parquet`   | `question_test.parquet`   |

## Loading the Dataset

The Parquet files can be loaded with `pandas`:

```python
import pandas as pd

image2tikz_train = pd.read_parquet("image2tikz_train.parquet")
image2tikz_test = pd.read_parquet("image2tikz_test.parquet")

question_train = pd.read_parquet("question_train.parquet")
question_test = pd.read_parquet("question_test.parquet")
```

Base64-encoded images can be decoded as follows:

```python
import base64
from io import BytesIO
from PIL import Image

def decode_base64_image(image_base64):
    image_bytes = base64.b64decode(image_base64)
    return Image.open(BytesIO(image_bytes)).convert("RGB")

img = decode_base64_image(image2tikz_train.iloc[0]["image"])
img.show()
```

## Intended Use

TriGeoBench is intended for research on:

* multimodal mathematical reasoning;
* geometry-centric visual question answering;
* image-to-TikZ generation;
* evaluating whether models can reason over precise geometric structures;
* studying the interaction between textual math problems, visual diagrams, and symbolic diagram representations.

## Limitations

The dataset focuses on geometry-centric middle- and high-school mathematics problems. The annotations include LaTeX-formatted problem texts and TikZ code for figures. Although the dataset has been processed and checked, residual annotation errors may remain.

## Anonymous Review Notice

This repository is anonymized for peer review. Please do not attempt to identify the authors during the review process.