pfnet/amb-hmeg

AmbHMEG: Ambiguous Handwritten Mathematical Expression Dataset

This repository provides a dataset of ambiguous handwritten mathematical expressions generated by AmbHMEG, a model for rendering LaTeX expressions as visually ambiguous math images. It also includes the pretrained AmbHMEG model used for dataset generation.

• GitHub: https://github.com/pfnet-research/AmbHMEG

Contents

The resources are organized in the order of the data generation pipeline.

Training Dataset

• mathwriting_with_graph.tar.zst

A preprocessed version of the MathWriting dataset with graph annotations used for training the AmbHMEG model.

Pretrained Model

• gryphgen_graph_sd_mathwriting_epoch_50.pth

A model trained on the MathWriting dataset to generate handwritten mathematical expressions, including ambiguous variations.

Generated Dataset

• mathwriting_amb.tar.zst

A dataset of ambiguously generated handwritten mathematical expressions produced by AmbHMEG.

Structure

mathwriting_amb/
  basic/
    test/
    valid/
  layout/
    test/
    valid/
  symbol/
    test/
    valid/

Subsets

basic

Standard single-conditioned generated dataset.

layout

Dual-conditioned dataset:

• original expression
• expression with superscripts and subscripts removed

symbol

Dual-conditioned dataset:

• original expression
• expression where symbols are replaced with visually similar alternatives

Replacement Rules Used in Symbol Editing

pairs = [
    ("0", "6"),
    ("0", "8"),
    ("1", "7"),
    ("1", "9"),
    ("2", "7"),
    ("3", "8"),
    ("5", "6"),
    ("5", "8"),
    ("0", "O"),
    ("0", "o"),
    ("1", "l"),
    ("1", "I"),
    ("2", "z"),
    ("2", "Z"),
    ("5", "S"),
    ("6", "b"),
    ("8", "B"),
    ("9", "g"),
    ("t", "+"),
    ("c", "e"),
    ("u", "v"),
    ("v", "r"),
    ("m", "n"),
    ("a", "d"),
    ("i", "j"),
    ("x", r"\times"),
    ("O", "Q"),
    ("I", "J"),
    ("v", r"\nu"),
    ("o", r"\omicron"),
    ("p", r"\rho"),
    ("n", r"\eta"),
    ("u", r"\mu"),
    ("a", r"\alpha"),
    ("y", r"\gamma"),
    ("2", r"\zeta"),
    ("2", r"\gamma"),
    ("x", r"\chi"),
    ("w", r"\omega"),
    ("e", r"\epsilon"),
    (r"\epsilon", r"\in"),
    (r"\phi", r"\varphi"),
    (r"\theta", r"\vartheta"),
    (r"\pi", r"\varpi"),
    ("k", r"\kappa"),
    (r"\sigma", "o"),
    ("r", r"\gamma"),
    ("z", r"\xi"),
    (r"\beta", "B"),
    ("-", r"\sim"),
    (r"\cdot", "."),
    ("1", "|"),
    ("|", "l"),
    (r"\sum", "E"),
    (r"\prod", r"\Pi"),
    (r"\partial", "d"),
    (r"\infty", "8"),
    (r"\subset", "c"),
    (r"\in", r"\epsilon"),
    (r"\subseteq", r"\subset"),
    (r"\approx", r"\sim"),
    (r"\equiv", "="),
    ("0", r"\emptyset"),
    (r"\emptyset", r"\phi"),
    (r"\ell", "1"),
    ("C", "c"),
    ("I", "l"),
    ("I", "i"),
    ("K", "k"),
    ("M", "m"),
    ("N", "n"),
    ("O", "o"),
    ("P", "p"),
    ("S", "s"),
    ("U", "u"),
    ("V", "v"),
    ("W", "w"),
    ("X", "x"),
    ("Y", "y"),
    ("Z", "z"),
    ("I", "j"),
    ("L", "l"),
    ("Q", "q"),
    ("R", "r"),
    (r"\Gamma", r"\gamma"),
    (r"\Delta", r"\delta"),
    (r"\Theta", r"\theta"),
    (r"\Lambda", r"\lambda"),
    (r"\Xi", r"\xi"),
    (r"\Pi", r"\pi"),
    (r"\Sigma", r"\sigma"),
    (r"\Phi", r"\phi"),
    (r"\Psi", r"\psi"),
    (r"\Omega", r"\omega"),
    (r"\Sigma", "E"),
    (r"\Pi", r"\prod"),
]

Notes

This dataset contains data derived from and includes original MathWriting samples. It is subject to the terms of the MathWriting dataset license (CC BY-NC-SA 4.0).

Data Format

Each sample consists of an image and a corresponding label file.

• Image: <id>.png
• Label: <id>.pkl (JSON-serializable structure)

Usage

Download and Extract

tar --zstd -xvf *.tar.zst

Training and Generation

Refer to the official repository:

https://github.com/pfnet-research/AmbHMEG

License

Code and Model

• Licensed under the MIT License

The model is trained on the MathWriting dataset, and its use and outputs may be subject to the dataset license.

Dataset

• Licensed under CC BY-NC-SA 4.0
• MathWriting Dataset https://github.com/google-research/google-research/tree/master/mathwriting

Usage Restrictions

• Commercial use is not allowed
• Derivative works must be shared under CC BY-NC-SA 4.0
• Attribution to the original MathWriting authors is required

Acknowledgements

We thank the authors of the MathWriting dataset for providing this resource.