PadishahIIIXXX/latex-ocr
Image-to-Text • Updated • 1
image imagewidth (px) 1 20.5k | text stringlengths 1 7.06k |
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n\to\infty | |
_{DD} | |
\begin{array}{rl}{\langle u|u|^{2},b_{j,1}\rangle}&{=\sum_{k,l,m}\frac{A_{k}A_{l}A_{m}}{L_{k}L_{l}L_{m}}\left\langle e^{i\Gamma_{k}+i\Gamma_{l}-i\Gamma_{m}}e^{-\frac{|y_{k}|^{2}+|y_{l}|^{2}+|y_{m}|^{2}}{2}},e^{i\Gamma_{j}}e^{-\frac{1}{2}|y_{j}|^{2}}\right\rangle}\end{array} | |
p | |
j | |
S=\textsf{Stabs}(\Pi)=\{ P_{i}\} | |
N\to\infty | |
a_{1} | |
\ddot{\mathrm{~o~}} | |
c=(m^{2}+n^{2})^{2}, | |
R | |
d_{n} | |
x | |
F_{3} | |
96\% | |
G_{F} | |
(x,y)\in\left[-10,10\right] | |
x_{0}=x^{u} | |
V(t) | |
s_{\mathrm{im}}^{2}\left(a_{1110}+a_{2001}-s_{\mathrm{im}}a_{2100}\right) | |
r<R_{\mathrm{phot}} | |
\rho | |
\overrightarrow{\xi} | |
\phi(t) | |
15.5H\times 4.5H\times 4H=6.2\times 1.8\times 1.6m^{3} | |
p_{L} | |
\sigma(r)=\frac{2E}{1+\nu}\frac{h\kappa}{4\pi r^{3}} | |
0 | |
k^{2}=k_{x}^{2}+k_{y}^{2} | |
\frac{d\rho}{dt}=-[\overline{{F}},\rho]\neq 0. | |
\leq | |
({\hat{T}}(\mathbf{x}))^{-1}\mathbf{\hat{r}}{\hat{T}}(\mathbf{x})=\mathbf{\hat{r}}+\mathbf{x}{\hat{\mathbb{I}}} | |
C_{\mathrm{G}}\approx 16\: \mathrm{\ muF/cm^{2}} | |
^* | |
i | |
{\cal Z}_{B}=Tr\; e^{-\beta\varepsilon_{\kappa}(\overline{{{\Phi}}}_{1,\kappa}\Phi_{1,\kappa}+\overline{{{\Phi}}}_{2,\kappa}\Phi_{2,\kappa})}e^{-\beta\mu(N_{1,\kappa}+N_{2,\kappa})}, | |
\begin{array}{r}{\xi\cos\theta_{\mathrm{L}}+\Delta\sin\theta_{\mathrm{L}}=\sqrt{\xi^{2}+\Delta^{2}}.}\end{array} | |
I-V | |
\mu\mathrm{m} | |
{\frac{\partial a_{k}^{s}}{\partial t}}=\frac{i\epsilon}{8k_{\perp}}\int_{\mathbb{R}^{6}}\sum_{s_{p}s_{q}}\left[s_{p}s_{q}k_{\perp}^{2}+\frac{k_{\parallel}}{pq}\left(p_{\parallel}q^{2}+q_{\parallel}p^{2}\right)\right. | |
\delta | |
\mathrm{mwnv}=\int_{-1}^{1}u_{2}(0,x_{2})dx_{2} | |
\overline{{\v x}}_{k}^{f}=\frac{1}{N_{e}}\sum_{n=1}^{N_{e}}\v x_{k}^{f,(n)} | |
G_{xx}(0,0)=g(\rho R^{2},\infty)/N | |
a_{P}a_{Q}^{\dagger}=S_{PQ}-a_{Q}^{\dagger}a_{P}, | |
\leftarrow c_{n-1}\cdot | |
\begin{array}{rl}{(\pi_{C|D}-\pi_{D|D})q_{D|D}=}&{\left[-c+w_{I}b+\frac{1-w_{I}}{k}(k-1)q_{C|C}b-\frac{1-w_{I}}{k}(k-1)q_{C|D}b\right]\left(1-\frac{k-2}{k-1}p_{C}\right)}\\ {=}&{\left(-c+w_{I}b+\frac{1-w_{I}}{k}b\right)\left(1-\frac{k-2}{k-1}p_{C}\right),}\end{array} | |
{\begin{array}{rl}{{F^{\alpha\beta}}_{;\beta}}&{=0}\\ {F_{[\alpha\beta;\gamma]}}&{={\frac{1}{3}}\left(F_{\alpha\beta;\gamma}+F_{\beta\gamma;\alpha}+F_{\gamma\alpha;\beta}\right)={\frac{1}{3}}\left(F_{\alpha\beta,\gamma}+F_{\beta\gamma,\alpha}+F_{\gamma\alpha,\beta}\right)=0.}\end{array}} | |
\begin{array}{rlr}{\sum_{i}P_{i,\nu}dQ_{i,\nu}}&{{}=}&{\frac{1}{2}\left[(P_{k}-P_{-k})d(Q_{k}-Q_{-k})-(Q_{k}+Q_{-k})d(P_{k}+P_{-k})\right]=}\end{array} | |
\varphi_{1} | |
R_{1} | |
F=\frac{v_{x}^{2}+v_{y}^{2}}{2g}. | |
\pm 2\% | |
F_{r{\tilde{\theta}}}^{1}=-\, \frac{1}{2\lambda}\, {\dot{a}}~~,~~F_{r{\tilde{\varphi}}}^{2}=\frac{1}{2\lambda}\, {\sin{\widetilde{\theta}}\, {\dot{a}}}~~,~~F_{{\tilde{\theta}}{\tilde{\varphi}}}^{3}=\frac{1}{2\lambda}\, {\sin{\widetilde{\theta}}}\left(1-a^{2}\right)~~. | |
s\gg\lambda | |
\operatorname{archavercos}(y)=2\operatorname{arccos}\left({\sqrt{y}}\right)=\operatorname{arccos}\left(2y-1\right) | |
x={\frac{-2t^{2}-1}{-t^{2}-1}}\qquad\ dx={\frac{2t}{(-t^{2}-1)^{2}}}\, \ dt, | |
g({\mathsf{d}})=0 | |
T^{2} | |
\sin(\theta)=-X_{3} | |
(\mathfrak{n}^{+}\otimes\mathbb C[t])v_{\pmb{\xi}}=0,\quad\, (h_{\alpha_{i}}\otimes t^{s})v_{\pmb{\xi}}=\lambda(h_{\alpha_{i}})\delta_{s,0}v_{\pmb{\xi}},\quad\, (x_{\alpha_{i}}^{-}\otimes 1)^{\lambda(h_{\alpha_{i}})+1}v_{\pmb{\xi}}=0,\quad\, \mathrm{for}\, i=1,2, | |
\sigma^{\perp}=61.2\mathrm{~m~} | |
> | |
^1 | |
\frac{\partial\langle\hat{\mathcal{L}}\rangle}{\partial\mu}=(\langle\hat{A}\rangle-a)\equiv 0, | |
C_{1}=a(I-P^{T})^{\dag} | |
\Phi={\left\{ \begin{array}{ll}{\tan{\frac{\pi\alpha}{2}}}&{{\mathrm{if~}}\alpha\neq 1}\\ {-{\frac{2}{\pi}}\log|c\, t|}&{{\mathrm{if~}}\alpha=1}\end{array}\right.} | |
2n_{\mathrm{ink}}h\cos{\theta_{i}}=m\lambda, | |
\mathrm{Nu}^{*,(drop)}<-2 | |
s | |
\begin{array}{r}{4\pi+\frac{\gamma\varepsilon^{3}}{2}(1+\varepsilon+\varepsilon^{2})-\left(\frac{2\pi{h^{\ast}}^{4}}{\varepsilon^{2}}-\frac{\gamma{h^{\ast}}^{2}\varepsilon^{2}}{2}\right)\log{(h^{\ast})}+\ensuremath{\operatorname{O}\left(\gamma\varepsilon^{6},(\gamma+1){h^{\ast}}^{2}\varepsilon^{2},\frac{{h^{\ast}}^{4}}... | |
v | |
a_{\mu}^{\mathrm{SUSY}}={\frac{\tan\beta}{48\pi}}{\frac{m_{\mu}^{2}}{M_{\mathrm{SUSY}}^{2}}}(5\alpha_{2}+\alpha_{1}) | |
\tilde{\Omega} | |
E_{c} | |
\Gamma(p)\rightarrow\Gamma(p^{\prime})=\Lambda\Gamma(p)\Lambda^{-1} | |
+{\frac{1}{2m^{2}}}\Pi_{\psi}^{2}+A_{0}\Pi_{\psi}+{\frac{m^{2}}{2}}((\partial_{i}\psi)^{2}+2A_{i}\partial_{i}\psi). | |
y_{0}=|H(\mathrm{j}\omega)| | |
\phi=0 | |
\begin{array}{rlr}{V(x,t)}&{=}&{\frac{1}{|\sqrt{2\lambda}\alpha_{0}|^{2q}}\sum_{m=0}^{q}(-1)^{m+q}\frac{(2^{m}q!)^{2}}{(2m)!(q-m)!}\lambda^{q-m}x^{2m}}\\ &{}&{-\frac{(-i)^{q}}{|\sqrt{2\lambda}\alpha_{0}|^{2q}}\Big[\Big(e^{-i\tau}\alpha_{0}\sqrt{2\lambda}\Big)^{q}+\Big(e^{i\tau}\alpha_{0}^{*}\sqrt{2\lambda}\Big)^{q}\Big... | |
BW=15 | |
{\mathcal{K}}(\hat{M}_{f},\hat{M}_{b})=\mathrm{const}\; \int{\mathcal{D}}{\mathcal{F}}{\mathcal{D}}{\mathcal{B}}\exp\left\{ -{\mathcal{W_{F}}}-{\mathcal{W_{B}}}-{\mathcal{W_{FB}}}\right\} | |
\begin{array}{rlr}{E_{12}(a,c,W\rightarrow 0)}&{{}=}&{\left\{ \begin{array}{lcl}{-\frac{1}{2}\cos 2\theta}&{,}&{d=0}\\ {\frac{\pi}{4}\sin 2\theta\cos 2\theta-\cos 2\theta+\ln[|\tan\theta|^{\sin^{2}2\theta/2}]}&{,}&{d=2}\\ {-\cos 2\theta}&{,}&{d=4}\\ {-\frac{1}{2}\cos 2\theta\left[1+24(19+5\cos 4\theta)^{-1}\right]}&{,}... | |
\lambda=L/H | |
U | |
\begin{array}{rlr}&{}&{\left.\frac{\partial}{\partial b}\left\{ I(u,v)\right\} \right|_{b=0}}\\ &{=}&{-j\left[\int_{0}^{2\pi}\int_{0}^{1}e^{j[aZ_{5}(r,\theta)-2\pi\rho rcos(\phi-\theta)}rdrd\theta\right.}\\ &{}&{\times\int_{0}^{2\pi}\int_{0}^{1}Z_{4}(r,\theta)e^{-j[aZ_{5}(r,\theta)-2\pi\rho rcos(\phi-\theta)}rdrd\theta... | |
n_{g}=v_{g}/c | |
f=1,2 | |
\mathcal{W} | |
|\mathscr{W}|=-2 | |
H^{2}(\mathrm{~\boldmath~q~}^{(1)},\mathrm{~\boldmath~q~}^{(2)})=\frac{1}{2}\sum_{j}\left(\sqrt{q_{j}^{(1)}}-\sqrt{q_{j}^{(2)}}\right)^{2}, | |
\neg(A\land B) | |
\forall^{p}L:=\left\{ x\in\{ 0,1\} ^{*}\ \left|\ \left(\forall w\in\{ 0,1\} ^{\leq p(|x|)}\right)\langle x,w\rangle\in L\right.\right\} | |
\frac{dn_{i}}{dt}=\frac{\partial n_{i}}{\partial t}+\triangledown\cdot(D\triangledown n_{i})=\frac{\delta n_{i}}{\delta t}, | |
\mathcal{H}=-J\sum_{\langle ij\rangle}\pmb{\sigma}_{i}\pmb{\sigma}_{j}, | |
\ldots | |
^{\circ} | |
1\% | |
m=1 | |
u(t) |
End of preview. Expand in Data Studio
Synthetic LaTeX OCR Dataset
Overview
This dataset contains synthetically generated LaTeX formula images designed to augment training data for LaTeX OCR models. The dataset applies style enrichment techniques to existing real-world LaTeX datasets, creating diverse visual representations of mathematical formulas through PDF-rendering and font styling.
Dataset Structure
synth/
├── plain/
│ ├── train/
│ │ ├── images/
│ │ │ ├── train_0000000.png
│ │ │ ├── train_0000001.png
│ │ │ └── ...
│ │ └── metadata.jsonl
│ └── validation/
│ ├── images/
│ └── metadata.jsonl
├── styled/
│ ├── train/
│ │ ├── images/
│ │ └── metadata.jsonl
│ └── validation/
│ ├── images/
│ └── metadata.jsonl
└── README.md
Data Format
Each metadata.jsonl file contains one JSON object per line:
{"text": "x^2 + y^2 = z^2", "file_name": "images/train_0000001.png"}
{"text": "\\frac{a}{b} + \\frac{c}{d}", "file_name": "images/train_0000002.png"}
{"text": "\\int_{0}^{\\infty} e^{-x} dx", "file_name": "images/train_0000003.png"}
Fields:
text(str): LaTeX formula stringfile_name(str): Relative path to the image file
Dataset Statistics
Plain Dataset
| Split | Samples | Avg Length | Median Length | Min Length | Max Length | Std Length | P95 Length | P99 Length |
|---|---|---|---|---|---|---|---|---|
| Train | 1,143,025 | 86.1 chars | 35.0 chars | 1 chars | 7,058 chars | 142.3 chars | 341.0 chars | 651.0 chars |
| Validation | 30,461 | 136.4 chars | 60.0 chars | 1 chars | 3,257 chars | 195.1 chars | 490.0 chars | 894.0 chars |
| Total | 1,173,486 | - | - | - | - | - | - | - |
Styled Dataset
| Split | Samples | Avg Length | Median Length | Min Length | Max Length | Std Length | P95 Length | P99 Length |
|---|---|---|---|---|---|---|---|---|
| Train | 154,616 | 75.0 chars | 49.0 chars | 10 chars | 3,111 chars | 80.9 chars | 237.0 chars | 367.0 chars |
| Validation | 4,133 | 98.1 chars | 71.0 chars | 10 chars | 845 chars | 87.6 chars | 291.4 chars | 400.0 chars |
| Total | 158,749 | - | - | - | - | - | - | - |
Combined Statistics
- Total Plain Dataset: 1,173,486 samples
- Total Styled Dataset: 158,749 samples
- Grand Total: 1,332,235 samples
Dataset Constitution
This synthetic dataset is generated from the following sources:
Distribution
1. Source Datasets
UniMER-1M
- Description: Large-scale mathematical expression recognition dataset
- Source: UniMER-1M training set
- Formulas:
XXX,XXXmathematical expressions - Coverage: Diverse mathematical notation including algebra, calculus, geometry, and advanced mathematics
pix2tex Dataset
- Description: HuggingFace pix2tex LaTeX OCR dataset
- Source: Loaded automatically from HuggingFace Hub
- Splits: Training + Validation splits
- Formulas: LaTeX expressions from academic sources
- Coverage: Academic papers, textbooks, and research documents
2. Synthetic Plain Dataset
Generation Method: PDF-style rendering without font styling
- Formula Source: Combined UniMER-1M + pix2tex datasets
- Processing:
- Sanitized formulas with comprehensive space normalization
- Normalized legacy LaTeX commands (
\bf→\mathbf, etc.) - Rendered using MathJax + CairoSVG pipeline (LaTeX → SVG → PDF → PNG)
- Rasterized at 150 DPI for screenshot-style images
- RGB format with white background
- Train/Validation Split: Train from
unimer_train+pix2tex_train; Validation fromunimer_test+pix2tex_val - Usage in Training: 20% random subset used in mixed training dataset
Characteristics:
- Clean, PDF-quality rendering
- Consistent font style (default LaTeX fonts)
- Minimal visual variation
- Serves as baseline/anchor for style robustness
3. Synthetic Styled Dataset
Generation Method: Style-enriched PDF rendering with font macros
- Formula Source: Combined UniMER-1M + pix2tex datasets
- Style Injection Strategy (Section 3.2):
- Random injection of
\mathxxfont macros (\mathbf,\mathbb,\mathcal,\mathit,\mathrm,\mathsf,\mathtt,\mathfrak,\mathscr) - Semantic heuristics for variable types:
- Sets (R, C, N, Z, Q): 35%
\mathbb, 15%\mathcal, 50% plain - Vectors (x, y, z, u, v, w, A, B, M): 30%
\mathbf, 10%\mathit, 60% plain - Operators (d, e, i): 20%
\mathrm, 80% plain - Generic: 2% each specialty font, 90% plain
- Sets (R, C, N, Z, Q): 35%
- Global cap: ~40% of identifiers styled per formula
- Consistency rule: Same variable gets same style throughout formula
- Random injection of
- Styled Formula Ratio: ~10-50% of original formulas produce distinct styled variants
- Rendering: MathJax with full TeX package support (amsmath, amssymb, mathrsfs, amsfonts)
- Train/Validation Split: Train from
unimer_train+pix2tex_train; Validation fromunimer_test+pix2tex_val - Usage in Training: 100% used in mixed training dataset
Characteristics:
- Rich visual diversity in mathematical typography
- Realistic font variations from academic publications
- Maintains semantic correctness
- Improves model robustness to font styling
Generation Pipeline
Pipeline Steps
- Extract Formulas: Extract LaTeX formulas from UniMER and pix2tex source datasets
- Sanitize Formulas: Apply LaTeX normalization rules for robust tokenization
- Inject Macros & Render: Generate styled variants and render images via MathJax
Technical Details
- Style Injection: Probability-based identifier selection with semantic heuristics
- Rendering: MathJax (Node.js) for LaTeX → SVG conversion with full TeX package support
- Rasterization: CairoSVG for SVG → PDF conversion, then PDF → PNG at 150 DPI
Rendering Pipeline
LaTeX Formula → MathJax (SVG) → CairoSVG (PDF) → pdf2image (PNG)
Source Dataset Citations
@inproceedings{unimer2024,
title={UniMER: Universal Mathematical Expression Recognition},
author={UniMER Authors},
booktitle={Conference},
year={2024}
}
@dataset{latex_ocr_dataset,
title={LaTeX-OCR Dataset},
author={lukbl},
year={2023},
publisher={HuggingFace},
howpublished={\url{https://huggingface.co/datasets/lukbl/LaTeX-OCR-dataset}}
}
License
This dataset is released under the MIT License. See source dataset licenses for additional restrictions:
- UniMER-1M: [Original License]
- LaTeX-OCR Dataset: [Original License]
The synthetic generation code and methodology are provided under MIT License.
Changelog
Version 2.0.0 (Formula Sanitization)
🔧 Added LaTeX formula sanitization with comprehensive space normalization rules:
- Control word boundary protection: Prevents token merging (e.g.,
\mathcal Astays as\mathcal A) - Text-like command preservation: Maintains spaces in
\text{},\mathrm{},\operatorname{}, etc. - Control symbol handling: Preserves spaces after control symbols (
\,,\;,\\, etc.) - Verbatim command exemption:
\verband\lstinlinecommands remain untouched - Array/tabular optimization: Removes unnecessary spaces around
&and\\in structured environments - General space cleanup: Removes all other redundant whitespace
- Control word boundary protection: Prevents token merging (e.g.,
📈 Improved formula consistency and reduced tokenization errors
Example:
Old: \mathcal A + \text{ cost } + \begin{array}{c} x \\ y \end{array} New: \mathcal A+\text{ cost }+\begin{array}{c}x\\y\end{array}
Version 1.0.0 (Initial Release)
- ✨ Initial release with plain and styled variants
- ✨ HuggingFace JSONL format
- ✨ Train/validation splits (90/10)
- ✨ Quality-controlled generation pipeline
- 📊 Total samples: 1,332,235 (Plain: 1,173,486 | Styled: 158,749)
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Models trained or fine-tuned on PadishahIIIXXX/latex-ocr-dataset