Datasets:

krotreaksmey
/

synthetic_khmer_math

image imagewidth (px) 24 1.05k	text stringlengths 2 982	class stringclasses 2 values
	ជាភាពដែលត្រូវធ្វើអ្វីៗ	khmer
	\rho^2 \ln(\Lambda l)^2 \ll \frac{1}{l^2} \ln\frac{1}{(\rho l)^2}\label{eq20}	expression
	S^{\rm W}(p) = -i\gamma\cdot p \sigma_{V}^{\rm W}(p) \label{Csym}	expression
	{}\label{hamac}S^G [h_{ij}, \pi^{ij}, N, N^i] = \int_{\cal M} dt \, d^3x \left( {\pi}^{ij} {\dot h}_{ij} - N H^G - N^i H^G_i \right),	expression
	រស្សជាតិ	khmer
	X^{A{A^\prime}}_{0}:=i{\sqrt2}(\sigma^{A} \beta^{A^\prime}- \varsigma^{A} \alpha^{A^\prime})=-i{\sqrt2}({\bar \sigma}^{A^\prime}{\bar \beta}^{A} -{\bar \varsigma}^{A^\prime}{\bar \alpha}^{A}),	expression
	P[R>s]\ \ge\ \lim_{m\to\infty} P[\cap_{n\ge m}A_n(t^{2n})^c]\ .	expression
	\Gamma(b_1 \to \gamma + \gamma)= \zeta \left({M_1\over2m_P}\right)^4 \left({A\over\ell_P^2}\right)^2{M_1\over2\hbar}.	expression
	ពិព្យាយាម	khmer
	ស្នោ	khmer
	ប៉ុន្មាន?	khmer
	។តើសិទ្ធិកាតព្វកិច្ចនិង	khmer
	{\widehat \Gamma}_{\; \; \; BC}^{A'} \equiv \Gamma_{\; \; \; BC}^{A'}+\nabla_{\; \; \; B}^{A'} \; \nu_{C} \; ,	expression
	\lambda^2 - \mbox{Tr} Z \, \lambda +\mbox{det}Z =0 \label{simple}	expression
	straight for the nearest	khmer
	\label{5} [x_0, x_i] = -\frac{i}{\kappa}\, x_i, \quad [x_i, x_j] = 0.,	expression
	{\cal L} = - \frac{1}{4} F^a_{\mu\nu} F^{\mu\nu,a} + \frac{1}{2}m^2A_\mu^aA^{\mu,a} \label{4.1}	expression
	\bar{Z}(j) = 1 + \bar{X}(j\bar{Z}(j)), \;\;\;\;\;\; \bar{Z}(j) = \sum_{w}j^{\bar{w}}<\phi^{w}> \label{ff}	expression
	D_i=\sum_j (X_{ji}^\dagger X_{ji}-X_{ij}X_{ij}^\dagger )=\theta_i,\label{eq:D-flatness}	expression
	ទៅវិញទៅមកអនុវត្តសកម្មភាព	khmer
	x(t)=x_{r}(t)={1\over t},\quad y(t)=y_{r}(t)=-{1\over{t^2}}, \quad z(t)=z_{r}(t)=-{1\over{t^2}}. \label{eq:functions}	expression
	\int_0^{\Delta t(r_P)} dt = \int_{r_P}^c e^{-r} dr.	expression
	បាបកម្ម	khmer
	១៩៧៦ ។ ពិធិសារ វិសោធនកម្ម សន្ធិសញ្ញា មិត្តភាព និង សហប្រតិបត្តិការ នៅ អាស៊ី	khmer
	N^{AB}=\bar{\epsilon}_1\Gamma^{ABC}D_C\epsilon_2+\textstyle{1\over 8}\bar{\epsilon_1}\Gamma^{C_1C_2}\epsilon_2F^{AB}_{\ \ C_1C_2}+\textstyle{1\over{96}}\bar{\epsilon}_1\Gamma^{ABC_1\cdots C_4}\epsilon_2F_{C_1\cdots C_4}.\label{11dsgnester}	expression
	\overline{g}=\sqrt{g^{2}+g^{\prime 2}} = \frac{1}{2\sqrt{\omega}}\sqrt{\tilde{g}^{2}+\tilde{g}^{\prime 2}} \label{VII34}	expression
	ចំលង កំដៅ និង	khmer
	\{w,z\} = \{w,u\}~(\frac{du}{dz})^{2} + \{u,z\}	expression
	រដ្ឋាភិបាលបាន	khmer
	ស្រួចស្រាល់	khmer
	K_{i}E_{\alpha}=q^{(\alpha,\alpha_{i})}E_{\alpha}K_{i},K_{i}F_{\alpha}=q^{-(\alpha,\alpha_{i})}F_{\alpha}K_{i},	expression
	\label{obh:matter}{\delta L\over \delta\Psi} = {\partial L\over \partial\Psi} -(-1)^{p}D{\partial L \over \partial D\Psi}=0.	expression
	%F_{2,a} - F_{2,-a}, F_{2,b} - F_{2,-b}%\label{5.16}%	expression
	{\cal P} : T \mapsto -T, \qquad Q_\pm \mapsto\bar{Q}_\mp , \qquad \bar{Q}_\pm \mapsto Q_\mp\,.	expression
	F(g)= -\frac{3}{8} -\frac{5 A^2}{48}-\frac{A^4}{384} -\frac{1}{2} \log\frac{A^2}{4} + \frac{C_1}{g^2},\label{sol1}	expression
	\Psi_D =\left( \begin{array}{c}A\\B\\C\\D\end{array} \right).	expression
	\label{quater.constr.}\phi_2^4=\frac{\sqrt{g}}{\alpha}\left[p_1^2-m^2+\sqrt{g}~\frac{\alpha m+\beta\sigma\sqrt{m^2-p_1^2}}{(q_2^2)^{3/2}}\right],~~~~~~\sigma=\mbox{sign}~\varepsilon(p_1q_2q_3),	expression
	បញ្ញាវាចានិងសម្ភារ។អប់រំ	khmer
	មាន តួនាទី ជា ប្រវត្តិសាស្ត្រ ដោយ	khmer
	E_{eff(3+1)}=-\frac{1}{2\pi^{2}}\int_{0}^{+\infty}k\ln\left(\frac{k^{2}+m^{2}_{f}}{m_{f}^{2}}\right) (\Delta(k)-c) dk	expression
	[\partial_A-\Phi_A,\partial_B-\Phi_B]=\partial_B\Phi_A-\partial_A\Phi_B+[\Phi_A,\Phi_B]=0	expression
	{\sum_{j=1}^{m+1} \sum_{k=0}^{\infty} E^{(-2k-1)}_{jj}u^{(-2k-1)}_j}	expression
	\{\gamma ^{\mu },\gamma ^{\nu }\}=2g^{\mu \upsilon }, \label{Dirac}	expression
	ចូរ បកស្រាយ	khmer
	\label{tension}T_{Dp}= \frac{1}{l_s^{p+1} g_s}	expression
	%V(x) = \frac{3}{4}\frac{1}{\cos^2 x}-\frac{1}{4}.%\label{potential}%	expression
	S_{ij}(i\pi -\theta )=S_{ij}(h\theta _{h}+H\theta _{H}-\theta)=\prod\limits_{x=1}^{h}\prod\limits_{y=1}^{H}\left\{ x+h,y+H\right\}_{\theta }^{-\mu _{ij}(x+h,y+H)}\,\,. \label{133}	expression
	ភព ផែនដី	khmer
	ដល់ យុវជន ខ្មែរ	khmer
	C(r)=\ln(2\sqrt{2\pi}e^{\gamma +1} r)\quad . \label{l3}	expression
	\omega_\xi(X,Y)=\langle[X,Y],\xi\rangle=-\langle Y,[X,\xi]\rangle	expression
	សត្វ មនុស្ស ពុំ មែន នៅលើ ជញ្ជាំង ទេ គឺ ដាច់ ពី ជញ្ជាំង ដោយ មាន	khmer
	\bar\delta S^{(2)}=\int_{t_0}^tdt\int dx\,\epsilon^{\mu\nu}\frac{\epsilon^{\rho\lambda}}{\sqrt{-g}}\,D_\rho\partial_\mu\phi\,\bar\delta\bigl(D_\lambda\partial_\nu\phi\bigr)\,,\label{4.2}	expression
	see you can't get her out	khmer
	\sum_{\pi(1,2,...n)} \mbox{Tr}\Big[\tau^{(l_0)} \tau^{(l_{\pi(1)})} .....\tau^{(l_{\pi(n)})} \Big]\frac{1}{\tilde{x}_0 - \tilde{x}_{\pi(1)}}\frac{1}{\tilde{x}_{\pi(1)} - \tilde{x}_{\pi(2)}} .....\frac{1}{\tilde{x}_{\pi(n)} - \tilde{x}_0} \; ,	expression
	ឈ្ងៀម	khmer
	\beta F = - \frac{N}{\beta^3 } \int d \theta d \phi \int_{r_+ + h}^L dr \frac{\sqrt{g_4}}{ ( - g^{'}_{tt } )^2 } = - N \int_0^\beta d \tau \int d \theta d \phi \int_{r_+ + h}^L dr \sqrt{g_4} \frac{1}{ \beta_{local}^4}, \label{free}	expression
	\delta \phi = \delta \phi_0 + \delta \phi_{-} t^{-1},	expression
	\begin{array}{rcl}\omega(\lambda)\wedge\omega(\lambda) & = & 0 \,, \\d \omega(\lambda) & = & 0 \,.\end{array}	expression
	ស្មាក្ដី	khmer
	\label{ctildeocho}\begin{array}{rcl}{\tilde C}^{(8)\prime}_{\mu_1\dots\mu_7 z}&=&(i_k N^{(8)})_{\mu_1\dots\mu_7}+7(i_k N^{(7)})_{[\mu_1\dots\mu_6}(C^{(1)}_{\mu_7]}-C^{(1)}_z \frac{g_{z\mu_7]}}{g_{zz}})\\& & \\& & +35(C^{(3)}_{[\mu_1\dots\mu_3}-3C^{(3)}_{[\mu_1\mu_2 z}\frac{g_{z\mu_3}}{g_{zz}})C^{(3)}_{\mu_4\mu_5 z}C^{(...	expression
	\frac{\delta ^{P}I[\phi +\psi ]}{\delta \eta }	expression
	មួយ ទៀត អញ្ជើញ ព្រាហ្មណ៍ អ្នក មាន ចំណេះដឹង មក ធ្វើជា ទីប្រឹក្សា	khmer
	និង ភ្លៀង អាស៊ីត ។	khmer
	។ឯពពួកសត្វចតុបាតខ្លះវា	khmer
	ពពក នឹង	khmer
	រតូវ	khmer
	E_C^{(2)\;reg}(R\to\infty,\Lambda)=-\frac{\Lambda}{2\pi}\ln\left[\sinh\left(R\sqrt{\Lambda^2+\omega_0^2}\right)\right]+\frac{1}{2\pi}\int\limits_{0}^{\Lambda}dy\left(R\sqrt{y^2+\omega_0^2}-\ln 2\right)-\frac{\omega_0^2}{4}.\label{b3.17}	expression
	នៅខ្ពង់រាបឆ្លូងលើ។	khmer
	S= \int dt d^2x\left\{\mbox{ Tr }(2Kg^{-1}\dot g)-\frac{\kappa}{2}\epsilon^{ij}A^A_i \dot A^A_j-{\cal H}+A_0^AG^A\right\}	expression
	\lambda tK_{\left\| n\right\| }(\mu t)I_{\left\| n\right\| }(\mu t)q_{-i}q_i.\label{dh}	expression
	សភាមួយជាន់មាន	khmer
	I_{\mu}^{\ \nu}\equiv \left[ \delta_\mu^\nu + \phi^{-1}\phi_{\mu\alpha}h^{\alpha\nu}\right] \;,\quad I^{-1}\ _\mu^{\ \alpha} I_\alpha^{\ \nu} =\delta_\mu^\nu \;,\quad I\equiv detI_\mu^{\ \nu}\; . \label{defI}	expression
	ជើងទើន	khmer
	\label{hyper1}(1+z)(1-z) \frac{d^2}{dz^2} u(z) + \left( (c-2)z + c -2a -2b \right)\frac{d}{dz}u(z) + \frac{2ab}{1+z} = 0,	expression
	\eta_{11}= - {4\Gamma(d-2) \over \Gamma(2-{d \over 2})\Gamma({d \over 2}-1)\Gamma({d \over 2}-2)\Gamma({d \over 2}+1)},	expression
	ធ្លាប់ ជិះ ពីមុន	khmer
	f_{\rm em}=-{\pi^2\over 240}{1\over a^4}.\label{casimirclassic}	expression
	កុមារី	khmer
	ព្រះចន្ទថាដូចម្តេច?	khmer
	គ្មាន ក្រោម បន្ទះ គឺ គ្មាន	khmer
	ជា កោះ តាំង នៅ ត្រង់	khmer
	ខ្មែរ ធ្លាក់ចុះ	khmer
	\Psi(\theta)= \left( \begin{array}{lr} \psi_{n,m-1}(\theta) \\ \psi_{n,m}(\theta) \\ \psi_{n,m-1}(\theta) \\ \psi_{n,m}(\theta) \\ \,\,\,\,\,\,\,\vdots\\ \psi_{n,m-1}(\theta) \\ \end{array} \right)_{(2k+1) \times 1}	expression
	ដើម្បីវាស់វែង	khmer
	N=T^a \mbox{\tiny $\wedge$} T_a - R_{ab}\mbox{\tiny $\wedge$}e^a\mbox{\tiny $\wedge$} e^b.\label{NY}	expression
	ប្រភេទ កំរិត និង របៀបរបប នៃ ការប្រមូល	khmer
	{\cal L}_{\rm hyp.kin.} \rightarrow {\cal L}_{\rm hyp.kin.} - \frac32 \sigma'' \phi^*_i \phi^i.	expression
	អនុត្តរ	khmer
	comewithalockerwherewecan	khmer
	\left\{ A,B\right\} _{{\footnotesize PB}}=\sum_{i}\frac{\partial\left(A,B\right) }{\partial\left( x_{i},p_{i}\right) }=-\left\{ B,A\right\}_{{\footnotesize PB}}\;.	expression
	Was it possible that men	khmer
	\{C^a,g,\Theta_{\mu},\partial_{\mu}\Theta_{\nu},\ldots\},	expression
	មានគុណ(សម្មាទិដ្ឋិ	khmer
	គ្រាន់តែ ជា បែក ចេញ ពី អាត្ម័ន	khmer
	ប្រៃ	khmer
	រយៈពេល ធ្វើ សមាធិ ( ផ្កា ឈូក ព្រះបដិមា ព្រះធម៍ ជាដើម )ការផ្ចង់ អារម្ម ណ៏ ត្រូវ	khmer
	t_2 \frac{t_0^4}{4!}+ 2 \frac{t_1^2}{2!} \frac{t_0^3}{3!}	expression
	[\frac{1}{u^{3}}\partial _{u}(u^{3}\partial _{u})-\frac{Nk^{2}}{u^{2}}-k'^{2}-\frac{l(l+2)}{u^{2}}]\tilde{\varphi }(u)=0	expression
	\hat{K}=\left(\begin{array}{ccc} \frac{B}{4} \delta^{\mu \nu \alpha \beta} & 0 & 0\\ 0 & -\frac{B}{16} & -\frac{B_1}{4} \\ 0 & -\frac{B_1}{4} & \frac{B_1^2}{2B} -A\end{array}\right)	expression

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Synthetic Khmer Math OCR Dataset

Large-scale OCR dataset for Khmer text and LaTeX math expression recognition, generated from synthetic document images. This is the full training set with 146,914 cropped text regions.

Dataset Summary

Split	Samples	Khmer	LaTeX
train	117,541	50,484	67,057
validation	29,373	12,568	16,805
Total	146,914	63,052	83,862

Features

Feature	Type	Description
`image`	PIL Image	Cropped text region from synthetic document
`text`	string	Ground truth text (Khmer or LaTeX source code)
`class`	string	`"khmer"` or `"expression"`

Classes

ID	Name	Count	Description
0	`khmer`	63,052	Khmer script text (books, newspapers, conversations, poetry)
1	`expression`	83,862	LaTeX math formulas (integrals, matrices, physics equations)

Examples

Khmer:

លើកកម្ពស់បៀវត្សគ្រូបង្រៀន
បទប្បញ្ញត្តិ នៃ ច្បាប់
ជាង គេ នៅ ប្រទេស កម្ពុជា

LaTeX:

\rho^2 \ln(\Lambda l)^2 \ll \frac{1}{l^2} \ln\frac{1}{(\rho l)^2}
\tilde{F}(y)= \int_0^{\infty}dx\ln\left(1+\frac{\sin^2xy}{(e^x-\cos x)^2}\right)
\hat{K}=\left(\begin{array}{ccc} \frac{B}{4} \delta^{\mu \nu \alpha \beta} & 0 & 0\\ 0 & -\frac{B}{16} & -\frac{B_1}{4} \\ 0 & -\frac{B_1}{4} & \frac{B_1^2}{2B} -A\end{array}\right)

Usage

from datasets import load_dataset

ds = load_dataset("krotreaksmey/synthetic_khmer_math")

# View a sample
example = ds["train"][0]
print(f"Class: {example['class']}")
print(f"Text: {example['text']}")
example["image"]

# Filter by class
khmer_only = ds["train"].filter(lambda x: x["class"] == "khmer")
expression_only = ds["train"].filter(lambda x: x["class"] == "expression")

Image Stats

Width: 60–1,046 px (avg ~380 px)
Height: 38–171 px (avg ~74 px)
Format: PNG with transparency

Generation Pipeline

Text collection — 62,680 Khmer texts from local books + 83,884 LaTeX formulas from arXiv
LaTeX rendering — LuaLaTeX + HarfBuzz for proper Khmer Unicode shaping
Page composition — Random placement on colored backgrounds (in-memory, 35-40 pages/sec)
YOLOv8 OBB detection — Trained model detects text regions with oriented bounding boxes
Crop + match — Detection regions cropped and matched to ground truth OCR labels via IoU

Related Datasets

krotreaksmey/khmer_math — Smaller curated subset (10,499 samples)
krotreaksmey/Yolo_Detect_khmer_math — Trained YOLOv8 OBB model

Citation

@misc{synthetic_khmer_math_ocr_2026,
  title={Synthetic Khmer Math OCR Dataset},
  author={krotreaksmey},
  year={2026},
  url={https://huggingface.co/datasets/krotreaksmey/synthetic_khmer_math}
}

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