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| <title>MathJax Example</title> |
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| <p> ${}_{mm\_morph}$ </p> |
| <p> $c=\frac{max(|A|,|B|)}{min(|A|,|B|)}$ </p> |
| <p> $J\_{mm\_syn}$ </p> |
| <p> $C_{WALS}$ </p> |
| <p> $m:\mathbb{L}\mapsto\mathbb{R}$ </p> |
| <p> $\rho=0.69$ </p> |
| <p> $J_{mm}$ </p> |
| <p> $1\dots|Z|$ </p> |
| <p> $J_{mm\_syn}$ </p> |
| <p> $J_{mm}(\mathbf{a},\mathbf{b})=\frac{\sum_{j=1}^{|Z|}min(a_{j},b_{j})}{\sum_{j=% |
| 1}^{|Z|}max(a_{j},b_{j})}$ </p> |
| <p> $\{Z=t(y):y\in Y\}=\{(y_{i},z_{j})\}$ </p> |
| <p> $\{Y=m(x):x\in X\}=\{(x_{i},y_{i})\}$ </p> |
| <p> $J_{mm\_morph}$ </p> |
| <p> ${}_{mm}$ </p> |
| <p> $1\dots|X|$ </p> |
| <p> $J\_{mm\_morph}$ </p> |
| <p> $ch\_ttr_{500}$ </p> |
| <p> $s_{l}=r\cdot ch\_ttr_{l\_500}$ </p> |
| <p> ${}_{morph}$ </p> |
| <p> ${}_{mm\_syn}$ </p> |
| <p> ${}_{syn}$ </p> |
| <p> $S=\textbf{C}\circ\textbf{U}(X)$ </p> |
| <p> $val_{1}$ </p> |
| <p> $\sigma(G;D)$ </p> |
| <p> $\log P(G|D,\lambda)\propto\log P(D|G)+\log P(G|\lambda)$ </p> |
| <p> $\sigma(G;D)=\sum_{i=1}^{n}\sigma\left(v_{i},\operatorname{pa}\left(v_{i}\right% |
| );D\right)$ </p> |
| <p> $X=\{x_{1},x_{2},\cdots,x_{n}\}$ </p> |
| <p> $sym_{1}$ </p> |
| <p> $P\left(v_{i}\mid\text{pa}\left(v_{i}\right)\right)$ </p> |
| <p> $val_{n}$ </p> |
| <p> $x_{i_{1}}\rightarrow x_{j_{1}}$ </p> |
| <p> $S{\prime}$ </p> |
| <p> $\mathcal{A}=\{x_{i}\leadsto x_{j}\mid(x_{i},x_{j})\in S^{\prime}\}$ </p> |
| <p> $P(G\mid D,\lambda)=\frac{P(D\mid G,\lambda)P(G\mid\lambda)}{P(D\mid\lambda)}$ </p> |
| <p> $Domain$ </p> |
| <p> $sym_{i}$ </p> |
| <p> $val_{i}$ </p> |
| <p> $\text{pa}(v_{i})$ </p> |
| <p> $x\leadsto y$ </p> |
| <p> $P(D|\lambda)$ </p> |
| <p> $S=\{(x_{i},x_{j})\}$ </p> |
| <p> $\sigma(G;D,\lambda)=\sigma(G;D)+\sigma(G;\lambda)$ </p> |
| <p> $PromtU$ </p> |
| <p> $sym_{n}$ </p> |
| <p> $x_{i}\leadsto x_{j}\Rightarrow x_{j}\not\in\text{pa}(x_{i}),x_{i}<x_{j}$ </p> |
| <p> $x\not\rightarrow y$ </p> |
| <p> $S^{\prime}={(x_{i},x_{j})}$ </p> |
| <p> $S=\{(x_{i_{1}},x_{j_{1}}),\cdots,(x_{i_{m}},x_{j_{m}})\mid x_{i_{k}},x_{j_{k}}% |
| \in X\}$ </p> |
| <p> $\frac{2\cdot\text{precision}\cdot\text{recall}}{\text{precision}+\text{recall}}$ </p> |
| <p> $x_{i_{m}}\rightarrow x_{j_{m}}$ </p> |
| <p> $S^{\prime}=\textbf{R}\circ\textbf{C}\circ\textbf{U}(X)$ </p> |
| <p> $P(D\mid G,\lambda)=P(D\mid G)$ </p> |
| <p> $T=\textbf{U}(X)$ </p> |
| <p> $\sigma(G;\lambda)$ </p> |
| <p> $x_{i}\leadsto x_{j}$ </p> |
| <p> $T=\{t_{1},t_{2},\cdots,t_{n}\}$ </p> |
| <p> $g_{i}(\textbf{x})$ </p> |
| <p> $h_{j}(\textbf{x})$ </p> |
| <p> $\displaystyle\mathrm{s.t.}:$ </p> |
| <p> $\displaystyle f({\bf{x}}),x\in D$ </p> |
| <p> $\displaystyle\mathrm{Min}:$ </p> |
| <p> $\displaystyle g_{i}({\bf{x}})\leq 0,{i}=1,\dots,{p}$ </p> |
| <p> $\displaystyle h_{j}({\bf{x}})\leq 0,{j}=1,\dots,{q}$ </p> |
| <p> $S\neq\phi$ </p> |
| <p> $W=\phi$ </p> |
| <p> $W=W\cup(S\cap T)$ </p> |
| <p> $E^{\prime}[i]=E^{\prime}[j]$ </p> |
| <p> $\lvert E^{\prime}\rvert$ </p> |
| <p> $\rm{LayoutLMv3_{LARGE}}$ </p> |
| <p> $V[j]=V[j]+1$ </p> |
| <p> $T=P[j*2-1]$ </p> |
| <p> $batch\_size=8$ </p> |
| <p> $S=S[j+1:\lvert S\rvert]$ </p> |
| <p> $L=L[1:\lvert L\rvert]$ </p> |
| <p> $E=E\cup ParseEntityValue(D,J^{\prime})$ </p> |
| <p> $<segment~{}text>~{}XX|YY_{segment}$ </p> |
| <p> $T.subtypes=\phi$ </p> |
| <p> $G=\phi$ </p> |
| <p> $\lvert E\rvert$ </p> |
| <p> $M=\{``s.x|s.y"\mapsto s|s\in D.segments\}$ </p> |
| <p> $G^{\prime}.value=\bigcup_{w\in W}w.text\_value$ </p> |
| <p> $P[j*2]\notin M$ </p> |
| <p> $\bigcup_{T^{\prime}\in T}MajorityVoting(\bigcup_{S^{\prime}\in S}DecodeForType% |
| (ParseJson(S^{\prime}),T^{\prime},D))$ </p> |
| <p> $800train/100dev/100test$ </p> |
| <p> $E^{\prime}.subtypes=\bigcup_{T^{\prime}\in T.subtypes}DecodeForType(J^{\prime}% |
| ,T^{\prime},D)$ </p> |
| <p> $R.split(E[i])$ </p> |
| <p> $(segment~{}text,segment~{}identifier)$ </p> |
| <p> $S=D.pages[i].segments$ </p> |
| <p> $G^{\prime}.bounding\_box=\{\min(b.x),\min(b.y),\max(b.x),\max(b.y)\}_{w\in W,b% |
| =w.bounding\_box}$ </p> |
| <p> $E=\phi$ </p> |
| <p> $F(S[1:j])\leq L$ </p> |
| <p> $V=[0,0,...,0]\in\mathbb{R}\textsuperscript{$\lvert E\rvert$}$ </p> |
| <p> $L=\{T\}$ </p> |
| <p> $\lvert P\rvert/2$ </p> |
| <p> $G=G\cup\{G^{\prime}\}$ </p> |
| <p> $learning\_rate=2\cdot 10^{-5}$ </p> |
| <p> $E=E\cup\{E^{\prime}\}$ </p> |
| <p> $\mathbf{LayoutLMv3_{LARGE}}$ </p> |
| <p> $T^{\prime}=L[0]$ </p> |
| <p> $C=C\cup\{S[1:j]\}$ </p> |
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