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| <p> $\mathfrak{L}_{T}$ </p> | |
| <p> $\tau_{e}=2$ </p> | |
| <p> $ct\leftarrow G.centroid$ </p> | |
| <p> $O(4^{n})$ </p> | |
| <p> $dividing\_line\leftarrow$ </p> | |
| <p> $\tau_{e}=3$ </p> | |
| <p> $4^{3}\cdot n/4$ </p> | |
| <p> $\mathfrak{L}_{\mathbf{T}}$ </p> | |
| <p> $E_{area}=\sum_{i=1}^{S_{T}}(Area(Sb_{i}^{*})\cdot p_{triangle}(\mathbf{G})),$ </p> | |
| <p> $N_{I}>N_{p}$ </p> | |
| <p> $N_{I}>>N_{p}$ </p> | |
| <p> $\mathfrak{R}_{\mathbf{T}}$ </p> | |
| <p> $\mathbf{G_{\mathbf{T}}}$ </p> | |
| <p> $\mathbf{S}_{i}=\big{[}N_{I}\cdot\dfrac{Area(p_{i})}{Area(\mathbf{X})}\big{]},$ </p> | |
| <p> $slope\leftarrow Axial(ct)$ </p> | |
| <p> $Sb$ </p> | |
| <p> $N_{c}=N_{I}$ </p> | |
| <p> $CR(v_{i},v_{j})=dist^{B}(v_{i},v_{j})-Length(\overline{v_{i}v_{j}}),$ </p> | |
| <p> $\Phi(p^{e}_{i})$ </p> | |
| <p> $\mathbf{\mathcal{O}}^{*}$ </p> | |
| <p> $Axial(z)$ </p> | |
| <p> $\|\;\;\|$ </p> | |
| <p> $\mathbf{G}_{T}$ </p> | |
| <p> $dist^{B}$ </p> | |
| <p> $\mathbf{G}\leftarrow p_{2}$ </p> | |
| <p> $\bigcup_{i}S_{i}$ </p> | |
| <p> $\mathbb{R}^{2}\setminus\mathbf{X}$ </p> | |
| <p> $\mathbf{\mathcal{O}}$ </p> | |
| <p> $z\in\mathbf{X}$ </p> | |
| <p> $M_{a}=\dfrac{|\bigcup_{i}S_{i}|}{P_{\mathbf{X}}},$ </p> | |
| <p> $\tau_{e}=1$ </p> | |
| <p> $slope$ </p> | |
| <p> $dividing\_line$ </p> | |
| <p> $p_{triangle}(polygon)=\begin{cases}0.8&polygon\text{ is a triangle}\\ | |
| 1.0&\text{otherwise.}\end{cases}$ </p> | |
| <p> $8/2$ </p> | |
| <p> $R^{m}_{i}$ </p> | |
| <p> $S_{i}-1$ </p> | |
| <p> $p_{1},p_{2}\leftarrow G$ </p> | |
| <p> $dist^{M(X)}$ </p> | |
| <p> $S_{T}-1$ </p> | |
| <p> $4^{1}\cdot n/2$ </p> | |
| <p> $M_{c}=\dfrac{P_{w}}{P_{\mathbf{X}}},$ </p> | |
| <p> $\gamma^{u}$ </p> | |
| <p> $4^{2^{\tau_{e}}-1}\cdot n/2^{\tau_{e}}$ </p> | |
| <p> $\Phi(z,M(\mathbf{X}))=\operatorname*{arg\,min}_{m\in M(\mathbf{X})}\|z-m\|$ </p> | |
| <p> $ac_{k}$ </p> | |
| <p> $L_{ci}$ </p> | |
| <p> $M_{s}=1-\dfrac{|\bigcup_{i}S_{i}|}{\sum_{i}|S_{i}|}.$ </p> | |
| <p> $\mathfrak{R}_{T}$ </p> | |
| <p> $slope\leftarrow Crosswise(ct)$ </p> | |
| <p> $p^{\prime}\in ac_{k}$ </p> | |
| <p> $\mathbf{G}\leftarrow p_{1}$ </p> | |
| <p> $\mathbf{P}=\{p_{1},\dots,p_{N_{p}}\}$ </p> | |
| <p> $p^{e}_{i}$ </p> | |
| <p> $Sb=[bx_{1},by_{1},bx_{2},by_{2}]$ </p> | |
| <p> $\mathcal{T}_{t}^{(d)}(m)$ </p> | |
| <p> $\mathcal{T}_{r}^{(d)}(m)=\lVert(\mathcal{T}^{(d)}(s,m))_{s\in\mathcal{M},s\neq | |
| t% | |
| }\rVert_{2}$ </p> | |
| <p> $\mathcal{T}_{t}^{(d)}(m)=\lVert(\mathcal{T}^{(d)}(m,t))_{t\in\mathcal{M},t\neq | |
| s% | |
| }\rVert_{2}$ </p> | |
| <p> $\alpha=\frac{2}{255}$ </p> | |
| <p> $\displaystyle x^{t+1}=\prod_{x+\mathcal{B}}(x^{t}+\alpha\text{sgn}(\nabla_{x}L% | |
| (\theta,x,y)))$ </p> | |
| <p> $\mathcal{T}_{r}^{(d)}(m)$ </p> | |
| <p> $\mathcal{T}^{(d)}(s,t)$ </p> | |
| <p> $\mathcal{A}_{s}^{(d)}=\{(x,y)\}$ </p> | |
| <p> $\mathcal{A}_{s}^{(d)}$ </p> | |
| <p> $(s,t)\in\mathcal{M}^{2}$ </p> | |
| <p> $(7,308+4,542+7,517)*6=116,202$ </p> | |
| <p> $\mathcal{T}^{(d)}(s,t)=\frac{|\{(x,y)\in\mathcal{A}_{s}^{(d)};\hat{y}_{t}\neq y% | |
| \}|}{|\mathcal{A}_{s}^{(d)}|}$ </p> | |
| <p> $N_{e}=100$ </p> | |
| <p> $l^{\eta}_{i,j\in B}$ </p> | |
| <p> $BNM$ </p> | |
| <p> $L^{\textit{AttnMask}}_{DM}=L_{DM}(\mathcal{M}\odot x,\mathcal{M}\odot\tilde{x}),$ </p> | |
| <p> $[v^{*},\ldots,v^{\&}]:=\operatorname*{arg\,min}_{\mathcal{V}}E_{x_{0},{% | |
| \epsilon}\sim N(0,I)}\\ | |
| \|{\epsilon}-{\epsilon}_{\theta}(x_{t},t,[c_{\theta}(y),v^{*},\ldots,v^{\&}]\|% | |
| ^{2}$ </p> | |
| <p> $V=f_{V}(v)$ </p> | |
| <p> $v^{\eta}_{i}$ </p> | |
| <p> $[y,p^{*}]$ </p> | |
| <p> $v^{\eta}_{j}$ </p> | |
| <p> $L_{PromptCL}$ </p> | |
| <p> $\overline{M}^{p}=1/T\sum_{t=1}^{T}M_{t}^{p}$ </p> | |
| <p> $\{v^{*},\ldots,v^{\&}\}$ </p> | |
| <p> $v^{*}=c_{\theta}(p^{*})$ </p> | |
| <p> $L_{DM}=L_{DM}(x,\tilde{x}):=E_{x_{0},{\epsilon}\sim N(0,I),t\sim\text{Uniform}% | |
| (1,T)}\|{\epsilon}-{\epsilon}_{\theta}(x_{t},t,c_{\phi}(p))\|^{2},$ </p> | |
| <p> $6100$ </p> | |
| <p> $L=L^{\textit{AttnMask}}_{DM}+\gamma L_{PromptCL}^{adj},$ </p> | |
| <p> $M=\text{Softmax}(QK^{T}/\sqrt{d})$ </p> | |
| <p> $step=1,\ldots,S$ </p> | |
| <p> $\{v^{\&}\}$ </p> | |
| <p> $(0.2,0.0005)$ </p> | |
| <p> $\mathcal{V}=[v^{*},\ldots,v^{\&}]$ </p> | |
| <p> $(p^{*},v^{*})$ </p> | |
| <p> $(\mathcal{P},\mathcal{V})$ </p> | |
| <p> ${\bm{\epsilon}}\sim\mathcal{N}(\mathbf{0},\textbf{I})$ </p> | |
| <p> $L_{PromptCL}^{adj}$ </p> | |
| <p> $v=c_{\phi}(p)$ </p> | |
| <p> $\eta\in MN$ </p> | |
| <p> $L^{\textit{AttnMask}}_{DM}$ </p> | |
| <p> $(0.3,0.00075)$ </p> | |
| <p> $Q=f_{Q}(z)$ </p> | |
| <p> $\mathcal{P}=[p^{*},\ldots,{p}^{\&}]$ </p> | |
| <p> $\mathcal{M}=\bigcup_{p\in\mathcal{P}}B(M^{p})$ </p> | |
| <p> $\{v^{*}\}$ </p> | |
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