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\begin{tabular}{c|c|c|c} Parameter & RNG & PSO & GA\\ \hline \emph{num-boost-round} & 295 & 153 & 451\\ \emph{learning-rate} & 0.062 & 0.300 & 0.085\\ \emph{max-depth} & 5 & 4 & 5\\ \emph{gamma} & 0.98 & 3.86 & 2.99\\ \emph{min-child-weight} & 173 & 323.6 & 442.2\\ \emph{subsample} & 0.83 & 0.830 & 0.907\\ \emph{colsample-bytree} & 0.7 & 1.0 & 0.3\\ \hline \end{tabular}
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\begin{tabular}{l||c|c|c||c|c|c} & \multicolumn{3}{c||}{\textbf{ELBO} $\mathcal{L}$}& \multicolumn{3}{c} {\textbf{Uncond. Exp. Reward $\mathcal{J}$}} \\ \hline \textbf{Stock} & \textbf{sessions} &\textbf{learning rates} & \textbf{epochs} & \textbf{sessions} & \textbf{rates} & \textbf{epochs}\\ \hline FB & 3 & $1 \times 10^{-4}$, $1 \times 10^{-6}$, $1 \times 10^{-8}$ & 500, 500, 50 & 1 & $5 \times 10^{-5}$ & 150 \\ INTC & 1 & $1 \times 10^{-4}$ & 500 & 1 & $5 \times 10^{-4}$& 100 \\ MSFT & 3 &$1 \times 10^{-4}$, $1 \times 10^{-6}$, $1 \times 10^{-7}$ & 500, 250, 10&1 & $1 \times 10^{-7}$ & 130 \\ VOD & 2 & $1 \times 10^{-4}$,$1 \times 10^{-6}$ & 150, 20 & 1 & $3 \times 10^{-5}$& 20\\ \end{tabular}
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\begin{tabular}{|c|cc|} \hline Parameter & Posterior mean & 95\% credible interval \\ \hline $\sigma^2$ & 0.0107 & (0.0106, 0.0107) \\ $\sigma_Z$ & 1.557 & (1.496, 1.618) \\ $\rho_Z$ & 428.2 & (409.5, 446.8) \\ \hline \end{tabular}
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\begin{tabular}{|c|c|ccc|c|} \hline Model number & Model form & WAIC & CPO & RMSE$_{\text{CV}}$ & Run-time\\ \hline 1 & $x\cdot\alpha(s-s_0,t-t_0) + \{Z^0(s,t)\}$ & 108 & -0.0003 & 0.001 & 99\\ 3 & $x\cdot\alpha(s-s_0,t-t_0) + \gamma(s-s_0,t-t_0) + \{Z^0(s,t)\}$ & 59 & 0 & 0 & 206\\ 4 & $x\cdot\alpha(s-s_0,t-t_0) + \gamma(s-s_0,t-t_0) + x^\beta \cdot \{Z^0(s,t)\}$ & 0 & -0.0018 & 0.091 & 71\\ 5 & $x\cdot\alpha(s-s_0,t-t_0) + x^\beta \cdot \{Z^0(s,t)\}$ & 47 & -0.0004 & 0.094 & 89\\ \hline \end{tabular}
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\begin{tabular}{|c|cc|} \hline Model & $\{Z(s)\}-Z(s_0)$ & $\{Z(s)\}\mid Z(s_0)=0$ \\ \hline 0 & 337 & \bf 298 \\ 1 & \bf 43 & 65 \\ 2 & 80 & \bf 71 \\ 3 & \bf 0 & 18 \\ 4 & \bf 20 & 23 \\ 5 & \bf 55 & 61 \\ \hline \end{tabular}
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\begin{tabular}{|c|cc|} \hline Model & $\zeta=1.5$ & $\zeta=2$ \\ \hline 0 & \bf 2438 & 2447 \\ 1 & \bf 614 & 624 \\ 2 & \bf 743 & 746 \\ 3 & \bf 4 & 15 \\ 4 & \bf 0 & 12 \\ 5 & \bf 611 & 639 \\ 6 & 4394961 & \bf 4394960 \\ \hline \end{tabular}
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\begin{tabular}{lccc} \hline \rule[-1ex]{0pt}{3.5ex} & Laboratory & SRM & HabEx \\ \hline\hline \rule[-1ex]{0pt}{3.5ex} Telescope diameter $(D)$ & 5.0 mm & 2.37 m & 4.0 m\\ \rule[-1ex]{0pt}{3.5ex} Starshade diameter $(2R)$ & 25.06 mm$^\dagger$ & 26 m & 52 m\\ \rule[-1ex]{0pt}{3.5ex} Wavelength $(\lambda)$ range & 641 - 725 nm$^\dagger$ & 616 - 800 nm & 300 - 1000 nm\\ \rule[-1ex]{0pt}{3.5ex} Telescope - starshade sep. $(Z_\text{tel})$ & 50.0 m & 26,000 km & 76,600 km\\ \rule[-1ex]{0pt}{3.5ex} Source - starshade sep. $(Z_\text{src})$ & 27.45 m & $>3$ parsec & $>3$ parsec\\ \rule[-1ex]{0pt}{3.5ex} {\bf Fresnel number} $(N)$ & {\bf12.2 $-$ 13.8}$^\dagger$ & {\bf 8.1 $-$ 10.5} & {\bf8.8 $-$ 29}\\ \hline \end{tabular}
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\begin{tabular}{cl} \hline \rule[-1ex]{0pt}{3.5ex} Symbol & Description\\ \hline\hline \rule[-1ex]{0pt}{3.5ex} $C^i$ & Contrast at pixel $i$ \\ \rule[-1ex]{0pt}{3.5ex} $\Gamma^i$ & Transfer function mapping to pixel $i$\\ \rule[-1ex]{0pt}{3.5ex} $\gamma$ & Ratio of PSF peak after propagation through free space\\ &\hspace{20pt} to that of the calibration mask\\ \rule[-1ex]{0pt}{3.5ex} $A$ & Peak value of apodization function $(=0.9)$\\ \rule[-1ex]{0pt}{3.5ex} $s^i$ & Counts collected in pixel $i$ during exposure of length $t$ [ct]\\ \rule[-1ex]{0pt}{3.5ex} $P$ & Laser power [W]\\ \rule[-1ex]{0pt}{3.5ex} $\nu$ & Neutral density filter transmission\\ \rule[-1ex]{0pt}{3.5ex} $\varepsilon$ & Transmission through atmosphere \\ \rule[-1ex]{0pt}{3.5ex} $\tau$ & Throughput of camera optics \\ \rule[-1ex]{0pt}{3.5ex} $Q$ & Quantum efficiency of detector [$e^-$/ph]\\ \rule[-1ex]{0pt}{3.5ex} $E$ & Photon energy [J/ph] \\ \rule[-1ex]{0pt}{3.5ex} $G$ & Camera inverse-gain [$e^-$/ct] \\ \rule[-1ex]{0pt}{3.5ex} $t$ & Exposure time [s]\\ \rule[-1ex]{0pt}{3.5ex} $m$ & Denotes {\it mask} measurement\\ \rule[-1ex]{0pt}{3.5ex} $u$ & Denotes {\it unocculted / calibration} measurement\\ \hline \end{tabular}
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\begin{tabular}{ccc} \toprule Process & Hyperparameter & Value \\ \midrule \multirow{4}{*}{Sequential SIFT Matching} & \texttt{min\_inlier\_ratio} & \texttt{0.65} \\ & \texttt{max\_distance} & \texttt{0.55} \\ & \texttt{min\_num\_inliers} & \texttt{50} \\ & \texttt{overlap\_num} & \texttt{15} \\ \midrule \multirow{3}{*}{RANSAC} & \texttt{dyn\_num\_trials\_multiplier} & \texttt{3.0} \\ & \texttt{confidence} & \texttt{0.99} \\ & \texttt{min\_inlier\_ratio} & \texttt{0.1} \\ \midrule \multirow{3}{*}{Sparse Reconstucion} & \texttt{abs\_pose\_min\_inlier\_ratio} & \texttt{0.25} \\ & \texttt{filter\_max\_reproj\_error} & \texttt{4.0} \\ & \texttt{filter\_min\_tri\_angle} & \texttt{1.5} \\ \midrule \multirow{2}{*}{Dense Reconstucion} & \texttt{geom\_consistency\_max\_cost} & \texttt{3.0} \\ & \texttt{geom\_consistency\_regularizer} & \texttt{0.3} \\ \bottomrule \end{tabular}
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\begin{tabular}{lllllll} \toprule {Vector attributes} & BZR & COX2 & CUNEIFORM & ENZYMES & PROTEIN & SYNTHETIC \\ \midrule \midrule \small{FGW} & \textbf{85.12$\pm$4.15}* & 77.23$\pm$4.86 & \textbf{76.67$\pm$7.04} & 71.00$\pm$6.76 & \textbf{74.55$\pm$2.74} & \textbf{100.00$\pm$0.00} \\ \midrule \small{HOPPERK} & 84.15$\pm$5.26 & \textbf{79.57$\pm$3.46} & 32.59$\pm$8.73 & 45.33$\pm$4.00 & 71.96$\pm$3.22 & 90.67$\pm$4.67 \\ \small{PROPAK} & 79.51$\pm$5.02 & 77.66$\pm$3.95 & 12.59$\pm$6.67 & \textbf{71.67$\pm$5.63}* & 61.34$\pm$4.38 & 64.67$\pm$6.70 \\\midrule \small{PSCN k=10} & 80.00$\pm$4.47 & 71.70$\pm$3.57 & 25.19$\pm$7.73 & 26.67$\pm$4.77 & 67.95$\pm$11.28 & \textbf{100.00$\pm$0.00} \\ \small{PSCN k=5 } & 82.20$\pm$4.23 & 71.91$\pm$3.40 & 24.81$\pm$7.23 & 27.33$\pm$4.16 & 71.79$\pm$3.39 & \textbf{100.00$\pm$0.00} \\ \bottomrule \end{tabular}
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\begin{tabular}{llll} \toprule {Discrete attr.} & MUTAG & NCI1 & PTC-MR \\ \midrule \midrule FGW raw & 83.26$\pm$10.30 & 72.82$\pm$1.46 & 55.71$\pm$6.74 \\ FGW wl h=2 & 86.42$\pm$7.81 & 85.82$\pm$1.16 & {63.20$\pm$7.68} \\ FGW wl h=4 & \textbf{88.42$\pm$5.67} & \textbf{86.42$\pm$1.63} & \textbf{65.31$\pm$7.90} \\ \midrule GK k=3 & 82.42$\pm$8.40 & 60.78$\pm$2.48 & 56.46$\pm$8.03 \\ RWK & 79.47$\pm$8.17 & 58.63$\pm$2.44 & 55.09$\pm$7.34 \\ SPK & 82.95$\pm$8.19 & 74.26$\pm$1.53 & 60.05$\pm$7.39 \\ WLK & 86.21$\pm$8.48 & 85.77$\pm$1.07 & 62.86$\pm$7.23 \\ WLK h=2 & 86.21$\pm$8.15 & 81.85$\pm$2.28 & 61.60$\pm$8.14 \\ WLK h=4 & 83.68$\pm$9.13 & 85.13$\pm$1.61 & 62.17$\pm$7.80 \\\midrule PSCN k=10 & 83.47$\pm$10.26 & 70.65$\pm$2.58 & 58.34$\pm$7.71 \\ PSCN k=5 & 83.05$\pm$10.80 & 69.85$\pm$1.79 & 55.37$\pm$8.28 \\ \bottomrule \end{tabular}
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\begin{tabular}{lll} \toprule {Without attribute} & IMDB-B & IMDB-M \\ \midrule \midrule GW & \textbf{63.80$\pm$3.49} & \textbf{48.00$\pm$3.22} \\ \midrule GK k=3 & 56.00$\pm$3.61 & 41.13$\pm$4.68 \\ SPK & 55.80$\pm$2.93 & 38.93$\pm$5.12 \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccccccccc} \hline \multirow{2}{*}{Data set} &\multicolumn{10}{c}{Algorithms}\\ \cline{2-11} & K-means&NMF&DKM&Tri-NMF&GLBM&ITCC&RBC&CCOT&CCOT-GW & COOT\\ \hline D1&$.018\pm{.003}$&$.042\pm{.037}$&$.025\pm{.048}$&$.082\pm{.063}$&$.021\pm{.011}$&$.021\pm{.001}$&$.017\pm{.045}$&$.018\pm{.013}$&$.004\pm{.002}$ & $\mathbf{0}$ \\ D2&$.072\pm{.044}$&$.083\pm{.063}$&$.038\pm{.000}$&$.052\pm{.065}$&$.032\pm{.041}$&$.047\pm{.042}$&$.039\pm{.052}$&$.023\pm{.036}$&$.011\pm{.056}$ & $\mathbf{.009\pm{0.04}}$\\ D3&--&--&$.310\pm{.000}$&--&$.262\pm{.022}$&$.241\pm{.031}$&--&$.031\pm{.027}$&$\mathbf{.008\pm{.001}}$ & $.04\pm{.05}$\\ D4&$.126\pm{.038}$&--&$.145\pm{.082}$&--&$.115\pm{.047}$&$.121\pm{.075}$&$.102\pm{.071}$&$.093\pm{.032}$&$.079\pm{.031}$ & $\mathbf{0.068\pm{0.04}}$\\ \hline \end{tabular}
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\begin{tabular}{cc} \hline M1 &M20\\ \hline Shawshank Redemption (1994)& Police Story 4: Project S (Chao ji ji hua) (1993)\\ Schindler's List (1993) & Eye of Vichy, The (Oeil de Vichy, L') (1993) \\ Casablanca (1942) & Promise, The (Versprechen, Das) (1994)\\ Rear Window (1954) & To Cross the Rubicon (1991)\\ Usual Suspects, The (1995) & Daens (1992)\\ \hline \end{tabular}
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\begin{tabular}{llll} \toprule {Discrete attr.} & MUTAG & NCI1 & PTC \\ \midrule \midrule FGW raw sp & 100\% & 100\% & 98\% \\ FGW wl h=2 sp & 100\% & 100\% & 88\% \\ FGW wl h=4 sp & 100\% & 100\% & 88\% \\ \midrule \end{tabular}
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\begin{tabular}{lllllll} \toprule {Vector attributes} & BZR & COX2 & CUNEIFORM & ENZYMES & PROTEIN & SYNTHETIC \\ \midrule \midrule \small{FGW sp} & 100 \% & 90\% & 100\% & 100\% & 100\% & 100\% \\ \midrule \end{tabular}
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\begin{tabular}{llll} \toprule {Discrete attr.} & MUTAG & NCI1 & PTC-MR \\ \midrule \midrule FGW raw sp & 83.26$\pm$10.30 & 72.82$\pm$1.46 & 55.71$\pm$6.74 \\ FGW wl h=2 sp & 86.42$\pm$7.81 & 85.82$\pm$1.16 & {63.20$\pm$7.68} \\ FGW wl h=4 sp & \textbf{88.42$\pm$5.67} & \textbf{86.42$\pm$1.63}* & 65.31$\pm$7.90 \\ \midrule W raw sp & 79.36$\pm$3.49 & 70.5$\pm$4.63 & 54.79$\pm$5.76 \\ W wl h=2 sp & 87.78$\pm$8.64 & 85.83$\pm$1.75 & 63.90$\pm$7.66 \\ W wl h=4 sp & 87.15$\pm$8.23 & 86.42$\pm$1.64 & \textbf{66.28$\pm$6.95}* \\ \midrule GW sp &82.73$\pm$9.59 & 73.40$\pm2.80$ & 54.45$\pm$ 6.89\\ \bottomrule \end{tabular}
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\begin{tabular}{lllllll} \toprule {Vector attributes} & BZR & COX2 & CUNEIFORM & ENZYMES & PROTEIN & SYNTHETIC \\ \midrule \midrule \small{FGW sp} & 85.12$\pm$4.15 & \textbf{77.23$\pm$4.86}* & \textbf{76.67$\pm$7.04} & 71.00$\pm$6.76 & 74.55$\pm$2.74 & \textbf{100.00$\pm$0.00} \\ \midrule \small{W} & \textbf{85.36$\pm$4.87}* & 77.23$\pm$3.16 & 61.48$\pm$10.23 &\textbf{71.16$\pm$6.32}* & \textbf{75.98$\pm$ 1.97}* & 34.07$\pm$11.33 \\ \midrule \small{GW sp} & 82.92$\pm$6.72 & 77.65$\pm$5.88 & 50.66$\pm$8.91 & 23.66$\pm$3.63 & 71.96$\pm$ 2.40 & 41.66$\pm$4.28 \\ \bottomrule \end{tabular}
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\begin{tabular}{llll} \toprule {Discrete attr.} & MUTAG & NCI1 & PTC-MR \\ \midrule \midrule FGW & 2.5 ms & 7.3 ms & 3.7 ms \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \toprule \multicolumn{5}{c}{GoogleNet $\rightarrow$ Decaf }\\ \midrule {Domains} & {CCA} & {KCCA} & {EGW} & {COOT}\\ \midrule C$\rightarrow$A & $11.30$$\pm 4.04$ & $\underline{ 14.60}$$\pm 8.12$ & $8.20$$\pm 2.69$ & $\bf 25.10$$\pm 11.52$\\ C$\rightarrow$C & $13.35$$\pm 4.32$ & $\underline{ 17.75}$$\pm 10.16$ & $11.90$$\pm 2.99$ & $\bf 37.20$$\pm 14.07$\\ W$\rightarrow$A & $14.55$$\pm 10.68$ & $\underline{ 25.05}$$\pm 24.73$ & $14.55$$\pm 2.05$ & $\bf 39.75$$\pm 17.29$\\ A$\rightarrow$C & $13.80$$\pm 6.51$ & $\underline{ 20.70}$$\pm 17.94$ & $16.00$$\pm 2.44$ & $\bf 30.25$$\pm 18.71$\\ A$\rightarrow$A & $16.90$$\pm 10.45$ & $\underline{ 28.95}$$\pm 30.62$ & $12.70$$\pm 1.79$ & $\bf 41.65$$\pm 16.66$\\ W$\rightarrow$W & $14.50$$\pm 6.72$ & $\underline{ 24.05}$$\pm 19.35$ & $9.55$$\pm 1.77$ & $\bf 36.85$$\pm 9.20$\\ W$\rightarrow$C & $13.15$$\pm 4.98$ & $\underline{ 14.80}$$\pm 8.79$ & $11.40$$\pm 2.65$ & $\bf 30.95$$\pm 17.18$\\ A$\rightarrow$W & $10.85$$\pm 4.62$ & $\underline{ 14.40}$$\pm 12.36$ & $12.70$$\pm 2.99$ & $\bf 40.85$$\pm 16.21$\\ C$\rightarrow$W & $18.25$$\pm 14.02$ & $\underline{ 25.90}$$\pm 25.40$ & $11.30$$\pm 3.87$ & $\bf 34.05$$\pm 13.82$\\ \bf Mean & $14.07$$\pm 2.25$ & $\underline{ 20.69}$$\pm 5.22$ & $12.03$$\pm 2.23$ & $\bf 35.18$$\pm 5.24$\\ \bottomrule \end{tabular}
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\begin{tabular}{|l||r|r|r||rr|rr|rr||rr|} \hline & $\{a\}$ & $\{b\}$ & $\{d\}$ & \multicolumn{2}{c|}{$\{a,b\}$} & \multicolumn{2}{c|}{$\{a,d\}$} & \multicolumn{2}{c|}{$\{b,d\}$}& \multicolumn{2}{c|}{$\{a,b,d\}$}\\ \hline Vertex & $l^*$ & $l^*$ & $l^*$ & $l$ & $l^*$ & $l$ & $l^*$ & $l$ & $l^*$ & $l$ & $l^*$\\ \hline a & 0 & 1 & 16 & 1 &1 & 16 &16 & 17 &16 & 16& \\ b & 1 & 0 & 15 & 1 &1 & 16 &16 & 15 &15 & 16& \\ c & 12 & 11 & 16 & 23 &17 & 28 &22 & 27 &26 & 33&\emph{22} \\ d & 16 & 15 & 0 & 31 &16 & 16 &16 & 15 &15 & 31& \\ E & 8 & 7 & 12 & 15 &8 & 20 &18 & 19 &17 & 20&\\ F & 6 & 5 & 10 & 11 &6 & 16 &16 & 15 &15 & 16&\\ G & 32 & 31 & 36 & 63 &32 & 68 &42 & 67 &41 & 68&\\ H & 32 & 31 & 16 & 63 &32 & 48 &42 & 47 &41 & 48&\\ I & 11 & 10 & 5 & 21 &11 & 16 &16 & 15 &15 & 16&\\ J & 9 & 8 & 13 & 17 &9 & 22 &19 & 21 &18 & 22&\\ \hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|} \hline \textbf{Experiment} & \textbf{P($R_1$)} & \textbf{R($R_1$)} & \textbf{F($R_1$)} & \textbf{P($R_2$)} & \textbf{R($R_2$)} & \textbf{F($R_2$)} \\ \hline Word2Vec-CNN & 0.77 & 0.84 & 0.81 & 0.82 & 0.74 & 0.77 \\ \hline Word2Vec-Bi-GRU & 0.90 & 0.88 & 0.89 & 0.77 & 0.80 & 0.78\\ \hline ELMo-Bi-LSTM & 0.92 & 0.90 & 0.91 & 0.80 & 0.85 & 0.83 \\ \hline \end{tabular}
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\begin{tabular}{|l|l|l|l|} \hline \textbf{Model} & \textbf{Acc@1} & \textbf{Acc@5} & \textbf{Acc@10} \\ \hline f & 0.0095 & 0.087 & 0.175 \\ \hline BIM & 0.0093 & 0.037 & 0.0578 \\ \hline CHI & 0.0019 & 0.0336 & 0.0664 \\ \hline RSV & 0.0107 & 0.0873 & 0.170 \\ \hline KLD & 0.0016 & 0.0654 & 0.138 \\ \hline NN & 0.13 & 0.26 & 0.34 \\ \hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline $T_{\text{in}~\text{out}}$ & $T_{++}$ & $T_{0+}$ & $T_{-+}$ & $T_{+0}$ & $T_{00}$ & $T_{-0}$ & $T_{+-}$ & $T_{0-}$ & $T_{--}$ \\ \hline Theory & 3 & 5.5 & 6 & 5 & 3 & 5 & 6 & 5.5 & 3 \\ Simulation & 3.06 & 5.56 & 5.97 & 5.02 & 3.02 & 5.02 & 5.94 & 5.58 & 3.02 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c} \hline $T$ & $E = (x,y)$ & $P$ \\\hline web-scale image classification & (ImageNet, crowdsourced labels) & test accuracy \\\hline intelligent healthcare & (medical data, annotations by variability) & error rate \\\hline service call analysis & (perceived speech, user rating) & quality rate of call \\\hline \end{tabular}
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\begin{tabular}{lr} \hline \hline \textbf{Hidden Layer} & \textbf{Hidden Sizes}\\ \hline Word/GloVe/Char & 100\\ POS & 50 \\ GloVe Linear & 125 \\ BERT Linear & 125 \\ BiLSTM & 3*600 \\ Char LSTM & 1*400 \\ Unary Arc (UD) & 500\\ \textbf{Local1O}/\textbf{Local2O} Unary Arc (Others) & 450\\ \textbf{Single1O}/\textbf{Single2O} Unary Arc (Others) & 550\\ Label & 150\\ Binary Arc & 150\\ \hline \textbf{Dropouts} & \textbf{Dropout Prob.}\\ \hline Word/GloVe/POS & 20\%\\ Char LSTM (FF/recur) & 33\%\\ Char Linear & 33\%\\ BiLSTM (FF/recur) & 45\%/25\%\\ Unary Arc/Label & 25\%/33\%\\ Binary Arc & 25\%\\ \hline \textbf{Optimizer \& Loss} & \textbf{Value}\\ \hline \textbf{Local1O}/\textbf{Local2O} Interpolation ($\lambda$)& 0.40\\ \textbf{Single1O}/\textbf{Single2O} Interpolation ($\lambda$)& 0.07\\ Adam $\beta_1$ & 0\\ Adam $\beta_2$ & 0.95\\ Decay Rate & 0.85 \\ Decay Step (without \textbf{dev} improvement) & 500 \\ \hline \textbf{Weight Initialization} & \textbf{Mean/Stddev}\\ \hline Unary weight & 0.0/1.0\\ Binary weight & 0.0/0.25\\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{\textbf{Methods}}& {$u_1$ Testing $RD$} & {$u_2$ Testing $RD$} & {Global Testing $RD$} & {Global Testing Accuracy}\\ \hline \text{AgnosticFair} & 0.0208 & 0.0177 & 0.0196 & 0.7626\\ \hline \text{AgnosticFair-b} & 0.0450 & 0.0795 & 0.0673 & 0.7885\\ \hline \end{tabular}
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\begin{tabular}{|l||l|l|} \hline \textbf{Dataset} & \textbf{MSE} & \textbf{Iterations}\\ \hline \hline Corridor & 0.31 & 14\\ Office & 0.42 & 19\\ Linkoping & 0.53 & 8\\ Bunny & 0.0025 & 19\\ Bremen & 0.45 & 8\\ \hline \end{tabular}
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\begin{tabular}{|l||l|l|} \hline \textbf{Dataset} & \textbf{MSE} & \textbf{Iterations}\\ \hline \hline Corridor & 0.66 & 100\\ Office & 0.48 & 100\\ Linkoping & 0.50 & 100\\ Bunny & 0.0024 & 100\\ Bremen & 0.48 & 100\\ \hline \end{tabular}
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\begin{tabular}{|l|l|l|l|l|} \hline \textbf{Sequence} & \textbf{median} & \textbf{0.75 quantile} & \textbf{0.95 quantile} & \textbf{iterations} \\ \hline \hline \textbf{box\_met} & 1.28 & 2.49 & 4.27 & 39.40 \\ \textbf{hauptgebaude} & 0.01 & 0.02 & 0.77 & 42.35 \\ \textbf{pioneer\_slam3} & 0.15 & 0.34 & 0.75 & 36.34 \\ \textbf{urban05} & 0.44 & 0.65 & 4.31 & 39.65 \\ \textbf{gazebo\_winter} & 0.02 & 0.03 & 0.05 & 41.09 \\ \textbf{planetary\_map} & 0.54 & 1.08 & 2.07 & 24.89 \\ \textbf{long\_office\_household} & 0.17 & 0.63 & 1.99 & 35.20 \\ \textbf{plain} & 0.17 & 0.46 & 0.93 & 31.78 \\ \textbf{pioneer\_slam} & 0.18 & 0.44 & 3.64 & 38.13 \\ \textbf{stairs} & 0.03 & 0.09 & 0.23 & 34.08 \\ \textbf{gazebo\_summer} & 0.05 & 0.19 & 0.74 & 35.96 \\ \textbf{wood\_autumn} & 0.02 & 0.03 & 0.06 & 40.41 \\ \textbf{apartment} & 0.06 & 0.28 & 1.50 & 33.36 \\ \textbf{wood\_summer} & 0.01 & 0.02 & 0.03 & 42.44 \\ \textbf{p2at\_met} & 0.47 & 0.97 & 1.96 & 29.75 \\ \hline \hline \textbf{total} & 0.10 & 0.45 & 1.86 & 29.75 \\ \hline \end{tabular}
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\begin{tabular}{|c|c||c|c|} \hline $\tilde{\nu}_{g'g}$ (cm$^{-1}$) & $\tilde{\nu}_{e'e}$ (cm$^{-1}$) & $|\mu_{eg'}|^2$ (AU)& $|\mu_{ge'}|^2$ (AU) \\ \hline 469 & 469 &0.7 & 0.1\\ \hline 494 & 489 &0.1 & 0.3\\ \hline 524 & 526 & 0.9 & 2.4\\ \hline 580 & 570 &0.6 & 2.1\\ \hline 592 & 589 &3.3 & 10\\ \hline 674 & 669 &0.04 & 4.2\\ \hline 753 & 726 &0.15 & 6.5\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline & $w=1/3$ & $w=1$ & $w=1/9$ \\ \hline \hline $A_s^{\rm max} $ & 0.015 & 0.007 & 0.0082\\ \hline $A_s^{\rm min}$ & 0.002 & 0.001 & 0.003\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline & $w=1/3$ & $w=1$ & $w=1/9$ \\ \hline \hline Range of $k_*$ in Mpc$^{-1}$ & $2\times 10^6$ - $7 \times 10^6$ & $2\times 10^6$ - $7 \times 10^6$ & $2\times 10^7$ - $7 \times 10^7$\\ \hline Range of $M/M_{\odot}$ at $k_{*,{\rm min}}$ & 0.2-2 & 1-10 & $10^{-4}$ - $5\times 10^{-3}$\\ \hline Range of $M/M_{\odot}$ at $k_{*,{\rm max}}$ & 0.01 - 0.33 & 0.08-2 & $3\times 10^{-6}$ - $3\times 10^{-4}$\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline $P_{\zeta}(k)$ & $k_*$ in Mpc$^{-1}$ & $M/M_{\odot} (w=1/3)$ & $M/M_{\odot} (w=1)$ & $M/M_{\odot} (w=1/9)$ \\ \hline \hline Lognormal with exponential cutoff & $10^6$ & $0.8-40$ & $2-200$ & $0.08 - 100$\\ \hline & $10^7$ & $7\times 10^{-3} - 0.5$ & $0.07 - 8$ & $5\times 10^{-4} - 0.5$\\ \hline Broken power law & $10^6$ & $0.2 - 10$ & $1 - 30$ & $0.02 - 8$\\ \hline & $10^7$ & $2\times 10^{-3} - 0.2$ & $0.025 - 1$ & $10^{-4} - 0.03$\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline $P_{\zeta}(k)$ & $k_*$ (Mpc$^{-1}$) & $w=1/3$ & $w=1$ & $w=1/9$ \\ \hline \hline Gaussian & $10^6$ & consistent at $2\sigma$ with $A_s\simeq 0.01$ & inconsistent & inconsistent ($f_{\rm PBH}>1$)\\ \hline & $10^7$ & consistent at $2\sigma$ with $A_s\simeq 0.01$ & inconsistent & consistent with $A_s\simeq 0.007$\\ \hline Lognormal with exponential cutoff & $10^6$ & inconsistent at $2\sigma$ with $A_s\simeq 0.011$ & inconsistent & inconsistent (large $\gamma _{\rm CP}$) \\ \hline & $10^7$ & consistent at $2\sigma$ with $A_s\simeq 0.011$ & inconsistent & consistent with $A_s\simeq 0.0078$ \\ \hline Broken power law & $10^6$ & consistent at $1\sigma$ with $A_s\simeq 0.012$ & inconsistent & inconsistent ($f_{\rm PBH}>1$) \\ \hline & $10^7$ & consistent at $2\sigma$ with $A_s\simeq 0.0122$ & inconsistent & inconsistent ($f_{\rm PBH}>1$)\\ \hline \end{tabular}
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\begin{tabular}{llllllllll} \hline $\beta$ & $\epsilon_1$ & $\epsilon_2$ & $l_{hit}$ & $l_{miss}$ & $\lambda_1$ & $\lambda_2$ & $\lambda_3$ & $\lambda_4$ & $\lambda_5$ \\ \hline 1.0 & 1.0 & 1.2 & 0.4 & 0.05 & 0.2 & 0.9 & 1.0 & 0.1 & 0.4 \\ \hline \end{tabular}
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\begin{tabular}{cccc} Method & Average Rank & Method & Average Rank \\ \hline Franceschi & 1.79 & 1-NN DTW & 2.58\\ TOTOPO & 2.5 & 1-NN Euclidean & 3.11\\ \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|} \hline \hline \hline \multicolumn{7}{|c|}{\textbf{Independent Tensor Structures}} \\ \hline \hline \hline \multicolumn{1}{|c|}{\multirow{2}{*}{Co-Dimension}} & \multicolumn{1}{c|}{\multirow{2}{*}{Cross-Ratio}} & \multicolumn{2}{c|}{Vector} & \multicolumn{1}{c|}{\multirow{2}{*}{Bi-Vector}} & \multicolumn{2}{c|}{2-Tensor} \\ \cline{3-4} \cline{6-7} \multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{} &\multicolumn{1}{c|}{at $x$} &\multicolumn{1}{c|}{at $x'$} & \multicolumn{1}{c|}{} &\multicolumn{1}{c|}{at $x$} &\multicolumn{1}{c|}{at $x'$} \\ \hline $q>2$ & $\xi_1$, $\xi_2$ & $\Xi^{(1)}_{\mu}$, $\Xi^{(2)}_{\mu}$ & $\Xi'^{(1)}_{\alpha}$, $\Xi'^{(2)}_{\alpha}$ & $I_{\mu \alpha}$, $\mathcal{J}'_{\mu\alpha}$ &$\delta_{\mu \nu}$, $\mathcal{J}_{\mu \nu}$ &$\delta_{\alpha \beta}$, $\mathcal{J}''_{\alpha \beta}$ \\ \hline $q=2 $ & $\xi_1$, $\xi_2$ & $\Xi^{(1)}_{\mu}$, $\Xi^{(2)}_{\mu}$ & $\Xi'^{(1)}_{\alpha}$, $\Xi'^{(2)}_{\alpha}$ & $I_{\mu \alpha}$ & $\delta_{\mu \nu}$ & $\delta_{\alpha \beta}$ \\ \hline $q=1$ & $\xi_1$ & $\Xi^{(1)}_{\mu}$ & $\Xi'^{(1)}_{\alpha}$ & $I_{\mu \alpha}$ & $\delta_{\mu \nu}$ & $\delta_{\alpha \beta}$ \\ \hline \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline \hline \hline \multirow{2}{*}{Correlators} & \multicolumn{3}{c|}{\# of functions} & \multicolumn{3}{c|}{Conservation} \\ \cline{2-7} & $q > 2$ & $ q = 2$ & $q = 1$ & $q > 2$ & $q = 2$ & $q = 1$ \\ \hline $\langle J_{\mu} \mathcal{O} \rangle$ & 2 & 2 & 1 & 1 & 1 & 1 \\ \hline $\langle J_{\mu} J_{\nu} \rangle$ & 5 & 4 & 2 & 2 & 2 & 1 \\ \hline $\langle T_{\mu \nu} \mathcal{O} \rangle$ & 4 & 4 & 1 & 2 & 2 & 1 \\ \hline $\langle T_{\mu \nu} J_{\alpha}\rangle$ & 12 & 8 & 2 & 10 & 8 & 3 \\ \hline $\langle T_{\mu \nu} T_{\alpha \beta} \rangle$ & 19 & 10 & 3 & 12 & 8 & 2 \\ \hline \hline \hline \multirow{2}{*}{Correlators, $d=4$} & \multicolumn{3}{c|}{\# of functions} & \multicolumn{3}{c|}{EoM} \\ \cline{2-7} & \multicolumn{1}{l|}{$q = 3$} & \multicolumn{1}{l|}{$q = 2$} & \multicolumn{1}{l|}{$q = 1$} & \multicolumn{1}{l|}{$q = 3$} & \multicolumn{1}{l|}{$q = 2$} & \multicolumn{1}{l|}{$q = 1$} \\ \hline $\langle F_{\mu \nu} \mathcal{O} \rangle$ & 1 & 1 & 0 & 2 & 2 & 0 \\ \hline $\langle F_{\mu \nu} F_{\alpha \beta} \rangle$ & 10 & 5 & 2 &6 & 4 & 1 \\ \hline \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline \hline \hline \multicolumn{10}{|c|}{\textbf{Independent Tensor Structures for Bulk-to-Defect}} \\ \hline \hline \hline \multicolumn{3}{|c|}{Vectors} & \multicolumn{2}{c|}{\multirow{2}{*}{Bivector}} & \multicolumn{5}{c|}{2-Tensor} \\ \cline{1-3} \cline{6-10} \multirow{2}{*}{at $x$} & \multicolumn{2}{c|}{at $\textbf{x}'$} & \multicolumn{2}{c|}{} & \multirow{2}{*}{at $x$} & \multicolumn{4}{c|}{at $\textbf{x}'$} \\ \cline{2-5} \cline{7-10} & spin $=a$ & $i$ & $(\mu,a)$ & $(\mu,i)$ & & (a,b) &(a,i) &(i,a) &(i,j) \\ \hline $\hat{\Xi}^{(1)}_{\mu}$ & 0 & $\hat{\mathcal{X}}'_{i}$ & $\hat{\mathcal{I}}_{\mu a}$ & $\hat{\mathcal{I}}_{\mu i} $ & \multicolumn{1}{l|}{$\mathcal{J}_{\mu \nu}$, $\delta_{\mu \nu}$} & $\delta_{ab}$ & 0 & 0 & $\delta_{ij}$ \\ \hline \hline \hline \end{tabular}
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\begin{tabular}{|lcccc|} \hline Method & $\mathit{F_{l<10}}$ & $\mathit{J_{l<10}}$ & $\mathit{F_{l>20}}$ & $\mathit{J_{l>20}}$ \\ \hline\hline S2S* & 74.4 & 73.7 & 54.5 & 54.6 \\ HS2S~(ours) & \textbf{77.1} & \textbf{76.3} & \textbf{65.5} & \textbf{64.2} \\ \hline \end{tabular}
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\begin{tabular}{|lcccc|} \hline Method & $\mathit{avg}$ & $\mathit{th: 0}$ & $\mathit{th: 50}$ & $\mathit{th: 100}$ \\ \hline\hline S2S* & 63.3 & 33.6 & 30.8 & 33.1\\ HS2S~(ours) & \textbf{69.0} & \textbf{40.2} & \textbf{39.3} & \textbf{47.7}\\ \hline \end{tabular}
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\begin{tabular}{|l|c|c|c|c|c|c|} \hline & $a_{0}$ & $a_{1}$ & $a_{2}$ & $a_{3}$ & $a_{4}$ & $a_{5}$ \\ \hline $\widetilde{c}>0.01$ & -5.73 & $1.25 \times 10^{-2}$ & 1.38 & $2.61 \times 10^{-5}$ & $-4.01 \times 10^{-3}$ & $3.26 \times 10^{-1}$ \\ $-0.01<\widetilde{c}$ & -6.45 & $2.09 \times 10^{-2}$ & $-4.65 \times 10^{-2}$ & $3.06 \times 10^{-5}$ & $9.25 \times 10^{-3}$ & $-4.59 \times 10^{-1}$ \\ $-0.01<\widetilde{c} \leq 0.01$ & -5.80 & $1.35 \times 10^{-2}$ & $9.97 \times 10^{-1}$ & $3.80 \times 10^{-5}$ & $1.51 \times 10^{-5}$ & $-4.87 \times 10^{-4}$ \\ \hline \end{tabular}
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\begin{tabular}{l|r|r} \textbf{Property} & Natural & Selective \\ \hline Training sentences~ & 97842 & 97842 \\ Ratio of Singular to Plural main nouns & 67\% & 45\% \\ Ratio of Singular to Plural nouns (total) & 79\% & 71\% \\ Fraction of 0 attractors & 93\% & - \\ Fraction of 1 attractors & 5.6\% & 79\% \\ Fraction of 2 attractors & 1.1\% & 15\% \\ Fraction of 3 attractors & 0.3\% & 3.7\% \\ \hline \hline Testing Sentences & 157k & 157k \end{tabular}
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\begin{tabular}{l|cccc|cccc} Training set & \multicolumn{4}{c|}{Natural Sampling} & \multicolumn{4}{c}{Selective Sampling} \\ \hline Test attractors & 0 & 1 & 2 & 3 & 0 & 1 & 2 & 3 \\ \hline & \multicolumn{8}{c}{LANGUAGE MODEL} \\ \hline LSTM & \textbf{0.98} & 0.91 & 0.84 & 0.78 & 0.89 & \textbf{0.98} & \textbf{0.98} & 0.95 \\ ONLSTM &\textbf{ 0.98} & 0.92 & 0.86& 0.82& 0.90 & \textbf{0.98} & \textbf{0.98} & 0.95 \\ GRU & \textbf{0.97} & 0.88& 0.78 & 0.73& 0.87 & \textbf{0.98} & 0.97 & 0.94 \\ DRNN & \textbf{0.96} & 0.69 & 0.47 & 0.36 & 0.83 & \textbf{0.97} & 0.94 & 0.91 \\ \hline & \multicolumn{8}{c}{BINARY CLASSIFIER} \\ \hline LSTM &\textbf{ 0.97} & 0.93 & 0.87& 0.82& 0.60& \textbf{0.98} & 0.96 & 0.97 \\ ONLSTM &\textbf{ 0.97} & 0.91 & 0.84 & 0.81 & 0.64 & \textbf{0.98} & 0.97 & \textbf{0.98} \\ GRU &\textbf{ 0.97} & 0.88 & 0.76 & 0.69 & 0.62 & 0.95 & 0.94& \textbf{0.96} \\ DRNN & \textbf{0.97 }& 0.90& 0.81 & 0.77& 0.70 &\textbf{ 0.97 }& 0.96 & 0.96 \\ \hline \end{tabular}
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\begin{tabular}{l|c|c|c|c} Training set & \multicolumn{2}{c|}{ Natural} & \multicolumn{2}{c}{ Selective} \\ \hline Test attractors & 0 & 1 & 0 & 1 \\ \hline LSTM & \textbf{0.77} {($\pm$ 0.05)} & 0.66 ($\pm$ 0.04) & 0.63 ($\pm$ 0.04) & \textbf{0.83} {($\pm$ 0.06)} \\ ONLSTM & \textbf{0.76} {($\pm$ 0.07)} & 0.70 ($\pm$ 0.06) & 0.60 ($\pm$ 0.05) & \textbf{0.85} {($\pm$ 0.01)} \\ GRU & \textbf{0.74} {($\pm$ 0.02)} & 0.64 ($\pm$ 0.02) & 0.51 ($\pm$ 0.02) & \textbf{0.81} {($\pm$ 0.04)} \\ DRNN & \textbf{0.67} {($\pm$ 0.04)} & 0.44 ($\pm$ 0.04) & 0.48 ($\pm$ 0.04) & \textbf{0.79} {($\pm$ 0.03)} \\ \bottomrule \end{tabular}
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\begin{tabular}{l|c|c|c|c} \multicolumn{1}{c|}{Training set} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c|}{Selective} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c}{Selective} \\ \hline Test metric & \multicolumn{2}{c|}{Prediction Confidence} & \multicolumn{2}{c}{ \(\frac{P(grammatical)}{P(ungrammatical)}\)} \\ \hline LSTM & \textbf{5.72} & 2.56 & \textbf{303.91} & 12.90 \\ ONLSTM & \textbf{5.80} & 2.64 & \textbf{331.83} & 14.08 \\ GRU & \textbf{5.13} & 2.40 & \textbf{169.28} & 11.02 \\ DRNN & \textbf{5.15} & 2.38 & \textbf{172.78} & 10.77 \\ \end{tabular}
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\begin{tabular}{l|r|r|r|r|r|r} \multicolumn{1}{l|}{Architecture} & \multicolumn{3}{c|}{Natural Sampling} & \multicolumn{3}{c}{Selective Sampling} \\ \hline \multicolumn{1}{l|}{} & LM & BC & \multicolumn{1}{c|}{$\frac{BC}{LM}$} & LM & BC & \multicolumn{1}{c}{$\frac{BC}{LM}$} \\ \multicolumn{1}{l|}{} & & & \multicolumn{1}{c|}{} & & & \multicolumn{1}{c}{} \\ \hline DRNN & 44.85 & 168.81 & 3.76 & 40.80 & 458.80 & 11.24 \\ GRU & 220.36 & 626.24 & 2.84 & 83.93 & 624.06 & 7.44 \\ LSTM & 66.03 & 941.76 & 14.26 & 57.68 & 729.18 & 12.64 \\ ONLSTM & 71.48 & 586.42 & 8.20 & 58.41 & 698.10 & 11.95 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c} \multicolumn{1}{l|}{Architecture} & \multicolumn{1}{l|}{} & \multicolumn{2}{c|}{$\mathscr{N}$=535} & \multicolumn{2}{c|}{$\mathscr{N}$=1069} & \multicolumn{2}{c}{$\mathscr{N}$=1601} \\ \hline \multicolumn{1}{l|}{} & No fine-tune & Epoch=1 & Epoch=5 & Epoch=1 & Epoch=5 & Epoch=1 & Epoch=5 \\ \hline LSTM & \textbf{0.90} & 0.86 & 0.64 & 0.83 & 0.72 & 0.78 & 0.75 \\ ONLSTM & \textbf{0.91} & 0.87 & 0.48 & 0.84 & 0.44 & 0.78 & 0.60 \\ GRU & \textbf{0.87} & 0.85 & 0.80 & 0.83 & 0.78 & 0.80 & 0.78 \\ DRNN & \textbf{0.83} & 0.80 & 0.77 & 0.78 & 0.76 & 0.77 & 0.78 \\ \hline \end{tabular}
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\begin{tabular}{ccc} \toprule GPU & CPU & Memory \\ \midrule 0 & 1 & 1GB\\ 0 & 1 & 2GB\\ 1 & 2 & 4GB\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule GPU & CPU & Memory & Count \\ \midrule 0 & 1 & 2GB & 1.5\\ 1 & 2 & 4GB & 1\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule Name & Time Range & Baseline Instance & Test Set Time Range\\ \midrule Our cluster trace & 2 months & g4.xlarge and m5.xlarge & 1 week\\ Microsoft Philly cluster trace & 3 months & g4.xlarge & 1 week\\ Alibaba Fuxi cluster trace & 1 week & m5.24xlarge & 1 day \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \toprule Data & Model & MSE & PMSE & Time \\ \midrule \multirow{5}{*}{Ours} & Transformer & 2.51e-7 & 1.97e-7 & 44min\\ & LSTM & 0.0047 & 0.0039 & 28min \\ & SES & 0.0110 & 0.0046 & 37min \\ & ARIMA & 0.027 & 0.0063 & 130min \\ & Static & 0.7841 & 0.7841 \\ \toprule \multirow{5}{*}{Fuxi} & Transformer & 0.0021 & 0.0010 & 11min\\ & LSTM & 0.0035 & 0.0074 & 8min \\ & SES & 0.0026 & 0.0025 & 28s \\ & ARIMA & 0.025 & 0.021 & 20min\\ & Static & 0.8927 & 0.8927 \\ \toprule \multirow{5}{*}{Philly} & Transformer & 0.0003 & 0.0004 & 38min\\ & LSTM & 0.0040 & 0.0028 & 31min\\ & SES & 0.1470 & 0.1470 & 46min \\ & ARIMA & 0.020 & 0.093 & 84min \\ & Static & 0.7054 & 0.7054 \\ \bottomrule \end{tabular}
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\begin{tabular}{|c|c|} \hline \hline {\bf Methods} & {\bf Steps} \\ \hline \bf{ETCNet} & $\bf{16.50 \pm 6.03}$ \\ Gated-ACML & $33.83 \pm 10.08$ \\ SchedNet & $39.49 \pm 3.27$ \\ Message-Dropout & $35.09 \pm 7.96$ \\ \hline A3C2(Full communication) & $16.20 \pm 5.85$ \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|} \hline \hline \multirow{2}{*} & {2 agents} & \multicolumn{2}{|c|}{3 agents} & \multicolumn{2}{|c|}{4 agents} \\ \cline{2-6} ~ & {$\le $ 50\%} & {$\le $ 33.3\%} & {$\le $ 66.6\%} & {$\le $ 25\%} & {$\le $ 50\%} \\ \hline \bf{ETCNet} & $\bf{52.19 \pm 14.63}$ & $\bf{54.59 \pm 18.63}$ & $53.52 \pm 17.81$ & $47.79 \pm 19.02$ & $\bf{46.04 \pm 17.39}$ \\ {Gated-ACML} & $93.80 \pm 13.33$ & $65.87 \pm 22.05$ & $60.35 \pm 20.40$ & $70.67 \pm 28.86$ & $46.28 \pm 18.43$ \\ {SchedNet} & $54.06 \pm 13.14$ & $54.95 \pm 17.41$ & $\bf{52.78 \pm 17.71}$ & $\bf{45.52 \pm 16.69}$ & $46.66 \pm 18.05$ \\ {Message-Dropout} & $91.385 \pm 13.94$ & $85.33 \pm 19.32$ & $61.01 \pm 19.53$ & $73.933 \pm 26.404$ & $59.63 \pm 23.98$ \\ \hline {A3C2 (Full communication)} & {$51.08 \pm 12.68$} & \multicolumn{2}{|c|}{$50.68 \pm 16.75$} & \multicolumn{2}{|c|}{$45.256 \pm 16.755$} \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline \hline ~ & Cooperative Navigation & Predator and Prey & Activation function \\ \hline EncoderNet & 6-20-6 & 52-40-15 & -relu-tanh \\ \hline ActorNet & 12-40-40-5 & \#-80-40-15 & -relu-relu-softmax \\ \hline CriticNet & 12-40-40-1 & \#-120-80-1 & -relu-relu-None \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline \hline ~ & Cooperative Navigation & Predator and Prey \\ \hline training time steps & 600000 & 600000 \\ \hline message length & 6 & 15 \\ \hline discount factor & 0.95 & 0.95 \\ \hline learning rate for ActorNet/EncoderNet & 0.0002 & 0.0002 \\ \hline learning rate for CriticNet & 0.0004 & 0.0004 \\ \hline entropy regularization weight & 0.01 & 0.01 \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline \hline ~ & ~ & Cooperative Navigation & Predator and Prey & Activation function \\ \hline \multirow{3}*{ETCNet} & GateNet & 6-40-40-2 & 52-80-80-2 & -relu-relu-softmax \\ \cline{2-5} ~ & LagrangeNet & 12-60-60-1 & \#-120-80-1 & -relu-relu-None \\ \cline{2-5} ~ & PenaltyNet & 12-60-60-1 & 52-60-40-1 & -relu-relu-relu-None \\ \hline \multirow{2}*{SchedNet} & wNet & 6-20-20-1 & 52-20-20-1 & -relu-relu-sigmoid \\ \cline{2-5} ~ & QNet & 14-100-50-1 & \#-100-50-1 & -relu-relu-None \\ \hline \multirow{2}*{Gated-ACML} & QNet & 14-60-60-1 & \#-120-60-1 & -relu-relu-None \\ \cline{2-5} ~ & ClassfyNet & 6-40-40-2 & 52-80-80-2 & -relu-relu-softmax \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline \hline ~ & Cooperative Navigation & Predator and Prey \\\hline learning rate for GateNet & \multicolumn{2}{|c|}{0.0002} \\\hline learning rate for LagrangeNet & \multicolumn{2}{|c|}{0.0004} \\\hline learning rate for PenaltyNet & \multicolumn{2}{|c|}{0.0004} \\\hline \hline \end{tabular}
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\begin{tabular}{lc|lc|lc} \toprule Relations & Proportion(\%) & Relations & Proportion(\%) & Relations & Proportion(\%)\\ \midrule MotivatedByGoal & 1.7 & HasProperty & 0.8 & CausesDesire & 4.2 \\ HasPrerequisite & 5.1 & Desires & 0.8 & CapableOf & 5.9 \\ HasSubevent & 5.1 & RelatedTo & 8.5 & DistinctFrom & 1.7 \\ HasA & 1.7 & NotDesires & 0.8 & HasLastSubevent & 0.8 \\ PartOf & 2.5 & UsedFor & 4.2 & AtLocation & 36.4 \\ FormOf & 0.8 & Antonym & 5.9 & Causes & 12.7 \\ \bottomrule \end{tabular}
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\begin{tabular}{|l|c|} \hline \textbf{Constant} & \textbf{Value}\\ \hline $k_1$ & $10$\\ $k_2$ & $10$\\ $k_3$ & $-2$\\ $k_4$ & $-1$\\ $k_5$ & $1$\\ \hline \end{tabular}
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\begin{tabular}{|l|c|l|c|} \hline \textbf{Constant} & \textbf{Value} & \textbf{Constant} & \textbf{Value}\\ \hline $\mu$ & $0.05$ & $h$ & $0.07$\\ $\gamma$ & $10$ & $\gamma_u$ & $0.001$\\ $\alpha$ & $0.1$ & $\gamma_\mu$ & $0.1$\\ $\gamma_p$ & $0.1$ & $\gamma^0_s$ & $0.1$\\ $\lambda_s$ & $10$ & $\gamma^1_s$ & $0.01$\\ \hline \end{tabular}
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\begin{tabular}{lrrc} \toprule[0.5pt] Method & GFLOPs ($\blacktriangle$) & Memory(M $\blacktriangle$) & mIoU \% \\ \hline\hline Baseline & 0.00 & 0.00 & 75.37\\ self-attention & 121.62 & 471.04 & 78.83\\ HCNet &71.63 & 70.08 & 79.86 \\ \bottomrule[0.5pt] \end{tabular}
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\begin{tabular}{lcccccc} \toprule[0.5pt] Method & Imp surf & Building & Low veg &Tree& Car & OA \\ \hline\hline ADL\_3 & 89.5 &93.2 &82.3 &88.2 &63.3 & 88.0\\ DST\_2 & 90.5 &93.7 &83.4 & 89.2 & 72.6 & 89.1\\ ONE\_7 &91.0 & 94.5 & 84.4 & 89.9 & 77.8 & 89.8\\ DLR\_10 & 92.3 & 95.2 & 84.1 & 90.0 & 79.3 & 90.3\\ GSN & 92.2 & 95.1 & 83.7 & 89.9 &82.4 & 90.3\\ HCNet & 93.1 & 96.1 & 84.9 & 90.1 & 88.6 & 91.4\\ \bottomrule[0.5pt] \end{tabular}
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\begin{tabular}{lcc} \hline\hline Parameters & two sectors & one sector \\ \hline ${kT_{e1}}\,\mathrm(keV)$ & $1.38^{+0.42}_{-0.25}$ & $1.37^{+0.28}_{-0.21}$\\ ${kT_{e2}}\,\mathrm(keV)$ & $0.33^{+0.01}_{-0.03}$ & $0.31^{+0.01}_{-0.02}$\\ $n_\mathit{e}\,t,(10^{10}\,\mathrm{cm}^{-3}\mathrm{s})$ & $6.20^{+2.68}_{-1.80}$ & $7.08^{+1.85}_{-1.75}$\\ $Norm_{1},(10^{-6})$ & $2.47^{+0.74}_{-0.69}$ & $3.12^{+0.71}_{-0.62}$\\ $Norm_{2},(10^{-6})$ & $2.53^{+0.83}_{-0.76}$ & $3.26^{+0.82}_{-0.36}$\\ Oxygen & $ 1.86^{+0.31}_{-0.31}$ & $2.03^{+0.36}_{-0.28}$\\ Neon & $ 3.77^{+1.10}_{-0.71}$ & $4.15^{+0.76}_{-0.62}$\\ Magnesium & $ 2.10^{+0.70}_{-0.45}$ & $2.03^{+0.46}_{-0.34}$\\ Silicon & $1.51^{+0.54}_{-0.37}$ & $1.43^{+0.37}_{-0.29}$\\ Sulfur & $1.25^{+0.71}_{-0.51}$ & $1.48^{+0.56}_{-0.44}$\\ \textit{C-statistic}& 6830 & 7338\\ \textit{$\chi^2_{P}$} & 12676 & 12680\\ dof & 12438& 12438\\ goodness & 0.71& 0.76\\ \hline \end{tabular}
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\begin{tabular}{lcc} \hline\hline Parameters & two sectors & one sector \\ \hline ${kT_{e}}\,\mathrm(keV)$ & $0.97^{+0.21}_{-0.14}$ & $0.91^{+0.19}_{-0.13}$\\ $n_\mathit{e}\,t_{1},(10^{10}\,\mathrm{cm}^{-3}\mathrm{s})$ & $7.24^{+5.38}_{-2.65}$ & $6.81^{+5.75}_{-2.54}$\\ $Norm,(10^{-5})$ & $1.82^{+0.52}_{-0.49}$ & $2.02^{+0.63}_{-0.55}$\\ Oxygen & $ 0.16^{+0.20}_{-0.09}$ & $0.14^{+0.15}_{-0.07}$\\ Neon & $ 0.34^{+0.13}_{-0.11}$ & $0.27^{+0.12}_{-0.05}$\\ Magnesium & $ 0.14^{+0.12}_{-0.10}$ & $0.13^{+0.11}_{-0.10}$\\ near background in source & $0.98^{+0.14}_{-0.14}$ & $0.81^{+0.12}_{-0.11}$ \\ near background scale & $1.00^{+0.02}_{-0.02}$ & $1.00^{+0.01}_{-0.01}$ \\ \textit{C-statistic}& 9669 & 10173\\ \textit{$\chi^{2}_{P}$} & 18486 & 18575\\ dof & 18665 & 18665\\ goodness& 0.46 & 0.49\\ \hline \end{tabular}
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\begin{tabular}{|l|c|c|c|} \hline & & vnei & blackbody\\ Region & observation & simulation & simulation \\ & [counts] & [counts] & [counts] \\ \hline two-sector near-background & 1784 & 1784 & 1784 \\ source ellipse & \phantom{0}983 & \phantom{0}981 & \phantom{0}979\\ \hline one-sector near-background & 3248 & 3248 & 3248 \\ source ellipse & \phantom{0}983 & \phantom{0}987 & \phantom{0}984\\ \hline \end{tabular}
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\begin{tabular}{|l|cc|} \hline two-sector background & \texttt{vnei} & blackbody \\ & [counts] & [counts] \\ \hline scaled background & \phantom{0}552 & \phantom{0}669 \\ source & \phantom{0}425 & \phantom{0}306 \\ S3/sky background & \phantom{000}4 & \phantom{000}4 \\ \hline \hline one-sector background & \texttt{vnei} & blackbody \\ & [counts] & [counts] \\ \hline scaled background & \phantom{0}592 & \phantom{0}699 \\ source & \phantom{0}391 & \phantom{0}281 \\ S3/sky background & \phantom{000}4 & \phantom{000}4 \\ \hline \end{tabular}
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\begin{tabular}{|l|cccc|} \hline Near-Background &\multicolumn{4}{c|}{Point Source: vnei}\\ \hline & m & n & $D_{0.999}(m,n)$ & $D$\\ \hline two-sector& 86499 & 809 & 0.069 & 0.16\\ one-sector& 86159 & 809 & 0.069 & 0.15\\ \hline \hline Near-Background &\multicolumn{4}{c|}{Point Source: blackbody}\\ \hline & m & n & $D_{0.999}(m,n)$ & $D$\\ \hline two-sector& 83766 & 809 & 0.069 & 0.10 \\ one-sector& 83831 & 809 & 0.069 & 0.08 \\ \hline \end{tabular}
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\begin{tabular}{|l|ccc|} \hline Near-Background &\multicolumn{3}{c|}{Point Source: vnei}\\ \hline & $\chi^{2}$ & P-value & Dof\\ \hline two-sector& 178.91 & $4.02\times10^{-23}$ & 30\\ one-sector& 144.46 & $6.39\times10^{-17}$ & 30\\ \hline \hline Near-Background &\multicolumn{3}{c|}{Point Source: blackbody}\\ \hline & $\chi^{2}$ & P-value & Dof\\ \hline two-sector& 74.68 & $1.12\times10^{-5}$ & 30\\ one-sector& 61.93 & $5.33\times10^{-4}$ & 30\\ \hline \end{tabular}
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\begin{tabular}{lccc|ccc} \hline \multirow{2}{*}{\textbf{Main Frame Elements}} & \multicolumn{3}{c}{\textbf{Gold spatial triggers}} & \multicolumn{3}{c}{\textbf{Predicted spatial triggers}} \\ \cline{2-7} & \textbf{P(\%)} & \textbf{R(\%)} & \textbf{F1} & \textbf{P(\%)} & \textbf{R(\%)} & \textbf{F1} \\ \hline \textsc{Figure} & 81.39 & 84.26 & 82.77 & 67.53 & 71.08 & 69.14 \\ \hline \textsc{Ground} & 92.01 & 93.41 & 92.69 & 70.87 & 80.13 & 75.09 \\ \hline \textsc{Hedge} & 75.51 & 83.08 & 78.91 & 68.94 & 74.05 & 71.19 \\ \hline \textsc{Diagnosis} & 54.73 & 78.41 & 64.06 & 48.49 & 67.67 & 55.95 \\ \hline \textsc{Relative Position} & 87.47 & 81.01 & 83.54 & 60.13 & 66.35 & 62.17 \\ \hline \textsc{Distance} & 75.83 & 80.83 & 75.53 & 73.63 & 80.00 & 74.25 \\ \hline \textsc{Position Status} & 68.59 & 66.20 & 66.97 & 61.42 & 64.45 & 61.55 \\ \hline \textsc{Overall} & 82.60 & 85.31 & 83.92 & 66.95 & 73.17 & 69.81 \\ \hline \end{tabular}
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\begin{tabular}{lccc} \hline \textbf{Spatial triggers used}&\textbf{Overall P (\%)}&\textbf{Overall R (\%)}&\textbf{Overall F1} \\ \hline Gold annotated triggers & 72.80 & 80.87 & 76.62 \\ \hline Predicted triggers & 65.71 & 73.48 & 69.38 \\ \hline \end{tabular}
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\begin{tabular}{l|l|c|c|c} \hline \textbf{Phenotype variant} & \textbf{Example} & \textbf{Precision(\%)} & \textbf{Recall(\%)} & \textbf{F1} \\ \hline BR & \textit{cerebellum} & \textcolor{black}{$73.58$} & \textcolor{black}{$89.62$} & \textcolor{black}{$80.81$} \\ \hline BR $+$ CS & \textit{cerebellum, left} & \textcolor{black}{$68.34$} & \textcolor{black}{$85.47$} & \textcolor{black}{$75.95$} \\ \hline BR $+$ SS\_CO & \textit{cerebellum, chronic} & \textcolor{black}{$55.53$} & \textcolor{black}{$82.0$} & \textcolor{black}{$66.22$} \\ \hline BR $+$ CS $+$ SS\_CO & \textit{cerebellum, left, chronic} & \textcolor{black}{$49.67$} & \textcolor{black}{$74.11$} & \textcolor{black}{$59.48$} \\ \hline BR $+$ CS $+$ SS & \textit{cerebral hemisphere - frontal lobe, bilateral, subacute} & \textcolor{black}{$46.32$} & \textcolor{black}{$56.96$} & \textcolor{black}{$51.09$} \\ \hline BR $+$ CS $+$ LC & \textit{basal ganglia, bilateral, yes} & \textcolor{black}{$62.53$} & \textcolor{black}{$77.2$} & \textcolor{black}{$69.09$} \\ \hline BR $+$ CS $+$ SS\_CO $+$ LC & \textit{basal ganglia, bilateral, chronic, yes} & \textcolor{black}{$48.59$} & \textcolor{black}{$72.49$} & \textcolor{black}{$58.18$} \\ \hline \end{tabular}
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\begin{tabular}{clccccccc} \toprule \textbf{\#}& \textbf{Metrics} & \textbf{en-de} & \textbf{en-zh} & \textbf{ro-en} & \textbf{et-en} & \textbf{ne-en} & \textbf{si-en} & \textbf{ru-en}\\ \midrule 1&Baseline (test) & 0.146 & 0.190 & 0.685 & 0.477 & 0.386 & 0.374 & 0.548 \\ \midrule 2&BERT & \textbf{0.120} & 0.167 & 0.650 & 0.306 & 0.475 & - & \textbf{0.354} \\ 3&BERT (align) & 0.091 & 0.170 & 0.672 & 0.307 & \textbf{0.478} & - & 0.340 \\ 4&BERT (ppl) & 0.068 & 0.187 & 0.671 & 0.321 & 0.468 & - & 0.311 \\ 5&BERT (align+ppl) & 0.099 & \textbf{0.189} & \textbf{0.677} & \textbf{0.324} & 0.477 & - & 0.332 \\ \bottomrule \end{tabular}
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\begin{tabular}{clccccccc} \toprule \textbf{\#}& \textbf{Metrics} & \textbf{en-de} & \textbf{en-zh} & \textbf{ro-en} & \textbf{et-en} & \textbf{ne-en} & \textbf{si-en} & \textbf{ru-en}\\ \midrule 1&BERT & \textbf{0.143} & 0.131 & 0.389 & 0.217 & 0.318 & - & \textbf{0.259} \\ 2&BERT (align) & 0.122 & 0.133 & 0.422 & 0.219 & \textbf{0.322} & - & 0.251 \\ 3&BERT (ppl) & 0.105 & 0.145 & 0.416 & 0.225 & 0.315 & - & 0.240 \\ 4&BERT (align+ppl) & 0.132 & \textbf{0.152} & \textbf{0.439} & \textbf{0.228} & 0.320 & - & 0.247 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule & mBERT & XLM \\ \midrule \textbf{en-de} & 0.120 & 0.056 \\ \textbf{en-zh} & 0.167 & 0.008 \\ \textbf{ro-en} & 0.650 & 0.568 \\ \textbf{et-en} & 0.306 & 0.254 \\ \textbf{ne-en} & 0.475 & 0.398 \\ \textbf{si-en} & - & 0.362 \\ \textbf{ru-en} & 0.354 & 0.228 \\ \bottomrule \end{tabular}
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\begin{tabular}{|l|c|c|} \hline \textbf{Workload} & \textbf{QPS range} & \textbf{Number of clients} \\ \hline img-dnn & 100 -- 2000 & 12 \\ masstree & 250 -- 2500 & 12 \\ moses & 10 -- 500 & 6 \\ shore & 10 -- 300 & 12 \\ silo & 250 -- 6000 & 18 \\ specjbb & 250 -- 7000 & 18 \\ sphinx & 0.2 -- 2.0 & 2 \\ xapian & 100 -- 1100 & 4 \\\hline \end{tabular}
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\begin{tabular}{|l|c|c|} \hline \textbf{Workload} & \textbf{Tail latency QoS} & \textbf{QPS single-thread} \\ \hline img-dnn & 3.6 ms & 650 \\ masstree & 1.4 ms & 1000 \\ moses & 7.1 ms & 30 \\ shore & 25 ms* & 100 \\ silo & 0.5 ms & 1000\\ specjbb & 0.7 ms & 1500\\ sphinx & 4275.4 ms** & 0.7 \\ xapian & 6.2 ms & 350 \\\hline \end{tabular}
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\begin{tabular}{c|cc|cc|cc|cc|cc} \hline $\alpha$ & $\beta$ & $\tilde \Omega$ & $\beta$ & $\tilde\Omega$ & $\beta$ & $\tilde\Omega$ & $\beta$ & $\tilde\Omega$ & $\beta$ & $\tilde\Omega$\\ \hline & $f = -3$ & & $f = -2$ & & $f = 0$ & & $f = 2$ & & $f = 3$ \\ \hline 1.0 & 0.96 & 0.160 & 1.00 & 0.267 & 0.58 & 0.374 & 0.30 & 0.110 & 0.32 & 0.071 \\ 0.9 & 0.91 & 0.161 & 0.95 & 0.267 & 0.55 & 0.373 & 0.29 & 0.110 & 0.30 & 0.071 \\ 0.8 & 0.86 & 0.163 & 0.88 & 0.268 & 0.52 & 0.367 & 0.27 & 0.111 & 0.28 & 0.072 \\ 0.7 & 0.79 & 0.167 & 0.81 & 0.269 & 0.48 & 0.356 & 0.25 & 0.112 & 0.26 & 0.073 \\ 0.6 & 0.72 & 0.172 & 0.73 & 0.269 & 0.43 & 0.337 & 0.23 & 0.114 & 0.24 & 0.075 \\ 0.5 & 0.63 & 0.179 & 0.63 & 0.266 & 0.38 & 0.310 & 0.21 & 0.116 & 0.21 & 0.077 \\ 0.4 & 0.53 & 0.184 & 0.52 & 0.253 & 0.33 & 0.270 & 0.19 & 0.117 & 0.18 & 0.080 \\ 0.3 & 0.41 & 0.178 & 0.38 & 0.221 & 0.26 & 0.215 & 0.17 & 0.114 & 0.15 & 0.082 \\ 0.2 & 0.26 & 0.142 & 0.24 & 0.156 & 0.18 & 0.144 & 0.14 & 0.097 & 0.12 & 0.077 \\ 0.1 & 0.12 & 0.064 & 0.11 & 0.065 & 0.10 & 0.060 & 0.09 & 0.052 & 0.08 & 0.047 \\ \hline \hline \end{tabular}
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\begin{tabular}{lccccc} \hline \textbf{Dataset} & \textbf{Train} &\textbf{Valid} & \textbf{Test} & \textbf{\#Intent} & \textbf{\#Slot} \\ \hline ATIS & 4,478 & 500 & 893 & 26 & 83 \\ SNIPS & 13,084 & 700 & 700 & 7 & 39 \\ Facebook TOP & 31,279 & 4,462 & 9,042 & 25 & 36 \\ \hline \end{tabular}
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\begin{tabular}{ccccccc} \hline \textbf{Epoch} & \textbf{MeanEucDist} &\textbf{NN-cos} & \textbf{NN-Euc} & \textbf{SNIPS} & \textbf{ATIS} & \textbf{TOP}\\ \hline 100 & 0.3677$\pm$0.25\% & 0.66$\pm$1.90\% & 0.65$\pm$2.00\% & 79.29 & 82.31 & 78.09 \\ 200 & 0.3254$\pm$0.08\% & 2.20$\pm$0.69\% & 2.30$\pm$0.84\% & 85.43 & 84.99 & 81.59 \\ 300 & 0.3023$\pm$0.09\% & 3.66$\pm$0.92\% & 3.96$\pm$0.55\% & 86.86 & 86.11 & 83.17 \\ 400 & 0.2841$\pm$0.23\% & 4.84$\pm$0.58\% & 5.26$\pm$0.83\% & \textbf{89.71} & 87.01 & 83.45 \\ 500 & 0.2685$\pm$0.26\% & 5.72$\pm$0.48\% & 6.21$\pm$0.78\% & 87.71 & 87.23 & 83.82 \\ 600 & 0.2573$\pm$0.12\% & 6.20$\pm$0.39\% & 6.72$\pm$0.18\% & 88.14 & 85.69 & 83.41 \\ 700 & 0.2499$\pm$0.20\% & 6.42$\pm$0.49\% & 6.94$\pm$0.33\% & 88.00 & \textbf{87.35} & 84.27 \\ 800 & 0.2444$\pm$0.07\% & 6.54$\pm$0.39\% & 7.07$\pm$0.15\% & 88.57 & 86.90 & 84.09 \\ 900 & 0.2407$\pm$0.10\% & 6.62$\pm$0.31\% & 7.14$\pm$0.14\% & 88.57 & 86.56 & \textbf{84.42} \\ 1000 & 0.2380$\pm$0.07\% & 6.65$\pm$0.39\% & 7.16$\pm$0.10\% & 89.14 & 87.12 & 83.86 \\ \hline \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule oracle/reset & $93.78_{0.12}$ & $93.81_{0.11}$ & $93.82_{0.10}$ & $93.82_{0.10}$ \\ continue & $94.04_{0.07}$ & $94.05_{0.07}$ & $94.05_{0.07}$ & $94.06_{0.07}$ \\ stop & $93.86_{0.09}$ & $93.90_{0.07}$ & $93.90_{0.07}$ & $93.91_{0.07}$ \\ \midrule oracle/reset & $73.20_{0.31}$ & $76.55_{0.24}$ & $77.42_{0.27}$ & $77.54_{0.22}$ \\ continue & $81.99_{0.04}$ & $82.30_{0.03}$ & $82.37_{0.08}$ & $82.41_{0.08}$ \\ stop & $74.35_{0.23}$ & $77.06_{0.14}$ & $77.73_{0.13}$ & $77.82_{0.09}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule oracle & $94.10_{0.08}$ & $92.98_{0.07}$ & $91.66_{0.22}$ & $85.95_{0.79}$ \\ reset & $94.20_{0.11}$ & $94.34_{0.06}$ & $94.33_{0.01}$ & $94.42_{0.04}$ \\ reset (mult.) & $94.15_{0.07}$ & $93.98_{0.08}$ & $94.06_{0.06}$ & $94.16_{0.05}$ \\ continue & $94.15_{0.02}$ & $94.35_{0.05}$ & $94.37_{0.04}$ & $94.33_{0.04}$ \\ stop & $93.95_{0.09}$ & $94.11_{0.05}$ & $94.24_{0.07}$ & $94.25_{0.06}$ \\ \midrule oracle & $75.09_{0.17}$ & $80.67_{0.40}$ & $78.69_{1.27}$ & $47.38_{1.79}$ \\ reset & $75.06_{0.16}$ & $87.21_{0.14}$ & $91.24_{0.02}$ & $92.46_{0.09}$ \\ reset (mult.) & $75.04_{0.18}$ & $86.19_{0.12}$ & $90.76_{0.11}$ & $92.16_{0.03}$ \\ continue & $82.01_{0.06}$ & $89.17_{0.08}$ & $91.80_{0.12}$ & $92.69_{0.01}$ \\ stop & $75.08_{0.54}$ & $87.16_{0.08}$ & $90.98_{0.13}$ & $92.18_{0.06}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule percep. (first) & $92.81_{0.06}$ & $93.22_{0.04}$ & $93.44_{0.02}$ & $93.52_{0.06}$ \\ percep. (last) & $92.84_{0.11}$ & $93.57_{0.06}$ & $93.86_{0.09}$ & $93.77_{0.04}$ \\ m. (last) & $94.10_{0.07}$ & $94.29_{0.07}$ & $94.27_{0.03}$ & $94.43_{0.04}$ \\ cost-s. m. (last) & $93.98_{0.03}$ & $94.32_{0.10}$ & $94.37_{0.03}$ & $94.33_{0.13}$ \\ log loss (beam) & $92.29_{0.07}$ & $92.09_{0.11}$ & $94.24_{0.08}$ & $94.32_{0.02}$ \\ log loss (neig.) & $94.22_{0.00}$ & $94.29_{0.03}$ & $94.27_{0.06}$ & $94.38_{0.01}$ \\ \midrule percep. (first) & $77.62_{0.14}$ & $86.32_{0.05}$ & $89.83_{0.05}$ & $91.00_{0.07}$ \\ percep. (last) & $77.67_{0.07}$ & $87.62_{0.03}$ & $90.82_{0.16}$ & $91.98_{0.11}$ \\ m. (last) & $81.75_{0.04}$ & $88.80_{0.02}$ & $91.91_{0.05}$ & $92.81_{0.05}$ \\ cost-s. m. (last) & $81.76_{0.05}$ & $88.92_{0.06}$ & $91.81_{0.03}$ & $92.81_{0.03}$ \\ log loss (beam) & $77.50_{0.07}$ & $88.25_{0.08}$ & $91.46_{0.06}$ & $92.56_{0.11}$ \\ log loss (neig.) & $81.94_{0.02}$ & $89.01_{0.10}$ & $91.75_{0.03}$ & $92.60_{0.03}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule log loss (neighbors); no acc. & $94.25_{0.02}$ & $93.61_{0.07}$ & $92.77_{0.11}$ & $92.08_{0.08}$ \\ log loss (beam); no acc. & $92.31_{0.08}$ & $86.89_{0.20}$ & $87.58_{0.27}$ & $89.51_{0.28}$ \\ cost-sensitive margin (last); no acc. & $93.94_{0.11}$ & $93.31_{0.06}$ & $92.30_{0.05}$ & $90.61_{0.14}$ \\ \midrule log loss (neighbors); acc. & $94.23_{0.03}$ & $94.30_{0.06}$ & $94.31_{0.05}$ & $94.37_{0.09}$ \\ log loss (beam); acc. & $92.33_{0.08}$ & $92.16_{0.50}$ & $94.26_{0.05}$ & $94.37_{0.05}$ \\ cost-sensitive margin (last); acc. & $94.07_{0.07}$ & $94.26_{0.07}$ & $94.28_{0.04}$ & $94.26_{0.04}$ \\ \midrule \midrule log loss (neighbors); no acc. & $81.95_{0.03}$ & $88.01_{0.06}$ & $89.48_{0.08}$ & $88.77_{0.09}$ \\ log loss (beam); no acc. & $77.70_{0.04}$ & $86.76_{0.06}$ & $88.58_{0.09}$ & $88.12_{0.06}$ \\ cost-sensitive margin (last); no acc. & $81.74_{0.05}$ & $87.35_{0.11}$ & $89.18_{0.12}$ & $88.89_{0.17}$ \\ \midrule log loss (neighbors); acc. & $82.00_{0.05}$ & $89.14_{0.08}$ & $91.68_{0.02}$ & $92.60_{0.04}$ \\ log loss (beam); acc. & $77.61_{0.26}$ & $88.18_{0.05}$ & $91.44_{0.06}$ & $92.58_{0.03}$ \\ cost-sensitive margin (last); acc. & $81.73_{0.01}$ & $88.83_{0.02}$ & $91.85_{0.03}$ & $92.87_{0.02}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule log loss (neighbors); always & $94.27_{0.10}$ & $94.37_{0.02}$ & $94.39_{0.06}$ & $94.33_{0.07}$ \\ log loss (beam); always & $92.26_{0.08}$ & $92.23_{0.66}$ & $94.33_{0.05}$ & $94.30_{0.04}$ \\ \midrule log loss (neighbors); on-cost increase & $92.06_{0.78}$ & $93.65_{0.07}$ & $93.67_{0.16}$ & $92.22_{0.32}$ \\ log loss (beam); on-cost increase & $92.23_{0.11}$ & $93.00_{0.33}$ & $93.10_{0.57}$ & $91.98_{0.32}$ \\ \midrule \midrule log loss (neighbors); always & $82.01_{0.04}$ & $89.11_{0.05}$ & $91.75_{0.01}$ & $92.62_{0.06}$ \\ log loss (beam); always & $77.52_{0.17}$ & $88.19_{0.05}$ & $91.43_{0.03}$ & $92.49_{0.04}$ \\ \midrule log loss (neighbors); on-cost increase & $79.35_{0.07}$ & $88.53_{0.08}$ & $91.44_{0.03}$ & $92.45_{0.06}$ \\ log loss (beam); on-cost increase & $77.57_{0.06}$ & $86.69_{0.07}$ & $90.47_{0.03}$ & $91.72_{0.05}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule & 1 & 2 & 4 & 8 \\ \midrule oracle & $94.09_{0.09}$ & $92.92_{0.11}$ & $91.29_{0.27}$ & $86.47_{0.62}$ \\ reset & $94.06_{0.07}$ & $94.15_{0.07}$ & $94.16_{0.02}$ & $94.14_{0.07}$ \\ reset (mult.) & $93.97_{0.03}$ & $93.87_{0.04}$ & $93.95_{0.01}$ & $94.05_{0.09}$ \\ continue & $94.16_{0.03}$ & $94.23_{0.09}$ & $94.23_{0.04}$ & $94.29_{0.11}$ \\ stop & $93.88_{0.02}$ & $94.02_{0.04}$ & $94.09_{0.06}$ & $94.18_{0.07}$ \\ \midrule oracle & $74.55_{0.21}$ & $81.54_{0.43}$ & $77.18_{0.74}$ & $49.67_{3.23}$ \\ reset & $75.38_{0.44}$ & $87.00_{0.14}$ & $90.98_{0.05}$ & $92.31_{0.18}$ \\ reset (mult.) & $74.85_{0.46}$ & $86.19_{0.17}$ & $90.45_{0.11}$ & $91.78_{0.07}$ \\ continue & $81.55_{0.01}$ & $88.86_{0.02}$ & $91.53_{0.19}$ & $92.36_{0.06}$ \\ stop & $74.61_{0.35}$ & $86.66_{0.10}$ & $90.78_{0.12}$ & $91.97_{0.04}$ \\ \bottomrule \end{tabular}
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\begin{tabular}{c|ccccccc} \toprule Teacher & WRN-40-2 & WRN-40-2 & resnet56 & resnet110 & resnet110 & resnet32x4 & vgg13 \\ Student & WRN-16-2 & WRN-40-1 & resnet20 & resnet20 & resnet32 & resnet8x4 & vgg8 \\ \midrule Teacher & 75.61 & 75.61 & 72.34 & 74.31 & 74.31 & 79.42 & 74.64 \\ Student & 73.26 & 71.98 & 69.06 & 69.06 & 71.14 & 72.50 & 70.36 \\ \midrule KD & $74.92\,(71\%\uparrow)$ & $73.54\,(43\%\uparrow)$ & $70.66\,(49\%\uparrow)$ & $70.67\,(31\%\uparrow)$ & $73.08\,(61\%\uparrow)$ & $73.33\,(12\%\uparrow)$ & $72.98\,(61\%\uparrow)$ \\ $\ell_2$ loss & $75.53\,(97\%\uparrow)$ & $74.33\,(65\%\uparrow)$ & $71.42\,(72\%\uparrow)$ & $71.30\,(43\%\uparrow)$ & $73.81\,(84\%\uparrow)$ & $74.01\,(22\%\uparrow)$ & $72.33\,(46\%\uparrow)$ \\ LSH loss & $75.61\,(100\%\uparrow)$ & $74.20\,(61\%\uparrow)$ & $71.51\,(75\%\uparrow)$ & $71.73\,(51\%\uparrow)$ & $73.69\,(80\%\uparrow)$ & $73.49\,(14\%\uparrow)$ & $72.69\,(54\%\uparrow)$ \\ $\ell_2$ loss + LSH loss & $75.62\,(100\%\uparrow)$ & $74.54\,(71\%\uparrow)$ & $71.65\,(79\%\uparrow)$ & $71.39\,(44\%\uparrow)$ & $73.99\,(90\%\uparrow)$ & $73.37\,(13\%\uparrow)$ & $73.68\,(78\%\uparrow)$ \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc} \toprule Teacher & vgg13 & ResNet50 & ResNet50 & resnet32x4 & resnet32x4 & WRN-40-2 \\ Student & MobileNetV2 & MobileNetV2 & vgg8 & ShuffleNetV1 & ShuffleNetV2 & ShuffleNetV1 \\ \midrule Teacher & 74.64 & 79.34 & 79.34 & 79.42 & 79.42 & 75.61 \\ Student & 64.60 & 64.60 & 70.36 & 70.50 & 71.82 & 70.50 \\ \midrule KD & $67.37\,(28\%\uparrow)$ & $67.35\,(19\%\uparrow)$ & $73.81\,(38\%\uparrow)$ & $74.07\,(40\%\uparrow)$ & $74.45\,(35\%\uparrow)$ & $74.83\,(85\%\uparrow)$ \\ $\ell_2$ loss & $66.98\,(24\%\uparrow)$ & $65.73\,(8\%\uparrow)$ & $71.90\,(17\%\uparrow)$ & $74.65\,(47\%\uparrow)$ & $75.73\,(51\%\uparrow)$ & $75.37\,(95\%\uparrow)$ \\ LSH loss & $67.48\,(29\%\uparrow)$ & $67.02\,(16\%\uparrow)$ & $74.15\,(42\%\uparrow)$ & $75.49\,(56\%\uparrow)$ & $75.56\,(49\%\uparrow)$ & $75.89\,(105\%\uparrow)$ \\ $\ell_2$ loss + LSH loss & $67.16\,(25\%\uparrow)$ & $68.99\,(30\%\uparrow)$ & $74.89\,(50\%\uparrow)$ & $75.36\,(54\%\uparrow)$ & $76.70\,(64\%\uparrow)$ & $76.25\,(113\%\uparrow)$ \\ \bottomrule \end{tabular}
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\begin{tabular}{c|ccccccc} \toprule Teacher & WRN-40-2 & WRN-40-2 & resnet56 & resnet110 & resnet110 & resnet32x4 & vgg13 \\ Student & WRN-16-2 & WRN-40-1 & resnet20 & resnet20 & resnet32 & resnet8x4 & vgg8 \\ \midrule $std_{t}$ & 0.17 & 0.17 & 0.24 & 0.23 & 0.23 & 0.11 & 0.07 \\ $std_{s}$ & 0.20 & 0.26 & 0.27 & 0.27 & 0.26 & 0.16 & 0.10 \\ $D_t$ & 128 & 128 & 64 & 64 & 64 & 256 & 512 \\ $D_s$ & 128 & 64 & 64 & 64 & 64 & 256 & 512 \\ \midrule $(1, 1, 2048)$ & 75.33 & 73.50 & 71.25 & 71.17 & 73.37 & 73.64 & 73.06 \\ $(3, 1, 2048)$ & 75.47 & 74.16 & 71.70 & 71.68 & 73.87 & 74.11 & 72.91 \\ $(5, 1, 2048)$ & 75.99 & 74.43 & 71.41 & 71.66 & 73.32 & 73.66 & 73.77 \\ $(6, 1, 2048)$ & 75.62 & 74.54 & 71.65 & 71.39 & 73.99 & 73.37 & 73.68 \\ $(7, 1, 2048)$ & 76.34 & 74.36 & 71.18 & 71.78 & 73.96 & 73.70 & 73.89 \\ \midrule $(6, std_{t}, 2048)$ & 76.11 & 74.42 & 70.96 & 71.75 & 74.00 & 73.91 & 73.57 \\ $(6, std_{s}, 2048)$ & 75.53 & 74.25 & 71.43 & 71.60 & 74.19 & 73.82 & 73.61 \\ \midrule $(6, std_{t}, 4\times D_t)$ & 76.43 & 74.15 & 71.27 & 71.13 & 73.55 & 74.13 & 73.57 \\ $(6, std_{t}, 32\times D_t)$ & 75.84 & 74.51 & 70.96 & 71.75 & 74.00 & 73.77 & 73.25 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc} \toprule Teacher & vgg13 & ResNet50 & ResNet50 & resnet32x4 & resnet32x4 & WRN-40-2 \\ Student & MobileNetV2 & MobileNetV2 & vgg8 & ShuffleNetV1 & ShuffleNetV2 & ShuffleNetV1 \\ \midrule $std_{t}$ & 0.07 & 0.04 & 0.04 & 0.11 & 0.11 & 0.17 \\ $std_{s}$ & 0.06 & 0.06 & 0.10 & 0.06 & 0.06 & 0.06 \\ $D_t$ & 512 & 2048 & 2048 & 256 & 256 & 128 \\ $D_s$ & 640 & 640 & 512 & 960 & 1024 & 960 \\ \midrule $(1, 1, 2048)$ & 66.82 & 65.79 & 72.12 & 75.23 & 75.42 & 74.98 \\ $(3, 1, 2048)$ & 67.95 & 67.33 & 73.47 & 74.94 & 76.12 & 76.17 \\ $(5, 1, 2048)$ & 68.01 & 67.60 & 74.64 & 75.38 & 75.56 & 76.06 \\ $(6, 1, 2048)$ & 67.16 & 68.99 & 74.89 & 75.36 & 76.70 & 76.25 \\ $(7, 1, 2048)$ & 67.88 & 69.20 & 74.43 & 75.25 & 76.70 & 76.35 \\ \midrule $(6, std_t, 2048)$ & 68.12 & 67.57 & 72.89 & 75.22 & 76.52 & 75.63 \\ $(6, std_s, 2048)$ & 67.77 & 67.47 & 73.68 & 74.93 & 76.27 & 75.70 \\ \midrule $(6, std_t, 4\times D_t)$ & 68.12 & 67.95 & 72.80 & 75.02 & 76.46 & 76.36 \\ $(6, std_t, 32\times D_t)$ & 67.78 & 67.33 & 72.76 & 75.36 & 76.25 & 75.83 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|ccccccc} \toprule Teacher & WRN-40-2 & WRN-40-2 & resnet56 & resnet110 & resnet110 & resnet32x4 & vgg13 \\ Student & WRN-16-2 & WRN-40-1 & resnet20 & resnet20 & resnet32 & resnet8x4 & vgg8 \\ \midrule KD & 74.92 & 73.54 & 70.66 & 70.67 & 73.08 & 73.33 & 72.98 \\ 0 & \textbf{76.04} & 74.46 & 71.16 & \textbf{71.79} & \textbf{74.18} & \textbf{73.70} & 73.92 \\ mean & 75.39 & 74.11 & 71.52 & 70.95 & 73.85 & 73.64 & \textbf{73.98} \\ median & 75.62 & \textbf{74.54} & \textbf{71.65} & 71.39 & 73.99 & 73.37 & 73.68 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc} \toprule Teacher & vgg13 & ResNet50 & ResNet50 & resnet32x4 & resnet32x4 & WRN-40-2 \\ Student & MobileNetV2 & MobileNetV2 & vgg8 & ShuffleNetV1 & ShuffleNetV2 & ShuffleNetV1 \\ \midrule KD & 67.37 & 67.35 & 73.81 & 74.07 & 74.45 & 74.83 \\ 0 & 67.14 & 68.64 & 74.25 & \textbf{75.57} & \textbf{76.71} & 75.76 \\ mean & \textbf{68.16} & 68.07 & 74.54 & 75.55 & 75.32 & 75.99 \\ median & 67.16 & \textbf{68.99} & \textbf{74.89} & 75.36 & 76.70 & \textbf{76.25} \\ \bottomrule \end{tabular}
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\begin{tabular}{l|cc} \toprule Teacher & ResNet34 & ResNet34 \\ Student & ResNet18 & ResNet18 (pretrained by KD) \\ \midrule Teacher & 91.69 & 91.69 \\ Student & 89.15 & 89.88 \\ \midrule KD & $89.26\,(4\%\uparrow)$ & $89.85\,(2\%\downarrow)$ \\ $\ell_2$ (1FC) & $88.75\,(20\%\downarrow)$ & $90.89\,(56\%\uparrow)$ \\ $\ell_2$ (2FC) & $89.98\,(33\%\uparrow)$ & $90.77\,(49\%\uparrow)$ \\ \bottomrule \end{tabular}
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\begin{tabular}{l|cc} \toprule Teacher & ResNet101 & ResNet101\\ Student & ResNet50 & MobileNetV2\\ \midrule Teacher & 93.27 & 93.27 \\ Student & 92.76 & 89.53 \\ \midrule LSHL2 $\rightarrow$ KD & $92.69\,(14\%\downarrow)$ & $89.64\,(3\%\uparrow)$ \\ LSHL2 $\rightarrow$ L2 & $\textbf{93.17}\,(80\%\uparrow)$ & $\textbf{90.14}\,(16\%\uparrow)$ \\ LSHL2 $\rightarrow$ LSH & $92.40\,(71\%\downarrow)$ & $89.91\,(10\%\uparrow)$\\ LSHL2 $\rightarrow$ LSHL2 & $92.85\,(18\%\uparrow)$ & $89.90\,(10\%\uparrow)$\\ \bottomrule \end{tabular}
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\begin{tabular}{l|cc} \toprule Teacher & ResNet101 & ResNet101\\ Student & ResNet50 & MobileNetV2\\ \midrule Teacher & 77.67 & 77.67 \\ Student & 75.54 & 71.06 \\ \midrule LSHL2 $\rightarrow$ KD & $75.14\,(19\%\downarrow)$ & $71.47\,(6\%\uparrow)$ \\ LSHL2 $\rightarrow$ L2 & $77.04\,(70\%\uparrow)$ & $73.28\,(34\%\uparrow)$ \\ LSHL2 $\rightarrow$ LSH & $76.59\,(49\%\uparrow)$ & $73.73\,(40\%\uparrow)$\\ LSHL2 $\rightarrow$ LSHL2 & $\textbf{77.16}\,(76\%\uparrow)$ & $\textbf{73.73}\,(40\%\uparrow)$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lcc|cc|cc} \toprule & \multicolumn{2}{c}{\bf QNLI } & \multicolumn{2}{c}{\bf {CoNLL-2003 NER} } & \multicolumn{2}{c}{\bf SQuAD 2.0 } \\ Models & Original & Attack & Original & Attack & Original & Attack \\ \midrule BERT & 90.7 & 63.4 & 91.24 & 60.79 & 76.3 & 50.1 \\ AdvBERT & 90.8 & 75.8 & 90.68 & 71.47 & 76.6 & 52.4 \\ BERT+WordRec & 84.0 & 76.1 & 82.52 & 67.79 & 63.5 & 55.2 \\ CharBERT & \bf 91.7 & \bf 80.1 & \bf 91.81 & \bf 76.14 & \bf 78.6 & \bf 56.3 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccl} \toprule Dataset& \#Nodes&\#Edges&\#Features(Node)&\#Classes\\ \midrule PPI & 56,944 & 818,716 & 50 &121(multilabel) \\ Reddit & 232,965& 11,606,919 & 602& 41(single) \\ \bottomrule \end{tabular}
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\begin{tabular}{ccl} \toprule Models / Metrics& AUC(\%)& Logloss\\ \midrule GraphSAGE-MEAN & 71.33$\pm$0.1011 & 0.4526$\pm$0.0165\\ GraphSAGE-MAX & 68.34$\pm$0.3253 & 0.4640$\pm$0.0035\\ GraphSAGE-LSTM & 67.30$\pm$0.1710 & 0.4741$\pm$0.0171\\ GraphSAGE-GCN & 66.72$\pm$0.4274 & 0.4600$\pm$0.0052\\ GAT & 70.52$\pm$0.5625 & 0.4521$\pm$0.0172\\ FM & 60.24$\pm$ 0.0760 & 0.5065$\pm$0.0008\\ DNN & 65.09$\pm$ 0.1297 & 0.4894$\pm$0.0010\\ DeepFM & 65.33$\pm$ 0.0052 & 0.4850$\pm$0.0050\\ xDeepFM & 65.97$\pm$0.0010 & 0.4808$\pm$0.0031\\ DCN & 67.08$\pm$0.0003 & 0.4911$\pm$0.0016\\ \textbf{GAIN(ours)} & \textbf{74.15$\pm$0.0351} & \textbf{0.4250$\pm$0.0004}\\ \bottomrule \end{tabular}
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\begin{tabular}{|l|l|l|l|} \hline & Brazilian & American & European \\ \hline Hyperboloid & \textbf{0.780} & \textbf{0.670} &\textbf{0.581} \\ Struct2vec & 0.732 & 0.651 & 0.577 \\ Node2vec & 0.267 & 0.473 & 0.329 \\ \hline \end{tabular}
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