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\begin{tabular}{|c|c|c|} \hline Final state & BP1 & BP2 \\ \hline \hline $1\mu ^- 1e^+$ & 149.2 & 508.2 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c} \toprule & \# nodes &The percentage of top 5 labels ($v_c$'s label is 11)\\ \hline 2-hop neigh. $\mathcal{N}^2(v_c)$ & 3,600& 13 (23.2\%), 12 (21.8\%), \textbf{11 (19.7\%)}, 10 (17.3\%), 14 (12.9\%)\\ Ego-AE set $\mathcal{A}_{3,2} (v_c)$ & 46& \textbf{11 (45.3\%)}, 10 (17.2\%), 12 (14.1\%), 13 (12.5\%), 9 (7.8\%)\\ Ego-AE set $\mathcal{A}_{5,2} (v_c)$ & 222& \textbf{11 (46.0\%)}, 12 (24.9\%), 10 (13.8\%), 13 (11.0\%), 9 (2.8\%)\\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule \noalign{\smallskip} Model & With BN & Set5 & Set14 & BSD100 & Urban100 \\ \noalign{\smallskip} \hline \noalign{\smallskip} PACT-EDSR & \checkmark & 0.531/0.0083 & 0.273/0.0068 & 0.166/0.0056 & 0.354/0.0125 \\ PACT-EDSR & $\times$ & 0.575/0.0085 & 0.395/0.0101 & 0.274/0.0094 & 0.790/0.0278 \\ PAMS-EDSR & $\times$ & 0.029/0.0002 & 0.009/-0.0002 & 0.003/-0.0003 & -0.019/-0.0005 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \toprule \noalign{\smallskip} Init. & Set5 & Set14 & BSD100 & Urban100 \\ \noalign{\smallskip} \hline \noalign{\smallskip} Random & 31.782/0.8896 & 28.383/0.7779 & 26.273/0.6879 & 23.488/0.6780 \\ EMA & 32.002/0.8923 & 28.497/0.7797 & 28.497/0.7797 & 25.806/0.7788 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccc} \toprule\noalign{\smallskip} Dataset & bits & without $L_{SKT}$ & with $L_{SKT}$ & metrics. $\uparrow$ \\ \noalign{\smallskip} \hline \noalign{\smallskip} \multirow{2}*{Set5} & 8 &32.127/0.8939& 32.124/0.8940 & -0.003/0.0001 \\ & 4 & 31.538/0.8842 & 31.591/0.8851 & \textbf{0.053/0.0009}\\ \noalign{\smallskip} \hline \noalign{\smallskip} \multirow{2}*{Set14} & 8 &28.541/0.7807 & 28.585/0.7811 & \textbf{0.044/0.0004} \\ & 4 & 28.177/0.7723 & 28.199/0.7725 & 0.022/0.0002 \\ \noalign{\smallskip} \hline \noalign{\smallskip} \multirow{2}*{BSD100} & 8 & 27.550/0.7352 & 27.565/0.7352& 0.015 /0.0000 \\ & 4 & 27.302/0.7280 & 27.322/0.7282 & \textbf{0.020/0.0002}\\ \noalign{\smallskip} \hline \noalign{\smallskip} \multirow{2}*{Urban100} & 8 & 25.984/0.7835 & 26.016/0.7843 & 0.032/0.0008 \\ & 4 & 25.250/0.7607 & 25.321/0.7624 & \textbf{0.071/0.0017 } \\ \bottomrule \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|}\hline Scheme & QEC Code &$\eta_{\rm th}$& $\eta$, computational error rate & Resource &$N$ for $p_{\rm L}= 10^{-6}$ & $N$ for $p_{\rm L}=10^{-15}$ \\ \hline OCQC & 7-qubit Steane code&$\it{4\times10^{-3}}$ & $4\times10^{-4},~4\times10^{-5}$ & Bell pair &$2.6\times10^{19}$& $7.1\times10^{24}$\\ PLOQC & 7-qubit Steane code& $\it{2\times10^{-3}}$ & $4\times10^{-4},~4\times10^{-5}$ &Bell pair&$6.8\times10^{14}$ &$3.5\times10^{19}$\\ EDQC & Error detecting codes& $\it{1.57\times10^{-3}}$ &$1\times10^{-4},~1\times10^{-5}$ &Bell pair &$\mathcal{O}(10^{13})$&$\mathcal{O}(10^{16})$\\ CSQC & 7-qubit Steane code& $2.3\times10^{-4}$ & $8\times10^{-5},~1.97\times10^{-5}$& CSS qubits&$2.1\times10^{11}$&$6.9\times10^{15}$\\ MQQC & 7-qubit Steane code &$1.7\times10^{-3}$ & $\mathcal{O}(10^{-4}),~\mathcal{O}(10^{-4})$ &Bell pair&$2.7\times10^{14}$&$1.4\times10^{19}$\\ HQQC & 7-qubit Steane code& $4.6\times10^{-4}$ & $\mathcal{O}(10^{-4}),~\mathcal{O}(10^{-4})$ &Hybrid qubits&$8.2\times10^{9}$&$2.3\times10^{12}$\\ TPQC &Topological&$\it{5.3\times10^{-4}}$ & 0,~$1\times10^{-3}~(5.3\times10^{-4},~0)$& Entangled photons& $>2\times10^9$ & $>4.2\times10^{10}$\\ HTQC &Topological &$3.3\times10^{-3}$ & $1.5\times10^{-3},~3\times10^{-3}$ &Hybrid qubits&$8.5\times10^5$ & $1.7\times10^7$\\ PHTQC-2 & Topological & $5\times10^{-3}$ & $2.4\times10^{-3},~3\times10^{-3}$ &Hybrid qubits& $ 1.1\times10^6$ & $1.8\times10^7$\\ {\bf PHTQC-3} & Topological & $\bf 5.7\times10^{-3}$ & $2.6\times10^{-3},~2.3\times10^{-3}$ &Hybrid qubits& $2.9\times10^7$& $4.9\times10^8$\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Instance & Time (MIP) & Time (PADP) & GAP(\%) \\ \hline $\mathcal{I}(5,5,0.4,0.25)$ & 0.2 & 0.084 & 0 \\ $\mathcal{I}(5,10,0.4,0.25)$ & 2.371 & 0.204 & 0 \\ $\mathcal{I}(5,20,0.4,0.25)$ & 8.241 & 0.683 & 0.13 \\ $\mathcal{I}(5,30,0.4,0.25)$ & 10.31 & 1.127 & 0.16 \\ $\mathcal{I}(5,40,0.4,0.25)$ & 9.63 & 1.567 & 0.16 \\ $\mathcal{I}(10,5,0.4,0.25)$ & 0.225 & 0.115 & 0 \\ $\mathcal{I}(10,10,0.4,0.25)$ & 6.8 & 0.36 & 0 \\ $\mathcal{I}(10,20,0.4,0.25)$ & 53.848 & 1.041 & 0.02 \\ $\mathcal{I}(10,30,0.4,0.25)$ & 101.423 & 1.742 & 0.05 \\ $\mathcal{I}(10,40,0.4,0.25)$ & 138.449 & 2.437 & 0.06 \\ $\mathcal{I}(25,5,0.4,0.25)$ & 0.511 & 0.149 & 0 \\ $\mathcal{I}(25,10,0.4,0.25)$ & 256.734 & 0.466 & 0 \\ $\mathcal{I}(25,20,0.4,0.25)$ & 1891.068 & 1.332 & 0.14 \\ $\mathcal{I}(25,30,0.4,0.25)$ & 1425.692 & 2.248 & 0.2 \\ $\mathcal{I}(25,40,0.4,0.25)$ & 3015.04 & 3.176 & 0.22 \\ $\mathcal{I}(50,5,0.4,0.25)$ & 9.664 & 0.17 & 0.02 \\ $\mathcal{I}(50,10,0.4,0.25)$ & 3643.571 & 0.555 & 0.24 \\ $\mathcal{I}(100,5,0.4,0.25)$ & 106.115 & 0.245 & 0 \\ $\mathcal{I}(10,10,0.4,0.25)$ & 9669.398 & 0.802 & 0.13 \\ $\mathcal{I}(250,5,0.4,0.25)$ & 193.304 & 0.304 & 0 \\ $\mathcal{I}(500,5,0.4,0.25)$ & 742.221 & 0.434 & 0 \\ \hline min & 0.2 & 0.084 & 0 \\ max & 9669.398 & 3.176 & 0.24 \\ mean & 1013.563 & 0.916 & 0.073 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline Instance & CPLEX Time(sec) & CPLEX Gap(\%) & PADP Time(sec) & Improvement(\%) \\ \hline $\mathcal{I}(50,20,0.4,0.25)$ & 14401.456 & 0.6 & 1.628 & -0.33 \\ $\mathcal{I}(50,30,0.4,0.25)$ & 14401.767 & 0.5 & 2.699 & -0.36 \\ $\mathcal{I}(50,40,0.4,0.25)$ & 14470.37 & 1.1 & 4.025 & -0.37 \\ $\mathcal{I}(100,20,0.4,0.25)$ & 14404.549 & 2 & 2.251 & 0.05 \\ $\mathcal{I}(100,30,0.4,0.25)$ & 14421.458 & 2.1 & 3.635 & 0.01 \\ $\mathcal{I}(100,40,0.4,0.25)$ & 14406.975 & 1.8 & 4.9 & -0.14 \\ $\mathcal{I}(250,10,0.4,0.25)$ & 14405.094 & 1.9 & 0.98 & 0.09 \\ $\mathcal{I}(250,20,0.4,0.25)$ & 14406.464 & 5.4 & 3.005 & 0.66 \\ $\mathcal{I}(250,30,0.4,0.25)$ & 14404.798 & 6.4 & 5.658 & 0.87 \\ $\mathcal{I}(250,40,0.4,0.25)$ & 14406.866 & 5.7 & 7.724 & 0.13 \\ $\mathcal{I}(500,10,0.4,0.25)$ & 14407.241 & 4.5 & 1.502 & 0.62 \\ $\mathcal{I}(500,20,0.4,0.25)$ & 14406.308 & 7 & 5.662 & 1.13 \\ $\mathcal{I}(500,30,0.4,0.25)$ & 14406.978 & 7.6 & 8.255 & 1.48 \\ $\mathcal{I}(500,40,0.4,0.25)$ & 14405.674 & 8.9 & 10.203 & 2.66 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline $\epsilon$ & nStage & Value of stochastic solution($\%$) \\ \hline \multicolumn{ 1}{|c|}{0.1} & 5 & 2.97 \\ \multicolumn{ 1}{|c|}{} & 10 & 4.52 \\ \multicolumn{ 1}{|c|}{} & 20 & 4.47 \\ \multicolumn{ 1}{|c|}{} & 30 & 4.53 \\ \hline \multicolumn{ 1}{|c|}{0.25} & 5 & 4.03 \\ \multicolumn{ 1}{|c|}{} & 10 & 5.70 \\ \multicolumn{ 1}{|c|}{} & 20 & 6.83 \\ \multicolumn{ 1}{|c|}{} & 30 & 7.31 \\ \hline \multicolumn{ 1}{|c|}{0.5} & 5 & 3.95 \\ \multicolumn{ 1}{|c|}{} & 10 & 5.89 \\ \multicolumn{ 1}{|c|}{} & 20 & 7.80 \\ \multicolumn{ 1}{|c|}{} & 30 & 9.30 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline $\epsilon$ & nStage & Value of perfect information($\%$) \\ \hline \multicolumn{ 1}{|c|}{0.1} & 5 & 1.72 \\ \multicolumn{ 1}{|c|}{} & 10 & 2.14 \\ \multicolumn{ 1}{|c|}{} & 20 & 1.84 \\ \multicolumn{ 1}{|c|}{} & 30 & 1.76 \\ \hline \multicolumn{ 1}{|c|}{0.25} & 5 & 5.62 \\ \multicolumn{ 1}{|c|}{} & 10 & 7.09 \\ \multicolumn{ 1}{|c|}{} & 20 & 5.81 \\ \multicolumn{ 1}{|c|}{} & 30 & 5.17 \\ \hline \multicolumn{ 1}{|c|}{0.5} & 5 & 12.44 \\ \multicolumn{ 1}{|c|}{} & 10 & 16.36 \\ \multicolumn{ 1}{|c|}{} & 20 & 17.66 \\ \multicolumn{ 1}{|c|}{} & 30 & 16.92 \\ \hline \end{tabular}
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\begin{tabular}{|ccc|ccc|} \hline {nScenario} & {nStage} & Price of Fairness (\%) & {nScenario} & {nStage} & Price of Fairness (\%) \\ \hline 5 & 5 & 4.10 & 25 & 5 & 5.96\\ 5 & 10 & 4.66 & 25 & 10 & 6.98\\ 5 & 20 & 4.15 & 25 & 20 & 6.45\\ 5 & 30 & 3.89 & 25 & 30 & 6.31\\ 5 & 40 & 3.80 & 25 & 40 & 6.27\\ 10 & 5 & 4.19 & 50 & 5 & 6.81\\ 10 & 10 & 5.02 & 50 & 10 & 7.99\\ 10 & 20 & 4.89 & 100 & 5 & 7.13\\ 10 & 30 & 4.82 & 100 & 10 & 8.39\\ 10 & 40 & 4.80 & 250 & 5 & 7.08\\ & & & 500 & 5 & 7.07 \\ \hline \end{tabular}
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\begin{tabular}{|ccc|ccc|} \hline {nScenario} & {nStage} & value of Flexibility (\%) & {nScenario} & {nStage} & value of Flexibility (\%) \\ \hline 5 & 5 & 2.53 & 25 & 5 & 2.12\\ 5 & 10 & 5.38 & 25 & 10 & 5.34\\ 5 & 20 & 10.24 & 25 & 20 & 13.33\\ 5 & 30 & 12.39 & 25 & 30 & 17.61\\ 5 & 40 & 13.25 & 25 & 40 & 19.59\\ 10 & 5 & 2.16 & 50 & 5 & 1.55\\ 10 & 10 & 5.88 & 50 & 10 & 4.73\\ 10 & 20 & 11.81 & 100 & 5 & 1.23\\ 10 & 30 & 15.11 & 100 & 10 & 4.15\\ 10 & 40 & 16.63 & 250 & 5 & 1.21\\ & & & 500 & 5 & 1.25 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c} \toprule Subset & Duration(hrs) & \#Sentences & \#Male & \#Female \\ \midrule Training & 150 & 120098 & 161 & 179 \\ Development & 10 & 14326 & 12 & 28 \\ Test & 5 & 7200 & 13 & 7 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|c|c} \toprule Subset & SNRs & Noise corpus \\ \midrule Training & \begin{tabular}[c]{@{}c@{}}randomly sampled \\ between {[}0dB, 20dB{]}\end{tabular} & 100 Nonspeech Sounds \\ \midrule Development & 0, 5, 10, 15 and 20dB & \begin{tabular}[c]{@{}c@{}}100 Nonspeech Sounds \\ and NOISE-92\end{tabular} \\ \midrule Test & 0, 5, 10, 15 and 20dB & \begin{tabular}[c]{@{}c@{}}100 Nonspeech Sounds \\ and NOISE-92\end{tabular} \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Test Set} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 107.03 & 72.71 & 45.49 & 26.37 & 18.01 & 53.33 & 10.74 \\ \midrule E2E\_ASR-SpecAugment & 68.44 & 43.74 & 25.89 & 14.97 & 11.59 & 32.55 & 8.78 \\ \midrule E2E\_ASR-MCT & 27.92 & 19.13 & 14.72 & 11.96 & 10.36 & 16.71 & 9.64 \\ \midrule E2E\_ASR-MCT-SpecAugment & 24.43 & 16.85 & 14.11 & 11.16 & 9.66 & 15.14 & 9.30 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Development Set} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 98.30 & 62.64& 37.15 & 21.81 & 14.76 & 46.81 & 9.10 \\ \midrule E2E\_ASR-SpecAugment & 63.01 & 38.07 & 21.56 & 13.51 & 10.36 & 29.24 & 7.96 \\ \midrule E2E\_ASR-MCT & 25.26 & 16.11 & 12.16 & 10.09 & 9.22 &14.55 & 8.51 \\ \midrule E2E\_ASR-MCT-SpecAugment & 21.76 & 14.44 & 11.13 & 9.92 & 9.24 & 13.28 & 8.44 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Enhanced Test Set} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 44.11 & 29.85 & 20.12 & 14.75 & 12.51 & 24.06 & 14.23 \\ \midrule E2E\_ASR-SpecAugment & 34.82 & 22.22 & 15.50 & 11.45 & 10.02 & 18.64 & 11.21 \\ \midrule E2E\_ASR-MCT & 28.74 & 18.82 & 14.18 & 11.63 & 10.37 & 16.63 & 12.73 \\ \midrule E2E\_ASR-MCT-SpecAugment & 27.04 & 18.01 & 13.88 & 10.80 & 9.56 & 15.74 & 11.38 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Enhanced Development Set} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 37.81 & 24.13 & 16.36 & 12.34 & 10.60 & 20.21 & 11.84 \\ \midrule E2E\_ASR-SpecAugment & 30.62& 18.87 & 12.82 & 10.19 & 9.15 & 16.31 & 9.95 \\ \midrule E2E\_ASR-MCT & 24.32 & 15.52 & 11.34 & 9.95 & 9.00 & 14.01 & 10.99 \\ \midrule E2E\_ASR-MCT-SpecAugment & 23.37 & 14.92 & 11.21 & 9.77 & 9.17 & 13.67 & 10.13 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Test Set with SNR Data} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 99.91 & 68.33 & 42.82 & 24.84 & 17.39 & 50.11 & 10.73 \\ \midrule E2E\_ASR-SpecAugment & 64.41 & 40.44 & 23.97 & 14.36 & 11.30 & 30.55 & 8.73 \\ \midrule E2E\_ASR-MCT & 26.44& 18.44 & 14.41 & 11.77 & 10.32 & 16.17 & 9.68 \\ \midrule E2E\_ASR-MCT-SpecAugment & 23.25 & 16.34 & 13.77 & 11.00 & 9.57 & 14.70 & 9.34 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Speech transformer} & \multicolumn{7}{c}{CER Results(\%) on Development Set with SNR Data} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule E2E\_ASR-clean & 92.28 & 57.44 & 34.47 & 20.61 & 14.06 &43.67 & 9.12\\ \midrule E2E\_ASR-SpecAugment & 58.74 & 35.17 & 20.01 & 12.89 & 10.25 & 27.35 & 7.96 \\ \midrule E2E\_ASR-MCT & 24.01& 15.50 & 11.94 & 10.04 & 9.17 & 14.11 & 8.50 \\ \midrule E2E\_ASR-MCT-SpecAugment & 20.62 & 13.93 & 10.99 & 9.89 & 9.20 & 12.91 & 8.44 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccccc|c} \toprule \multirow{2}{*}{Models} & \multicolumn{7}{c}{CER Results(\%) on Development Set} \\ \cline{2-8} & 0dB & 5dB & 10dB & 15dB & 20dB & AVG. & clean \\ \midrule Joint-Enhance-E2E\_ASR & 22.14 & 14.42 & 11.70 & 10.27 & 9.54 & 13.60 & 8.88 \\ \midrule Joint-Enhance-E2E\_ASR-concat & 20.61 & 13.35 & 10.59 & 9.40 & 8.94 & 12.56 & 8.45 \\ \midrule Joint-Enhance-E2E\_ASR-GRF (our) & \textbf{19.76} & \textbf{12.71} & \textbf{9.93} & \textbf{9.09} & \textbf{8.74} & \textbf{12.03} & \textbf{8.18} \\ \bottomrule \end{tabular}
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\begin{tabular}{|c|c|} \hline Model & Parameters(Million) \\ \hline Speech Enhancement & 16.02 \\ \hline Speech Transformer & 25.40 \\ \hline Speech Transformer(concat) & 39.76 \\ \hline Speech Transformer(GRF) & 40.78 \\ \hline \end{tabular}
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\begin{tabular}{lccccccc} \toprule & Order & Order & Order & Trade & Tick & Security & Security \\ & add & cancel & modify & & table data & definition & status \\ \midrule Count & 4,435,738 (20.65\%) & 4,428,798 (20.62\%) & 12,593,071 (58.62\%) & 12,438 (0.06\%) & 193 (0\%) & 3,653 (0.02\%) & 7,642 (0.04\%) \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccccccc} \toprule Event & msgType & timestamp & securityId & orderRef & price & quantity & side & tradeRef \\ & $\langle$ \textit{Int} $\rangle$ & $\langle$ \textit{Int}, \textit{Unix} $\rangle$ & $\langle$ \textit{Int} $\rangle$ & $\langle$ \textit{Int} $\rangle$ & $\langle$ \textit{Int}, \textit{ZAC}$\cdot 10^5$$\rangle$ & $\langle$ \textit{Int} $\rangle$ & $\langle$ \textit{String} $\rangle$ & $\langle$ \textit{Int} $\rangle$ \\ \midrule Add LO & 2 & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & - \\ Cancel LO & 3 & \checkmark & \checkmark & \checkmark & - & - & - & - \\ Modify LO & 4 & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & - & - \\ Add MO (trade) & 5 & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & & \checkmark \\ Cancel MO (trade bust) & 6 & \checkmark & \checkmark & - & \checkmark & \checkmark & - & \checkmark \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccccccccc} \toprule TimeStamp & EventType & Bid & BidVol & Ask & AskVol & Trade & TradeVol & TradeSign & MicroPrice & MidPrice & InterArrivals \\ \midrule 2018-12-27T09:00:01.026 & ASK & NaN & NaN & 2.99499e10 & 85.0 & NaN & NaN & - & NaN & NaN & NaN \\ 2018-12-27T09:00:01.026 & BID & 2.96759e10 & 85.0 & NaN & NaN & NaN & NaN & - & 2.98129e10 & 2.98129e10 & NaN \\ 2018-12-27T09:00:11.024 & BID & 2.75102e10 & 92.0 & NaN & NaN & NaN & NaN & - & 2.86818e10 & 2.873005e10 & NaN \\ 2018-12-27T09:00:11.024 & ASK & NaN & NaN & 2.77892e10 & 92.0 & NaN & NaN & - & 2.76497e10 & 2.76497e10 & NaN \\ 2018-12-27T09:00:29.569 & ASK & NaN & NaN & NaN & NaN & NaN & NaN & - & NaN & NaN & NaN \\ 2018-12-27T09:00:29.569 & BID & 2.96001e10 & 86.0 & NaN & NaN & NaN & NaN & - & NaN & NaN & NaN \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccc} \toprule times & type & value & size & condcode \\ \midrule 2018-12-31T07:00:00.0 & BID & 279278.25 & 400.0 & - \\ 2018-12-31T07:00:00.0 & ASK & 286046.38 & 10.0 & - \\ 2018-12-31T07:00:00.0 & ASK & 286046.38 & 30.0 & - \\ 2018-12-31T08:30:00.0 & TRADE & 0.0,0.0 & IP \\ 2018-12-31T08:32:30.0 & BID & 279278.25 & 413.0 & - \\ 2018-12-31T08:32:30.0 & ASK & 281198.16 & 3.0 & - \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccccccccc} \toprule TimeStamp & EventType & Bid & BidVol & Ask & AskVol & Trade & TradeVol & MicroPrice & MidPrice & InterArrivals & TradeSign \\ \midrule 2019-01-02T09:00:00.0 & BID & 279258.84 & 1195.0 & NaN & NaN & NaN & NaN & NaN & NaN & NaN & - \\ 2019-01-02T09:00:04.0 & BID & 279258.84 & 1196.0 & NaN & NaN & NaN & NaN & NaN & NaN & NaN & - \\ 2019-01-02T09:00:35.0 & ASK & NaN & NaN & 261475.48 & 2869.0 & NaN & NaN & 266707.68 & 270367.16 & NaN & - \\ 2019-01-02T09:00:35.0 & BID & 279258.84 & 1193.0 & NaN & NaN & NaN & NaN & 266698.41 & 270367.16 & NaN & - \\ 2019-01-02T09:00:35.0 & ASK & NaN & NaN & 261475.48 & 2868.0 & NaN & NaN & 266699.70 & 270367.16 & NaN & - \\ 2019-01-02T09:00:35.0 & BID & 279258.84 & 1192.0 & NaN & NaN & NaN & NaN & 266696.60 & 270367.16 & NaN & - \\ \bottomrule \end{tabular}
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\begin{tabular}{lc|lc} \toprule \multicolumn{2}{c}{A2X} & \multicolumn{2}{c}{JSE} \\ \cmidrule{1-2} \cmidrule{3-4} Security name & Security code & Security name & Security code \\ \midrule Aspen Pharmacare Holdings Ltd & APN & Absa Group Ltd & ABG \\ African Rainbow Min Ltd & ARI & Anglo American Plc & AGL \\ AVI Ltd & AVI & British American Tobacco Plc & BTI \\ Coronation Fund Managers Ltd & CML & FirstRand Ltd & FSR \\ Growthpoint Prop Ltd & GRT & Nedbank Group Ltd & NED \\ Mr Price Group Ltd & MRP & Naspers Ltd & NPN \\ Naspers Ltd & NPN & Standard Bank Group Ltd & SBK \\ Standard Bank Group Ltd & SBK & Shoprite Holdings Ltd & SHP \\ Sanlam Ltd & SLM & Sanlam Ltd & SLM \\ Santam Ltd & SNT & Sasol Ltd & SOL \\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccc} \toprule & Quote Rule & Tick Rule & Lee--Ready Rule \\ \midrule NPN & 99.41\% & 51.58\% & 99.41\% \\ SBK & 97.10\% & 45.37\% & 97.12\% \\ SLM & 99.14\% & 48.25\% & 99.16\% \\ \bottomrule \end{tabular}
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\begin{tabular}{l|cccccccccc} \toprule Security & NPN & SLM & SNT & GRT & CML & APN & AVI & MRP & ARI & SBK\\ \midrule Percentage & 13.81\% & 11.16\% & 32.74\% & 13.22\% & 16.7\% & 28.66\% & 25.92\% & 19.24\% & 13.72\% & 15.86\% \\ \bottomrule \end{tabular}
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\begin{tabular}{lc|rrrrrc} Dataset & Version & Classes & Images & Instances & Ins/Img & Cls/Img & Thr.\\ \hline\hline Pascal VOC & 07+12 & 20 & 8k & 23k & 2.9 & 1.6 & \checkmark\\ COCO & 2017 & 80 & 118k & 860k & 7.3 & 2.9 & \checkmark\\ LVIS & v1 & 1,203 & 100k & 1.27M & $\geq$12.8$^*$\hspace{-4.4pt} & $\geq$3.6$^*$\hspace{-4.4pt} & \ding{55}\\ Objects365 & v2 & 365 & 1.94M & 28M & 14.6 & 6.1 & \checkmark\\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc} & \multicolumn{2}{c}{COCO} & \multicolumn{2}{c}{Pascal VOC}\\ Categories$\rightarrow$ & Train & Held-Out & Train & Held-Out\\ \hline \hline Siam. Faster R-CNN & 49.7 & 22.8 & 82.7 & 37.6\\ --- empty Refs. & 10.1 & 4.4 & 59.6 & 33.2\\ \hline \end{tabular}
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\begin{tabular}{l|cc|ccc|ccc} \multicolumn{9}{c}{\textbf{COCO}} \\ \multicolumn{3}{c|}{} & \multicolumn{3}{c|}{1-shot} & \multicolumn{3}{c}{5-shot} \\ Model & Backb. & Sched. & Train C. & Held-Out C. & Delta & Train C. & Held-Out C. & Delta \\ \hline \hline Siam. RetinaNet & R50 & 1x & 50.6 & 18.9 & 31.7 & 55.5 & 22.1 & 33.4\\ Siam. FRCNN & R50 & 1x & 49.7 & 22.8 & 26.9 & 54.9 & 27.6 & 27.3\\ Siam. FRCNN & R50 & 3x & 51.7 & 21.9 & 29.8 & 57.6 & 26.7 & 30.9\\ Siam. FRCNN & X101 & 1x & 56.4 & 23.5 & 32.9 & 61.9 & 28.6 & 33.3\\ \hline \multicolumn{9}{c}{} \\ \multicolumn{9}{c}{\textbf{LVIS}} \\ \multicolumn{3}{c|}{} & \multicolumn{3}{c|}{1-shot} & \multicolumn{3}{c}{5-shot} \\ Model & Backb. & Sched. & Train C. & Held-Out C. & Delta & Train C. & Held-Out C. & Delta \\ \hline \hline Siam. RetinaNet & R50 & 1x & 28.4 & 24.7 & 3.7 & 31.6 & 27.5 & 4.1\\ Siam. FRCNN & R50 & 1x & 31.5 & 28.0 & 3.5 & 37.0 & 33.0 & 4.0\\ Siam. FRCNN & R50 & 3x & 32.7 & 28.7 & 4.0 & 38.2 & 33.5 & 4.7\\ Siam. FRCNN & X101 & 1x & 35.4 & 31.3 & 4.1 & 41.4 & 36.3 & 5.1\\ \hline \multicolumn{9}{c}{} \\ \multicolumn{9}{c}{\textbf{Objects365}} \\ \multicolumn{3}{c|}{} & \multicolumn{3}{c|}{1-shot} & \multicolumn{3}{c}{5-shot} \\ Model & Backb. & Sched. & Train Cats. & Held-Out C. & Delta & Train C. & Held-Out C. & Delta \\ \hline \hline Siam. RetinaNet & R50 & 1x & 19.7 & 14.5 & 5.2 & 23.4 & 17.2 & 6.2\\ Siam. FRCNN & R50 & 1x & 19.4 & 14.8 & 4.6 & 25.7 & 19.9 & 5.8\\ Siam. FRCNN & R50 & 3x & 22.0 & 16.5 & 5.5 & 27.7 & 20.9 & 6.8\\ Siam. FRCNN & X101 & 1x & 25.0 & 17.9 & 7.1 & 30.6 & 22.4 & 8.2\\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc|cc} \multicolumn{3}{c|}{} & \multicolumn{2}{c|}{1-shot} & \multicolumn{2}{c}{5-shot} \\ Model & Backb. & Train Data & Train C. & Held-Out C. & Train C. & Held-Out C. \\ \hline \hline Siam. Mask R-CNN$^{*}$ & R50 & COCO & 37.6 & 16.3 & 41.3 & 18.5\\ CoAE$^{**}$ & R50 & COCO & 40.9 & 22.0 & - & -\\ AIT$^{***}$ & R50 & COCO & 47.5 & 24.3 & - & -\\ \hline Siam. RetinaNet & R50 & COCO & 50.6 & 18.9 & 55.5 & 22.1\\ Siam. Faster R-CNN & R50 & COCO & 49.7 & 22.8 & 54.9 & 27.6\\ Siam. Mask R-CNN & R50 & COCO & 51.9 & 22.9 & 57.9 & 27.8\\ Siam. Cascade R-CNN & R50 & COCO & 50.3 & 22.0 & 56.2 & 27.2\\ Siam. Faster R-CNN & X101 32x4d & COCO & \textbf{56.4} & 23.5 & \textbf{61.9} & 28.6\\ \hline Siam. Faster R-CNN & R50 & LVIS & 36.2 & 25.0 & 43.5 & 31.7\\ Siam. Faster R-CNN & X101 32x4d & LVIS & 42.5 & \textbf{27.4} & 50.3 & \textbf{34.8}\\ \hline \end{tabular}
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\begin{tabular}{c|cccc} \toprule Planner & $d_{\rm{fly}}$(m) & $t_{\rm{fly}}$(s) & Collision & $t_{\rm{cal}}{}^*$ \\ \midrule DMPC & 20.6 & \bf 10.8 & \bf 0 & 0.668 (s) \\ RBP & 22.9 & 23.6 & \bf 0 & 1.18 (s) \\ ORCA & 21.3 & 28.5 & 0.375 & \bf 0.0225 (ms) \\ Proposed & \bf 20.3 & 14.3 & \bf 0 & 0.514 (ms) \\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccc} \toprule Density(obs/$m^2$) & $d_{\rm{fly}}$(m) & vel.(m/s) & $d_{\rm{safe}}$(m) & $t_{\rm{cal}}$(ms) \\ \midrule 0.42 & 49.4 & 1.61 & 0.208 & 5.00 \\ 0.28 & 45.4 & 1.59 & 0.22 & 2.87 \\ 0.14 & 43.7 & 1.57 & 0.266 & 1.21 \\ 0 & 42.2 & 1.55 & / & 0.49 \\ \bottomrule \end{tabular}
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\begin{tabular}{|c|c|c|} \hline \textbf{Ensemble} & \textbf{Heat Function} & \textbf{Entropy}\\ \hline Microcanonical & Internal Energy & \\ $(N,V,E)$ & $E$ &$S(N,V,E)$\\ \hline Isoenthalpic-isobaric & Enthalpy & \\ $(N,P,H)$ &$H=E+PV$ &$S(N,P,H)$\\ \hline Third Adiabatic ensemble &Hill Energy &\\ $(\mu,V,L)$ &$L=E-\mu N$ &$S(\mu,V,L)$\\ \hline Fourth adiabatic ensemble &Ray Energy &\\ $(\mu,P,R)$ &$R=E+PV-\mu N$ &$S(\mu,P,R)$\\ \hline \end{tabular}
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\begin{tabular}{|r|c|c|c|} \hline $x$ & $W_\mathcal{L}(x)$ & Approximate & Relative Error\\ & & Value &\\ \hline $302.7564$ & $4$ & $3.8914$ & $2.71438\times 10^{-2}$\\ \hline $1194.3088$ & $5$ & $4.8766$ & $2.46807\times 10^{-2}$\\ \hline $4337.0842$ & $6$ & $5.8756$ & $2.07321\times 10^{-2}$\\ \hline $14937.6471$ & $7$ & $6.8792$ & $1.72518\times 10^{-2}$\\ \hline $49589.8229$ & $8$ & $7.8844$ & $1.44500\times 10^{-2}$\\ \hline $160238.6564$ & $9$ & $8.8899$ & $1.22306\times 10^{-2}$ \\ \hline $507178.1179$ & $10$ & $9.8953$ & $ 1.04662\times 10^{-2}$\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|} \hline \textbf{Method} & \textbf{Close} & \textbf{Open} & \textbf{High} & \textbf{Low} & \textbf{NAV}\\ \hline DeConFuse & \textbf{0.016} & \textbf{0.007} & \textbf{0.012} & \textbf{0.013} & \textbf{0.410} \\ \hline ConvTimeNet & 1.550 & 1.550 & 1.530 & 1.560 & 2.350 \\ \hline TimeNet & 0.295 & 0.295 & 0.294 & 0.295 & 0.511 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Experiment & Our Method & Weight-Decay & Best $\lambda$ \\ \hline MNIST-CNV & $\mathbf{94.47 \pm 0.26\%}$ & 93.92 $\pm$ 0.57\% & $10^{-4}$ \\ \hline MNIST-FF & 89.01 $\pm$ 0.42\% & $\mathbf{89.60 \pm 0.46\%}$ & $10^{-4}$ \\ \hline CIFAR10-CNV & $\mathbf{36.96 \pm 0.87\%}$ & 35.38 $\pm$ 1.10\% & $10^{-2}$ \\ \hline IRIS-FF & $\mathbf{96.67 \pm 0.0\%}$ & $\mathbf{96.67 \pm 0.0\%}$ & $10^{-3}$ \\ \hline MPG-FF & $\mathbf{5.36 \pm 0.27}$ & 9.00 $\pm$ 0.73 & $10^{-4}$ \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline \textbf{\textit{(-1,1)}}& \textbf{\textit{(0,1)}}& \textbf{\textit{(1,1)}} \\ \cline{1-3} \textbf{\textit{(-1,0)}}& \textbf{\textit{(0,0)}}& \textbf{\textit{(1,0)}} \\ \hline \textbf{\textit{(-1,-1)}}& \textbf{\textit{(0,-1)}}& \textbf{\textit{(1,-1)}} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline \textbf{\textit{a$_1$*r$_1$}}& \textbf{\textit{a$_2$*r$_2$}}& \textbf{\textit{a$_3$*r$_3$}} \\ \cline{1-3} \textbf{\textit{a$_4$*r$_4$}}& \textbf{\textit{a$_5$*r$_5$}}& \textbf{\textit{a$_6$*r$_6$}} \\ \hline \textbf{\textit{a$_7$*r$_7$}}& \textbf{\textit{a$_8$*r$_8$}}& \textbf{\textit{a$_9$*r$_9$}} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\textbf{YOLOv3}} \\ \cline{1-6} \textbf{\textit{category}}& \textbf{\textit{Label Confidence}}& \textbf{\textit{Left}}& \textbf{\textit{Top}}& \textbf{\textit{Right}}& \textbf{\textit{Bottom}} \\ \cline{1-6} \textbf{\textit{hat}}& \textbf{\textit{0.981}}& \textbf{\textit{598.40}}& \textbf{\textit{5.74}}& \textbf{\textit{718.82}}& \textbf{\textit{143.52}} \\ \cline{1-6} \textbf{\textit{hat}}& \textbf{\textit{0.965}}& \textbf{\textit{106.98}}& \textbf{\textit{74.34}}& \textbf{\textit{188.41}}& \textbf{\textit{177.79}} \\ \hline \textbf{\textit{hat}}& \textbf{\textit{0.968}}& \textbf{\textit{314.11}}& \textbf{\textit{60.32}}& \textbf{\textit{395.96}}& \textbf{\textit{158.78}} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\textbf{Improved YOLOv3}} \\ \cline{1-6} \textbf{\textit{category}}& \textbf{\textit{Label Confidence}}& \textbf{\textit{Left}}& \textbf{\textit{Top}}& \textbf{\textit{Right}}& \textbf{\textit{Bottom}} \\ \cline{1-6} \textbf{\textit{hat}}& \textbf{\textit{0.999}}& \textbf{\textit{598.08}}& \textbf{\textit{5.79}}& \textbf{\textit{718.31}}& \textbf{\textit{143.43}} \\ \cline{1-6} \textbf{\textit{hat}}& \textbf{\textit{0.995}}& \textbf{\textit{106.91}}& \textbf{\textit{74.47}}& \textbf{\textit{188.49}}& \textbf{\textit{177.79}} \\ \hline \textbf{\textit{hat}}& \textbf{\textit{0.977}}& \textbf{\textit{314.10}}& \textbf{\textit{60.35}}& \textbf{\textit{395.93}}& \textbf{\textit{158.73}} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|} \hline \cline{1-2} \textbf{\textit{Model}}& \textbf{\textit{Label Confidence}} \\ \cline{1-2} \textbf{\textit{YOLOv3}}& \textbf{\textit{0.966}} \\ \cline{1-2} \textbf{\textit{Improved YOLOv3}}& \textbf{\textit{0.982}}\\ \hline \end{tabular}
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\begin{tabular}{l|lll} \toprule Data set & dimension $p$ & classes $K$ & samples $n_k$ \\ \midrule Sonar & 59 & 2 & $n_1=111$, $n_2 = 97$ \\ \midrule Vowel & 9 & 11 & $n_k = 90$ for all $k$ \\ \midrule Ionosphere & 32 & 2 & $n_1=126$, $n_2 = 225$ \\ \bottomrule \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline \hline Phase&a$_{x}$&a$_{d}$&h&$\theta$&$\Delta E$&C11&C12&C66\\ \hline s(I)&5.85&8.27&3.44&0&-2.893&23.460&5.953&12.301\\ \hline s(II)&5.61&7.93&3.55&15.28&-2.897&34.798&19.006&14.199\\ \hline \hline \end{tabular}
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\begin{tabular}{l|c|c|c|c} \hline & \textbf{RIS}& \textbf{AF Relay} & \textbf{DF Relay} & \textbf{FD Relay} \\ \hline With RF Chains? &No& Yes&Yes&Yes\\ \hline SP Capability? &No& No&Yes&Yes\\ \hline Noise?&No & Yes&Yes&Yes\\ \hline Duplex &Full& Half&Half& Full\\ \hline Hardware cost& Low&Median& High& Very high\\ \hline Power Consumption& Low &Median& High& Very high\\ \hline \end{tabular}
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\begin{tabular}{l|l|l|l|l|l} \hline \textbf{Graph} & \textbf{Entities} & \textbf{Relations} & \textbf{Train} & \textbf{Validation} & \textbf{Test}\\ \hline WN18 & 40943 & 18 & 141442 & 5000 & 5000 \\ WN18RR & 40943 & 11 & 86835 & 3034 & 3134 \\ FB15K & 14951 & 1345 & 483142 & 50000 & 59071 \\ FB15K-237 & 14541 & 237 & 272115 & 17535 & 20466 \\ YAGO3-10 & 123182 & 37 & 1079040 & 5000 & 5000 \\ \end{tabular}
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\begin{tabular}{l|l} \hline \textbf{Tool} & \textbf{Version}\\ \hline python & 3.7.7 \\ ampligraph & 1.3.1 \\ tensorflow & 1.15.0 \\ Keras-Applications & 1.0.8 \\ Keras-Preprocessing & 1.1.0 \\ CUDA Toolkit & 10.0.130 \\ cuDNN & 7.6.5 \\ numpy & 1.18.1\\ pandas & 1.0.3 \\ \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline $\boldsymbol{T}$ & $\boldsymbol{\lvert V \rvert}$ & $\boldsymbol{W}$ & \textbf{Critical Path} \\ \hline 4 & 21 & 116 & 74 \\ \hline 8 & 121 & 536 & 158 \\ \hline 16 & 817 & 3056 & 326 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|} \hline $\boldsymbol{T}$ & $\boldsymbol{p}$ & \textbf{Agent} & \textbf{ASAP} & \textbf{Greedy} & \textbf{Random} \\ \hline 4 & 4 & \textbf{74} & \textbf{74} & \textbf{74} & 74.8 (0.87)\\ \hline 8 & 4 & 163 & \textbf{160} & 173 & 196.5 (5.57) \\ \hline 16 & 4 & 792 & \textbf{787} & 814 & 832.9 (6.09) \\ \hline 8 & 2 & \textbf{280} & 282 & 286 & 300.2 (5.39) \\ \hline 8 & 6 & \textbf{158} & \textbf{158} & 174 & 174.2 (3.24) \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline $\boldsymbol{T}$ & $\boldsymbol{p}$ & \textbf{CP} & $\boldsymbol{w}$ & \textbf{makespan} \\ \hline & & $+$ & 0 & 163 (3.28) \\ \cline{3-5} & & $+$ & 1 & 163 (4.54) \\ \cline{3-5} & & $-$ & 0 & 173 (40.13) \\ \cline{3-5} 8 & 4 & $-$ & 1 & 170 (16.53) \\ \cline{3-5} & & $-$ & 2 & 171 (0.89) \\ \cline{3-5} & & $-$ & 3 & 166 (0.83) \\ \cline{3-5} & & $-$ & 4 & 164 (10.58) \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline $\mathbf{T_{\mbox{test}}}$ & $\mathbf{T_{\mbox{train}}}$ & $\mathbf{p_{\mbox{test}}}$ & $\mathbf{p_{\mbox{train}}}$ & \textbf{makespan} \\ \hline & 4 & & & 74 \\ 4 & 8 & & & 74 \\ & 16 & & & 74 \\ \cline{1-2} \cline{5-5} & 4 & & & 215 \\ 8 & 8 & 4 & 4 & 163 \\ & 16 & & & 175 \\ \cline{1-2} \cline{5-5} & 4 & & & 911 \\ 16 & 8 & & & 805 \\ & 16 & & & 792 \\ \hline & & & 2 & 280 \\ & & 2 & 4 & 285 \\ & & & 6 & 296\\ \cline{3-5} & & & 2 & 172\\ 8 & 8 & 4 & 4 & 163 \\ & & & 6 & 178 \\ \cline{3-5} & & & 2 & 158\\ & & 6 & 4 & 159 \\ & & & 6 & 158\\ \hline \end{tabular}
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\begin{tabular}{lccccc} \hline & 12+log(O/H)$_{\rm S}$ & log(U)$_{\rm D}$ & 12+log(O/H)$_{\rm B}$ & log(U$_{\rm S}$)$_{\rm B}$ & (Z$_{\rm ISM}$)$_{\rm B}$ \\ [0.5ex] \hline ULX-1 (\textbullet) & 8.04$\pm${ 0.17} & -3.03 $\pm$ {0.09} & 8.26 {$\pm$ 0.02} & -3.13 {$\pm$ 0.02} & 0.0070 {$\pm$ 0.0003}\\ ULX-1 ($\ast$) & 8.10 $\pm$ {0.16} & -2.75 $\pm$ {0.09 } & 8.22 {$\pm$ 0.01} & -2.99 {$\pm$ 0.01} & 0.0064 {$\pm$ 0.0002}\\ ULX-3 ($\blacktriangle$)& 8.37 $\pm$ {0.09} & -2.50 $\pm$ {0.06 } & 8.7078 {$\pm$ 0.0001}& -3.1253 {$\pm$ 0.0005} & 0.0134 {$\pm$ 0.0001}\\ \hline \end{tabular}
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\begin{tabular}{lrrrr} \toprule \textsc{Name} & \textsc{Dimension} & \textsc{Classes} & \textsc{Training Samples} & \textsc{Test Samples}\\ \midrule MNIST & 784 & 10 & 60K & 10K \\ CIFAR10 & 3072 & 10 & 50K & 10K\\ CIFAR100 & 3072 & 100 & 50K & 10K\\ \midrule IMDB & 104083 & 2 & 25K & 25K\\ SST2 & 14583 & 2 & 67K & 872 \\ YELP & 175710 & 5 & 500K & 50K\\ \bottomrule \end{tabular}
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\begin{tabular}{lrrr} \toprule Transformation & MNIST & CIFAR10 & CIFAR100 \\ \midrule \emph{Identiy - Raw} & 0.029 (k=3) & 0.646 (k=1) & 0.825 (k=1) \\ PCA (d=32) & \textbf{0.025 (k=8)} & 0.575 (k=16) & 0.811 (k=1) \\ PCA (d=64) & \textbf{0.025 (k=3)} & 0.601 (k=18) & 0.806 (k=1) \\ PCA (d=128) & 0.028 (k=3) & 0.619 (k=1) & 0.810 (k=1) \\ NCA (d=64) & 0.026 (k=5) & 0.600 (k=18) & 0.837 (k=39) \\ AlexNet & 0.165 (k=13) & 0.244 (k=13) & 0.509 (k=19) \\ GoogleNet & 0.113 (k=9) & 0.171 (k=10) & 0.431 (k=18) \\ VGG16 & 0.133 (k=16) & 0.208 (k=19) & 0.476 (k=15) \\ VGG19 & 0.138 (k=15) & 0.205 (k=19) & 0.470 (k=16) \\ ResNet50-V2 & 0.092 (k=5) & 0.152 (k=9) & 0.397 (k=17) \\ ResNet101-V2 & 0.092 (k=6) & 0.126 (k=9) & 0.371 (k=10) \\ ResNet152-V2 & 0.094 (k=3) & 0.137 (k=6) & 0.373 (k=14) \\ InceptionV3 & 0.049 (k=13) & 0.150 (k=10) & 0.407 (k=17) \\ EfficientNet-B0 & 0.535 (k=7) & 0.159 (k=9) & 0.410 (k=17) \\ EfficientNet-B1 & 0.691 (k=7) & 0.125 (k=7) & 0.368 (k=24) \\ EfficientNet-B2 & 0.630 (k=8) & 0.120 (k=10) & 0.352 (k=10) \\ EfficientNet-B3 & 0.789 (k=7) & 0.090 (k=6) & 0.312 (k=13) \\ EfficientNet-B4 & 0.745 (k=25) & \textbf{0.085 (k=7)} & \textbf{0.307 (k=13)} \\ EfficientNet-B5 & 0.804 (k=23) & 0.092 (k=8) & 0.317 (k=12) \\ EfficientNet-B6 & 0.649 (k=25) & 0.092 (k=6) & 0.326 (k=10) \\ EfficientNet-B7 & 0.543 (k=14) & 0.087 (k=12) & 0.316 (k=9) \\ \bottomrule \end{tabular}
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\begin{tabular}{lrrr} \toprule Transformation & IMDB & SST2 & YELP \\ \midrule \emph{Identiy - BOW} & 0.334 (k=36) & 0.349 (k=6) & - \\ BOW-TFIDF & 0.243 (k=247) & 0.249 (k=26) & - \\ PCA (d=8) & 0.274 (k=155) & 0.408 (k=81) & - \\ PCA (d=16) & 0.226 (k=159) & 0.382 (k=236) & - \\ PCA (d=32) & 0.216 (k=175) & 0.375 (k=174) & - \\ PCA (d=64) & 0.228 (k=157) & 0.377 (k=147) & - \\ PCA (d=128) & 0.241 (k=196) & 0.374 (k=170) & - \\ ELMO & 0.255 (k=37) & \textbf{0.195 (k=206)} & 0.424 (k=166) \\ NNLM (d=50) & 0.287 (k=77) & 0.294 (k=227) & 0.475 (k=86) \\ NNLM (d=128) & 0.255 (k=57) & 0.241 (k=148) & 0.452 (k=43) \\ NNLM (d=50, w/ normalize) & 0.259 (k=45) & 0.288 (k=36) & 0.455 (k=92) \\ NNLM (d=128, w/ normalize) & 0.227 (k=47) & 0.241 (k=162) & 0.427 (k=45) \\ Universal Sentence Encoder (USE) & \textbf{0.188 (k=183)} & 0.201 (k=186) & \textbf{0.387 (k=75)} \\ BERT-Base & 0.266 (k=45) & 0.267 (k=8) & 0.441 (k=51) \\ \bottomrule \end{tabular}
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\begin{tabular}{|l|c||c|c|} \hline Parameter & Value & Parameter & value \\ \hline\hline Domain (m) & 40, 40, 1 & Grid size (m) & 1\\ Time (year) & 10 & \# of time steps & 10\\ Porosity & 1 & Top depth (m) & 5,000\\ $\rho_{oil}\ (kg/m^3)$ & 600 & $\rho_{water}\ (kg/m^3)$ & 999\\ $\mu_{oil}\ (cP)$ & 2 & $\mu_{water}\ (cP)$ & 1\\ Input dims. & (40,40) & Output dims & (10,40,40) \\ \hline \end{tabular}
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\begin{tabular}{|l|c|c|c|} \hline Loss & Method & SegNet & SegNet-ConvLSTM \\ \hline\hline \multirow{3}{*}{MSE} & Training Set & 5.21e-3 & 2.3e-3 \\ & Validation loss & 3.70e-2 & 1.12e-2 \\ & Test loss & 3.55e-2 & 1.23e-2\\ \hline \multirow{3}{*}{Physical} & Training Set & 5.13e-2 & 4.01e-2 \\ & Validation loss & 9.73e-2 & 8.79e-2 \\ & Test loss & 9.28e-2 & 9.14e-2\\ \hline \end{tabular}
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\begin{tabular}{ccccccccc} \hline \noalign{\smallskip} Nucleus & & $\Delta R_{p}$ & & Mirror Nucleus & & $\Delta R_{n}$ & & $\Delta R_{mirr}$ \\ \noalign{\smallskip}\hline\noalign{\smallskip} $^{16}$Ne & & 0.366 & & $^{16}$C & & 0.308 & & -0.360 \\ $^{18}$Ne & & 0.160 & & $^{18}$O & & 0.111 & & -0.147 \\ $^{20}$Ne & & 0.024 & & $^{20}$Ne & & -0.024 & & 0.000 \\ \noalign{\smallskip}\hline\noalign{\smallskip} $^{30}$Ar & & 0.327 & & $^{30}$Mg & & 0.238 & & -0.308 \\ $^{32}$Ar & & 0.222 & & $^{32}$Si & & 0.136 & & -0.188 \\ $^{34}$Ar & & 0.128 & & $^{34}$S & & 0.041 & & -0.088 \\ $^{36}$Ar & & 0.044 & & $^{36}$Ar & & -0.044 & & 0.000 \\ \noalign{\smallskip}\hline \end{tabular}
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\begin{tabular}{|l|c|c|c|c|} \hline & $T_c$ & $\Delta_0$ & $-dH_{c2}/dT$ & $-dH^2_{c\parallel}/dT$ \\ & [$K$] & [meV] & [$T/K$] & [$T^2/K$]\\ \hline Re 6 nm & 4.76 & 1.0 & 8.1 & 303 \\ Re 3 nm & 3.83 & 0.8 & 6.9 & 795 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c} \hline Network & Setting & FLOPs(G) & Top-1(\%) & Top-5(\%) & Inference Time(ms)\\ \hline \multirow{4}{*}{\shortstack{HS-ResNet50\\(Same Params)}}& 18$w$-8$s$ & 11.6 &\textbf{81.43} & 95.53 & 6.19\\ & 22$w$-7$s$ &12.3 &81.40 & 95.57 & 5.90 \\ & 28$w$-6$s$ &13.1 &81.28 & \textbf{95.61} & 5.34 \\ & 40$w$-5$s$ &15.1 &81.11 & 95.40 & \textbf{5.28} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Dataset & Training & Validation & Testing \\ \hline Tamil-English & 1,335 & 1,260 & 3,149\\ Malayalam-English & 4,716 & 674 & 1,348 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline Data & Classes & Precision & Recall & F1 Score & Weighted Average-F1 & Accuracy \\ \hline \multirow{5}{*}{Malayalam-English} & Mixed feelings & 0.03 & 0.22 & 0.05 & \multirow{5}{*}{0.52} & \multirow{5}{*}{ 0.49 }\\ & Negative & 0.12 & 0.40 & 0.19&&\\ & Positive & 0.72 & 0.50 & 0.59&&\\ & not-malayalam & 0.36 & 0.58 & 0.44&&\\ & unknown state & 0.42 & 0.46 & 0.44&&\\ \hline \multirow{5}{6em}{Tamil-English} & Mixed feelings & 0.23 & 0.13 & 0.17 & \multirow{5}{3em}{0.32} & \multirow{5}{3em}{ 0.35 }\\ & Negative & 0.50 & 0.16 & 0.24&&\\ & Positive & 0.39 & 0.73 & 0.51&&\\ & not-Tamil & 0.10 & 0.40 & 0.16&&\\ & unknown state & 0.03 & 0.31 & 0.05&&\\ \hline \end{tabular}
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\begin{tabular}{|l||c|c|c|c||c|c|c|} \multicolumn{1}{c}{} & \multicolumn{4}{c}{Disparity (lower is better)} & \multicolumn{3}{c}{Accuracy (higher is better)} \\ \hline ~ & Abs Rel & Sq Rel & RMSE & RMSE log & $\delta < 1.25$ & $\delta < 1.25^2$ & $\delta < 1.25^3$ \\ \hline No wrapping & 0.301 & 2.543 & 6.220 & 0.395 & 0.668 & 0.828 & 0.901 \\ Wrapping & \textbf{0.299} & \textbf{2.514} & \textbf{6.037} & \textbf{0.387} & \textbf{0.675} & \textbf{0.835} & \textbf{0.906} \\ \hline \end{tabular}
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\begin{tabular}{|r|r|l||r|r|} \hline Seq. & FOV (deg) & Wrap & ATE Mean & ATE Std. Dev. \\ \hline 02 & 360 & Yes & \textbf{0.0139} & \textbf{0.0210} \\ 02 & 360 & No & 0.0143 & 0.0211 \\ 02 & 270 & No & 0.0150 & 0.0230 \\ 02 & 180 & No & 0.0203 & 0.0296 \\ 02 & 100 & No & 0.0324 & 0.0498 \\ \hline 05 & 360 & Yes & 0.0138 & 0.0195 \\ 05 & 360 & No & 0.0132 & \textbf{0.0189} \\ 05 & 270 & No & \textbf{0.0131} & 0.0191 \\ 05 & 180 & No & 0.0167 & 0.0224 \\ 05 & 100 & No & 0.0258 & 0.0383 \\ \hline 04 & 360 & Yes & \textbf{0.0342} & 0.0351 \\ 04 & 360 & No & 0.0345 & \textbf{0.0322} \\ 04 & 270 & No & 0.0355 & 0.0348 \\ 04 & 180 & No & 0.0384 & 0.0372 \\ 04 & 100 & No & 0.0371 & 0.0359 \\ \hline \end{tabular}
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\begin{tabular}{|l||c|c|c|c||c|c|c|} \multicolumn{1}{c}{} & \multicolumn{4}{c}{Disparity (lower is better)} & \multicolumn{3}{c}{Accuracy (higher is better)} \\ \hline ~ & Abs Rel & Sq Rel & RMSE & RMSE log & $\delta < 1.25$ & $\delta < 1.25^2$ & $\delta < 1.25^3$ \\ \hline No wrapping & 0.550 & 16.266 & 12.868 & 0.560 & 0.475 & 0.745 & 0.856 \\ Wrapping & \textbf{0.497} & \textbf{14.212} & \textbf{12.032} & \textbf{0.528} & \textbf{0.565} & \textbf{0.781} & \textbf{0.867} \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Statistic&Observables&Model&Variance$/{\mathcal V}^2$\\ \hline &&&\\ EE Only&$\widetilde C^{EE}_{\ell}$&$(1+2m)[C^{EE}_{\ell}+N_{\ell}]$&$(C^{EE}_{\ell})^2+N^2_{\ell}$\\ &&&\\ \hline &&&\\ EE-BB&$\widetilde C^{EE}_{\ell}-\widetilde C^{BB}_{\ell}$&$(1+2m)[C^{EE}_{\ell}]$&$(C^{EE}_{\ell})^2+2N^2_{\ell}$\\ &&&\\ \hline &&&\\ EE and BB (joint likelihood)&$\widetilde C^{EE}_{\ell}$, $\widetilde C^{BB}_{\ell}$&$(1+2m)[C^{EE}_{\ell}+N_{\ell}]$,$(1+2m)N_{\ell}$&$(C^{EE}_{\ell})^2+N^2_{\ell}$, $N^2_{\ell}$\\ &&&\\ \hline \end{tabular}
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\begin{tabular}{c||c|c||c|c} \hline \multirow{2}{*}{\textbf{Scenarios}} & \multicolumn{2}{c||}{\textbf{Market-1501}} & \multicolumn{2}{c}{\textbf{DukeMTMC}} \\ \cline{2-5} & mAP & Rank-1 & mAP & Rank-1 \\ \hline Global feature only & 38.3 & 62.0 & 26.9 & 41.2 \\ \hline Local feature only & 42.4 & 70.8 & 34.1 & 57.8 \\ \hline Our joint usage & \textbf{54.4} & \textbf{82.2} & \textbf{47.2} & \textbf{69.9} \\ \hline \end{tabular}
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\begin{tabular}{c||c|c||c|c} \hline \multirow{2}{*}{\textbf{Scenarios}} & \multicolumn{2}{c||}{\textbf{Market-1501}} & \multicolumn{2}{c}{\textbf{DukeMTMC}} \\ \cline{2-5} & mAP & Rank-1 & mAP & Rank-1 \\ \hline $N_+=1,N_-=all$ & 37.1 & 70.9 & 37.9 & 60.3 \\ \hline $N_+=7,N_-=all$ & 53.6 & 79.6 & 42.4 & 65.8 \\ \hline Ours ($N_+=7,N_-=500$) & \textbf{54.4} & \textbf{82.2} & \textbf{47.2} & \textbf{69.9} \\ \hline \end{tabular}
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\begin{tabular}{ll|l} \textbf{Parameter} & & \textbf{Value}\\ \midrule Magnetic permeability & $\mu_0$ & $4\pi\times 10^{-7} \text{ H/m}$\\ Boltzmann constant & $k_\mathrm{B}$ & $1.38064852\times 10^{-23} \text{ J/K}$\\ \midrule \multicolumn{3}{l}{{\it Scanner (sinusoidal)}} \\ \midrule Excitation frequency & $f$& $25000 \text{ Hz}$\\ Excitation amplitudes & $A$& $0.02\text{ T} /\mu_0$\\ Gradient strength & $G$ & $7\text{ T/m} /\mu_0$\\ \midrule \multicolumn{3}{l}{{\it Scanner (pulsed)}} \\ \midrule Excitation frequency & $f_\mathrm{pulsed}$& $2500 \text{ Hz}$\\ Excitation amplitudes & $A_\mathrm{pulsed}$& $0.001\text{ T} /\mu_0$\\ Gradient strength & $G$ & $7\text{ T/m} /\mu_0$\\ \midrule \multicolumn{3}{l}{{\it Particle (spherical shape); Brownian rotation}} \\ \midrule Temperature & $T_\textrm{B}$ & $293 \text{ K}$ \\ Sat. magnetization & $M_{\mathrm{S}}$ & $474000 \text{ J/m$^3$/T}$\\ Particle core diameter & $D_\mathrm{core}$ & variable \\ Particle core volume & $V_\mathrm{C}$ & $1/6 \pi D_\mathrm{core}^3$ \\ Particle core diameter & $D_\mathrm{hydro}$ & variable \\ Particle hydrodynamic volume & $V_\mathrm{H}$ & $1/6 \pi D_\mathrm{hydro}^3$ \\ Dynamic viscosity & $\eta$ & $1.0 \times 10^{-5} \text{ Pa s} $\\ \end{tabular}
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\begin{tabular}{l|cc} \hline Model & Relative MSFE & Standard Error \\ \hline Lasso AR-X - Static Eval Period & 1.0000 & 0.00241\\ Lasso AR-X - Rolling Window Eval Period & 0.9921 & 0.00234\\ Online Lasso AR-X - Gradient Descent & {\bf 0.9813} & 0.00225\\ Online Lasso AR-X - Newton & 0.9845 & 0.00226\\ Sample Mean & 2.8367 &0.00856 \\ Random Walk & 4.4431 &0.00856 \\ AR-X with lag order selected by AIC & 5.1585& 0.02049\\ AR-X with lag order selected by BIC & 5.4009 & 0.02049\\ \hline \end{tabular}
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\begin{tabular}{l|rrrrrr} \hline Lasso AR-X Model & Min & Lower Quartile & Mean & Median & Upper Quartile & Max \\ \hline Conventional Rolling & 1266.31 & 1277.94 & 1306.63 & 1288.18 & 1309.65 & 1527.03 \\ Online - Newton & 345.45 & 355.25 & 367.76 & 359.25 & 367.23 & 490.37 \\ Online - Gradient Descent & 334.89 & 343.83 & 359.44 & 348.95 & 355.62 & 472.98 \\ \hline \end{tabular}
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\begin{tabular}{lll}\hline Language & Connection rules & Connectors\\\hline SysML & 31 & 62\\\hline BPMN & 72 & 133\\\hline UPDM & 396 & 792\\\hline EASTADL & 215 & 233\\\hline OPM & 39 & 54 \\\hline \end{tabular}
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\begin{tabular}{l|cccc|cccc} & \multicolumn{4}{|c}{PAR10} & \multicolumn{4}{|c}{\# Solved} \\ & B & W & M & std & B & W & M & std \\ \hline \multicolumn{9}{c}{\bf CityCar} \\ \hline arvandherd & 203.09 & 788.74 & 498.80 & 161.13 & 19 & 15 & 17 & 1.41 \\ Bfs-f & 2116.23 & 2258.57 & 2253.84 & 41.08 & 6 & 5 & 5 & 0.18\\ Cedalion & 2137.34 & 2138.13 & 2137.44 & 0.27 & 6 & 6 & 6 & 0.0 \\ Freelunch & 3000.00 & 3000.00 & 3000.00 & 0.0 & 0 & 0 & 0 & 0.0 \\ IbaCoP & 1713.18 & 2570.38 & 1997.55 & 223.69 & 9 & 3 & 7 & 2.41 \\ Jasper & 2258.35 & 3000.00 & 2265.04 & 342.01 & 5 & 0 & 5 & 2.54 \\ Mercury & 2430.31 & 2702.90 & 2429.63 & 77.40 & 4 & 2 & 4 & 0.15 \\ Mpc & 1384.71 & 1811.22 & 1532.23 & 112.60 & 11 & 8 & 10 & 1.07 \\ Probe & 763.78 & 2401.24 & 1662.58 & 373.69 & 15 & 4 & 9 & 2.45 \\ SIW & 2255.80 & 2255.95 & 2255.87 & 0.04 & 5 & 5 & 5 & 0.00 \\ use & 2721.95 & 3000.00 & 3000.00 & 73.78 & 2 & 0 & 0 & 0.20 \\ Yahsp3 & 3000.00 & 3000.00 & 3000.00 & 0.0 & 0 & 0 & 0 & 0.00 \\ \hline \end{tabular}
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\begin{tabular}{l|c|cccccc} Planners & \multicolumn{7}{|c}{PAR10} \\ & Or & Js & LPG & Mp & Me & Pb & Y3 \\ \hline Jasper & 1372.3 & {\bf 1293.2} & 1376.9 & 1318.2 & 1338.7 & 1360.7 & 1354.9\\ LPG & 923.7 & 867.9 & {\bf 701.4} & 893.0 & 918.9 & 894.6 & 757.2 \\ Mp & 1799.3 & 1833.3 & 1818.3 & 1802.6 & 1796.6 & {\bf 1781.1} & 1796.2 \\ Mercury & 1377.9 & 1327.1 & 1341.8 & 1349.0 & {\bf 1312.7} & 1320.0 & 1319.9 \\ Probe & 1062.0 & 672.4 & 593.3 & 707.6 & 588.3 & {\bf 578.9} & 619.8\\ Yahsp3 & 389.6 & 311.4 & 319.6 & 391.0 & 352.5 & 326.2 & {\bf 309.8} \\ \hline \hline Planners &\multicolumn{7}{|c}{\% Solved Problems} \\ & Or & Js & LPG & Mp & Me & Pb & Y3 \\ \hline Jasper & 56.4 & {\bf 59.1} & 56.1 & 58.3 & 57.5 & 56.7 & 57.0 \\ LPG & 69.8 & 71.7 & {\bf 77.3} & 70.9 & 70.1 & 70.9 & 75.4 \\ Mp & 41.0 & 39.3 & 39.8 & 40.4 & 40.6 & {\bf 41.2} & 40.6 \\ Mercury & 57.0 & 57.8 & 57.2 & 57.0 & {\bf 58.3} & 58.0 & 58.0 \\ Probe & 70.8 & 78.9 & 81.6 & 77.8 & 81.8 & {\bf 82.1} & 80.7 \\ Yahsp3 & 87.4 & 90.1 & 89.8 & 87.4 & 88.8 & 89.6 & {\bf 90.1}\\ \hline \hline Planners &\multicolumn{7}{|c}{IPC score} \\ & Or & Js & LPG & Mp & Me & Pb & Y3 \\ \hline Jasper & 86.9 & {\bf 90.6} & 89.0 & 87.8 & 88.6 & 86.8 & 86.5\\ LPG & 163.5 & 170.3 & {\bf 192.6} & 167.2 & 164.8 & 167.5 & 183.9\\ Mp & 103.2 & 100.1 & 100.4 & {\bf 104.4} & 102.7 & 103.3 & 102.2\\ Mercury & 87.9 & 90.3 & 89.5 & 89.1 & {\bf 91.1} & 90.7 & 90.6\\ Probe & 125.9 & 147.4 & 156.8 & 142.5 & 154.2 & {\bf 158.1} & 152.2\\ Yahsp3 & 277.0 & 285.6 & 285.9 & 272.0 & 259.6 & 285.0 & {\bf 292.3}\\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc|cc} & \multicolumn{2}{|c|}{IPC score} & \multicolumn{2}{|c|}{PAR10} & \multicolumn{2}{c}{Solved} \\ Planner & O & B & O & B & O & B\\ \hline Jasper &195.9& {\bf 252.2} &1375.9&975.3& 56.3&69.4\\ LPG &192.1& {\bf 261.2} &926.2&826.0& 69.7&72.9\\ Mpc &167.9& {\bf 232.5} &1637.5&1109.4& 46.1&63.8\\ Mercury &183.9& {\bf 236.8} &1381.5&1126.6& 55.8&63.5\\ Probe &205.5& {\bf 294.2} &1265.3&602.3& 58.7&81.0\\ Yahsp3 &260.0& {\bf 310.9} &390.6&310.7& 87.4 &90.1\\ \hline \end{tabular}
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\begin{tabular}{l|c|c|c} \hline Pos & {\bf Original} & {\bf Configured} & {\bf Best} \\ \hline 1&Yahsp3 (297)& Yahsp3 (303)& Yahsp3 (306)\\ \hline 2&Lpg (168)& Lpg (198)& Lpg (189)\\ \hline 3&Mpc (121)& Probe (123)& Probe (173)\\ \hline 4&Probe (112)& Mpc (117)& Jasper (123)\\ \hline 5&Mercury (91)& Mercury (95)& Mpc (119)\\ \hline 6&Jasper (90)& Jasper (94)& Mercury (105)\\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc|cc} & \multicolumn{2}{|c|}{PAR10} & \multicolumn{2}{|c|}{IPC Score} & \multicolumn{2}{c}{Solved (\%)} \\ Planner & O& B & O& B & O & B\\ \hline Bfs-f & 1977.1 & 1871.3 & 71.6 & \textbf{80.5} & 34.5 & 38.2 \\ Mpc & 1994.8 & \textbf{1740.4} & 64.1 & \textbf{83.0} & 34.1 & \textbf{43.2} \\ Yahsp3 & 2256.6 & \textbf{2012.4} & 46.0 & \textbf{67.7} & 25.0 & \textbf{33.2} \\ Probe & 1876.3 & \textbf{1561.3} & 73.6 & \textbf{93.4} & 38.2 & \textbf{48.7}\\ arvandherd & 1350.4 & 1278.8 & 104.6 & \textbf{116.8} & 57.3 & 59.1 \\ Freelunch & 2416.0 & 2415.6 & 43.0 & 44.0 & 20.0 & 20.0 \\ Mercury & 1771.0 & 1770.6 & 90.9 & 91.4 & 41.4 & 41.8 \\ Jasper & 1674.4 & 1582.8 & 86.6 & \textbf{94.8} & 45.0 & 47.3 \\ SIW & 1935.5 & 1894.9 & 77.0 & 80.0 & 36.4 & 36.8 \\ use & 1469.8 & \textbf{1300.5} & 100.5 & \textbf{112.5} & 51.7 & 57.3 \\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc|cc} & \multicolumn{2}{|c|}{PAR10} & \multicolumn{2}{|c|}{Solved (\%)} & \multicolumn{2}{c}{IPC score} \\ Planner & B & W & B & W & B & W\\ \hline Jasper & {\bf 2402.1} & 2777.8 & 75.1 & 70.7 & 307.0 & 285.5 \\ LAMA & 2012.1 & 2084.3 & 79.7 & 79.2 & 326.0 & 318.0 \\ Lpg & {\bf 1438.8} & 1940.5 & 73.8 & 68.8 & 277.2 & 254.1 \\ Mpc & {\bf 2796.4} & 2887.2 & 64.7 & 64.7 & 256.2 & 247.1 \\ Probe & {\bf 1162.1} & 1417.9 & 88.4 & 86.0 & 358.4 & 342.8 \\ SGPlan & {\bf 2245.7} & 2372.0 & 64.5 & 63.3 & 265.6 & 256.4 \\ Yahsp3 & {\bf 1355.3} & 1628.9 & 85.0 & 82.1 & 342.3 & 292.7 \\ \hline \end{tabular}
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\begin{tabular}{l|ccccccc|c} Planner & Bar & Bw & D & Mbw & R & S & T & Total\\ \hline Jasper & A & B(b) & B(b) & $\blacksquare$ & $\blacksquare$ & F & $\blacksquare$ & 3 \\ LAMA & F & B & B(b) & F & b & B & $\blacksquare$ & 1 \\ Lpg & -- & F & B(b) & A & A & B & B(b) & 0 \\ Mpc & -- & B(b) & B(b) & b & b & B & F & 0 \\ Probe & F & B(b) & B & b & $\blacksquare$ & B & b & 1 \\ SGPlan & A & -- & B(b) & A & B & $\blacksquare$ & B(b) & 1 \\ Yahsp3 & $\blacksquare$ & B(b) & B(b) & A & B & $\blacksquare$ & B(b) & 2 \\ \hline \end{tabular}
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\begin{tabular}{l|cc|cc|cc} & \multicolumn{2}{|c|}{PAR10} & \multicolumn{2}{|c|}{Solved (\%)} & \multicolumn{2}{c}{IPC score} \\ Planner & B & L & B & L & B & L\\ \hline Bfs-f & 2364.9 & 2554.4 & 61.7 & 58.3 & 37.0 & 34.5 \\ Freelunch & 4119.7 & 4200.8 & 30.0 & 30.0 & 17.9 & 17.9 \\ Mercury & 4505.7 & 4506.0 & 25.0 & 25.0 & 15.0 & 14.8 \\ use & 4106.4 & 4304.2 & 31.7 & 28.3 & 19.0 & 16.9 \\ SIW & 1869.9 & 2069.8 & 70.0 & 66.7 & 40.2 & 39.6 \\ \hline \end{tabular}
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\begin{tabular}{l|cccc|cccc} & \multicolumn{4}{|c}{PAR10} & \multicolumn{4}{|c}{\# Solved} \\ & B & W & M & std & B & W & M & std \\ \hline \multicolumn{9}{c}{\bf Visitall} \\ \hline arvandherd & 2434.78 & 2435.65 & 2435.37 & 0.22 & 4 & 4 & 4 & 0.00 \\ Bfs-f & 2266.40 & 2266.98 & 2266.64 & 0.22 & 5 & 5 & 5 & 0.00 \\ Cedalion & 6.79 & 7.02 & 6.88 & 0.06 & 20 & 20 & 20 & 0.00 \\ Freelunch & 2101.71 & 2101.84 & 2101.72 & 0.03 & 6 & 6 & 6 & 0.00 \\ IbaCoP & 3000.00 & 3000.00 & 3000.00 & 0.00 & 0 & 0 & 0 & 0.00 \\ Jasper & 1860.37 & 2271.11 & 2132.25 & 146.50 & 8 & 5 & 6 & 1.35 \\ Mercury & 1712.02 & 1712.55 & 1712.27 & 0.37 & 9 & 9 & 9 & 0.00 \\ Mpc & 3000.00 & 3000.00 & 3000.00 & 0.00 & 0 & 0 & 0 & 0.00 \\ Probe & 2427.55 & 2427.98 & 2427.74 & 0.14 & 4 & 4 & 4 & 0.00 \\ SIW & 1141.64 & 1142.25 & 1141.65 & 0.15 & 13 & 13 & 13 & 0.00 \\ use & 3000.00 & 3000.00 & 3000.00 & 0.00 & 0 & 0 & 0 & 0.00 \\ Yahsp3 & 1701.89 & 1702.18 & 1702.12 & 0.18 & 9 & 9 & 9 & 0.00 \\ \hline \end{tabular}
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\begin{tabular}{l|c} \hline Exogenous variable & Accuracy\\ \hline Rotation (MNIST-R) & 3.020\\ Scale (dSprites) & 0.0291\\ Identity (LFW) & 98.95\\ \hline \end{tabular}
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\begin{tabular}{l|c|c} \hline Method & MNIST-R & dSprites \\ \hline \hline Baseline & 96.83 & 96.53 \\ \hline Simple deep ensemble & 96.81 & 92.68 \\ Tree-gated deep ensemble & 97.31 & 95.91 \\ Exogenous tree-gated deep ensemble & \underline{98.07} & \underline{98.1} \\ \hline Oracle$^\dagger$ & 98.06 & 98.43 \\ \hline THIN & \textbf{98.26} & \textbf{98.5} \\ \hline \end{tabular}
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\begin{tabular}{l|c} \hline Gating variable & MNIST-RS \\ \hline \hline Digit & 96.68 \\ \hline Scale & 97.22 \\ Rotation & \underline{97.4} \\ Rotation + Scale & \textbf{97.63} \\ \hline \end{tabular}
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\begin{tabular}{l|c|c|c} \hline Method & RAF-DB & AffectNet & ExpW \\ \hline \hline Baseline (VGG16) & 82.99 & 61.31 & 70.96 \\ Baseline (VGGFace) & 84.06 & 61.66 & 71.57 \\ \hline Simple deep ensemble & 85.59 & 63.00 & 75.05 \\ Tree-gated deep ensemble & 86.38 & 63.34 & 75.17 \\ Exogenous tree-gated deep ensemble & \underline{87.29} & \underline{63.71} & \underline{75.74} \\ \hline THIN & \textbf{87.81} & \textbf{63.97} & \textbf{76.08} \\ \hline \end{tabular}
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\begin{tabular}{|l|c|} \hline \textbf{Parameter} & \textbf{Parameter value} \\\hline Number of generations (G) & 50 \\\hline Population size (M) & 20 \\\hline Problem dimension (d) & 2 \\\hline CE coefficient ($\alpha$) for EB-QPSO & $\alpha = 0.5$ \\\hline Jumping percentage & 1 \\\hline Jumping rate & 0.2 \\\hline Number of transposons & 1 \\\hline Lambda ($\lambda$) & 3 \\\hline Minimum search point & (0.0001, 8) \\\hline Maximum search point & (1 $\times$ $10^6$, 4 $\times$ $10^4$) \\\hline \end{tabular}
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\begin{tabular}{|l|l|l|l|} \hline LSSVM optimizer strategy & RMSE & MAE & MAPE (\%) \\\hline PSO & 0.992 $\pm$ 0.0408 & 0.699 $\pm$ 0.013 & 10.72 $\pm$ 1.08 \\\hline QPSO & 1.046 $\pm$ 0.053 & 0.681 $\pm$ 0.037 & 9.88 $\pm$ 0.98 \\\hline EBQPSO & \textbf{0.981 $\pm$ 0.061} & \textbf{0.671 $\pm$ 0.051} & \textbf{9.43 $\pm$ 1.12} \\\hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|} \cline{2-7} & \multicolumn{6}{c|}{\textbf{Types of Arguments}} \\ \cline{2-7} \textbf{} & $a_1$ & $a_2$ & $a_3$ & $a_4$ & $a_5$ & $a_6$ \\ \hline \multicolumn{1}{|c|}{\textbf{Rebuttals}} & $a_2$ & $a_1$ & - & - & - & - \\ \hline \multicolumn{1}{|c|}{\textbf{Undercuts}} & - & - & $a_2$ & $a_3$ & $a_4$ & $a_5$ \\ \hline \end{tabular}
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\begin{tabular}{rccc} & Banknote & Heart (Statlog) & Adult Census \smallskip\\ \hline \noalign{\smallskip} instances & 1372 & 270 & 48842 (1000) \\ features & 4 & 13 & 14 (80) \smallskip\\ \hline \noalign{\smallskip} LR & 98.86\% & 81.21\% & 94.67\% \\ SVM & \textbf{100.00\%} & \textbf{81.95\%} & \textbf{95.93\%} \\ RF & 99.26\% & 81.89\% & 94.32\% \\ NN & 99.43 & 77.02\% & 94.42\% \smallskip\\ \hline \noalign{\smallskip} \\ \end{tabular}
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\begin{tabular}{c|c|c|c|c|c||c|c|c|c|c||c|c|c|c|c|} \cline{2-16} & LIME & SHAP & PI & Intrinsic & Altruist & LIME & SHAP & PI & Intrinsic & Altruist & LIME & SHAP & PI & Intrinsic & Altruist \\ \hline \multicolumn{1}{|c|}{LR} & 49.75\% & 37.30\% & \textbf{0.00\%} & \textbf{0.00\%} & \textbf{0.00\%} & 61.71\% & 51.80\% & \textbf{38.46\%} & \textbf{0.00\%} & \textbf{36.87\%} & 18.54\% & 23.96\% & \textbf{17.18\%} & \textbf{0.00\%} & \textbf{13.56\%} \\ \hline \multicolumn{1}{|c|}{SVM} & 40.73\% & 43.33\% & \textbf{29.05\%} & - & \textbf{21.50\%} & 59.21\% & 48.60\% & \textbf{46.21\%} & - & \textbf{40.91\%} & 25.21\% & 12.05\% & \textbf{10.79\%} & - & \textbf{10.06\%} \\ \hline \multicolumn{1}{|c|}{RF} & 86.61\% & \textbf{75.78\%} & 85.71\% & 85.30\% & \textbf{69.04\%} & 76.61\% & 75.98\% & 84.87\% & \textbf{73.88\%} & \textbf{70.68\%} & 70.01\% & \textbf{13.08\%} & 24.83\% & 62.613\% & \textbf{13.08\%} \\ \hline \multicolumn{1}{|c|}{NN} & 39.89\% & 44.57\% & \textbf{17.26\%} & - & \textbf{14.27\%} & 58.86\% & \textbf{47.58\%} & 69.23\% & - & \textbf{43,73}\% & 21.51\% & 26.64\% & \textbf{17.89\%} & - & \textbf{14,66\%} \\ \hline & \multicolumn{5}{c||}{Banknote} & \multicolumn{5}{c||}{Heart (Statlog)} & \multicolumn{5}{c|}{Adult Census} \\ \cline{2-16} \end{tabular}
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\begin{tabular}{ccccccccccccc} \textbf{Chemical } & & $\eta_h$ & & $N_{P^h}$ && $N_{Q^h}$ & & $\eta_e$ & & $N_{P^e}$ & &$N_{Q^e}$ \\ \textbf{Formula} & & (a.u.) && && && (a.u.) && && \\ \hline Ag$_{10}$ && -2.12E-01 && 3 && 92 && -4.65E-02 & & 2 & & 143 \\ Ag$_{20}$ && -2.11E-01 && 5 && 185 & & -4.31E-02 && 4 & & 286 \\ Ag$_{40}$ && -2.11E-01 && 9 & & 371 && -4.86E-02 && 7 & & 573 \\ Ag$_{60}$ && -2.11E-01 && 13 & & 557 && -5.07E-02 && 10 && 860 \\ Ag$_{80}$ & & -2.11E-01 && 17 & & 743 & & -5.17E-02 && 13 & & 1147 \\ Ag$_{100}$ && -2.03E-01 && 17 && 933 & & -5.84E-02 && 14 && 1436 \end{tabular}
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\begin{tabular}{cc|cc|cc} \hline \multirow{2}{*}{\textbf{Model}} & \multirow{2}{*}{\textbf{Reported}} & \multicolumn{4}{c}{\textbf{Our implementation}} \\ \cline{3-6} & & \textbf{SNLI} & \textbf{Cross} & $\mathbf{\Delta}$ & \textbf{$\mathbf{\Delta}$ / SNLI} \\ \hline Majority & 33.8 & 32.8 & 47.1 & 14.3 & 43.6\%\\ HOM & 67.0 & 66.9 & 45.8 & -21.1 & -31.5\%\\ RF & -- & 54.0 & 53.2 & -0.8 & -1.5\%\\ \hline LSTM & 77.6 & 72.7 & 49.0 & -23.7 & -32.6\%\\ InferSent & 84.5 & 83.7 & 52.7 & -31.0 & -37.0\%\\ DiSAN & 85.6 & 84.3 & 52.1 & -32.2 & -38.2\%\\ HBMP & 86.6 & 84.2 & 54.2 & -30.0 & -35.6\%\\ \hline DecompAtt & 86.3 & 83.1 & 54.2 & -28.9 & -34.8\%\\ BiMPM & 86.9 & 84.3 & 55.2 & -29.1 & -34.5\%\\ DIIN & 88.0 & 86.1 & 55.3 & -30.8 & -35.8\%\\ ESIM & 88.0 & 87.5 & 56.0 & -31.5 & -36.0\%\\ \hline BERT & -- & 90.6 & 62.2 & -28.4 & -31.3\%\\ \hline \end{tabular}
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\begin{tabular}{c|cccc} \hline \bf Method & \bf SNLI & \bf Impr & \bf Cross & \bf Impr\\ \hline BiLSTM & 79.6 & -- & 49.4 & -- \\ +ADV & 78.4 & -1.5\% & 50.5 & +2.2\%\\ +DRiFt & 71.3 & -10.4\% & 52.7 & +6.7\% \\ +Learned-Mixin & 56.4 & -29.1\% & 51.1 & +3.4\% \\ +Learned-Mixin+H & 55.0 & -30.9\% & 51.0 & +3.2\% \\ +Weighting & 75.4 & -5.3\% & 49.9 & +1.0\%\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c} \hline \textbf{Creation Protocol} & \textbf{Dataset} & \textbf{Validation Size} & \textbf{Test Size} & \textbf{Entailment} & \textbf{Not-Entailment} & \textbf{Contradiction} & \textbf{Neutral}\\ \hline \multirow{2}{*}{Human Elicited} & $\text{MultiNLI}_\text{Matched}$ & 9815 & 9815 & 32.8\% & - & 32.4\% & 34.8\%\\ & $\text{MultiNLI}_\text{Mismatched}$ & 4916 & 4916 & 35.2\% & - & 33.0\% & 31.8\%\\ \hline \multirow{7}{*}{Human Judged} & SICK & 4963 & 4964 & 28.8\% & -- & 14.7\% & 56.5\%\\ & JOCI & 2327 & 2328 & 16.3\% & -- & 26.1\% & 57.6\%\\ & SciTail & 10000 & 17026 & 37.4\% & -- & -- & 62.6\%\\ & MPE & 4999 & 5000 & 32.5\% & -- & 41.5\% & 26.0\%\\ & Diagnostic & 552 & 552 & 41.7\% & -- & 23.4\% & 35.0\%\\ & Add-1 & 1897 & 1897 & 15.7\% & 84.3\% & -- & --\\ & CB & 153 & 153 & 45.1\% & -- & 48.0\% & 6.9\%\\ \hline \multirow{5}{*}{\shortstack{Automatically \\ Recast}} & DPR & 1830 & 1831 & 50.0\% & 50.0\% & -- & --\\ & SPR & 10000 & 144607 & 34.8\% & 65.2\% & -- & --\\ & FN+ & 10000 & 144604 & 43.4\% & 56.6\% & -- & --\\ & RTE & 2876 & 2876 & 50.4\% & 49.6\% & -- & --\\ & WNLI & 353 & 353 & 48.6\% & 51.4\% & -- & --\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c} \hline \bf Model & \bf MM & \bf MMis & \bf SICK & \bf JOCI & \bf SciTail & \bf DPR & \bf SPR & \bf FN+ & \bf MPE & \bf Add-1 & \bf Diagnostic & \bf CB & \bf RTE & \bf Wnli & \bf Acc Mean & \bf SNLI\\ \hline \bf Majority & 31.8 & 31.8 & 56.8 & 58.4 & 62.9 & 48.4 & 65.2 & 56.6 & 26.1 & 83.8 & 34.1 & 5.9 & 49.3 & 48.7 & 47.1 & 32.8\\ \bf HOM & 43.7 & 44.2 & 34.3 & 36.3 & 56.0 & 48.3 & 53.0 & 56.2 & 35.9 & 83.2 & 34.0 & 19.0 & 49.1 & 47.9 & 45.8 & 66.9\\ \bf RF & 45.4 & 47.3 & 45.7 & 36.2 & 70.2 & 48.2 & 64.4 & 55.8 & 44.5 & 83.7 & 43.4 & 48.5 & 60.3 & 51.3 & 53.2 & 54.0\\ \hline \bf LSTM & 45.0 & 44.9 & 42.0 & 40.7 & 60.8 & 49.7 & 61.7 & 53.1 & 46.9 & 66.9 & 39.4 & 35.5 & 50.0 & 49.4 & 49.0 & 72.7\\ \bf InferSent & 54.4 & 55.6 & 54.0 & 40.3 & 61.9 & 50.7 & 43.8 & 50.4 & 57.9 & 70.4 & 46.6 & 44.1 & 57.7 & 50.0 & 52.7 & 83.7\\ \bf DiSAN & 55.9 & 57.3 & 50.8 & 43.1 & 58.1 & 48.6 & 49.9 & 54.9 & 56.5 & 69.6 & 43.8 & 34.3 & 54.7 & 51.6 & 52.1 & 84.3\\ \bf HBMP & 57.0 & 58.2 & 51.5 & 44.4 & 62.0 & 48.4 & 46.6 & 54.7 & 58.2 & 79.8 & 44.2 & 44.1 & 58.1 & 51.0 & 54.2 & 84.2\\ \hline \bf DecomAtt & 58.0 & 59.6 & 50.6 & 44.8 & 62.9 & 51.1 & 42.8 & 53.1 & 57.7 & 74.1 & 47.8 & 43.8 & 60.8 & 51.6 & 54.2 & 83.1\\ \bf BiMPM & 59.0 & 61.3 & 49.6 & 44.8 & 55.3 & 51.7 & 45.4 & 57.7 & 59.3 & 81.0 & 49.2 & 45.9 & 60.6 & 51.6 & 55.2 & 84.3\\ \bf DIIN & 60.3 & 62.7 & 52.6 & 45.8 & 59.8 & 49.0 & 47.7 & 57.3 & 56.5 & 83.7 & 47.6 & 37.7 & 61.8 & 51.9 & 55.3 & 86.1\\ \bf ESIM & 62.2 & 64.6 & 57.0 & 45.0 & 53.7 & 51.8 & 45.4 & 55.6 & 62.9 & 74.7 & 50.5 & 47.5 & 61.1 & 51.1 & 56.0 & 87.5\\ \hline \bf BERT & 73.7 & 73.9 & 56.4 & 48.8 & 64.2 & 51.8 & 59.6 & 56.1 & 65.8 & 83.7 & 51.9 & 62.3 & 70.8 & 51.9 & 62.2 & 90.6\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|} \hline Orientation & Sign & $A'$ \\ \hline Increasing & $\text{sgn}(a^{\uparrow}) = \text{sgn}(a^{\downarrow}) = 1$ & $(\mu_{A}^{\uparrow}, b^{\downarrow})$ \\ Increasing & $\text{sgn}(a^{\uparrow}) = \text{sgn}(a^{\downarrow}) = -1$ & $(b^{\uparrow}, \mu_{A}^{\downarrow})$ \\ Decreasing & $\text{sgn}(a^{\uparrow}) = \text{sgn}(a^{\downarrow}) = 1$ & $(b^{\uparrow}, \mu_{A}^{\downarrow})$ \\ Decreasing & $\text{sgn}(a^{\uparrow}) = \text{sgn}(a^{\downarrow}) = -1$ & $(\mu_{A}^{\uparrow}, b^{\downarrow})$ \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c} \toprule & \textbf{\#Keyphrases} & \textbf{\% duplicate keyphrases} & \textbf{\% duplicate tokens} \\ \midrule \textbf{Ground Truth} & 5.3 & 0.1 & 7.3 \\ \textbf{MLE Baseline} & 7.3 & 26.6 & 36.0 \\ \bottomrule \end{tabular}