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\begin{tabular}{cccccc} \hline Dataset & Cora & Citeseer & Pubmed & Coauthor CS & ogbn-arxiv \\ \hline $\xi$ & 0.20 & 0.15 & 0.35 & 0.40 & 0.25 \\ $\gamma_0$ & 0.3 & 0.5 & 0.7 & 0.4 & 0.4 \\ \hline \end{tabular}
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\begin{tabular}{cccccccccc} \hline \multirow{2}{*}{Methods} & \multicolumn{3}{c}{Cora} & \multicolumn{3}{c}{Citeseer} & \multicolumn{3}{c}{Pubmed} \\ \cline{2-10} & ACC & NMI & ARI & ACC & NMI & ARI & ACC & NMI & ARI \\ \hline \multicolumn{10}{c}{Supervised} \\ \hline GCN & 64.3 & 48.3 & 50.9 & 64.8 & 37.9 & 40.1 & 64....
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\begin{tabular}{ccccccc} \hline \multirow{2}{*}{Method} & \multicolumn{2}{c}{Cora} & \multicolumn{2}{c}{Citeseer} & \multicolumn{2}{c}{Pubmed} \\ \cline{2-7} & Confident & K-means & Confident & K-means & Confident & K-means \\ \hline Joint & 77.7$\pm{0.08}$ & 78.2$\pm{0.11}$ & 65.7$\pm{0.09}$ & 65.3$\pm{0.10}$ & 72.5$\...
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\begin{tabular}{cccccc} \hline Datasets & Citeseer & Cora & Pubmed & Coauthor CS & ogbn-arxiv \\ \hline $\xi$ in eq. (\ref{eq:label_update}) & 0.15 & 0.20 & 0.35 & 0.30 & 0.4\\ Estimated $K$ & 6 & 8 & 3 & 19& 48\\ Classes & 6 & 7 & 3 &15 & 40\\ \hline \end{tabular}
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\begin{tabular}{ccc} \toprule & Complexity & Communication load \\ \midrule AGD & $O(q_1C(mnr + mr^2))$& $2q_1mr$\\ ADMM & $O(q_2C(mnr + mr^2 + r^3))$& $2q_2mr$\\ CEASE &$O(tq_3C(mnr + mr^2))$ & $4q_3mr$\\ \bottomrule \end{tabular}
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\begin{tabular}{cccc} \toprule Dataset& \# Instances & \# Features & \# Classes \\ \midrule CoverType & \texttildelow 540,000 & 54 & 7\\ KDD-99 & \texttildelow 4,900,000 & 41 & 11 \\ MNIST & \texttildelow 400,000 & 784 & 10 \\ \bottomrule \end{tabular}
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\begin{tabular}{lcccccc} \toprule & \multicolumn{2}{c}{CoverType} & \multicolumn{2}{c}{KDD-99} & \multicolumn{2}{c}{MNIST} \\ \cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7} & Accuracy & Time (s) & Accuracy& Time (s) & Accuracy& Time (s) \\ \midrule Scalable-NMF & 33.79 & 2.14 & 79.35 & 13.90 & 20.55& 25.77\\ ...
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\begin{tabular}{cccccccc} Graph models & MUTAG & PROTEINS & PTC & NCL1 & IMDB-B & IMDB-M & COLLAB\\ \hline GCN &$85.6\pm5.8$ &$76.0\pm3.2$ &$64.2\pm4.3$ &$80.2\pm2.0$ &$74.0\pm3.4$ &$51.9\pm3.8$ &$79.0\pm1.8$ \\ (s)GCN &$86.23\pm6.71$ &$77.99\pm3.72$ &$69.23\pm5.59$ &$80.3\pm2.1$ &$76.1\pm2.86$ &$52.4\pm2.56$ & $80.89\...
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\begin{tabular}{ccccccc} Graph models & WINE & CANCER & DIGITS & CITESEER & CORA & 20NEWS\\ \hline KNN-LDS &$97.5\pm1.2$ &$94.9\pm0.5$ &$92.5\pm0.7$ &$71.5\pm1.1$ &$71.5\pm0.8$ &$46.4\pm1.6$\\ (s)KNN-LDS &$98.0\pm1.1$ &$95.7\pm0.6$ &$92.5\pm0.6$ &$73.7\pm0.9$ &$72.3\pm0.6$ &$47.9\pm1.5$\\ \end{tabular}
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\begin{tabular}{cccc} Graph models & CORA & CITESEER & PUBMED\\ \hline GMNN &$83.4\pm0.8$ &$73.0 \pm 0.8$ &$81.3\pm0.5$\\ (s)GMNN &$83.5\pm0.2$ &$73.4 \pm 0.1$ &$81.6\pm0.2$\\ \end{tabular}
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\begin{tabular}{cccc} Graph models & CORA & CITESEER & PUBMED\\ \hline VGAE &$90.1\pm0.15$ &$92.0 \pm 0.17$ &$92.3\pm0.06$\\ (s)VGAE &$93.4\pm0.12$ &$92.6 \pm 0.12$ &$92.7\pm0.05$\\ Graphite-VAE &$91.5\pm0.15$ &$93.5.0 \pm 0.13$ &$94.6\pm0.04$\\ (s)Graphite-VAE &$93.7\pm0.13$ &$94.1 \pm 0.10$ &$94.8\pm0.03$\\ \end{tabu...
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\begin{tabular}{cccc} Graph models & CORA & CITESEER & PUBMED\\ \hline VGAE &$92.3\pm0.12$ &$94.2 \pm 0.12$ &$94.2\pm0.04$\\ (s)VGAE &$93.0\pm0.10$ &$94.3 \pm 0.08$ &$94.5\pm0.02$\\ Graphite-VAE &$93.2\pm0.13$ &$95.0 \pm 0.10$ &$96.0\pm0.03$\\ (s)Graphite-VAE &$93.5\pm0.11$ &$95.4 \pm 0.09$ &$96.3\pm0.02$\\ \end{tabula...
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\begin{tabular}{ccccc} Models (data) & 25\% & 50\% & 75\% & 100\% (full graph)\\ \hline LDS (CITESEER) &$71.92\pm1.0$ &$73.26 \pm 0.6$ &$74.58\pm0.9$ &$75.54\pm0.4$\\ (s)LDS (CITESEER) &$74.60\pm0.9$ &$74.90 \pm 0.7$ &$75.50\pm0.7$ &$76.11\pm0.6$\\ LDS (CORA) &$74.18\pm1.0$ &$78.98 \pm 0.6$ &$81.54\pm0.9$&$84.08\pm0.4$...
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\begin{tabular}{cccc} \hline \multicolumn{4}{c}{ENZYMES dataset} \\ \hline Models & - & Batch normalization & Continuous node attribute \\ \hline GCN &32.33$\pm5.07$ &$-$ &$51.17\pm 5.63$ \\ (s)GCN &$40.11\pm3.27$ &$56.67\pm4.47$ &$75.33\pm3.93$ \\ MGCN &$40.50\pm5.58$ &$-$ &$59.83\pm6.56$ \\ (s)MGCN &$51.83\pm5.84$ &$...
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\begin{tabular}{ccc} Graph models & MUTAG & PROTEINS\\ \hline GCN &$76.5\pm1.4$ &$74.45 \pm 4.91$\\ (s)GCN &$91.39\pm6.56$ &$78.49 \pm 3.19$\\ MGCN &$84.4\pm1.6$ &$74.62 \pm 2.56$\\ (s)MGCN &$87.25\pm4.16$& $78.23\pm3.23$\\ MGCNK&$89.1\pm1.4$&$76.27\pm2.82$\\ (s)MGCNK&$89.42\pm5.97$&$78.04\pm2.97$\\ \end{tabular}
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\begin{tabular}{cccc} GCN & GCN+$A^{2}$ & GCN+$A^{2}$+$2I$ & (s)GCN\\ \hline $74.37\pm0.31$ &$74.56\pm0.26$ &$74.23 \pm 0.37$&$78.49\pm 3.19$\\ \hline Graph-Unet & Graph-Unet+$A^{2}$ & Graph-Unet+$A^{2}$+$2I$ & (s)Graph-Unet\\ $72.45\pm0.88$ &$72.87\pm0.52$ &$73.18 \pm 0.50$&$74.12\pm 4.17$\\ \hline \end{tabular}
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\begin{tabular}{cccc} Graph models & CORA & CITESEER & PUBMED\\ \hline Mixhop &$71.4\pm0.81$ &$81.9 \pm 0.40$ &$80.8\pm0.58$\\ (s)GMNN &$73.4\pm0.76$ &$83.5 \pm 0.57$ &$81.6\pm0.64$\\ \end{tabular}
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\begin{tabular}{c||cccccc} \hline & inf & 80 & 60 & 50 & 40 & 30 \\\hline $\lambda$ & 1000 & 100 & 100 & 10 & 10 & 10\\ $\gamma$ & 0.001 & 0.01 & 0.01 & 0.05 & 0.1 &0.2 \\ $\eta$ & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 & 0.5\\ \hline \end{tabular}
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\begin{tabular}{c|ccc} \hline purity & SNPA & min vol & GFPI \\ \hline 0.8 & 0.219 & 0.014 & 0.010 \\ 0.7 & 0.315 & 0.029 & 0.018 \\ 0.6 & 0.429 & 0.485 & 0.017 \\ \hline \end{tabular}
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\begin{tabular}{c||ccccc} \hline $p = 1$, SNR = $\infty$ & $n_1 = 10$ & $n_1 = 30$ & $n_1 = 50$ & $n_1 = 100$ & $n_1 = 200$ \\\hline $r = 3$ & 0.75 & 0.73 & 2.81 & 44.53 & NA \\ $r = 4$ & 0.61 & 5.48 & 44.66 & NA & NA \\ $r = 5$ & 1.61 & 49.82 & NA & NA & NA\\ $r = 7$ & 13.30 & NA & NA & NA & NA \\ \hline \end{tabular}
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\begin{tabular}{c||ccccc} \hline $p = 0.6$, SNR = $\infty$ & $n_1 = 10$ & $n_1 = 30$ & $n_1 = 50$ & $n_1 = 100$ & $n_1 = 200$ \\\hline $r = 3$ & 0.59 & 0.71 & 1.28 & 27.1 & 449.90 \\ $r = 4$ & 0.55 & 3.40 & 29.46 & 609.18 & NA \\ $r = 5$ & 1.35 & 39.76 & 653.19 & NA & NA \\ $r = 7$ & 10.53 & NA & NA & NA & NA \\ \hline...
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\begin{tabular}{c||ccccc} \hline $p = 1$, SNR = 40 & $n_1 = 10$ & $n_1 = 30$ & $n_1 = 50$ & $n_1 = 100$ & $n_1 = 200$ \\\hline $r = 3$ & 0.67 & 2.15 & 8.11 & 282.54 & NA \\ $r = 4$ & 0.87 & 18.05 & 606.67 & NA & NA \\ $r = 5$ & 3.37 & NA & NA & NA & NA \\ $r = 7$ & 119.56 & NA & NA & NA & NA \\ \hline \end{tabular}
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\begin{tabular}{c||ccccc} \hline $p = 0.6$, SNR = 40 & $n_1 = 10$ & $n_1 = 30$ & $n_1 = 50$ & $n_1 = 100$ & $n_1 = 200$ \\\hline r = 3 & 0.62 & 1.89 & 12.45 & 998.29 & NA \\ r = 4 & 0.66 & 12.01 & 155.02 & NA & NA \\ r = 5 & 2.94 & 516.09 & NA & NA & NA \\ r = 7 & 103.89 & NA & NA & NA & NA \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline \multirow{2}{*}{Model-Type} & \multicolumn{3}{c|}{Weighted Metrics} \\ \cline{2-4} & Precision & Recall & F1-Score \\ \cline{1-4} GMM-HMM & 75.4 & 72.5 & 73.2 \\ \hline NVP-HMM & 77.5 & 77.0 & 76.6 \\ \hline Glow-HMM & 78.6 & 76.4 & 74.8 \\ \hline \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{Model-Type} & \multirow{2}{*}{Clean} & \multicolumn{9}{c|}{Diff. SNR levels for adding \texttt{white} noise}\\ \cline{3-11} & & 30dB & 25dB & 22dB & 20dB & 17dB & 15dB & 12dB & 10dB & 5dB\\ \cline{1-11} GMM-HMM & 72.0 & 62.3 & 56.0 & 52.9 & 51.8 & 53.5 & 5...
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\begin{tabular}{lllc} \toprule Dataset & \#Vertices & \#Edges & \#Classes \\ \midrule Cora & 2,708 & 5,429 & 7 \\ BlogCatalog & 10,312 & 333,983 & 39 \\ CiteSeer & 3,312 & 4,732 & 6 \\ Facebook & 4,039 & 88,234 & - \\ Youtube & 1,134,890 & 2,987,624 & - \\ \bottomrule \end{tabular}
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\begin{tabular}{ll} \toprule Algorithm/Dataset&BlogCatalog\\ \midrule Deepwalk &27.84 (27.30) \\ HARP &24.84 (24.66) \\ Walklets & 41.37(41.19) \\ Node2Vec (p=q=0.25) & 26,96 (25.81) \\ Node2Vec (p=q=1) &26,52 \\ \bottomrule \end{tabular}
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\begin{tabular}{lccc} \toprule Algorithm/Dataset&Cora&BlogCatalog&CiteSeer\\ \midrule HALK & \textbf{81.65} $\pm$2.2 & \textbf{27.70} $\pm$0.4 & \textbf{56.97} $\pm$3.2 \\ HARP & \underline{81.33} $\pm$2.5 & \underline{27.65} $\pm$0.6 & \underline{56.16} $\pm$2.0 \\ Walklets & 81.10 $\pm$2.5 & 27.31 $\pm$0.5 & 55.76 $\...
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\begin{tabular}{lcc} \toprule Operator &Symbol& definition\\ \midrule L1 & $|\ominus |$ & $|\phi_i(u)-\phi_i(v)|$\\ L2 & $L_2$ & $|\phi_i(u)-\phi_i(v)|^2$\\ Subtraction & $\ominus $ & $\phi_i(u)-\phi_i(v)$\\ Concatenation & $\oplus$& $(\phi(u),\phi(v))$\\ Average & $\oslash$ & $\frac{\phi_i(u)+\phi_i(v)}{2}$ \\ Hadamar...
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\begin{tabular}{llll}\toprule Set & Loss & Jaccard Score & Dice Score \\\midrule training & -0.45 & 0.68 & 0.81 \\ test & -0.49 & 0.67 & 0.79 \\\bottomrule \end{tabular}
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\begin{tabular}{c|c} \toprule Algorithm & Iteration complexity \\ \midrule REINFORCE & \multirow{2}{*}{$O(1/\epsilon^2)$}\\ (off-policy variant\footnotemark) &\\\midrule OffP-SF & $O(1/\epsilon^2)$ \\\midrule OffP-SF-SVRG & $O(1/\epsilon)$ \\ \bottomrule \end{tabular}
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\begin{tabular}{llll} \toprule \textbf{Classification Aggregation Strategy} & \textbf{Tie Breaker} & \textbf{Success Rate} & \textbf{Percentage of Tie Breakers} \\ \midrule maxp & - & 58\% & 0\% \\ avgp & - & 61\% & 0\% \\ wm & - & 47\% & 0\% \\ maj & avgp & 62\% & 16\% \\ maj & maxp & 60\% & 17\% \\ maj & wm & 57\% & ...
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\begin{tabular}{l|rrrr} \toprule Model & Batch size (per GPU) & Memory (per GPU) & GPU hours & ImageNet zero-shot \\ \midrule CLIP & 128 & 13.7GB & 141 & 20.3 \\ CLOOB & 128 & 13.7GB & 148 & 24.0 \\ \bottomrule \end{tabular}
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\begin{tabular}{lcc} \toprule Layer & Input & Output \\ \midrule Embedding & 500 & (500,64) \\ Flatten & (500,64) & (32000) \\ FullyConnected & (32000) & 250 \\ ReLU & - & - \\ FullyConnected & 250 & 2 \\ Softmax & 2 & 2 \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule Layer & Width & Height & Depth & Kernel size & Stride \\ \midrule Input & 28(32) & 28(32) & 1(3) & - & - \\ Convolution & 28(32) & 28(32) & 32 & 5 & 1 \\ ReLU & 28(32) & 28(32) & 32 & - & - \\ MaxPooling & 14(16) & 14(16) & 32 & 2 & 2 \\ Convolution & 14(16) & 14(16) & 32 & 5 & 1 \\ ReL...
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\begin{tabular}{c|c|c|c|c|c|c} \hline \hline Dataset & $N$ & m & ${l}_{avg}$ & Micro F1 & Macro F1 & Classifier$_{target}$\\ \hline{Creepware} &966 &16 & 2.07 &0.76 & 0.66 & SVM \\ \hline{Genbase} &662 &27 & 1.25 & 0.99 &0.73 & SVM \\ \hline{VOC2012} &17,125 &20 & 1.39 & 0.83 &0.74 & Inception-V3 \\ \hline{Planet} &40,...
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\begin{tabular}{c|c|c|c|c|c|c} \hline \hline Dataset & $N$ & m & ${l}_{avg}$ & Micro F1 & Macro F1 & Classifier$_{target}$\\ \hline{VOC2012} &17,125 &20 & 1.39 & 0.79 &0.68 & Resnet50 \\ \hline{Planet} &40,479 &17 & 2.87 & 0.78 &0.35 & Resnet50 \\ \hline \hline \end{tabular}
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\begin{tabular}{lcc} \multicolumn{1}{c}{\bf structure} &\multicolumn{1}{c}{\bf Poisson equation} & \multicolumn{1}{c}{\bf Helmholtz equation} \\ \hline \\ BI-GreenNet &7.44e-3 &8.56e-3 \\ DB-GreenNet &5.54e-2 &8.75e-1 \\ \end{tabular}
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\begin{tabular}{lccc} \multicolumn{1}{c}{\bf } &\multicolumn{1}{c}{\bf FDM 1.25e-2} & \multicolumn{1}{c}{\bf FDM 6.25e-3} &\multicolumn{1}{c}{\bf BI-GreenNet} \\ \hline \\ Average of relative $L^2$ error & 0.1255 & 0.0559 & 0.0303 \\ Number of parameters & 19521 & 77441 & 39281 \\ \end{tabular}
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\begin{tabular}{llll} \hline Index & $i=1$ & $i=2$ & $i=3$ \\ \hline $c_1$ & 0.5550 & 0.9934 & 0.2986 \\ $k_1$ & 1.9959 & 1.6667 & -0.9091 \\ $k_2$ & -0.1282 & -1.1056 & 1.7814 \\ $c_2$ & 0.3963 & 0.3051 & 0.3642 \\ $x_0$ & 0.2850 & 0.1625 & 0.2190 \\ $y_0$ & 0.5724 & -0.1154 & 0.6809 \\ \hline \end{tabular}
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\begin{tabular}{lccccc} \toprule{Modeling framework} & Single & sTS & mTS & lTS & All \\ \midrule Local modeling & $0.7983$ & $0.7870$ & $0.7553$ & $0.7182$ & $0.7647$ \\ Global modeling & $0.8011$ & $0.7546$ & $0.7115$ & $0.6784$ & $0.7364$ \\ \midrule Improvement [in $\%$] & -0.28 & 3.24 & 4.38 & 3.98 & 2.83 \\ \bott...
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\begin{tabular}{lccccc} \toprule{Training data} & Single & sTS & mTS & lTS & All \\ \midrule Whole dataset & $0.8011$ & $0.7546$ & $0.7115$ & $0.6784$ & $0.7364$ \\ Subsampled by $12\times$ & $0.8048$ & $0.7574$ & $0.7146$ & $0.6829$ & $0.7399$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule{Modeling framework} & Single & sTS & mTS & lTS & All$^\dagger$ \\ \midrule Local modeling & $n/a$ & $10.2987$ & $8.9845$ & $7.5793$ & $8.9542$ \\ Global modeling &$n/a$ & $9.7199$ & $8.2061$ & $6.8396$ & $8.2552$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule{Modeling framework} & Single & sTS & mTS & lTS & All \\ \midrule Local modeling & $0.5688$ & $0.1069$ & $0.0910$ & $0.0746$ & $0.2103$ \\ Global modeling & $0.5768$ & $0.1025$ & $0.0857$ & $0.0701$ & $0.2088$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule{Modeling framework} & Single & sTS & mTS & lTS & All$^\dagger$ \\ \midrule Ours w/o localization& $n/a$& $9.7633$ & $8.2500$ & $6.8993$ & $8.3042$ \\ Ours w localization & $n/a$ & $9.5996$ & $8.1377$ & $6.7692$ & $8.1688$ \\ \bottomrule \end{tabular}
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\begin{tabular}{lccccc} \toprule{Model} & Single & sTS & mTS & lTS & All \\ \midrule Ours w/o localization & $0.5794$ & $0.1029$ & $0.0860$ & $0.0706$ & $0.2097$ \\ Ours w localization & $0.5536$ & $0.1012$ & $0.0848$ & $0.0692$ & $0.2022$ \\ \bottomrule \end{tabular}
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\begin{tabular}{|l|c|c|} \hline Methods & $c=1$, $s=0$ & $c=0.1$, $s=0$ \\ \hline 2-layer \texttt{ANNnet} & 1.8421$\times 10^{-19}$/1.3512$\times 10^{5}$ & 1.1500$\times 10^{-2}$/1.1143$\times 10^{2}$ \\ 5-layer \texttt{ANNnet} & 9.0015$\times 10^{-13}$/1.2507$\times 10^{6}$ & 7.6328$\times 10^{-14}$/1.2426$\times 10^{...
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\begin{tabular}{rccccc} \toprule & Base (CoPINet)~~ & +Analogy& +Analogy+Inf& +Analogy+Var& +Analogy+Gen\\ \# samples & (32) & (32) & (32) & (32) & (2)\\ \midrule 14 (0.049$\%$) & 6.26 & \textbf{7.68} & \textbf{7.48} & 5.60 & 6.53 \\ 35 (0.098$\%$) & 11.07 & 13.71 & \textbf{14.10} & 12.35 & \textbf{18.99} \\ 77 (0.195$...
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\begin{tabular}{lcccccccc} \toprule method & accuracy & Center & 2{\tiny{$\times$}}2Grid& 3{\tiny{$\times$}}3Grid& ~L-R~& ~U-D~& ~O-IC~& ~O-IG \\ \midrule WReN-NoTag-Aux & 17.62 & 17.66 & 29.02 & 34.67 & 7.69 & 7.89 & 12.30 & 13.94 \\ WReN-NoTag-NoAux & 15.07 & 12.30 & 28.62 & 29.22 & 7.20 & 6.55 & 8.33 & 13.10 \\ WReN...
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\begin{tabular}{lcc} \toprule ~~~~~~\multirow{2}{*}{method} & \multicolumn{2}{c}{minibatch size} \\ \cmidrule{2-3} & 2 & 32 \\ \midrule Base (CoPINet) & 48.75 & 25.00 \\ \midrule ~~+ Analogy & 58.75 & 51.25 \\ ~~+ Inference Analogy & 61.25 & 45.00 \\ ~~+ Variational Analogy & 56.25 & 43.75 \\ ~~+ Generative Analogy & \...
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\begin{tabular}{lcc} \toprule ~~~~~~\multirow{2}{*}{method} & \multicolumn{2}{c}{minibatch size} \\ \cmidrule{2-3} & 2 & 32 \\ \midrule Base (CoPINet) & 48.75 & 25.00 \\ Base (CoPINet) + MetaContrast & \underline{51.25} & \underline{48.75} \\ \midrule ~~+ Analogy & 58.75 & 51.25 \\ ~~+ Analogy + MetaContrast & \underli...
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\begin{tabular}{ccc} \toprule number of ways & Analogy Sampling & +Analogy Learning (Ours) \\ \midrule 2 &40.13 &59.17 \\ 3 &64.63 &82.58 \\ 4 &62.89 &90.43 \\ 5 &55.10 &89.90 \\ 6 &59.05 &\textbf{95.67} \\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule Target Domain & Base (CoPINet) & Analogy (Ours) \\ \midrule 2{{$\times$}}2Grid & 23.75 & 38.75 \\ 3{{$\times$}}3Grid & 18.75 & 36.25 \\ O-IC & 30.00 & 31.25 \\ O-IG & 26.25 & 48.75 \\ L-R & 18.75 & 25.00 \\ U-D & 26.25 & 26.25 \\ \bottomrule \end{tabular}
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\begin{tabular}{llllll} \toprule Tasks & Episodes & DQN & VDQN & NoisyNet & AVDQN \\ \midrule CartPole-v0 & 1500 & 1176 & 7531 & 7955 & 1286 \\ CartPole-v1 & 1500 & 2350 & 16461 & 16871 & 2196 \\ Acrobot-v1 & 1500 & 884 & 4241 & 3882 & 1223 \\ MountainCar-v0 & 1500 & 1241 & 6610 & 5428 & 1790 \\ MDP $N=5$ & 1000 & 55 &...
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\begin{tabular}{lllll} \toprule Tasks & DQN & AVDQN & VDQN & NoisyNet \\ \midrule CartPole-v0 & 10802 & 11004 & 21604 & 21604 \\ CartPole-v1 & 10802 & 11004 & 21604 & 21604 \\ Acrobot-v1 & 11103 & 11406 & 22206 & 22206 \\ MountainCar-v0 & 10703 & 11006 & 21406 & 21406 \\ MDP $N=5$ & 10902 & 11104 & 21804 & 21804 \\ MDP...
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\begin{tabular}{llllll} \toprule Tasks & Time(s) & DQN & VDQN & NoisyNet & AVDQN \\ \midrule CartPole-v0 & 1300 & 198.89 & 196.58 & 185.64 & \textbf{200} \\ CartPole-v1 & 2350 & 416.71 & 480.33 & 362.64 & \textbf{500} \\ Acrobot-v1 & 1250 & -104.69 & -104.76 & -92.18 & \textbf{-74.51} \\ MountainCar-v0 & 1800 & -178.27...
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\begin{tabular}{lllll} \toprule Algo/Dataset & \multicolumn{2}{c}{Ponpare} & \multicolumn{2}{c}{USCensus}\\ \midrule Eval. Metric & a-AUC & c-AUC & a-AUC & c-AUC \\ \midrule Random &1.15 & 0.50 &0.31 & 0.50 \\ \midrule R-learner &5.06 & 0.65 & 0.40 &0.54\\ Causal Forest &6.58 &0.61 & 0.53 &0.51 \\ Simple CT &11.12 &0.7...
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\begin{tabular}{lrrrr} \toprule Dataset & Linear & Non-linear & Num cat & Num cont \\ \hline Adult-Income & 0.82 & 0.82 & 6 & 2\\ LendingClub & 0.67 & 0.66 & 4 & 4\\ German-Credit & 0.73 & 0.77 & 15 & 5\\ COMPAS & 0.67 & 0.67 & 4 & 1\\ \bottomrule \end{tabular}
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\begin{tabular}{lccccccccc} \toprule & \multicolumn{9}{c}{\textbf{cycle}} \\ \cmidrule(r){2-10} \textbf{\textbf{parameter}} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6} & \textbf{7} & \textbf{8} & \textbf{9} \\ \midrule epochs & 15 & 15 & 10 & 10 & 10 & 10 & 10 & 10 & 10 \\ grace epochs...
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\begin{tabular}{lccccccc} \toprule & \multicolumn{2}{c}{\textbf{kernel sizes}} & \multicolumn{2}{c}{\textbf{dilations}} & \multicolumn{2}{c}{\textbf{expansions}} & \\ \cmidrule(r){2-3} \cmidrule(r){4-5} \cmidrule(r){6-7} \textbf{\textbf{setting}} & \textbf{min} & \textbf{max} & \textbf{min} & \textbf{max} & \textbf{max...
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\begin{tabular}{c|cc} \hline $X^1$ & $\mathbb{E}(Y(0))$ & $\mathbb{E}(Y(1))$ \\ \hline\hline 0 & 1 & 0.8 \\ \hline 1 & 0 & 0.2 \\ \hline \end{tabular}
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\begin{tabular}{cc|cc} \hline $X^1$ & $X^2$ & $\mathbb{E}(Y(0))$ & $\mathbb{E}(Y(1))$ \\ [0.5ex] \hline\hline 0 & 0 & 2 & 1.8 \\ \hline 1 & 0 & 1 & 1.2 \\ \hline 0 & 1 & 1 & 0.8 \\ \hline 1 & 1 & 0 & 0.2 \\ \hline \end{tabular}
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\begin{tabular}{lcccc} \toprule & \multicolumn{2}{c}{CE loss} & \multicolumn{2}{c}{BLEU}\\ \midrule & train & eval (best) & train & eval (best)\\ \midrule Teacher-forcing (Figure~\ref{fig:scg}A, CE opt.) & $5.96 \pm 0.03$ & $6.44 \pm 0.08$ & $31.8 \pm 4.9$ & $19.6 \pm 3.6$\\ \midrule Feed samples (Figure~\ref{fig:scg}B...
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\begin{tabular}{cl|cccccc} \toprule \multicolumn{2}{c}{} & \multicolumn{2}{c}{NEFT $\beta = 1.0$} & \multicolumn{2}{c}{NEFT $\beta = 0.6$} & \multicolumn{2}{c}{NEFT $\beta = 0.4$} \\ \cmidrule(lr){3-4} \cmidrule(lr){5-6} \cmidrule(lr){7-8} \multicolumn{2}{c}{} & Acc.($\%$) & Rob.($\%$) & Acc.($\%$) & Rob.($\%$) & Acc.(...
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\begin{tabular}{cccccccc} \toprule \multicolumn{2}{c}{\multirow{1}{*}{Method}} & \multicolumn{2}{c}{Case-4} & \multicolumn{2}{c}{Case-6} & \multicolumn{2}{c}{Case-8} \\ \cmidrule(lr){1-2} \cmidrule(lr){3-4} \cmidrule(lr){5-6} \cmidrule(lr){7-8} Source & Transfer & Acc.($\%$) & Rob.($\%$) & Acc.($\%$) & Rob.($\%$) & Acc...
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\begin{tabular}{c|cc} \toprule $\lambda_d$ & Acc.($\%$) & Rob.($\%$) \\ \midrule $0.1$ & 74.87 & 17.59 \\ $0.01$ & 81.45 & 16.67 \\ $0.005$ & 84.86 & 8.59 \\ $0.001$ & 89.87 & 0.22 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule Source & Target & Arch. \\ \midrule CIFAR-100 & CIFAR-10 & WRN 34-10 \\ CIFAR-10 & GTSRB & WRN 28-4 \\ CIFAR-10 & SVHN & WRN 28-4 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|ccc} \hline Average & Diagnosis & Medication & Procedure\\ \hline 1.34 & 1.59 & 0.95 & 1.47\\ \hline \end{tabular}
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\begin{tabular}{l|c|c} \hline Model & Future code prediction & CRG prediction\\ \hline Grouped codes & 0.7605 & 0.9150\\ Exact codes & 0.7574 & 0.9155\\ \hline \end{tabular}
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\begin{tabular}{cccccc} \hline ID & Dataset & Instances & Features & Labels & Cardinality \\ \hline D1 & Food Truck & 407 & 21 (29) & 12 & 2.29 \\ D2 & Water Quality & 1060 & 16 & 14 & 5.07 \\ D3 & Flags & 194 & 19 & 7 & 3.39 \\ D4 & AI4I & 10K (339) & 7 (6) & 6 (4) & 1.04 \\ \hline \end{tabular}
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\begin{tabular}{cccc} \hline Datasets & Algorithm & L & T\\ \hline \multirow{3}{*}{D1} & LF-a & 20.33$_{\pm{0.70}}$ & 6.25$_{\pm{0.96}}$ \\ & LF-l & 30.06$_{\pm{3.47}}$ & 10.30$_{\pm{0.86}}$ \\ & LF-p & 44.71$_{\pm{9.04}}$ & 11.33$_{\pm{1.16}}$ \\ \hline \multirow{3}{*}{D2} & LF-a & 16.37$_{\pm{0.40}}$ & 0.94$_{\pm{0.0...
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\begin{tabular}{cccccc} \hline Dataset & Algorithms & C & L & P & T \\ \hline \multirow{3}{*}{D1} & LF-l & 0.03$_{\pm{0.00}}$ & 41.85$_{\pm{4.8}}$ & 1.00$_{\pm{0.00}}$ & 10.26$_{\pm{0.90}}$ \\ & Anchors & 0.06$_{\pm{0.02}}$ & 8.95$_{\pm{2.3}}$ & 0.99$_{\pm{0.02}}$ & 341.62$_{\pm{105.93}}$ \\ & CHIRPS & 0.73$_{\pm{0.09}...
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\begin{tabular}{lcc} \hline \textbf{Feature} & \textbf{Range} & \textbf{Instance values} \\ \hline Type & $[1, 3]$ & $3$ \\ Air temperature [K] & $[295.6, 304.4]$ & $300.7$ \\ Process temperature [K] & $[306.1, 313.7]$ & $310.2$ \\ Rotational speed [rpm] & $[1212, 2874]$ & $1364$ \\ Torque [Nm] & $[4.2, 76.2]$ & $65.3$...
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\begin{tabular}{l|c|c|c} \hline \hline Time Series & Point & $\alpha$ & $\sigma^2$\\ \hline \multirow{4}{*}{Linear-1} & 1-3000 & $\{0.9, -0.2, 0.8, -0.5\}$ & 0.5\\ \cline{2-4} & 3001-6000 & $\{-0.3, 1.4, 0.4, -0.5\}$ & 1.5\\ \cline{2-4} & 6001-9000 & $\{1.5, -0.4, -0.3, 0.2\}$ & 2.5\\ \cline{2-4} & 9001-12000 & $\{-0.1...
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\begin{tabular}{c|c|c} \hline \hline \multirow{2}{*}{$\alpha$}& \multicolumn{2}{c}{False alarms}\\ \cline{2-3} & SAFE & time-domain FE\\ \hline 0.7 & 0.001 & 0.008\\ 0.4 & 0.004 & 0.015\\ 0.1 & 0.011& 0.023\\ 0.1 & 0.019& 0.030\\ 0.4 & 0.035 & 0.041\\ 0.7 & 0.052& 0.053\\ \hline Average & 0.020$\pm$0.018 & 0.028$\pm$0....
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\begin{tabular}{l|c|c|c|c|c|c|c} \hline \hline \multirow{2}{*}{Dataset}& \multicolumn{2}{c|}{SAFE-PAR} & \multicolumn{2}{c|}{SAFE-KSVR} & \multicolumn{2}{c|}{SAFE-DNN} & \multirow{2}{*}{\% update}\\ \cline{2-7} & mse ($\times 10^{-3}$) & ex. time (s) & mse ($\times 10^{-3}$) & ex. time (s) & mse ($\times 10^{-3}$) & ex...
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\begin{tabular}{l|c|c|c|c|c|c|c} \hline \hline \multirow{2}{*}{Dataset}& \multicolumn{3}{c|}{Time-DNN} & \multicolumn{3}{c|}{SAFE-DNN} & DNN\\ \cline{2-8} & mse ($\times 10^{-3}$) & ex. time (s) & \% update & mse ($\times 10^{-3}$) & ex. time (s) & \% update & mse ($\times 10^{-3}$)\\ \hline \multirow{2}{*}{IBM} & $1.6...
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\begin{tabular}{rrrrrrrrrrr} \hline Cluster& Num.& Num.& Batch& Batch& Grad& Forward& Backward& Backward& Step& allreduce\% \\ Network& node& GPU& size per& size& accum.& (ms)& allreduce& everything& (ms)& \\ Type& & & GPU& & step& & (ms)& else (ms)& & \\ \hline Ethernet& 64& 256& 16& 8K& 2& 55& 3579& 117& 191& \textbf...
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\begin{tabular}{|l|l|l|l|l|} \hline The Number of Action & 3 & 101 & 1001 & 2001 \\ \hline Sparse+SparseBellman-1 & 1164 & 692 & {742} & 864 \\ \hline Sparse+SparseBellman-0.1 & 1060 & 2923 & 3998 & 599 \\ \hline Sparse+SparseBellman-0.01 & 685 & 1431 & 1010 & 811 \\ \hline Sparse+SoftBellman-1 & 863 & 1316 & 1698 & 65...
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\begin{tabular}{|l|l|l|l|l|} \hline The Number of Action & 9 & 121 & 961 & 2601 \\ \hline Sparse+SparseBellman-1 & 9193 & 9648 & 7275 & 9065 \\ \hline Sparse+SparseBellman-0.1 & 9791 & 5837 & 5779 & {6851} \\ \hline Sparse+SparseBellman-0.01 & 9783 & 6456 & 6631 & 7941 \\ \hline Sparse+SoftBellman-1 & 9126 & 9834 & 760...
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\begin{tabular}{cccc} \hline ACR & $R_w$ & WCR & Acc \\ \hline \multirow{4}{*}{4} & 4 & 4 & 76.4 \\ & 8 & 8.05 & 76 \\ & 12 & 11.97 & 74.6 \\ & 16 & 14.87 & 71.54 \\ \hline \end{tabular}
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\begin{tabular}{l|l} \hline Symbols & Descriptions\\ \hline \hline $\mathcal{G}$& attributed network\\ $\mathcal{G_M}$& attributed multiplex network\\ $\mathcal{C}$ & corruption function \\ $\mathcal{R}$ & readout function \\ $\mathcal{E}$ & encoder function \\ $\mathcal{D}$ & discriminator\\ $\mathcal{L}$ & objective ...
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\begin{tabular}{c|c|c|c|c|c|c} \hline Datasets & \# Nodes & Relation Types & \# Edges & \# Attributes & \# Labeled Data & \# Classes\\ \hline \hline \multirow{2}{*}{ACM} & \multirow{2}{*}{3,025} & Paper-Subject-Paper (PSP) & 2,210,761 & 1,830 & \multirow{2}{*}{600} & \multirow{2}{*}{3}\\ & & Paper-Author-Paper (PAP) & ...
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\begin{tabular}{l|cc|cc|cc|cc} \hline Dataset & \multicolumn{2}{c|}{ACM} & \multicolumn{2}{c|}{IMDB} & \multicolumn{2}{c|}{DBLP} & \multicolumn{2}{c}{Amazon} \\ \hline Metric & Macro-F1 & Micro-F1 & Macro-F1 & Micro-F1 & Macro-F1 & Micro-F1 & Macro-F1 & Micro-F1\\ \hline DeepWalk & 0.739 & 0.748 & 0.532 & 0.550 & 0.533...
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\begin{tabular}{l|cc|cc|cc|cc} \hline Dataset & \multicolumn{2}{c|}{ACM} & \multicolumn{2}{c|}{IMDB} & \multicolumn{2}{c|}{DBLP} & \multicolumn{2}{c}{Amazon} \\ \hline Metric & NMI & Sim@5 & NMI & Sim@5 & NMI & Sim@5 & NMI & Sim@5\\ \hline DeepWalk & 0.310 & 0.710 & 0.117 & 0.490 & 0.348 & 0.629 & 0.083 & 0.726 \\ node...
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\begin{tabular}{|c|l|} \hline Symbols & Definitions \\ \hline \hline $n$ & Sample size \\ \hline $p$ & Dimension of features \\ \hline $\mathbf{X}=\{\mathbf{S},\mathbf{V}\}\in\{0,1\}^p$ & Features\\ \hline $\mathbf{S}\in\{0,1\}^{p_s}$ & Stable features\\ \hline $\mathbf{V}\in\{0,1\}^{p_v}$ & Noisy features\\ \hline $Y\...
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\begin{tabular}{lccccccccc} \hline \textbf{} & line & corner\ 1 & corner\ 2 & square\ 1 & square\ 2 & maze\ 1 & maze\ 2 & \% NSD & reward\\ \hline distance & 8.00 & 8.00 & 16.00 & 8.00 & 12.00 & 16.00 & 16.00 & - & -\\ \hline baseline & 5.38 & 5.13 & 10.42 & 5.83 & 9.68 & 2.55 & 4.27 & 57.87 & 1.16 \\ DE & 6.16 & 6.24 ...
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\begin{tabular}{ll} \multicolumn{1}{c}{\bf Feature} &\multicolumn{1}{c}{\bf Description} \\ \hline \\ *Read Error Rate &Rate of errors that occurred when reading data from disk surface \\ *Temperature &Device temperature \\ *Airflow Temperature &Contains same information as the Temperature feature \\ *Reallocated Secto...
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\begin{tabular}{crrrrrrrrr} \toprule{H\textbackslash}W & {Edu} & {Height} & {Weight} & {Health} & {Irres} & {Disc} & {Order} & {Clumsy} & {Detail} \\ \midrule Edu & 0.065 & -0.083 & -0.052 & -0.048 & 0.015 & -0.013 & -0.043 & -0.063 & -0.040 \\ Height & -0.056 & -0.461 & -0.280 & -0.239 &-0.054 & 0.182 &-0.232 &-0.338 ...
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\begin{tabular}{lrrr} \toprule & QQP & MNLI & SST-2 \\ \hline $\text{BERT medium}^{\text{ orig}}$ & 89.8\% & 79.6\% & 94.2\% \\ $\text{BERT medium}^{\text{ ours}}$ & 89.5\% & 78.9\% & 94.2\% \\ \hline $\text{BERT base}^{\text{ orig}}$ & 90.8\% & 83.8\% & 95.0\% \\ $\text{BERT base}^{\text{ ours}}$ & 90.6\% & 81.2\% & 9...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 12 & 0.862 (6.5E-37) & 0.876 (1.6E-39) & 0.763 (2.2E-24) & 0.849 (1.0E+00) & 0.846 (1.0E+00) \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 12 & 0.670 (1.1E-27) & 0.685 (7.4E-29) & 0.564 (3.2E-20) & 0.652 (1.0E+00) & 0.647 (1.0E+00) \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 12 & 0.890 (2.7E-42) & 0.905 (5.3E-46) & 0.829 (7.7E-32) & 0.857 (1.0E+00) & 0.854 (1.0E+00) \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 12 & 0.707 (1.2E-30) & 0.732 (1.0E-32) & 0.637 (3.1E-25) & 0.662 (1.0E+00) & 0.658 (1.0E+00) \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 8 & 0.764 (2.4E-36) & 0.668 (3.2E-25) & 0.776 (3.4E-38) & 0.700 (1.9E-28) & 0.700 (1.8E-28) \\ 9 & 0.813 (2.1E-44) & 0.706 (4.0E-29) & 0.825 (9.2E-47) & 0.728 (1.3E-31) & 0.728 (1.2E-31) \\ 10 &...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 8 & 0.560 (1.8E-29) & 0.479 (4.4E-22) & 0.573 (1.1E-30) & 0.512 (6.8E-25) & 0.512 (6.6E-25) \\ 9 & 0.602 (1.2E-33) & 0.509 (1.2E-24) & 0.618 (2.5E-35) & 0.542 (1.1E-27) & 0.543 (9.7E-28) \\ 10 &...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes ($p$) & CKA ($p$) & PWCCA ($p$) & $\bar \rho_{\text{CCA}}$ ($p$) & $R^2_{\text{CCA}}$ ($p$)\\ \midrule 1 & 0.425 (5.1E-06) & 0.361 (1.1E-04) & 0.405 (1.4E-05) & 0.388 (3.4E-05) & 0.389 (3.2E-05) \\ 2 & 0.510 (3.1E-08) & 0.410 (1.2E-05) & 0.486 (1.5E-07) & 0.488 (1.3E-...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes ($p$) & CKA ($p$) & PWCCA ($p$) & $\bar \rho_{\text{CCA}}$ ($p$) & $R^2_{\text{CCA}}$ ($p$)\\ \midrule 1 & 0.295 (6.7E-06) & 0.269 (3.6E-05) & 0.277 (2.2E-05) & 0.265 (4.7E-05) & 0.268 (4.0E-05) \\ 2 & 0.363 (4.6E-08) & 0.288 (1.1E-05) & 0.343 (2.1E-07) & 0.342 (2.3E-...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 1 & 0.252 (5.7E-03) & 0.241 (7.8E-03) & 0.168 (4.7E-02) & 0.305 (1.0E+00) & 0.327 (1.0E+00) \\ 2 & 0.213 (1.7E-02) & 0.145 (7.5E-02) & 0.131 (9.7E-02) & 0.047 (6.8E-01) & 0.031 (6.2E-01) \\ 3 & ...
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\begin{tabular}{cccccc} \toprule Layer & Procrustes & CKA & PWCCA & $\bar \rho_{\text{CCA}}$ & $R^2_{\text{CCA}}$ \\ \midrule 1 & 0.199 (1.7E-03) & 0.171 (5.9E-03) & 0.126 (3.3E-02) & 0.244 (1.0E+00) & 0.243 (1.0E+00) \\ 2 & 0.179 (4.3E-03) & 0.123 (3.5E-02) & 0.118 (4.2E-02) & 0.061 (8.1E-01) & 0.042 (7.3E-01) \\ 3 & ...