Datasets:

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\begin{tabular}{lllll}[NEWLINE]\hline[NEWLINE]\textbf{IntelCPUs}&\textbf{NVidiaGPUs}&\textbf{ARM}&\textbf{IBM}&\textbf{AMD}\tabularnewline[NEWLINE]\hline[NEWLINE]Sandy/IvyBridge&Kepler&ThunderX&BluegeneQ&AMDCPUs\tabularnewline[NEWLINE]Haswell&Maxwell&ARMv8.0&Power7&\tabularnewline[NEWLINE]Skylake&Pascal&ARMv8.1&Power8&\tabularnewline[NEWLINE]WestmereCPUs&Volta&&Power9&\tabularnewline[NEWLINE]KnightsLanding/CornerXeonPhi&Turing&&&\tabularnewline[NEWLINE]BroadwellXeonE-class&&&&\tabularnewline[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{lllll}[NEWLINE]\hline\noalign{\smallskip}[NEWLINE]%\toprule[NEWLINE]Parameter&Afferents&Interneurons\\%\colrule[NEWLINE]\noalign{\smallskip}\hline\noalign{\smallskip}[NEWLINE]$C_m$&\SI{2.0}{\nano\farad}&\SI{50}{\pico\farad}\\[NEWLINE]$G_{leak}$&\SI{500}{\nano\siemens}&\SI{3}{\nano\siemens}\\[NEWLINE]$E_{leak}$&\SI{-70.0}{\milli\volt}&\SI{-65.0}{\milli\volt}\\[NEWLINE]$E_{exc}$&-&\SI{0.0}{\milli\volt}\\[NEWLINE]$E_{inh}$&-&\SI{-80.0}{\milli\volt}\\[NEWLINE]$E_{th}$&\SI{-54.0}{\milli\volt}&\SI{-50.0}{\milli\volt}orEqs.\ref{eq:ad_thr_diff}and\ref{eq:ad_thr}\\[NEWLINE]$\tau_{ref}$&\SI{1.0}{\milli\second}&\SI{2.0}{\milli\second}\\[NEWLINE]$\tau_{exc}$&-&\SI{0.5}{\milli\second}\\[NEWLINE]$\tau_{inh}$&-&\SI{10.0}{\milli\second}\\[NEWLINE]$\tau_{th}$&-&\num{1.0d4}\si{\second}\\[NEWLINE]$C_{th}$&-&\SI{20}{\milli\volt\second}\\[NEWLINE]\noalign{\smallskip}\hline[NEWLINE]%\botrule[NEWLINE]\end{tabular}

\begin{tabular}{cccccc}[NEWLINE]%\toprule[NEWLINE]%&&FP&FN&DET&F1\\[NEWLINE]%\cmidrule{3-6}[NEWLINE]%\multirow{2}{*}{\textbf{C2}}&LR&0.67&96.82&3.18&4.76\\[NEWLINE]%&GNN&0.01&0.97&99.03&99.37\\[NEWLINE]%\multirow{2}{*}{\textbf{P2P}}&LR&7.89&99.02&0.98&0.43\\[NEWLINE]%&GNN&0.01&0.49&99.51&99.58\\[NEWLINE]%\bottomrule[NEWLINE]%\end{tabular}

\begin{tabular}{ccccc}[NEWLINE]\toprule[NEWLINE]&&FP&FN&DET\\[NEWLINE]\cmidrule{3-5}[NEWLINE]\multirow{3}{*}{\textsc{C2}}&LR&0.67&96.82&3.18\\[NEWLINE]&GNN-2&0.00&1.00&0.00\\[NEWLINE]&GNN&0.01&0.97&99.03\\[NEWLINE]\midrule[NEWLINE]\multirow{3}{*}{\textsc{P2P}}&LR&7.89&99.02&0.98\\[NEWLINE]&GNN-2&0.00&99.92&0.08\\[NEWLINE]&GNN&0.01&0.49&99.51\\[NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{ccccc}[NEWLINE]%\hline[NEWLINE]%\hline[NEWLINE]%&\multicolumn{2}{c}{2ndlargesteigenvalue}&\multicolumn{2}{c}{Averagedistance}\\[NEWLINE]%&1000&10000&1000&10000\\[NEWLINE]%\hline[NEWLINE]%deBruijn&0.7162&0.7493&2.77&3.76\\[NEWLINE]%Kademlia&0.9536&0.9458&5.51&6.94\\[NEWLINE]%Chord&0.9987&0.9997&18.78&20.61\\[NEWLINE]%LEET-Chord&0.9144&0.9350&6.27&8.73\\[NEWLINE]%\hline[NEWLINE]%\hline[NEWLINE]%\end{tabular}

\begin{tabular}{lcccr}[NEWLINE]%\toprule[NEWLINE]%Dataset&Naive&Flexible&Better?\\[NEWLINE]%\midrule[NEWLINE]%Breast&95.9$\pm$0.2&96.7$\pm$0.2&$\surd$\\[NEWLINE]%Cleveland&83.3$\pm$0.6&80.0$\pm$0.6&$\times$\\[NEWLINE]%Glass2&61.9$\pm$1.4&83.8$\pm$0.7&$\surd$\\[NEWLINE]%Credit&74.8$\pm$0.5&78.3$\pm$0.6&\\[NEWLINE]%Horse&73.3$\pm$0.9&69.7$\pm$1.0&$\times$\\[NEWLINE]%Meta&67.1$\pm$0.6&76.5$\pm$0.5&$\surd$\\[NEWLINE]%Pima&75.1$\pm$0.6&73.9$\pm$0.5&\\[NEWLINE]%Vehicle&44.9$\pm$0.6&61.5$\pm$0.4&$\surd$\\[NEWLINE]%\bottomrule[NEWLINE]%\end{tabular}

\begin{tabular}{l|c}[NEWLINE]%HMMtype&Improvement\\[NEWLINE]%\hline[NEWLINE]%HMM-4&19\%\\[NEWLINE]%HMM-6&42\%\\[NEWLINE]%HMM-8&58\%\\[NEWLINE]%HMM-10&46\%\\[NEWLINE]%Average&41\%[NEWLINE]%\end{tabular}

\begin{tabular}{l|c}[NEWLINE]%HMM-type&Improvement\\[NEWLINE]%\hline[NEWLINE]%HMM-4&11\%\\[NEWLINE]%HMM-6&16\%\\[NEWLINE]%HMM-8&23\%\\[NEWLINE]%HMM-10&27\%\\[NEWLINE]%Average&19\%[NEWLINE]%\end{tabular}

\begin{tabular}{lcc}\hline\vspace{-1.7mm}&&\\\vspace{1mm}[NEWLINE]Modulation&EVM($\%$)&EVM(dB)\\\hline&&\vspace{-2mm}\\[NEWLINE]16-QAM&12.5&-18\\[NEWLINE]64-QAM&8&-22\\&&\vspace{-2.75mm}\\\hline[NEWLINE]%256-QAM&3.5&-29.4\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{lc}\hline\vspace{-1.7mm}&\\\vspace{1mm}[NEWLINE]Frequencyband&ACLR($\text{dBc}$)\\\hline&\vspace{-2mm}\\[NEWLINE]24.25-33.4(GHz)&28\\[NEWLINE]37-52.6(GHz)&26\\&\vspace{-2.75mm}\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{lp{0.2cm}S[table-number-alignment=right]lp{0.1cm}SS}[NEWLINE]\hline\hline[NEWLINE]$A$&&\multicolumn{2}{c}{$\delta\nu^{60,A}$/MHz}&&{$\dmscr^{60,A}$/fm$^2$}&{$R_\mathrm{c}$/fm}\\[NEWLINE]\hline[NEWLINE]58&&-509.1(25)&\,\,\,\,\,[42]&&-0.275(7)&3.770(2)\\[NEWLINE]60&&0.0&&&0.0&3.806(2)\\[NEWLINE]61&&280.8(27)&\,\,\,\,\,[20]&&0.083(5)&3.817(2)\\[NEWLINE]62&&503.9(25)&\,\,\,\,\,[39]&&0.223(5)&3.835(2)\\[NEWLINE]64&&1027.2(25)&\,\,\,\,\,[77]&&0.368(9)&3.854(2)\\[NEWLINE]68&&1992.3(27)&\,\,\,\,\,[147]&&0.620(21)&3.887(3)\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}[NEWLINE]\hline[NEWLINE]&Square&Plate&Total\\[NEWLINE]Sample&Dimension&Thickness&Mass\\[NEWLINE]&(mm)&(mm)&(g)\\[NEWLINE]\hline[NEWLINE]McMaster&152.4&5&1250\\[NEWLINE]Aurubis&101.6&2($\times3$)&568\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccc}[NEWLINE]\hline[NEWLINE]MJD&mag&$\sigma$\\[NEWLINE]\hline[NEWLINE]53505.21965&13.034&0.06\\[NEWLINE]53767.31269&13.214&0.05\\[NEWLINE]53767.31765&13.204&0.05\\[NEWLINE]53767.32261&13.214&0.05\\[NEWLINE]53767.32757&13.214&0.05\\[NEWLINE]53860.36368&13.244&0.05\\[NEWLINE]53860.37032&13.264&0.05\\[NEWLINE]53860.37695&13.254&0.05\\[NEWLINE]53860.38362&13.244&0.05\\[NEWLINE]53884.24010&13.274&0.05\\[NEWLINE]53767.32261&13.214&0.05\\[NEWLINE]...&...&...\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{c|c|c}[NEWLINE]Abbreviation&Approximationspace&Hyper-reduction\\[NEWLINE]\hline[NEWLINE]Adp-SS-ROM&$\mcalX_m(z)$&online-adaptive(see\Cref{sec:hypadp})\\[NEWLINE]\hline[NEWLINE]N-Adp-SS-ROM&$\mcalX_m(z)$&non-adaptive(see\Cref{sec:hypnon-adp})\\[NEWLINE]\hline[NEWLINE]SS-ROM&$\mcalX_m(z)$&none\\[NEWLINE]\hline[NEWLINE]S-ROM&$\td{\mcalX}_m$&none\\[NEWLINE]\end{tabular}

\begin{tabular}{c|c|c|c|c}[NEWLINE]&N-Adp-SS-ROM&Adp-SS-ROM&SS-ROM&S-ROM\\[NEWLINE]\hline[NEWLINE]$E(N_\mu,N_t)$&$1.95\times10^{30}$&$0.22$&$0.11$&$1.07$[NEWLINE]\end{tabular}

\begin{tabular}{c|c|c}[NEWLINE]&\multicolumn{2}{c}{$E(N_\mu,N_t)$}\\[NEWLINE]\hline[NEWLINE]$n$$(\%N_x)$&Adp-SS-ROM&N-Adp-SS-ROM\\[NEWLINE]\hline[NEWLINE]$100$(10)&$0.13$&\underline{$5.6\times10^{27}$}\\[NEWLINE]\hline[NEWLINE]$200$(20)&$0.11$&\underline{$1.1\times10^{26}$}\\[NEWLINE]\hline[NEWLINE]$400$(40)&$0.11$&\underline{$1.01\times10^{13}$}\\[NEWLINE]\hline[NEWLINE]$800$(80)&$0.11$&$0.11$\\[NEWLINE]\end{tabular}

\begin{tabular}{c|c|c|c|c}[NEWLINE]&N-Adp-SS-ROM&Adp-SS-ROM&SS-ROM&S-ROM\\[NEWLINE]\hline[NEWLINE]$E(N_\mu,N_t)$&$1$&$0.19$&$0.18$&$0.84$[NEWLINE]\end{tabular}

\begin{tabular}{c|c|c|c|c}[NEWLINE]&N-Adp-SS-ROM&Adp-SS-ROM&SS-ROM&S-ROM\\[NEWLINE]\hline[NEWLINE]$E(N_\mu,N_t)$&$18.75\times10^{3}$&$0.29$&$0.21$&$1.06$[NEWLINE]\end{tabular}

\begin{tabular}{|r|c|c|}[NEWLINE][NEWLINE]%\multicolumn{1}{c|}{}&\multicolumn{4}{c|}{MW1}&\multicolumn{4}{c|}{MW2}&\multicolumn{4}{c}{MW8}\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]$n$&Median&Interquartilerange\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]200&$6.99\cdot10^{-4}$&$3.46\cdot10^{-4}$\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]500&$2.66\cdot10^{-4}$&$1.80\cdot10^{-4}$\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]1000&$1.33\cdot10^{-4}$&$2.77\cdot10^{-4}$\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{|r|c|c|c|c|c|c|}[NEWLINE]%\multicolumn{1}{c|}{}&\multicolumn{4}{c|}{MW1}&\multicolumn{4}{c|}{MW2}&\multicolumn{4}{c}{MW8}\\[NEWLINE]\hline[NEWLINE]$(r,m-r)$&Mean$\hath_{LO}$&SD$\hath_{LO}$&Mean$\hath_{CV}$&SD$\hath_{CV}$&Mean$\hath_{KL}$&SD[NEWLINE]$\hath_{KL}$\\[NEWLINE]\hline[NEWLINE]$(200,300)$&0.320&0.080&0.314&0.073&0.313&0.025\\[NEWLINE]\hline[NEWLINE]$(400,600)$&0.277&0.066&0.265&0.044&0.268&0.020\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|c|c|}[NEWLINE]%\multicolumn{1}{c|}{}&\multicolumn{4}{c|}{MW1}&\multicolumn{4}{c|}{MW2}&\multicolumn{4}{c}{MW8}\\[NEWLINE]\hline[NEWLINE]&P\'olyatree:Normal&P\'olyatree:Cauchy&\\[NEWLINE]Setting&basedistribution&basedistribution&CVBF\\[NEWLINE]\hline[NEWLINE]Scalechange&3.87&4.25&3.39\\[NEWLINE]\hline[NEWLINE]Locationshift&5.49&4.56&4.21\\[NEWLINE]\hline[NEWLINE]Differenttailbehavior&4.31&2.89&3.56\\[NEWLINE]\hline[NEWLINE]Finitesupport&5.78&6.48&4.45\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccc}[NEWLINE]\hline[NEWLINE]$$TrainingSize1&TrainingSize2&TrainingSize3&TrainingSize4&TrainingSize5\\[NEWLINE][NEWLINE]1000&2000&3000&4000&5000\\[NEWLINE]\hline[NEWLINE]315.626816&276.528732&231.051167&201.645194&182.201332\\[NEWLINE]\hline[NEWLINE]241.768886&253.465869&235.792813&200.283283&190.463302\\[NEWLINE]\hline[NEWLINE]225.082372&271.294111&233.426294&207.040254&213.035850\\[NEWLINE]\hline[NEWLINE]234.807414&236.023336&266.549639&176.003360&189.454365\\[NEWLINE]\hline[NEWLINE]226.983797&270.906060&236.911292&215.656253&193.865229\\[NEWLINE]\hline[NEWLINE]272.410573&219.497947&238.849194&186.675892&172.254056\\[NEWLINE]\hline[NEWLINE]207.588154&272.831183&249.044102&179.578062&153.103469\\[NEWLINE]\hline[NEWLINE]281.847096&243.758940&245.641404&212.265566&178.598610\\[NEWLINE]\hline[NEWLINE]251.889248&291.354832&208.003008&201.931878&185.385053\\[NEWLINE]\hline[NEWLINE]284.436650&209.200084&199.055476&224.828010&189.899732\\[NEWLINE]\hline[NEWLINE]288.740627&247.195517&229.092062&205.312284&178.194134\\[NEWLINE]\hline[NEWLINE]144.649449&235.758037&230.391203&205.150802&188.819247\\[NEWLINE]\hline[NEWLINE]308.260022&271.371078&240.710648&177.380156&184.602293\\[NEWLINE]\hline[NEWLINE]277.599795&231.646253&225.778910&202.822568&160.224786\\[NEWLINE]\hline[NEWLINE]256.997302&226.210176&214.835991&229.774330&167.417223\\[NEWLINE]\hline[NEWLINE]230.934041&281.785840&238.745298&203.106276&191.103679\\[NEWLINE]\hline[NEWLINE]153.586296&260.621065&227.981708&186.511799&172.520435\\[NEWLINE]\hline[NEWLINE]226.711328&245.456213&231.617107&183.804394&147.947613\\[NEWLINE]\hline[NEWLINE]249.792654&274.684006&221.902894&216.998590&198.912825\\[NEWLINE]\hline[NEWLINE]261.422628&263.855802&228.180606&224.607334&177.832400\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccc}[NEWLINE]\hline[NEWLINE]$$TrainingSize1&TrainingSize2&TrainingSize3&TrainingSize4&TrainingSize5\\[NEWLINE]1000&2000&3000&4000&5000\\[NEWLINE]\hline[NEWLINE]-202.687708&-103.398273&-59.832436&-70.917170&-41.128011\\[NEWLINE]\hline[NEWLINE]-234.199598&-197.738096&-69.573026&-47.048713&-50.052904\\[NEWLINE]\hline[NEWLINE]-140.790753&-140.575321&-78.945489&-56.774375&-15.670203\\[NEWLINE]\hline[NEWLINE]-242.362822&-119.831672&-99.877084&-54.597158&-57.545674\\[NEWLINE]\hline[NEWLINE]-196.762484&-157.441267&-146.700200&-66.234945&-42.047030\\[NEWLINE]\hline[NEWLINE]-181.849927&-114.273492&-71.632717&-60.670678&-35.118160\\[NEWLINE]\hline[NEWLINE]-243.757842&-87.941830&-94.459536&-53.619110&-48.399131\\[NEWLINE]\hline[NEWLINE]-180.293276&-140.176705&-79.977440&-77.168984&-44.091777\\[NEWLINE]\hline[NEWLINE]-197.247316&-78.976296&-180.468267&-76.424981&-39.493026\\[NEWLINE]\hline[NEWLINE]-309.781101&-152.026848&-129.534220&-48.770075&-46.855700\\[NEWLINE]\hline[NEWLINE]-125.814943&-88.685435&-60.688252&-49.966268&-61.991158\\[NEWLINE]\hline[NEWLINE]-177.628620&-114.238403&-73.096124&-97.450147&-30.138647\\[NEWLINE]\hline[NEWLINE]-185.724860&-148.393193&-68.157621&-78.081066&-58.391781\\[NEWLINE]\hline[NEWLINE]-192.324827&-169.942633&-44.303294&-59.815353&-71.885834\\[NEWLINE]\hline[NEWLINE]-280.950475&-114.254441&-49.488445&-82.080690&-78.209511\\[NEWLINE]\hline[NEWLINE]-172.168485&-146.288878&-58.983640&-57.666794&-35.536059\\[NEWLINE]\hline[NEWLINE]-150.879885&-143.450683&-66.215758&-43.332715&-46.623911\\[NEWLINE]\hline[NEWLINE]-264.136426&-146.592290&-82.306751&-73.318538&-47.099724\\[NEWLINE]\hline[NEWLINE]-215.183162&-111.888083&-85.629583&-47.007426&-72.872396\\[NEWLINE]\hline[NEWLINE]-195.004422&-123.995007&-71.439609&-58.718432&-34.357756\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{lcl}[NEWLINE]\hline[NEWLINE]Parameter&Value&Comment\\[NEWLINE]\hline[NEWLINE]$E({B-V})$[mag]&0.68$\pm$0.02&fitted\\[NEWLINE]$T_\text{eff}$[kK]&35$\pm$0.5&fitted\\[NEWLINE]$d$[kpc]&2.5$\pm$0.2&from\citet{BJ2018}\\[NEWLINE]$\log(L_\star/$L$_\odot)$&5.4$\pm$0.1&fitted\\[NEWLINE]$R_\star$[R$_\odot$]&15.3$\pm$0.4&from$L_{\star}$and$T_\mathrm{eff}$\\[NEWLINE]$D$(clumpingfactor)&20&depth-dependent\\[NEWLINE]$\log(\dot{M}/\mathrm{M}_\odot\,\text{yr}^{-1})$&$-$5.9$\pm$0.1&fromH$\alpha$\\[NEWLINE]$v_{\infty}$[km\,s$^{-1}$]&2000$\pm$100&fitted\\[NEWLINE]log\,$g$[cm~s$^{-2}$]&3.5$\pm$0.1&fitted\\[NEWLINE]$M_\star$[M$_\odot$]&27$\pm$7&from$d$andlog\,$g$\\[NEWLINE]\hline[NEWLINE]\multicolumn{3}{c}{Chemicalabundances(massfraction)}\\[NEWLINE]\hline[NEWLINE]H&0.74&solar\\[NEWLINE]He&0.25&solar\\[NEWLINE]C&(5.4$^{+6.6}_{-3.0}$)$\times10^{-4}$&0.25$\times$solar\\[NEWLINE]N&(2.8$^{+9.7}_{-1.4})\times10^{-3}$&4$\times$solar\\[NEWLINE]O&(1.2$^{+0.3}_{-0.3}$)$\times10^{-3}$&2$\times$solar\\[NEWLINE]Si&6.7$\times10^{-4}$&solar\\[NEWLINE]P&5.8$\times10^{-6}$&solar\\[NEWLINE]S&3.1$\times10^{-4}$&solar\\[NEWLINE]Fe-group&1.3$\times10^{-3}$&solar\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{lcccccc}[NEWLINE]\toprule[NEWLINE]&\multicolumn{3}{c}{DeterministicSparsification}&\multicolumn{3}{c}{StochasticSparsification}\\[NEWLINE]Upper-Bound&$\mu$-convex&convex&nonconvex&$\mu$-convex&convex&nonconvex\\[NEWLINE]%\midrule[NEWLINE]%$\epsilon$-measure&$F(x^i){-}F^{\star}$&$F(x^i){-}F^{\star}$&$||\nablaF(x^{i^{\star}})||^2$\\[NEWLINE]\midrule[NEWLINE][NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]No-Compression&$A_{\epsilon}^{\texttt{SC}}$&$A_{\epsilon}^{\texttt{C}}$&$A_{\epsilon}^{\texttt{NC}}$[NEWLINE]&$B_{\epsilon}^{\texttt{SC}}$&$B_{\epsilon}^{\texttt{C}}$&$B_{\epsilon}^{\texttt{NC}}$[NEWLINE]%$\frac{2}{\bar{\omega}_T}\left(1{+}\frac{2\sigma^2}{\epsilonL}\right)\frac{2L\epsilon_0}{\epsilon}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE]Data-Dependent&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{NC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE][NEWLINE][NEWLINE]Worst-Case[NEWLINE]&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{NC}}$&[NEWLINE]$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE]\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lcccccc}[NEWLINE]\toprule[NEWLINE]&\multicolumn{3}{c}{DeterministicSparsification}&\multicolumn{3}{c}{StochasticSparsification}\\[NEWLINE]Upper-Bound&$\mu$-convex&convex&nonconvex&$\mu$-convex&convex&nonconvex\\[NEWLINE]%\midrule[NEWLINE]%$\epsilon$-measure&$F(x^i){-}F^{\star}$&$F(x^i){-}F^{\star}$&$||\nablaF(x^{i^{\star}})||^2$\\[NEWLINE]\midrule[NEWLINE][NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]No-Compression&$A_{\epsilon}^{\texttt{SC}}$&$A_{\epsilon}^{\texttt{C}}$&$A_{\epsilon}^{\texttt{NC}}$[NEWLINE]&$B_{\epsilon}^{\texttt{SC}}$&$B_{\epsilon}^{\texttt{C}}$&$B_{\epsilon}^{\texttt{NC}}$[NEWLINE]%$\frac{2}{\bar{\omega}_T}\left(1{+}\frac{2\sigma^2}{\epsilonL}\right)\frac{2L\epsilon_0}{\epsilon}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE]Data-Dependent&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{NC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE][NEWLINE][NEWLINE]Worst-Case[NEWLINE]&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{NC}}$&[NEWLINE]$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE]\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lcccc}[NEWLINE]\toprule[NEWLINE]Algorithm&$\epsilon$-measure&GD&$T$-SGD&$T$-SGDWC\\\midrule[NEWLINE][NEWLINE]strongly-convex&$F(x^i){-}F^{\star}$[NEWLINE]&$\kappa\log({\epsilon_0}/{\epsilon})$[NEWLINE]&$({1}/{\bar{\alpha}_T})\kappa\log({\epsilon_0}/{\epsilon})$[NEWLINE]&$({d}/{T})\kappa\log({\epsilon_0}/{\epsilon})$\\[NEWLINE]convex&$F(x^i){-}F^{\star}$[NEWLINE]&$2LR^2/\epsilon$[NEWLINE]&$(1/\bar\alpha_T)(2LR^2/\epsilon)$[NEWLINE]&$(d/T)(2LR^2/\epsilon)$\\[NEWLINE]non-convex&$||\nablaF(x^{i^{\star}})||^2$[NEWLINE]&$2L\epsilon_0/\epsilon$[NEWLINE]&$(1/\bar\alpha_T)(2L\epsilon_0/\epsilon)$[NEWLINE]&$(d/T)(2L\epsilon_0/\epsilon)$\\[NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lcccc}[NEWLINE]\toprule[NEWLINE]Algorithm&$\epsilon$-measure&GD&$T$-SGD&$T$-SGDWC\\\midrule[NEWLINE][NEWLINE]$\mu$-convex&$F(x^i){-}F^{\star}$[NEWLINE]&$\kappa\log(\frac{\epsilon_0}{\epsilon})$[NEWLINE]&$\frac{1}{\bar{\alpha}_T}\kappa\log(\frac{\epsilon_0}{\epsilon})$[NEWLINE]&$\frac{d}{T}\kappa\log(\frac{\epsilon_0}{\epsilon})$\\[NEWLINE]convex&$F(x^i){-}F^{\star}$[NEWLINE]&$\frac{2LR^2}{\epsilon}$[NEWLINE]&$\frac{1}{\bar\alpha_T}\frac{2LR^2}{\epsilon}$[NEWLINE]&$\frac{d}{T}\frac{2LR^2}{\epsilon}$\\[NEWLINE]non-convex&$||\nablaF(x^{i^{\star}})||^2$[NEWLINE]&$\frac{2L\epsilon_0}{\epsilon}$[NEWLINE]&$\frac{1}{\bar\alpha_T}\frac{2L\epsilon_0}{\epsilon}$[NEWLINE]&$\frac{d}{T}\frac{2L\epsilon_0}{\epsilon}$\\[NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lrrrr}[NEWLINE]\toprule[NEWLINE]Algorithm&strongly-convex&convex&non-convex\\[NEWLINE]\midrule[NEWLINE]$\epsilon$-measure&$F(x^i){-}F^{\star}$&$F(x^i){-}F^{\star}$&$||\nablaF(x^{i^{\star}})||^2$\\[NEWLINE]\midrule[NEWLINE][NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]GD&$\kappa\log(\frac{\epsilon_0}{\epsilon})$&$\frac{2LR^2}{\epsilon}$&$\frac{2L\epsilon_0}{\epsilon}$\\[NEWLINE][NEWLINE]$T$-SGD&$\frac{1}{\bar{\alpha}_T}\kappa\log(\frac{\epsilon_0}{\epsilon})$&$\frac{1}{\bar{\alpha}_T}\frac{2LR^2}{\epsilon}$&$\frac{1}{\bar{\alpha}_T}\frac{2L\epsilon_0}{\epsilon}$\\[NEWLINE][NEWLINE][NEWLINE]$T$-SGDWC[NEWLINE]&$\frac{d}{T}\kappa\log(\frac{\epsilon_0}{\epsilon})$&$\frac{d}{T}\frac{2LR^2}{\epsilon}$&$\frac{d}{T}\frac{2L\epsilon_0}{\epsilon}$\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lcccccc}[NEWLINE]\toprule[NEWLINE]&\multicolumn{3}{c}{DeterministicSparsification}&\multicolumn{3}{c}{StochasticSparsification}\\[NEWLINE]Upper-Bound&$\mu$-convex&convex&nonconvex&$\mu$-convex&convex&nonconvex\\[NEWLINE]%\midrule[NEWLINE]%$\epsilon$-measure&$F(x^i){-}F^{\star}$&$F(x^i){-}F^{\star}$&$||\nablaF(x^{i^{\star}})||^2$\\[NEWLINE]\midrule[NEWLINE][NEWLINE]%\multicolumn{4}{l}{IterationComplexity:}\\[NEWLINE][NEWLINE]No-Compression&$A_{\epsilon}^{\texttt{SC}}$&$A_{\epsilon}^{\texttt{C}}$&$A_{\epsilon}^{\texttt{NC}}$[NEWLINE]&$B_{\epsilon}^{\texttt{SC}}$&$B_{\epsilon}^{\texttt{C}}$&$B_{\epsilon}^{\texttt{NC}}$[NEWLINE]%$\frac{2}{\bar{\omega}_T}\left(1{+}\frac{2\sigma^2}{\epsilonL}\right)\frac{2L\epsilon_0}{\epsilon}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE]Data-Dependent&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\alpha}_T}}A_{\epsilon}^{\texttt{NC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{blue}{\frac{1}{\bar{\omega}_T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE][NEWLINE][NEWLINE]\\[NEWLINE][NEWLINE][NEWLINE]Worst-Case[NEWLINE]&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}A_{\epsilon}^{\texttt{NC}}$&[NEWLINE]$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{SC}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{C}}$&$\textcolor{red}{\frac{d}{T}}B_{\epsilon}^{\texttt{NC}}$[NEWLINE]\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lrrrrr}[NEWLINE]&UT&TS&IW&TM&Score\\[NEWLINE]\hline[NEWLINE]Min.&2.00&2.00&3.50&1.50&11.50\\[NEWLINE]1stQuartile&17.50&14.50&18.50&9.50&60.00\\[NEWLINE]Median&23.00&18.00&20.50&11.50&71.50\\[NEWLINE]Mean&22.17&16.73&19.42&10.94&69.24\\[NEWLINE]3rdQuartile&28.50&20.50&21.50&12.50&82.50\\[NEWLINE]Max.&34.50&25.00&25.00&15.00&98.50\\[NEWLINE]\hline[NEWLINE]Krippendorff's$\alpha$&0.96&0.96&0.74&0.89&\\[NEWLINE]\end{tabular}

\begin{tabular}{ll}[NEWLINE]\hline[NEWLINE]wordembeddingsize&$d=200$\\[NEWLINE]windowsize&$k=[1,2,3,4]$\\[NEWLINE]initiallearningrate&$\alpha=0.001$\\[NEWLINE]dropoutrate&$p=0.5$\\[NEWLINE]regularization&$\lambda=1e-3$\\[NEWLINE]numberoflayer&1\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{llrrr}[NEWLINE]\hline[NEWLINE]{\bfModel}&{\bfTarget}&{\bf$r$}&{\bf$\rho$}&{\bfMSE}\\\hline[NEWLINE]%{\bfFeature-basedModel}\\\hline[NEWLINE]\multirow{4}{*}{QuEst}&UT&0.24&0.25&51.99\\[NEWLINE]&TS&0.08&0.09&29.26\\[NEWLINE]&IW&-0.01&0.01&10.19\\[NEWLINE]&TM&-0.01&0.01&6.07\\\hline[NEWLINE]\multirow{4}{*}{MoBiL}&UT&0.18&0.20&79.23\\[NEWLINE]&TS&0.08&0.08&34.47\\[NEWLINE]&IW&0.15&0.12&16.68\\[NEWLINE]&TM&0.07&0.06&9.25\\\hline[NEWLINE]%{\bfNeuralModel}\\\hline[NEWLINE]\multirow{4}{*}{CNN-BiLSTM}&UT&0.19&0.18&64.41\\[NEWLINE]&TS&0.21&0.21&25.65\\[NEWLINE]&IW&0.13&0.09&11.46\\[NEWLINE]&TM&0.12&0.11&5.45\\\hline[NEWLINE]\multirow{4}{*}{CNN-BiLSTM-Att}&UT&$0.41$&$0.39$&$40.96$\\[NEWLINE]&TS&$0.37$&$0.37$&$15.58$\\[NEWLINE]&IW&$0.24$&$0.21$&$4.63$\\[NEWLINE]&TM&$0.30$&$0.28$&$3.59$\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|c|}[NEWLINE]\hline[NEWLINE]pol.&$t^3$&$t^2$&$t$&$1$\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]$H_{K^r,1}$&$x-1$&$x^3+9x^2-48x-421$&$x^3-96x^2+2737x-22357$&$x^3+43x^2+355x+121$\\[NEWLINE]\hline[NEWLINE]$\hat{H}_{K^r,2}$&-&$9x^3-238x^2+1361x-2195$&$9x^3-812x^2-45328x-487744$&$9x^3-7549x^2+448286x-5820221$\\[NEWLINE]\hline[NEWLINE]$\hat{H}_{K^r,3}$&-&$x^3-9x^2-48x-25$&$x^3-156x^2+3532x-6424$&$x^3-63x^2-3641x-11825$\\[NEWLINE]\hline[NEWLINE]$\hat{H}_{K^r,4}$&-&$9x^3-238x^2+1361x-2195$&$9x^3-812x^2-45328x-487744$&$9x^3-7549x^2+448286x-5820221$\\[NEWLINE]\hline[NEWLINE]$\hat{H}_{K^r,5}$&-&$x-6$&$x^3+36x^2-768x-26944$&$x^3-192x^2+10948x-178856$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|}[NEWLINE]\hline[NEWLINE]coeff.&minimalpol.\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]$t^3$&$x-1$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t^2$}&$609125894427130745695834466763740170563639135833980928x^3$\\[NEWLINE]&$+767725829025607378425247292652111581405730035262610432x^2$\\[NEWLINE]&$+300061222092067234082658423678294482282672624903293536x$\\[NEWLINE]&$+37243744151263324949875407438939777569860345513286901$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t$}&$63402882286988579232480270348050635745503565534880222391610376192x^3$\\[NEWLINE]&$-13725192373693066840488231757093791171761630118575681645149421568x^2$\\[NEWLINE]&$+786342921318635510916127890581383360136229955111267984417588224x$\\[NEWLINE]&$-13516646075537145153192703242525175243162619024655881644192369$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{1}&$178186461969600322341142200214605756480742490360904642532008424549206957490176x^3$\\[NEWLINE]&$+2500238465575574956316922540016128195983221550816430781122824734688503922688x^2$\\[NEWLINE]&$+7942841558044400713140974757114936533108129843365204389947225517213646848x$\\[NEWLINE]&$+6573048087002947388939081561118123324940201519692560411907632812406461$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|l|}[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]\multirow{2}{*}{coeff.}&\multirow{2}{*}{\hspace*{8.5cm}$S_4$}\\[NEWLINE]&\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]$t^3$&$x-1$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t^2$}&$609125894427130745695834466763740170563639135833980928x^3$\\[NEWLINE]&$+767725829025607378425247292652111581405730035262610432x^2$\\[NEWLINE]&$+300061222092067234082658423678294482282672624903293536x$\\[NEWLINE]&$+37243744151263324949875407438939777569860345513286901$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t$}&$63402882286988579232480270348050635745503565534880222391610376192x^3$\\[NEWLINE]&$-13725192373693066840488231757093791171761630118575681645149421568x^2$\\[NEWLINE]&$+786342921318635510916127890581383360136229955111267984417588224x$\\[NEWLINE]&$-13516646075537145153192703242525175243162619024655881644192369$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{1}&$178186461969600322341142200214605756480742490360904642532008424549206957490176x^3$\\[NEWLINE]&$+2500238465575574956316922540016128195983221550816430781122824734688503922688x^2$\\[NEWLINE]&$+7942841558044400713140974757114936533108129843365204389947225517213646848x$\\[NEWLINE]&$+6573048087002947388939081561118123324940201519692560411907632812406461$\\[NEWLINE][NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]\multirow{2}{*}{coeff.}&\multirow{2}{*}{\hspace*{8.5cm}$S_6$}\\[NEWLINE]&\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]$t^3$&$x-1$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t^2$}&$36305243238982413890281145728640119544631251519339927191004989892595083547500347392x^3$\\[NEWLINE]&$-4562099625444542640326757150351501343961608027306073167762565630692397127965147136x^2$\\[NEWLINE]&$-38373945786414575731513083189904988026800112808692449136937354443072398826315008x$\\[NEWLINE]&$+4414650961793693104140503198846514725940832560953694614278134162355358444958089$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$t$}&$17918396199353355049058805088857384488383405667618139921548515288945465097396579931049284021849686016x^3$\\[NEWLINE]&$-127779926553579818761843900212549793508900714146887992364081265379646615684431729282349219465658368x^2$\\[NEWLINE]&$+173870801973972034188665861925383203311853045841476017423892114350599398335858780136987512078336x$\\[NEWLINE]&$-34420059650825478884547414485898422831449454499107719097111434114544516620821487531714046653$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{1}&$2387771057358159367290182151060570674330169223812328868107571288339171666253440282540613475209$\\[NEWLINE]&$61296035059355070744231936x^3$\\[NEWLINE]&$-252803368000795481224137548975625269232188032444010506173669474186687453303016936277559608353$\\[NEWLINE]&$37040318608580594892800x^2$\\[NEWLINE]&$+5398401954573885778797871623679405939013291830944663536859088092482449919401839107837170565278$\\[NEWLINE]&$01421676551340032x$\\[NEWLINE]&$-3173319027571342197457569660707432734035037164408107365485384034562528494733387662989363676838$\\[NEWLINE]&$10259545343$\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]\multirow{2}{*}{coeff.}&\multirow{2}{*}{\hspace*{8.5cm}$S_8$}\\[NEWLINE]&\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]$t^3$&$x-1$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{$t^2$}&$17896610229573747174863113237715437362555551124007560823368715534964490124049106086376218475171$\\[NEWLINE]&$803998476828672000x^3$\\[NEWLINE]&$-8632764461526815390006506282494230116166385098236548909260694165812944738921272704072567622170572$\\[NEWLINE]&$8388910284800x^2$\\[NEWLINE]&$-16025644434941891793190025881111099657866879313532342984394763561573741656582305902336968805129475$\\[NEWLINE]&$94035269120x$\\[NEWLINE]&$+32529447226138938988669905527920116558625244669244753609865721673571430611095621276909587434858843$\\[NEWLINE]&$21574283$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{$t$}&$1282932435619698492314773507177627929574723682784816214540704700755412687484862774112813753070$\\[NEWLINE]&$4707515861536346952627346410280321024000000x^3$\\[NEWLINE]&$-8299716559598714066625123496581422312446576620002557854941277709128003194818010807059424517$\\[NEWLINE]&$07026350404833519933010891504909025280000x^2$\\[NEWLINE]&$+11917877361233953970010282512530202208569610409193159992562994892937507196265843185621505728$\\[NEWLINE]&$014209932930350406577902992615014400x$\\[NEWLINE]&$-7123291218140354671417349541795074255778101849191965430930690889917518777576393756582739603434$\\[NEWLINE]&$903409080046466500094184843$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{1}&$919680103243938973033922868060563504875468133020309148624843871674616915700907555399703648849339503$\\[NEWLINE]&$9639144509259910868729803635874949685516535079108608000000000x^3$\\[NEWLINE]&$-73559035342600500295040776192553962202449203791679388033633296324431166276281136614284845993667$\\[NEWLINE]&$7866564005446966040649993887769623302774737002823680000000x^2$\\[NEWLINE]&$+124859453246417802749874443519286834888515955015727839481478027559413452197186695139754181396863$\\[NEWLINE]&$30771129612045565781011078163726078946693873664000x$\\[NEWLINE]&$-93156216301296264623691984297496230976086049395125259735730164341146872241062442916382140292172050$\\[NEWLINE]&$4373610916963617612989963293561961647$\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]\multirow{2}{*}{coeff.}&\multirow{2}{*}{\hspace*{8.5cm}$S_{10}$}\\[NEWLINE]&\\[NEWLINE]\Xhline{2\arrayrulewidth}[NEWLINE]$t^3$&$x-1$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{$t^2$}&$355559112646711805441533173187873498621252899864733702350096028638947$\\[NEWLINE]&$086434181869745058736889518310522032532646375388879517143627083022336000x^3$\\[NEWLINE]&$-1746673407594299251126586578459915177303446574135079461748793747543688357497$\\[NEWLINE]&$51251268047890484907368544601828099865254929376287650532556800x^2$\\[NEWLINE]&$-221926037560681297097463583452946777526823575009037624736284810874206769091545575$\\[NEWLINE]&$5758535100520982872331063889546506421674505437288222720x$\\[NEWLINE]&$-12712015828149450830947991623508633378439516962838487229521551449205444676181757419$\\[NEWLINE]&$6317114842504230031245936394117370332526149643871$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{$t$}&$120857237869098796749243849386021434183238111564262812773854488641003266260560109723706082$\\[NEWLINE]&$3605269494853912985274275370629735011102984094101536010019521818373425987584000000x^3$\\[NEWLINE]&$-44031291431601012366252978980559805207664034353140198557448777193058697175779212464$\\[NEWLINE]&$31509460802917257291378017545643516518179640662145686947311793204195606596157440000x^2$\\[NEWLINE]&$+39633030527996127828036163516427799270794225874823970274200867418047856664450955053469$\\[NEWLINE]&$30905281877052732103313929610944694425132139827112711532749595268140236800x$\\[NEWLINE]&$+7573459660397995154627991279690982518993463138446961229699989343988200478541388188029$\\[NEWLINE]&$8693671007527321130879566194815441715447240349610824132088378321443$\\[NEWLINE]\hline[NEWLINE]\multirow{8}{*}{1}&$123240874097869995256375628744147413507353413780686466185600538844710585952172273671281859545131359$\\[NEWLINE]&$62104749046597816477320750767810020106355459964636651413138949876841656437080639980977612914688000000000x^3$\\[NEWLINE]&$+631734108594739263421048849111225980235838610319305095154878283895084698019513801345125252253266$\\[NEWLINE]&$8191388231529613779472209762512685540915211230224111283342447639256324862020608604973826048000000x^2$\\[NEWLINE]&$+40831140498524759788167285099786677735212333529675141992372211716893625351825268656408230063653920$\\[NEWLINE]&$8808658845598223352036086838810875696551081698050828145247131187273402074829684736000x$\\[NEWLINE]&$+289760817269051161710247539111124531055540151755308643194080087839211242064815461147954$\\[NEWLINE]&$938189924314930566902032346905632969933471189766079230515290335739274989177970677409$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|m{4.5cm}|m{3cm}|}\hline[NEWLINE]%\begin{tabular}{|l|l|}\hline[NEWLINE]\textbf{Parameter}&\textbf{Value}\\\hline[NEWLINE]LTVDelay-Dopplerchannelmodel&`ExtendedVehicularA(EVA)'\cite{itu2135}\\\hline[NEWLINE]Dopplerslots($N$)&$16$\\\hline[NEWLINE]Delayslots($M$)&$256$\\\hline[NEWLINE]NumberofNOMAusers&2\\\hline[NEWLINE]Userspeed&$500$kmph\\\hline[NEWLINE]Carrierfrequency&$5.9$GHz\\\hline[NEWLINE]SubcarrierBandwidth$\Deltaf$&$15$KHz\\\hline[NEWLINE]TotalBandwidth$B$&$3.84$MHz\\\hline[NEWLINE]FrameDuration$T_f$&$1.08$ms\\\hline[NEWLINE]ErrorCorrectionCodes&LDPCcodes.Codelength=648,coderate(R)=2/3\cite{IEEE_80211n_standard}\\\hline[NEWLINE]DownlinkaverageSNR&$\SNR_1=15$dB,$\SNR_2=25$dB\\\hline[NEWLINE]UplinkaverageSNR&$\SNR_1^u=10$dB,$\SNR_2^u=30$dB\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{|m{2.2cm}|m{1.15cm}|m{1.15cm}|m{1.5cm}|}\hline[NEWLINE]%Metric&OTFS-NOMA&OFDM-NOMA&\%Gain\\\hline[NEWLINE]%MeanSE&7.1716&8.6769&-17.34\%\\\hline[NEWLINE]%5\%OutageSE&6.199&5.532&12.05\%\\\hline[NEWLINE]%\end{tabular}

\begin{tabular}{|c|c|c|}[NEWLINE]%\hline[NEWLINE]%\multicolumn{2}{|c|}{SNR(dB)}&Modulation\\[NEWLINE]%\hline[NEWLINE]%OTFS&OFDM&\\[NEWLINE]%\hline[NEWLINE]%9.5&10.8&QPSK\\[NEWLINE]%16&18&16QAM\\[NEWLINE]%23&25&64QAM\\[NEWLINE]%\hline[NEWLINE]%\end{tabular}

\begin{tabular}{|c|c|c|}[NEWLINE]%\hline[NEWLINE]%Modulation&\multicolumn{2}{|c|}{SNR(dB)}\\[NEWLINE]%\hline[NEWLINE]%&OTFS&OFDM\\[NEWLINE]%\hline[NEWLINE]%QPSK&9.5&10.8\\[NEWLINE]%16QAM&15.8&18\\[NEWLINE]%64QAM&23.5&26\\[NEWLINE]%\hline[NEWLINE]%\end{tabular}

\begin{tabular}{lllll}[NEWLINE]&Texts&Words&Lexicon&L10\\[NEWLINE]\hline[NEWLINE]OpenWebText&8653K&8706M&31189K&2425K\\[NEWLINE]ukWac&2542K&1875M&6286K&832K\\[NEWLINE]Wikipedia&2524K&1242M&8168K&1010K\\[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|}[NEWLINE]\hline[NEWLINE]manifold&tangentsubspaceat$I$&orthogonalsubspaceat$I$\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]symplectic&Hamiltonian&skew-Hamiltonian\\[NEWLINE]perplectic&perskew-Hermitian&per-Hermitian\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]Liegroup&Liealgebra&Jordanalgebra\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{l@{\quad}c@{\quad}c@{\quad}c}[NEWLINE]&Uncoupled&Coupled&\\[NEWLINE]&(IDEE)&(EEG)&\\[NEWLINE]&$\Omega_{\phi,i}$&$M_{*,i}^2,\,\beta$&Section\\[NEWLINE]\hline[NEWLINE]\multirow{2}{*}{Canonical+$\Lambda$}[NEWLINE]&PB,PBS&&\ref{sec:constraints_uncoupled}\\[NEWLINE]&&PB,PBS&\ref{sec:constraints_coupled}\\[NEWLINE]\hline[NEWLINE]Accelerating[NEWLINE](LUPE)&&&\\[NEWLINE]\quad+$\summ_\nu$\quad($\Lambda=0$)&PB&PB&\multirow{2}{*}{\ref{sec:constraints_late}}\\[NEWLINE]\quad+$\Lambda$\qquad($\summ_\nu$fixed)&-&PB&\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{lccc}[NEWLINE]\hline\hline[NEWLINE]&$xy$&$xz$&$yz$\\\hline[NEWLINE]$J_\textrm{H}$(inunitsof$t_1$)&$0.8(\pm0.2)$&$1.2(\pm0.2)$&$1.2(\pm0.2)$\\[NEWLINE]$t_2$(inunitsof$t_1$)&$0.5(\pm0.1)$&$0(\pm0.2)$&$0.7(\pm0.1)$\\[NEWLINE]$\Delta_\textrm{CF}$(eV)&1$.87(\pm0.03)$&$2.32(\pm0.03)$&$2.45(\pm0.03)$\\[NEWLINE]%$2\Gamma_L$(eV)&0.06&0.06&0.06\\[NEWLINE]\hline\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}[NEWLINE]\hline\hline[NEWLINE]material&$a$(\AA)&$b$(\AA)&$c$(\AA)\\[NEWLINE]\hline[NEWLINE]LaSrAlO$_4$&3.756&3.756&12.617\\[NEWLINE]Ca$_2$CuO$_3$bulk\cite{kondoh1988magnetic}&12.262&3.783&3.263\\[NEWLINE]Ca$_2$CuO$_3$film&12.288&3.758&3.262\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|}[NEWLINE]\hline[NEWLINE]\textbf{Nameanddescription}&\textbf{Rangeofvalues}\\[NEWLINE]\hline[NEWLINE]Road-distancetointersection&[0m,250m]\\[NEWLINE]Road-distancetotrafficlight&[0m,250m]\\[NEWLINE]Road-distancetopedestriancrossing&[0m,250m]\\[NEWLINE]Road-distancetoyieldsign&[0m,250m]\\[NEWLINE]\hline[NEWLINE]Legalspeedlimit&[0km/h,120km/h]\\[NEWLINE]Averagedrivingspeedbasedonroadgeometry&[0km/h,$\infty$km/h]\\[NEWLINE]Curvature(inverseofradius)&[0m$^{-1}$,$\infty$m$^{-1}$]\\[NEWLINE]\hline[NEWLINE]Turnnumber:whichwaytoturninnextintersection&[0,$\infty$]\\[NEWLINE]\hline[NEWLINE]Relativeheadingoftheroadafterintersection&[-180$\deg$,180$\deg$]\\[NEWLINE]Relativeheadingofallotherroads&[-180$\deg$,180$\deg$]\\[NEWLINE]\hline[NEWLINE]Relativeheadingsofmap-matchedGPScoordinate&[-180$\deg$,180$\deg$]x5\\[NEWLINE]in\{1,5,10,20,50\}meters&\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{p{30mm}cl}[NEWLINE]Metricname&Parameters&Metricdefinition\\[NEWLINE]\hline[NEWLINE]Squarederror&--&$\frac{1}{|V|}\sum\limits_{i\inV}\|a_i-\hat{a}_i\|^2$\\[NEWLINE]Absoluteerror&--&$\frac{1}{|V|}\sum\limits_{i\inV}\|a_i-\hat{a}_i\|_1$\\[NEWLINE]Speed-weightedabsoluteerror&--&$\frac{1}{|V|}\sum\limits_{i\inV}\|a_i-\hat{a}_i\|_1v_i$\\[NEWLINE]Cumulativespeed-weightedabsoluteerror&$T$&$\frac{1}{|V|}\sum\limits_{i\inV}\|\sum\limits_{t=0}^T(a_{i+t}-\hat{a}_{i+t})v_{i+t}\|_1$\\[NEWLINE]Quantizedclassificationerror&$\sigma$&$\frac{1}{|V|}\sum\limits_{i\inV}\left(1-\delta\left(Q(a_i,\sigma),Q(\hat{a}_i,\sigma)\right)\right)$\\[NEWLINE]Thresholdedrelativeerror&$\alpha$&$\frac{1}{|V|}\sum\limits_{i\inV}\theta\left(\|\hat{a}_i-a_i\|-\alpha\|a_i\|\right)$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|c|c|c|}[NEWLINE]\hline[NEWLINE]ARTICLE&DATATYPE&INPUTS&OUTPUTS&LOSSES(IL)/\emph{REWARDS(RL)}&EVALUATION&DATA\\[NEWLINE]\hline[NEWLINE][NEWLINE][NEWLINE]Bewley\emph{etal.}&transfers&singlefrontalcamera&steering&1)imagereconstructionloss2)cyclicreconstructionloss&OPEN:\quadMAE,Balanced-MAE&60Kframes\\[NEWLINE]2019\cite{bewley2019learning}&simulatedtoreal&&&3)controlloss4)cycliccontrolloss5)adversarialloss&CLOSED:distancetointervention&town/rural\\[NEWLINE][NEWLINE]&(customsimulator)&&&6)perceptualloss7)latentreconstructionloss&&clear/rain/overcast\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE]Codevilla\emph{etal.}&CARLA&singlefrontalcamera&steering,acceleration&MAE&&Train:100h,Test:80h\\[NEWLINE]%test80hdoesnotmakesense-itisthebenchmark...[NEWLINE]2019\cite{codevilla2019exploring}&&ego-speed,navigationcommand&AUXILIARY:speedfromvision&&CLOSED:CARLAbenchmark\footnotemark&twotowns,diverseweather\\[NEWLINE][NEWLINE]&&&&&NoCrashbenchmark\footnotemark&\&trafficdensity\\[NEWLINE][NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Chen\emph{etal.}&CARLA&singlefrontalcamera&waypoints&MAElossontrajectories&CLOSED:CARLAbenchmark\footnotemark&Train:154Kframes=4h\\[NEWLINE]2019\cite{chen2019learning}&&&(inthecamerareferenceframe)&(comparingwithprivilegedagent)&NoCrashbenchmark\footnotemark&twotowns,diverseweather\\[NEWLINE][NEWLINE][NEWLINE]\hline[NEWLINE]Hawke\emph{etal.}&real&1or3cameras&steering:valueandslope&future-discountedMSEon&OPEN:Balanced-MAEformodelselection&Train:30h,Test:26routes\\[NEWLINE][NEWLINE]2019\cite{hawke2019urban}&&2timesteps(onlyforflow)&speed:valueandslope&predictedvalues\&slopes&CLOSED:success\%ofturns,ofstoppingbehindpacecar&onecity,6months\\[NEWLINE][NEWLINE]&&navigationcommand&&vs.observedfuturevalues&collisionrate,trafficviolationrate&differenttimesofday\\[NEWLINE][NEWLINE]&&&&&Metersperintervention(overall,inlinefollow,inpacecarfollowing)&\\[NEWLINE][NEWLINE]\hline[NEWLINE]Hecker\emph{etal.}&real&singlefrontalcamera&steering,speed&MAEonspeedandsteering&OPEN:MAE&Train:60h,Test:10h\\[NEWLINE][NEWLINE]2019\cite{hecker2019learning}&&TomTomscreen&&MAEonsecondderivativeofspeedandsteeringovertime&&city+countryside\\[NEWLINE][NEWLINE]&&featuresfromHDmaps&&adversarial(logloss)onhumannessofcommandsequence&&\\[NEWLINE][NEWLINE]\hline[NEWLINE]Kendall\emph{etal.}&real&singlefrontalcamera&steering,speed&Reward:distancetravelledwithoutdrivertakingover&CLOSED:metersperdisengagement&[NEWLINE]250mruralroad\\[NEWLINE][NEWLINE]2019\cite{kendall2019learning}&&&&&&\\[NEWLINE][NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Xiao\emph{etal.}&CARLA&singlefrontalcamera&steering,throttle,brake&MAE&CLOSED:CARLAbenchmark\footnotemark&Train:25h\\[NEWLINE]2019\cite{xiao2019multimodal}&&depthimage(trueorestimated)&&&&twotowns,diverseweather\\[NEWLINE][NEWLINE]\hline[NEWLINE]Zhou\emph{etal.}&GTAV&singleormultiplecameras+&steering&MAEforsteering&CLOSED:\%ofsuccessfulepisodes,&Train:100Kframes=3.5h\\[NEWLINE][NEWLINE]2019\cite{zhou2019does}&&trueorpredicted:&&Ifpredicting:MAEfordepth,normals,flow,albedo&\%successweightedbytracklength&\\[NEWLINE]&&semantic\&instancesegmentation,monocular&&CEforsegmentationandboundaryprediction&&urban+off-roadtrail\\[NEWLINE]&&depth,surfacenormals,opticalflow,albedo&&&&\\[NEWLINE][NEWLINE]\hline[NEWLINE]Zeng\emph{etal.}&real&singlefrontalcamera&space-timecostvolume,&planningloss(costmaps)&OPEN:Atdifferenttimehorizons:&1.4Mframes,6500scenarios\\[NEWLINE][NEWLINE]2019\cite{zeng2019end}&&LiDAR,ego-speed&AUXILIARY:ego-speed,3Dobject&perceptionloss(objectdetection)&MAEandMSElossoftrajectory&multiplecities\\[NEWLINE][NEWLINE]&&&locationsandfuturetrajectories&&collision\&trafficviolationrate&\\[NEWLINE]\hline[NEWLINE][NEWLINE]Amini\emph{etal.}&real&3cameras,unroutedmap,&1)unrouted:weight,mean,variance&unrouted:negativelog-likelihoodofhumansteering,&OPEN:z-scoreofhumansteering&Train:25kmtest:separate1km\\[NEWLINE][NEWLINE]2018\cite{amini2019variational}&&(optional)routedmap&ofthe3gaussianmodels(GMs)&routed:steeringMSEloss,&accordingtotheGMM&suburbanwithturns,intersections,\\[NEWLINE][NEWLINE]&&&2)routed:deterministicsteeringcontrol&MAEpenaltyonnormoftheGaussian&&roundabouts,dynamicobstacles\\[NEWLINE]&&&&mixturemodelweightsvector,&&\\[NEWLINE]&&&&quadraticpenaltyonthelogofvarianceofGMs&&\\[NEWLINE][NEWLINE]\hline[NEWLINE]Bansal\emph{etal.}&real,&7topdownsemanticmaps&waypoints,headings,speeds,selfposition&1)waypoint(CE)2)agentboxloss(CE)&OPEN:MSEonwaypoints&26Mexamples[NEWLINE]=60days\\[NEWLINE][NEWLINE]2018\cite{bansal2018chauffeurnet}&Test:real+sim&(Roadmap,TrafficLights,SpeedLimit,&,&3)direction(MAE)4)p\_subpixelloss(MAE)&CLOSED:success\%atstop-signs,trafficlights,lanefollowing,&noinformationondiversity\\[NEWLINE][NEWLINE]&&Route,CurrentAgentBox,&AUXILLIARY:roadmask,perceptionboxes&5)speed(MAE)6)collisionloss7)onroadloss&navigatingaroundaparkedcar,&\\[NEWLINE][NEWLINE]&&DynamicBoxes,[NEWLINE]PastAgentPoses)&&8)geometrylossAUXILIARY:objectsloss\&roadloss&recoveringfromperturbations,slowingdownbehindaslowcar&\\[NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Codevilla\emph{etal.}&CARLA+&singlefrontalcamera&steering&MSE&CLOSEDCARLA:successrate,kmperinfraction&SIMULATION:train2h,twotowns,diverseweather\\[NEWLINE]2018\cite{codevilla2018end}&realtoytruck&ego-speed,navigationcommand&acceleration&&CLOSEDREAL:\%missedturns,\#interventions,timespent&REAL:Train2h,notdiverse\\[NEWLINE]\hline[NEWLINE][NEWLINE]Hecker\emph{etal.}&real&4cameras&steering,speed&MSE&OPEN:MSE&60h\quadmultiplecities,conditions\\[NEWLINE]2018\cite{hecker2018end}&&route:GPScoordinatesorTomTommap&&&&\\[NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Liang\emph{etal.}&CARLA&singlefrontalcamera&steering,acceleraton,brake&Trainedintwophases,&CLOSED:CARLAbenchmark\footnotemark&IL:14h+RL:12h\\[NEWLINE]2018\cite{liang2018cirl}&&navigationcommand&&InILphase:\quad\quadMSE&&twotowns,diverseweather\\[NEWLINE]&&&&InRLphase:speed(+),abnormalsteerangle(-)&&\\[NEWLINE]&&&&collisions(-),overlapwithsidewalkorotherlane(-)&&\\[NEWLINE][NEWLINE]\hline[NEWLINE]Müller\emph{etal.}&transfers&&&&&Train:28h(incleardaytimeweather)\\[NEWLINE]2018\cite{muller2018driving}&simulatedtoreal&singlefrontalcamera&twowaypoints(fixeddistance,predictedangle)&MSE&CLOSED:\%ofsucessfulepisodes&Test:2x25trials\\[NEWLINE]&(simulation:CARLA)&navigationcommand&&&inreal:timespent,missedturns,infractions&incloudyafterrainweather\\[NEWLINE]&(real:toytrucks)&&&&&twotowns\\[NEWLINE][NEWLINE]&&&&&&real:diversesituations,weatherdiversityunclear\\[NEWLINE][NEWLINE][NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Sauer\emph{etal.}&CARLA&singlefrontalcamera&6affordances:[NEWLINE]&3xCE&CLOSED:CARLAbenchmark\footnotemark[NEWLINE]&noinformationonamount\\[NEWLINE]2018\cite{sauer2018conditional}&&&Hazardstop(boolean),RedTrafficLight(boolean),[NEWLINE]&3xMAE&meandistance(km)betweenvarioustypesofinfractions[NEWLINE]&twotowns,diverseweather\\[NEWLINE][NEWLINE]&&&SpeedSign[categorical],Relativeangle[rad]&&inSI:distancetocenterline,jerk&\\[NEWLINE][NEWLINE]&&&Distancestovehicle[m]andcenterline[m]&&&\\[NEWLINE]\hline[NEWLINE]Sobh\emph{etal.}&CARLA&singlefrontalcameraasRGB&steering,throttle&MSE&CLOSED:timespentoff-road&Train:136KsamplesTest:20min\\[NEWLINE]2018\cite{sobh2018end}&&orassegmentation&&&timespentonlanemarkings&\\[NEWLINE]&&LiDARinBEVorPGM&&&numberofcrashes&weathernotdiverse(notspecified)\\[NEWLINE]&&navigationcommand&&&&\\[NEWLINE]\hline[NEWLINE]\setcounter{footnote}{0}[NEWLINE][NEWLINE]Dosovitsky\emph{etal.}&CARLA&singlefrontalcamera&forILmodel:specifiedas"action"&notspecified&CLOSED:CARLAbenchmark\footnotemark&ILmodel:14hofdrivingdata[NEWLINE]\\[NEWLINE]2017\cite{dosovitskiy2017carla}&&navigationcommand&RLmodel:noinformation&&distancebetweeninfractions&RLmodel:12daysofdriving\\[NEWLINE]\hline[NEWLINE]Bojarski\emph{etal.}&real&singlefrontalcamera&steering&MSE&CLOSED:autonomy(\%ofdrivingtime&Train:lengthnotspecified\\[NEWLINE][NEWLINE]2016\cite{bojarski2016end}&&&&&whencarwascontrolledbythemodel,notsafetydriver)&day,night,multipletowns,conditions\\[NEWLINE]&&&&&&test:3h=100km\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c||c|c||c|c||c|c|}[NEWLINE]\hline[NEWLINE]&\multicolumn{4}{c||}{TownI}&\multicolumn{4}{c|}{TownII}\\[NEWLINE]ARTICLE&\multicolumn{2}{c||}{Trainingweather}&\multicolumn{2}{c|}{Newweather}&\multicolumn{2}{c||}{Trainingweather}&\multicolumn{2}{c|}{Newweather}\\[NEWLINE][NEWLINE]&Empty&Dyn.objects&Empty&dyn.objects&Empty&Dyn.objects&Empty&dyn.objects\\\hline[NEWLINE]Chen\emph{etal.}2019\cite{chen2019learning}&100\textsuperscript{a}&100\textsuperscript{a}&100\textsuperscript{a}&100\textsuperscript{a}&100&99&100&100\\\hline[NEWLINE]Xiao\emph{etal.}2019\cite{xiao2019multimodal}\textsuperscript{b}&92&89&90&90&90&87&90&94\\\hline[NEWLINE]Codevilla\emph{etal.}2019\cite{codevilla2019exploring}&95&92&-&-&95&92&92&90\\\hline[NEWLINE]Sauer\emph{etal.}2018\cite{sauer2018conditional}&92&93&90&92&70&64&68&64\%\\\hline[NEWLINE]Liang\emph{etal.}2018\cite{liang2018cirl}&93&82&86&80&53&41&68&62\\\hline[NEWLINE]%Codevilla\emph{etal.}2018\cite{codevilla2018end}**&40\%&38\%&44\%&42\%\\\hline[NEWLINE]Dosovitsky\emph{etal.}2017\cite{dosovitskiy2017carla}&86&83&84&82&40&38&44&42\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c||c|c|c|}[NEWLINE]\hline[NEWLINE]&\multicolumn{3}{c||}{Trainingweather}&\multicolumn{3}{c|}{Newweather}\\[NEWLINE]ARTICLE&Notraffic&Regulartraffic&Densetraffic&Notraffic&Regulartraffic&Densetraffic\\\hline[NEWLINE]Chen\emph{etal.}2019\cite{chen2019learning}&100&96&89&100\%&94\%&85\%\\\hline[NEWLINE][NEWLINE]Codevilla\emph{etal.}2019\cite{codevilla2019exploring}&51&44&38&90\%&87\%&67\%\\\hline[NEWLINE][NEWLINE]Sauer\emph{etal.}2018\cite{sauer2018conditional}&36&26&9&25\%&14\%&10\%\\\hline[NEWLINE][NEWLINE]Codevilla\emph{etal.}2018\cite{codevilla2018end}&48&27&10&24\%&13\%&2\%\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|}[NEWLINE]\hline[NEWLINE]\textbf{VSIParameter}&\textbf{Value}\\\hline\hline[NEWLINE]RatedRMSOutputVoltage&$220$(V)\\\hline[NEWLINE]RatedOutputFrequency($\omega_o$)&$2\pi60$(rad/s)\\\hline[NEWLINE]DCLinkVoltage($V_{dc}$)&$500$(V)\\\hline[NEWLINE]SwitchingFrequency&$20$(kHz)\\\hline[NEWLINE]$LC$FilterInductance($L_f$)&$2$(mH)\\\hline[NEWLINE]$LC$FilterCapacitance($C_f$)&$20$($\mu$F)\\\hline[NEWLINE]RatedOutputPower&$2$(kVA)\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|l|}\hline[NEWLINE]&\multicolumn{2}{c|}{RMSE}&\multicolumn{2}{c|}{Runtime(ms)}\\[NEWLINE]&$d=10$&$d=20$&$d=10$&$d=20$\\\hline[NEWLINE]Set-valuedAAA&$6.522\cdot10^{-3}$&$1.707\cdot10^{-3}$&$14.7$&$24.7$\\[NEWLINE]SurrogateAAA&$1.278\cdot10^{-2}$&$2.501\cdot10^{-2}$&$11.6$&$18.5$\\[NEWLINE]VF(5iter)&$1.374\cdot10^{-2}$&$6.143\cdot10^{-3}$&$38.3$&$69.4$\\[NEWLINE]VF(10iter)&$1.139\cdot10^{-2}$&$6.069\cdot10^{-3}$&$55.1$&$103.6$\\[NEWLINE]RKFIT(5iter)&$6.619\cdot10^{-3}$&$1.568\cdot10^{-3}$&$80.2$&$182.6$\\[NEWLINE]RKFIT(10iter)&$6.246\cdot10^{-3}$&$1.233\cdot10^{-3}$&$132.5$&$302.2$\\[NEWLINE]Loewner&$1.795\cdot10^{-2}$&$1.675\cdot10^{-2}$&$21.7$&$33.3$\\[NEWLINE]block-AAA&$1.421\cdot10^{-4}$&$8.625\cdot10^{-12}$&$122.3$&$288.0$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|l|}\hline[NEWLINE]&\multicolumn{2}{c|}{RMSE}&\multicolumn{2}{c|}{Runtime(ms)}\\[NEWLINE]&$d=10$&$d=20$&$d=10$&$d=20$\\\hline[NEWLINE]Set-valuedAAA&$2.258\cdot10^{3}$&$8.564\cdot10^{-2}$&$15.3$&$16.9$\\[NEWLINE]SurrogateAAA&$1.129\cdot10^{0}$&$4.301\cdot10^{0}$&$8.7$&$13.8$\\[NEWLINE]VF(5iter)&$1.702\cdot10^{1}$&$1.675\cdot10^{1}$&$35.7$&$42.4$\\[NEWLINE]VF(10iter)&$1.683\cdot10^{1}$&$1.674\cdot10^{1}$&$75.4$&$59.5$\\[NEWLINE]RKFIT(5iter)&$3.675\cdot10^{0}$&$5.270\cdot10^{-1}$&$70.8$&$143.6$\\[NEWLINE]RKFIT(10iter)&$3.806\cdot10^{-1}$&$9.061\cdot10^{-3}$&$114$&$245.1$\\[NEWLINE]Loewner&$1.011\cdot10^{0}$&$1.784\cdot10^{-2}$&$11.3$&$17$\\[NEWLINE]block-AAA&$6.897\cdot10^{-2}$&$2.863\cdot10^{-2}$&$66$&$166.9$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|l|}\hline[NEWLINE]&\multicolumn{2}{c|}{RMSE}&\multicolumn{2}{c|}{Runtime(ms)}\\[NEWLINE]&$d=10$&$d=20$&$d=10$&$d=20$\\\hline[NEWLINE]Set-valuedAAA&$3.895\cdot10^{-4}$&$5.543\cdot10^{-5}$&$18.8$&$36.5$\\[NEWLINE]SurrogateAAA&$4.662\cdot10^{-4}$&$3.209\cdot10^{-5}$&$14.6$&$24.9$\\[NEWLINE]VF(5iter)&$6.811\cdot10^{-4}$&$3.523\cdot10^{-4}$&$49.2$&$97.1$\\[NEWLINE]VF(10iter)&$6.729\cdot10^{-4}$&$3.016\cdot10^{-4}$&$72.3$&$135.4$\\[NEWLINE]RKFIT(5iter)&$1.555\cdot10^{-4}$&$2.345\cdot10^{-5}$&$101.8$&$240$\\[NEWLINE]RKFIT(10iter)&$8.735\cdot10^{-5}$&$1.507\cdot10^{-5}$&$164.9$&$363.8$\\[NEWLINE]Loewner&$9.419\cdot10^{-4}$&$2.225\cdot10^{-4}$&$54.8$&$56.5$\\[NEWLINE]block-AAA&$5.378\cdot10^{-5}$&$4.678\cdot10^{-6}$&$165.4$&$418.9$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|l|c|c|c|c|c|l|}\hline[NEWLINE]&\multicolumn{2}{c|}{RMSE}&\multicolumn{2}{c|}{Runtime(ms)}\\[NEWLINE]&$d=10$&$d=20$&$d=10$&$d=20$\\\hline[NEWLINE]Set-valuedAAA&$2.543\cdot10^{-9}$&$1.258\cdot10^{-10}$&$18.4$&$27.3$\\[NEWLINE]SurrogateAAA&$7.640\cdot10^{-5}$&$3.132\cdot10^{-4}$&$20.7$&$31.8$\\[NEWLINE]VF(5iter)&$1.476\cdot10^{-4}$&$1.270\cdot10^{-11}$&$49.2$&$108.1$\\[NEWLINE]VF(10iter)&$1.476\cdot10^{-4}$&$2.216\cdot10^{-11}$&$63.6$&$146.4$\\[NEWLINE]RKFIT(5iter)&$2.924\cdot10^{-10}$&$2.969\cdot10^{-12}$&$112.9$&$269.1$\\[NEWLINE]RKFIT(10iter)&$2.924\cdot10^{-10}$&$2.389\cdot10^{-12}$&$171.7$&$341.2$\\[NEWLINE]Loewner&$6.309\cdot10^{-5}$&$4.397\cdot10^{-8}$&$83.8$&$86.8$\\[NEWLINE]block-AAA&$6.272\cdot10^{-12}$&$3.530\cdot10^{-12}$&$143.8$&$330.8$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|Sc|Sc|}[NEWLINE]%{|M{2.5cm}|M{3.2cm}|M{3.2cm}|}[NEWLINE]\hline[NEWLINE]&$d=10$&$d=20$\\[NEWLINE]\hline[NEWLINE]Set-valuedAAA&$1.124\cdot10^{0}$&$1.857\cdot10^{0}$\\[NEWLINE]\hline[NEWLINE]SurrogateAAA&$1.961\cdot10^{0}$&$7.438\cdot10^{-1}$\\[NEWLINE]\hline[NEWLINE]VF(5iter)&$5.556\cdot10^{-1}$&$4.702\cdot10^{-2}$\\[NEWLINE]\hline[NEWLINE]VF(10iter)&$5.557\cdot10^{-1}$&$4.693\cdot10^{-2}$\\[NEWLINE]\hline[NEWLINE]RKFIT(5iter)&$3.197\cdot10^{-1}$&$5.862\cdot10^{-2}$\\[NEWLINE]\hline[NEWLINE]RKFIT(10iter)&$6.280\cdot10^{-2}$&$3.798\cdot10^{-2}$\\[NEWLINE]\hline[NEWLINE]Loewner&$4.998\cdot10^{-1}$&$4.140\cdot10^{-1}$\\[NEWLINE]\hline[NEWLINE]block-AAA&$2.721\cdot10^{-1}$&$1.121\cdot10^{-1}$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|c||c|c|}[NEWLINE]\hline[NEWLINE]\rm{Bin}&$M_{h}$$[M_{\odot}/h]$&$N_{h}$&$r_{v}$$[{\rmMpc}/h]$&$N_{v}$\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]0&$5.25\times10^{12}$&56414&3.32&15657\\[NEWLINE]\hline[NEWLINE]1&$1.23\times10^{13}$&31453&4.03&11796\\[NEWLINE]\hline[NEWLINE]2&$2.88\times10^{13}$&15913&4.91&6693\\[NEWLINE]\hline[NEWLINE]3&$6.74\times10^{13}$&6574&5.99&3028\\[NEWLINE]\hline[NEWLINE]4&$1.57\times10^{14}$&2229&7.29&1109\\[NEWLINE]\hline[NEWLINE]5&$3.70\times10^{14}$&557&8.93&362\\[NEWLINE]\hline[NEWLINE]6&$8.07\times10^{14}$&88&10.89&80\\[NEWLINE]\hline[NEWLINE]7&$1.78\times10^{15}$&4&13.07&17\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|c|}[NEWLINE]\hline[NEWLINE]\rm{Parameter}&\rm{Abundance}&\rm{Bias}\\[NEWLINE]\hline[NEWLINE]$\beta_h$&0.38&0.08\\[NEWLINE]\hline[NEWLINE]$D_h$&0.23&0.18\\[NEWLINE]\hline[NEWLINE]$\beta_v$&0.09&0.92\\[NEWLINE]\hline[NEWLINE]$D_v$&0.06&0.07\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}[NEWLINE]\hline[NEWLINE]A&[NEWLINE]1&4&6&9&12&27&40&56&64&108&119&184&195&197&208\\\hline[NEWLINE]$\sigma_\text{DPS}^{\text{Pb}A}/A$&[NEWLINE]1.36&3.42&3.93&5.93&7.91&13.70&19.25&24.95&27.38&38.59&41.65&54.14&56.60&57.05&59.40\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}\hline[NEWLINE]{\bf}&{\bfTotal}&{\bfAlgTime}&{\bfIndexIOTime}\\\hline\hline[NEWLINE]NS1:LRU&263.6&117.6&146.0\\\hline[NEWLINE]NS2:Per-Bucket&279.5&260.8&18.7\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{lll}[NEWLINE]\hline[NEWLINE]Variable&Description&MPM\\\hline[NEWLINE]\texttt{cSES}&\citet{Vable2017}'schildhoodSEPindex.&$\emptyset$\\[NEWLINE]\texttt{education}&Educationalattainmentinyears.ProxyforearlyadulthoodSEP&\texttt{race,food\_stamp}\\[NEWLINE]\texttt{wealth}&Householdwealthin1998.Proxyforlater-lifeSEP&$\emptyset$\\[NEWLINE]\texttt{CESD}&ScoreonCES-Dscalefordepressionin1998.&\texttt{age}\\[NEWLINE]\texttt{BMI}&Bodymassindexin1998.&\texttt{age}\\[NEWLINE]\texttt{phy\_act}&Participatedinregularphysicalactivityin1998.&\texttt{age}\\[NEWLINE]\texttt{diab}&Diagnosedwithdiabetesin1998orearlier.&\texttt{age,marital}\\[NEWLINE]\texttt{hi\_bp}&Diagnosedwithhighbloodpressureorhypertensionby1998.&\texttt{age,race}\\[NEWLINE]\texttt{heart}&Diagnosedwithheartproblemsin1998orearlier.&\texttt{age,race}\\[NEWLINE]\texttt{stroke}&Sufferedatleastonestrokeby1998.&\texttt{southern}\\[NEWLINE]\texttt{lonely}&Experiencedlonelinessinby1998.&\texttt{age}\\\hline\hline[NEWLINE]\texttt{age}&Ageinmonths(modifier)&\\[NEWLINE]\texttt{chld\_hlth}&Self-ratedchildhoodhealth(modifier)&\\[NEWLINE]\texttt{race}&Race(modifier;4levels)&\\[NEWLINE]\texttt{gender}&Gender(modifier)&\\[NEWLINE]\texttt{southern}&WhethersubjectwasborninSouthernU.S.(modifier)&\\[NEWLINE]\texttt{foreign}&WhethersubjectwasbornoutsidetheU.S.(modifier)&\\[NEWLINE]\texttt{veteran}&Whethersubjectwasveteran(modifier)&\\[NEWLINE]\texttt{marital}&Maritalstatusin1998(modifier)&\\[NEWLINE]\texttt{labor}&Laborforcestatusin1998(modifier;3levels)\\[NEWLINE]\texttt{food\_stamp}&Whethersubjectreceivedfoodstampsin1998(modifier)&\\[NEWLINE]\texttt{food\_insec}&Whethersubjectexperiencedfoodinsecurityin1998(modifier)&\\\hline[NEWLINE]\end{tabular}

\begin{tabular}{lcccc}[NEWLINE]\toprule[NEWLINE]Technique&SuccessRate&CleanupSteps&Observation&Env\\\midrule[NEWLINE]SoRB&28.0$\pm$6.3\%&400k&Proprio&PointEnv\\[NEWLINE]SoRB+SGM&\textbf{100.0$\pm$.1}\%&400k&Proprio&PointEnv\\\midrule[NEWLINE]SPTM&39.3$\pm$4.0\%&-&Visual&ViZDoom\\[NEWLINE]SPTM+SGM&\textbf{60.7$\pm$4.0\%}&114k&Visual&ViZDoom\\\midrule[NEWLINE]%[NEWLINE]ConSPTM&68.2$\pm$4.1\%&1M&Visual&SafetyGym\\[NEWLINE]ConSPTM+SGM&\textbf{92.9$\pm$1.4}\%&1M&Visual&SafetyGym\\\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lcccc}[NEWLINE]\toprule[NEWLINE]\multirow{2}{*}{Technique}&Easy&Medium&Hard&\multirow{2}{*}{Overall}\\[NEWLINE]&{\small$\leq200$m}&{\small$\leq400$m}&{\small$\leq600$m}&\\\midrule[NEWLINE]Randomactions&58.0\%&21.5\%&12.0\%&30.5\%\\[NEWLINE]Visualcontroller&75.0\%&34.5\%&18.5\%&42.7\%\\[NEWLINE]%[NEWLINE]SPTM,subsampledobservations&70.0\%&34.0\%&14.0\%&39.3\%\\[NEWLINE]SPTM+SGM+54\textsc{K}cleanupsteps&88.0\%&52.0\%&\textbf{26.0\%}&55.3\%\\[NEWLINE]SPTM+SGM+114\textsc{K}cleanupsteps&\textbf{92.0\%}&\textbf{64.0\%}&\textbf{26.0\%}&\textbf{60.7\%}\\\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{lc}[NEWLINE]\toprule[NEWLINE]Method&TimetoTakeAction(s)\\\midrule[NEWLINE]SoRB&0.550$\pm$0.220\\[NEWLINE]SGM(ours)&\textbf{0.077$\pm$0.004}\\\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{cccccccccc}[NEWLINE]\hline[NEWLINE]$\text{N}$&$\text{T}$&$\text{NR}$&$\text{PR}$&$\text{NLUT}$&$\text{PLUT}$&$\text{NMULT}$&$\text{PNMULT}$&$t_s$($\text{ns}$)&$R_s$($\text{Msps}$)\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$8$}&$4$&\multirow{4}{*}{$217$}&\multirow{4}{*}{$\approx0.07\%$}&$6339$&$\approx4.21\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$79.72$&$12.54$\\[NEWLINE]&$6$&&&$6381$&$\approx4.23\%$&&&$80.95$&$12.35$\\[NEWLINE]&$8$&&&$6452$&$\approx4.28\%$&&&$81.96$&$12.20$\\[NEWLINE]&$10$&&&$6598$&$\approx4.38\%$&&&$83.76$&$11.94$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$10$}&$4$&\multirow{4}{*}{$259$}&\multirow{4}{*}{$\approx0.09\%$}&$6772$&$\approx4.49\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$84.18$&$11.88$\\[NEWLINE]&$6$&&&$6904$&$\approx4.58\%$&&&$82.70$&$12.09$\\[NEWLINE]&$8$&&&$7331$&$\approx4.86\%$&&&$83.94$&$11.91$\\[NEWLINE]&$10$&&&$7331$&$\approx4.86\%$&&&$83.00$&$12.05$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$12$}&$4$&\multirow{4}{*}{$324$}&\multirow{4}{*}{$\approx0.11\%$}&$7280$&$\approx4.83\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$82.65$&$12.10$\\[NEWLINE]&$6$&&&$7916$&$\approx5.25\%$&&&$83.28$&$12.01$\\[NEWLINE]&$8$&&&$7954$&$\approx5.28\%$&&&$87.02$&$11.49$\\[NEWLINE]&$10$&&&$8147$&$\approx5.41\%$&&&$85.99$&$11.63$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$14$}&$4$&\multirow{4}{*}{$384$}&\multirow{4}{*}{$\approx0.13\%$}&$8761$&$\approx5.81\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$84.12$&$11.89$\\[NEWLINE]&$6$&&&$8915$&$\approx5.91\%$&&&$85.08$&$11.75$\\[NEWLINE]&$8$&&&$8999$&$\approx5.97\%$&&&$86.39$&$11.58$\\[NEWLINE]&$10$&&&$9163$&$\approx6.08\%$&&&$86.75$&$11.53$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$16$}&$4$&\multirow{4}{*}{$428$}&\multirow{4}{*}{$\approx0.14\%$}&$9816$&$\approx6.51\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$86.42$&$11.54$\\[NEWLINE]&$6$&&&$9990$&$\approx6.63\%$&&&$84.80$&$11.79$\\[NEWLINE]&$8$&&&$10072$&$\approx6.68\%$&&&$88.31$&$11.32$\\[NEWLINE]&$10$&&&$10252$&$\approx6.80\%$&&&$88.65$&$11.28$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{cccccccccc}[NEWLINE]\hline[NEWLINE]$\text{N}$&$\text{T}$&$\text{NR}$&$\text{PR}$&$\text{NLUT}$&$\text{PLUT}$&$\text{NMULT}$&$\text{PNMULT}$&$t_s$($\text{ns}$)&$R_s$($\text{Msps}$)\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$8$}&$4$&\multirow{4}{*}{$746$}&\multirow{4}{*}{$\approx0.25\%$}&$5326$&$\approx3.53\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$56.73$&$17.62$\\[NEWLINE]&$6$&&&$5350$&$\approx3.55\%$&&&$55.81$&$17.92$\\[NEWLINE]&$8$&&&$5422$&$\approx3.60\%$&&&$56.18$&$17.80$\\[NEWLINE]&$10$&&&$5590$&$\approx3.71\%$&&&$56.97$&$17.55$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$10$}&$4$&\multirow{4}{*}{$917$}&\multirow{4}{*}{$\approx0.30\%$}&$6093$&$\approx4.04\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$57.21$&$17.48$\\[NEWLINE]&$6$&&&$6141$&$\approx4.07\%$&&&$57.88$&$17.28$\\[NEWLINE]&$8$&&&$6199$&$\approx4.11\%$&&&$57.63$&$17.35$\\[NEWLINE]&$10$&&&$6317$&$\approx4.19\%$&&&$56.72$&$17.63$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$12$}&$4$&\multirow{4}{*}{$1113$}&\multirow{4}{*}{$\approx0.37\%$}&$6910$&$\approx4.58\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$57.90$&$17.27$\\[NEWLINE]&$6$&&&$6982$&$\approx4.63\%$&&&$58.22$&$17.18$\\[NEWLINE]&$8$&&&$7016$&$\approx4.65\%$&&&$58.60$&$17.06$\\[NEWLINE]&$10$&&&$7172$&$\approx4.76\%$&&&$56.26$&$17.77$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$14$}&$4$&\multirow{4}{*}{$1301$}&\multirow{4}{*}{$\approx0.43\%$}&$7799$&$\approx5.17\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$58.60$&$17.06$\\[NEWLINE]&$6$&&&$7823$&$\approx5.19\%$&&&$58.22$&$17.18$\\[NEWLINE]&$8$&&&$7905$&$\approx5.24\%$&&&$58.26$&$17.16$\\[NEWLINE]&$10$&&&$8031$&$\approx5.33\%$&&&$60.00$&$16.66$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$16$}&$4$&\multirow{4}{*}{$1477$}&\multirow{4}{*}{$\approx0.49\%$}&$8713$&$\approx5.78\%$&\multirow{4}{*}{$49$}&\multirow{4}{*}{$\approx6.38\%$}&$59.43$&$16.83$\\[NEWLINE]&$6$&&&$8737$&$\approx5.80\%$&&&$58.14$&$17.20$\\[NEWLINE]&$8$&&&$8819$&$\approx5.85\%$&&&$57.89$&$17.27$\\[NEWLINE]&$10$&&&$8955$&$\approx5.94\%$&&&$58.90$&$16.98$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccccccc}[NEWLINE]\hline[NEWLINE]$\text{N}$&$\text{NR}$&$\text{PR}$&$\text{NLUT}$&$\text{PLUT}$&$\text{NMULT}$&$\text{PNMULT}$&$t_s$($\text{ns}$)&$R_s$($\text{Msps}$)\\[NEWLINE]\hline[NEWLINE]$8$&$261$&$\approx0.09\%$&$6834$&$\approx4.53\%$&$49$&$\approx6.38\%$&$92.87$&$10.77$\\[NEWLINE]$10$&$307$&$\approx0.10\%$&$7331$&$\approx4.86\%$&$49$&$\approx6.38\%$&$98.44$&$10.16$\\[NEWLINE]$12$&$375$&$\approx0.12\%$&$8409$&$\approx5.58\%$&$49$&$\approx6.38\%$&$98.68$&$10.13$\\[NEWLINE]$14$&$438$&$\approx0.15\%$&$9460$&$\approx6.28\%$&$49$&$\approx6.38\%$&$99.98$&$10.00$\\[NEWLINE]$16$&$488$&$\approx0.16\%$&$10595$&$\approx7.03\%$&$49$&$\approx6.38\%$&$104.31$&$9.59$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccccccc}[NEWLINE]\hline[NEWLINE]$\text{N}$&$\text{NR}$&$\text{PR}$&$\text{NLUT}$&$\text{PLUT}$&$\text{NMULT}$&$\text{PNMULT}$&$t_s$($\text{ns}$)&$R_s$($\text{Msps}$)\\[NEWLINE]\hline[NEWLINE]$8$&$790$&$\approx0.26\%$&$5826$&$\approx3.87\%$&$49$&$\approx6.38\%$&$66.08$&$15.13$\\[NEWLINE]$10$&$965$&$\approx0.32\%$&$6317$&$\approx4.19\%$&$49$&$\approx6.38\%$&$72.16$&$13.86$\\[NEWLINE]$12$&$1164$&$\approx0.39\%$&$7434$&$\approx4.93\%$&$49$&$\approx6.38\%$&$68.95$&$14.50$\\[NEWLINE]$14$&$1355$&$\approx0.45\%$&$8328$&$\approx5.53\%$&$49$&$\approx6.38\%$&$73.23$&$13.66$\\[NEWLINE]$16$&$1537$&$\approx0.51\%$&$9298$&$\approx6.17\%$&$49$&$\approx6.38\%$&$74.56$&$13.41$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccc}[NEWLINE]\hline[NEWLINE]$\text{N}$&$\text{T}$&$MSE$(seeEquation\ref{MSEEq})\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$8$}&$4$&\multirow{4}{*}{$2.4\times10^{-6}$}\\[NEWLINE]&$6$&\\[NEWLINE]&$8$&\\[NEWLINE]&$10$&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$10$}&$4$&\multirow{4}{*}{$1.3\times10^{-7}$}\\[NEWLINE]&$6$&\\[NEWLINE]&$8$&\\[NEWLINE]&$10$&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$12$}&$4$&\multirow{4}{*}{$7.2\times10^{-9}$}\\[NEWLINE]&$6$&\\[NEWLINE]&$8$&\\[NEWLINE]&$10$&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$14$}&$4$&\multirow{4}{*}{$4.9\times10^{-10}$}\\[NEWLINE]&$6$&\\[NEWLINE]&$8$&\\[NEWLINE]&$10$&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{$16$}&$4$&\multirow{4}{*}{$2.7\times10^{-11}$}\\[NEWLINE]&$6$&\\[NEWLINE]&$8$&\\[NEWLINE]&$10$&\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{cccccc}[NEWLINE]\hline[NEWLINE]Setpoint&$0-2\,\text{s}$&$2\,\text{s}-4\,\text{s}$&$4\,\text{s}-6\,\text{s}$&$6\,\text{s}-8\,\text{s}$&$8\,\text{s}-10\,\text{s}$\\[NEWLINE]\hline\noalign{\smallskip}[NEWLINE]$\theta^{sp}_1(n)$(Figure\ref{FigResultsTheta1})&$90\degree$&$0\degree$&$45\degree$&$-45\degree$&$90\degree$\\[.1cm][NEWLINE]$\theta^{sp}_2(n)$(Figure\ref{FigResultsTheta2})&$45\degree$&$45\degree$&$0\degree$&$22.5\degree$&$45\degree$\\[.1cm][NEWLINE]$\theta^{sp}_3(n)$(Figure\ref{FigResultsTheta3})&$45\degree$&$22.5\degree$&$0\degree$&$22.5\degree$&$45\degree$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccccccccc}[NEWLINE]\hline[NEWLINE]\multirow{2}{*}{References}&\multirow{2}{*}{IM}&\multirow{2}{*}{NI}&\multirow{2}{*}{NR}&\multirow{2}{*}{NO}&\multirow{2}{*}{NB}&\multirow{2}{*}{Msps}&\multirow{2}{*}{Mflips}&\multirow{2}{*}{Thiswork}&\multicolumn{2}{c}{Speedup}\\[NEWLINE]&&&&&&&&&Msps&Mflips\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl7A}(2013)}&\multirow{4}{*}{TS-IM}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$35$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$10$}&\multirow{4}{*}{$\approx6.63$}&\multirow{4}{*}{$\approx232.05$}&TS-FIMM-OS&$\approx1.82\times$&$\approx2.55\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx2.66\times$&$\approx3.72\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx1.53\times$&$\approx2.14\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx2.09\times$&$\approx2.93\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl1}(2014)}&\multirow{4}{*}{TS-IM}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$6$}&\multirow{4}{*}{$3$}&\multirow{4}{*}{$8$}&\multirow{4}{*}{$\approx1.00$}&\multirow{4}{*}{$\approx6.00$}&TS-FIMM-OS&$\approx11.94\times$&$\approx97.43\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx17.55\times$&$\approx143.20\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx10.77\times$&$\approx87.88\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx15.13\times$&$\approx123.46\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA3}(2015)}&\multirow{4}{*}{M-IM}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$49$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$16$}&\multirow{4}{*}{$\approx0.51$}&\multirow{4}{*}{$\approx25.00$}&TS-FIMM-OS&$\approx22.11\times$&$\approx22.11\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx33.28\times$&$\approx33.28\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx18.79\times$&$\approx18.79\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx26.28\times$&$\approx26.28\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzy4}(2016)}&\multirow{4}{*}{M-IM}&\multirow{4}{*}{$4$}&\multirow{4}{*}{$9$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$8$}&\multirow{4}{*}{$\approx5.36$}&\multirow{4}{*}{$\approx48.23$}&TS-FIMM-OS&$\approx2.18\times$&$\approx12.13\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx3.20\times$&$\approx17.83\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx1.97\times$&$\approx10.94\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx2.76\times$&$\approx15.37\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA1}(2018)}&\multirow{4}{*}{M-IM}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$25$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$16$}&\multirow{4}{*}{$\approx1.67$}&\multirow{4}{*}{$\approx41.75$}&TS-FIMM-OS&$\approx6.75\times$&$\approx13.23\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx10.17\times$&$\approx19.93\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx5.74\times$&$\approx11.25\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx8.03\times$&$\approx15.74\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA6}(2019)}&\multirow{4}{*}{M-IM}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$25$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$8$}&\multirow{4}{*}{$\approx1.00$}&\multirow{4}{*}{$\approx25.00$}&TS-FIMM-OS&$\approx11.94\times$&$\approx23.40\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx17.55\times$&$\approx34.40\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx10.77\times$&$\approx21.11\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx15.13\times$&$\approx29.65\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA8}(2019)}&\multirow{4}{*}{M-IM}&\multirow{4}{*}{$3$}&\multirow{4}{*}{$42$}&\multirow{4}{*}{$1$}&\multirow{4}{*}{$-$}&\multirow{4}{*}{$\approx1.00$}&\multirow{4}{*}{$\approx42.00$}&TS-FIMM-OS&$\approx11.94\times$&$\approx13.85\times$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx17.55\times$&$\approx20.36\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx10.77\times$&$\approx12.49\times$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx15.13\times$&$\approx17.55\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl3}(2019)}&\multirow{4}{*}{TS-IM}&\multirow{4}{*}{$3$}&\multirow{4}{*}{$-$}&\multirow{4}{*}{$2$}&\multirow{4}{*}{$24$}&\multirow{4}{*}{$\approx1.56$}&\multirow{4}{*}{$-$}&TS-FIMM-OS&$\approx7.23\times$&$-$\\[NEWLINE]&&&&&&&&TS-FIMM-P&$\approx10.88\times$&$-$\\[NEWLINE]&&&&&&&&Fuzzy-PI-OS&$\approx6.15\times$&$-$\\[NEWLINE]&&&&&&&&Fuzzy-PI-P&$\approx8.59\times$&$-$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccccccccc}[NEWLINE]\hline[NEWLINE]\multirow{2}{*}{References}&\multirow{2}{*}{FPGA}&\multirow{2}{*}{NLC}&\multirow{2}{*}{NMULT}&\multirow{2}{*}{NBitsM}&\multirow{2}{*}{Thiswork}&\multicolumn{3}{c}{$R_{\text{occupation}}$}\\[NEWLINE]&&&&&&NLC&NMULT&NBitsM\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl7A}(2013)}&\multirow{4}{*}{Spartan3A}&\multirow{4}{*}{$447$}&\multirow{4}{*}{$4$}&\multirow{4}{*}{$1512\,\text{K}$}&TS-FIMM-OS&$\approx26.24\times$&\multirow{4}{*}{$\approx12.25\times$}&\multirow{4}{*}{$\approx10^{-6}\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx22.61\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx26.24\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx22.61\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl1}(2014)}&\multirow{4}{*}{CycloneII}&\multirow{4}{*}{$1622$}&\multirow{4}{*}{$0$}&\multirow{4}{*}{$8.19\,\text{K}$}&TS-FIMM-OS&$\approx6.51\times$&\multirow{4}{*}{$49\times$}&\multirow{4}{*}{$\approx10^{-3}\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx5.51\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx6.74\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx5.75\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA3}(2015)}&\multirow{4}{*}{ArriaVGX}&\multirow{4}{*}{$6496$}&\multirow{4}{*}{$0$}&\multirow{4}{*}{$6.592\,\text{K}$}&TS-FIMM-OS&$\approx2.53\times$&\multirow{4}{*}{$49\times$}&\multirow{4}{*}{$\approx10^{-3}\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx2.21\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx2.61\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx2.29\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzy4}(2016)}&\multirow{4}{*}{Spartan6}&\multirow{4}{*}{$871$}&\multirow{4}{*}{$32$}&\multirow{4}{*}{$0\,\text{K}$}&TS-FIMM-OS&$\approx12.13\times$&\multirow{4}{*}{$\approx1.53\times$}&\multirow{4}{*}{$1\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx10.28\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx12.56\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx10.71\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA1}(2018)}&\multirow{4}{*}{Spartan6}&\multirow{4}{*}{$11425$}&\multirow{4}{*}{$5$}&\multirow{4}{*}{$0\,\text{K}$}&TS-FIMM-OS&$\approx1.44\times$&\multirow{4}{*}{$\approx9.8\times$}&\multirow{4}{*}{$1\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx1.25\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx1.48\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx1.30\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA8}(2019)}&\multirow{4}{*}{Virtex5}&\multirow{4}{*}{$13108$}&\multirow{4}{*}{$53$}&\multirow{4}{*}{$0\,\text{K}$}&TS-FIMM-OS&$\approx1.25\times$&\multirow{4}{*}{$\approx0.93\times$}&\multirow{4}{*}{$1\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx1.09\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx1.29\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx1.13\times$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl3}(2019)}&\multirow{4}{*}{Virtex7}&\multirow{4}{*}{$12468$}&\multirow{4}{*}{$38$}&\multirow{4}{*}{$0\,\text{K}$}&TS-FIMM-OS&$\approx1.32\times$&\multirow{4}{*}{$\approx1.29\times$}&\multirow{4}{*}{$1\times$}\\[NEWLINE]&&&&&TS-FIMM-P&$\approx1.15\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-OS&$\approx1.36\times$&&\\[NEWLINE]&&&&&Fuzzy-PI-P&$\approx1.19\times$&&\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{cccccccc}[NEWLINE]\hline[NEWLINE]\multirow{2}{*}{References}&\multirow{2}{*}{FPGA}&\multirow{2}{*}{$N^{\text{ref}}_g$}&\multirow{2}{*}{$F^{\text{ref}}_{\text{clk}}$(MHz)}&\multirow{2}{*}{Thiswork}&\multirow{2}{*}{$N^{\text{work}}_g$}&\multirow{2}{*}{$F^{\text{work}}_{\text{clk}}$(MHz)}&\multirow{2}{*}{$S_d$}\\[NEWLINE]&&&&&&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl7A}(2013)}&\multirow{4}{*}{Spartan3A}&\multirow{4}{*}{$451$}&\multirow{4}{*}{$66.251$}&TS-FIMM-OS&$11779$&\multirow{4}{*}{$6.63$}&$\approx38.20\times$\\[NEWLINE]&&&&TS-FIMM-P&$10157$&&$\approx44.30\times$\\[NEWLINE]&&&&Fuzzy-PI-OS&$11779$&&$\approx38.20\times$\\[NEWLINE]&&&&Fuzzy-PI-P&$10157$&&$\approx44.30\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA3}(2015)}&\multirow{4}{*}{ArriaVGX}&\multirow{4}{*}{$6496$}&\multirow{4}{*}{$125$}&TS-FIMM-OS&$16453$&\multirow{4}{*}{$0.51$}&\multirow{4}{*}{$\approx10^6\times$}\\[NEWLINE]&&&&TS-FIMM-P&$14377$&&\\[NEWLINE]&&&&Fuzzy-PI-OS&$17001$&&\\[NEWLINE]&&&&Fuzzy-PI-P&$14926$&&\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzy4}(2016)}&\multirow{4}{*}{Spartan6}&\multirow{4}{*}{$903$}&\multirow{4}{*}{$20$}&TS-FIMM-OS&$6598$&\multirow{4}{*}{$5.36$}&$\approx4.42\times$\\[NEWLINE]&&&&TS-FIMM-P&$5590$&&$\approx5.22\times$\\[NEWLINE]&&&&Fuzzy-PI-OS&$6834$&&$\approx4.27\times$\\[NEWLINE]&&&&Fuzzy-PI-P&$5826$&&$\approx5.01\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFuzzyControlFPGA1}(2018)}&\multirow{4}{*}{Spartan6}&\multirow{4}{*}{$11430$}&\multirow{4}{*}{$10$}&TS-FIMM-OS&$10252$&\multirow{4}{*}{$1.67$}&$\approx149.16\times$\\[NEWLINE]&&&&TS-FIMM-P&$8955$&&$\approx170.70\times$\\[NEWLINE]&&&&Fuzzy-PI-OS&$10595$&&$\approx144.35\times$\\[NEWLINE]&&&&Fuzzy-PI-P&$9298$&&$\approx164.42\times$\\[NEWLINE]\hline[NEWLINE]\multirow{4}{*}{\cite{PaperFPGAFuzzySugenoControl3}(2019)}&\multirow{4}{*}{Virtex7}&\multirow{4}{*}{$12506$}&\multirow{4}{*}{$150$}&TS-FIMM-OS&$10252$&\multirow{4}{*}{$1.56$}&\multirow{4}{*}{$\approx10^5\times$}\\[NEWLINE]&&&&TS-FIMM-P&$8955$&&\\[NEWLINE]&&&&Fuzzy-PI-OS&$10595$&&\\[NEWLINE]&&&&Fuzzy-PI-P&$9298$&&\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|}[NEWLINE]%\hline[NEWLINE]%One&Two\\[NEWLINE]%\hline[NEWLINE]%Three&Four\\[NEWLINE]%\hline[NEWLINE]%\end{tabular}

\begin{tabular}{lcc}[NEWLINE]\hline\hline[NEWLINE]Model&NDP&BIC\\[NEWLINE]\hline[NEWLINE](1)M1&2&178.5\\[NEWLINE](2)M4&5&164.2\\[NEWLINE](3)M1$\times$M4&7&137.9\\[NEWLINE](4)M1$\times$M4$\times$MX&8&142.3\\[NEWLINE](5)M1$\times$M4$\times$MY&8&143.1\\[NEWLINE](6)M1$\times$M4$\times$(MX+MY)&9&143.7\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|}[NEWLINE]\hline[NEWLINE]$d=$dim$(\pa\cm)$&Conditions\\[NEWLINE]\hline[NEWLINE]2&Euler$(\pa\cm)=0$\\[NEWLINE]3&--\\[NEWLINE]even$>2$&Weyl$(\pa\cm)=0$\&Euler$(\pa\cm)=0$\\[NEWLINE]odd$>3$&Weyl$(\pa\cm)=0$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{rcccccccccccccc}[NEWLINE][NEWLINE]\multicolumn{3}{c}{\footnotesize{\textbf{Cats\&Dogsexperiment}}}\\[NEWLINE][NEWLINE]\toprule[NEWLINE][NEWLINE][NEWLINE]&\multicolumn{1}{c}{\textbf{TrainonTB1}}&\multicolumn{1}{c}{\textbf{TrainonTB2}}\\[NEWLINE][NEWLINE]\cmidrule(r){2-3}\cmidrule(r){4-5}[NEWLINE][NEWLINE]\textbf{Method}&\textbf{TB2}&\textbf{TB1}\\[NEWLINE][NEWLINE]\midrule[NEWLINE][NEWLINE]%&\multicolumn{4}{c}{\textbf{LearnGender,UnlearnAge}}\\[NEWLINE][NEWLINE]%\cmidrule(r){2-5}[NEWLINE][NEWLINE]ERM($\lambda=0.0$)&$0.749\pm0.020$&$0.692\pm0.007$\\[NEWLINE][NEWLINE][NEWLINE]Alvietal.~\cite{zisserman2018}&$0.852$~\cite{kim2019cvpr}&$0.781$~\cite{kim2019cvpr}\\[NEWLINE][NEWLINE][NEWLINE]Kimetal.~\cite{kim2019cvpr}&$0.903$&$0.873$\\[NEWLINE][NEWLINE][NEWLINE]\textit{Ours}&$0.882$&$0.793$\\[NEWLINE][NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{rcccccccccccccc}[NEWLINE][NEWLINE]\multicolumn{6}{c}{\footnotesize{\textbf{Germanexperiment}}}\\[NEWLINE][NEWLINE]\toprule[NEWLINE][NEWLINE]&\multicolumn{5}{c}{\textbf{Method}}\\[NEWLINE]\cmidrule(r){2-6}[NEWLINE][NEWLINE]&SVM~\cite{donini2018empirical}&FERM~\cite{donini2018empirical}&NN~\cite{mary2019fairness}&NN+$\chi^2$~\cite{mary2019fairness}&\textit{Ours($\lambda=1.0$)}\\[NEWLINE][NEWLINE]\midrule[NEWLINE][NEWLINE]Acc.&$0.74\pm0.03$&$0.73\pm0.04$&$0.74\pm0.04$&$0.73\pm0.03$&$0.72\pm0.03$\\[NEWLINE][NEWLINE][NEWLINE]EO&$0.10\pm0.06$&$0.05\pm0.03$&$0.47\pm0.19$&$0.25\pm0.14$&$0.05\pm0.05$\\[NEWLINE][NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{rcccc}[NEWLINE][NEWLINE]\multicolumn{5}{c}{}\\[NEWLINE][NEWLINE]\toprule[NEWLINE][NEWLINE][NEWLINE]&\multicolumn{2}{c}{\textbf{TrainonEB1}}&\multicolumn{2}{c}{\textbf{TrainonEB2}}\\[NEWLINE][NEWLINE]\cmidrule(r){2-3}\cmidrule(r){4-5}[NEWLINE][NEWLINE]\textbf{Method}&\textbf{EB2}&\textbf{Test}&\textbf{EB1}&\textbf{Test}\\[NEWLINE][NEWLINE]\midrule[NEWLINE][NEWLINE]ERM($\lambda=0.0$)&$0.650\pm0.020$&$0.849\pm0.007$&$0.576\pm0.013$&$0.708\pm0.008$\\[NEWLINE]%ERM&$0.6503\pm0.020$&$0.8493\pm0.007$&$0.5758\pm.013$&$0.7079\pm0.008$\\[NEWLINE][NEWLINE]Alvietal.~\cite{zisserman2018}&$0.637$~\cite{kim2019cvpr}&$0.856$~\cite{kim2019cvpr}&$0.573$~\cite{kim2019cvpr}&$0.699$~\cite{kim2019cvpr}\\[NEWLINE]%Alvietal.~\cite{zisserman2018}&$0.6374$&$0.8556$&$0.5733$&$0.6990$\\[NEWLINE][NEWLINE]Kimetal.~\cite{kim2019cvpr}&$0.680$&$0.867$&$0.642$&$0.745$\\[NEWLINE]%Kimetal.~\cite{kim2019cvpr}&$0.6800$&$0.8666$&$0.6418$&$0.7450$\\[NEWLINE][NEWLINE]\textit{Ours}&$0.684\pm0.010$&$0.872\pm0.010$&$0.631\pm0.034$&$0.745\pm0.021$\\[NEWLINE]%\textit{Ours}&$0.6835\pm0.010$&$0.8718\pm0.010$&$0.5955\pm0.005$&$0.7226\pm0.003$\\[NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{rcccccccccccccc}[NEWLINE][NEWLINE]\multicolumn{5}{c}{\footnotesize{\textbf{IMBDexperiment}}}\\[NEWLINE][NEWLINE]\toprule[NEWLINE][NEWLINE][NEWLINE]&\multicolumn{2}{c}{\textbf{TrainonEB1}}&\multicolumn{2}{c}{\textbf{TrainonEB2}}\\[NEWLINE][NEWLINE]\cmidrule(r){2-3}\cmidrule(r){4-5}[NEWLINE][NEWLINE]\textbf{Method}&\textbf{EB2}&\textbf{Test}&\textbf{EB1}&\textbf{Test}\\[NEWLINE][NEWLINE]\midrule[NEWLINE][NEWLINE]%&\multicolumn{4}{c}{\textbf{LearnGender,UnlearnAge}}\\[NEWLINE][NEWLINE]%\cmidrule(r){2-5}[NEWLINE][NEWLINE]ERM($\lambda=0.0$)&$0.650\pm0.020$&$0.849\pm0.007$&$0.576\pm0.013$&$0.708\pm0.008$\\[NEWLINE]%ERM&$0.6503\pm0.020$&$0.8493\pm0.007$&$0.5758\pm.013$&$0.7079\pm0.008$\\[NEWLINE][NEWLINE]Alvietal.~\cite{zisserman2018}&$0.637$~\cite{kim2019cvpr}&$0.856$~\cite{kim2019cvpr}&$0.573$~\cite{kim2019cvpr}&$0.699$~\cite{kim2019cvpr}\\[NEWLINE]%Alvietal.~\cite{zisserman2018}&$0.6374$&$0.8556$&$0.5733$&$0.6990$\\[NEWLINE][NEWLINE]Kimetal.~\cite{kim2019cvpr}&$0.680$&$0.867$&$0.642$&$0.745$\\[NEWLINE]%Kimetal.~\cite{kim2019cvpr}&$0.6800$&$0.8666$&$0.6418$&$0.7450$\\[NEWLINE][NEWLINE]\textit{Ours}&$0.684\pm0.010$&$0.872\pm0.010$&$0.6279\pm0.036$&$0.744\pm0.022$\\[NEWLINE][NEWLINE][NEWLINE]\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|}[NEWLINE]\hline[NEWLINE]Method&Accuracy\\[NEWLINE]\hline[NEWLINE]Petridis\cite{petridis2018end}&82.00\%\\[NEWLINE]\hline[NEWLINE]Petridis\cite{petridis2018end}(ourre-implement)&81.70\%\\[NEWLINE]\hline\hline[NEWLINE]TheModifiedBaselineArchitecture&\textbf{82.14\%}\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}[NEWLINE]\hline[NEWLINE]Class&Baseline&BaselinewithLMIM&Improvement\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]MAKES&62\%&74\%&\textbf{12\%}\\[NEWLINE]\hline[NEWLINE]MAKING&80\%&92\%&\textbf{12\%}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]POLITICAL&82\%&90\%&\textbf{8\%}\\[NEWLINE]\hline[NEWLINE]POLITICS&84\%&92\%&\textbf{8\%}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]STAND&48\%&60\%&\textbf{12\%}\\[NEWLINE]\hline[NEWLINE]STAGE&70\%&80\%&\textbf{10\%}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]NORTH&78\%&90\%&\textbf{12\%}\\[NEWLINE]\hline[NEWLINE]NOTHING&78\%&86\%&\textbf{8\%}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]SPEND&36\%&46\%&\textbf{10\%}\\[NEWLINE]\hline[NEWLINE]SPENDING&78\%&82\%&\textbf{4\%}\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{|c||c|}[NEWLINE]\hline[NEWLINE]Method&Accuracy\\[NEWLINE]\hline\hline[NEWLINE]Chung[2018]\cite{chung2018learning}&71.50\%\\[NEWLINE]Chung[2017]\cite{chung2017lip}&76.20\%\\[NEWLINE]Petridis[2018]\cite{petridis2018end}&82.00\%\\[NEWLINE]Stafylakis[2017]\cite{stafylakis2017combining}&83.00\%\\[NEWLINE]Wang[2019]\cite{wang2019multi}&83.34\%\\[NEWLINE]\hline\hline[NEWLINE]Baseline&82.14\%\\[NEWLINE]Baseline+LMIM&83.33\%\\[NEWLINE]TheProposedGLMIM&\textbf{84.41\%}\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|}[NEWLINE]\hline[NEWLINE]Method&Accuracy\\[NEWLINE]\hline\hline[NEWLINE]LSTM-5&25.76\%\\[NEWLINE]D3D[2018]\cite{yang2018lrw}&34.76\%\\[NEWLINE]3D+2D&38.19\%\\[NEWLINE]Wang[2019]\cite{wang2019multi}&36.91\%\\[NEWLINE]\hline\hline[NEWLINE]Baseline&\textbf{38.35\%}\\[NEWLINE]Baseline+LMIM&\textbf{38.69\%}\\[NEWLINE]TheProposedGLMIM&\textbf{38.79\%}\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{@{}rcrr@{}}[NEWLINE]\toprule[NEWLINE]&\multicolumn{1}{r}{$K=1$}&$K=5$&$K=10$\\\midrule[NEWLINE]NGSLL&\multicolumn{1}{r}{{\bf2.55}($\pm{0.04}$)}&{\bf6.19}($\pm{0.07}$)&{\bf10.76}($\pm{0.17}$)\\[NEWLINE]SHAP&\multicolumn{3}{c}{699.65($\pm{60.39}$)}\\[NEWLINE]LIME&\multicolumn{3}{c}{1109.95($\pm{22.11}$)}\\\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{|c||c|c||c|c|c||c|c|}[NEWLINE]\hline[NEWLINE]&$\ell_{{L}_{D(S)}}$&$\ell_{{R}_{D(S)}}$&$\Delta_{L}$&$\Delta_{R}$&$\Phi$&$\eta$&$\chi$\tabularnewline[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]$\text{SU}\left(2\right)_{L}$&\textbf{2}&\textbf{1}&\textbf{3}&\textbf{1}&\textbf{2}&\textbf{1}&\textbf{1}\tabularnewline[NEWLINE]\hline[NEWLINE]$\text{SU}\left(2\right)_{R}$&\textbf{1}&\textbf{2}&\textbf{1}&\textbf{3}&\textbf{2}&\textbf{1}&\textbf{1}\tabularnewline[NEWLINE]\hline[NEWLINE]$\text{U}\left(1\right)_{B-L}$&-1&-1&2&2&0&0&0\tabularnewline[NEWLINE]\hline[NEWLINE]$D_{4}$&\textbf{2$\oplus$1}&\textbf{2$\oplus$1}&\textbf{1}&\textbf{1}&\textbf{1}&\textbf{2}&\textbf{1}\tabularnewline[NEWLINE]\hline[NEWLINE]$Z_{2}$&1&1&1&1&-1&-1&-1\tabularnewline[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}[NEWLINE]\hline[NEWLINE]\textbf{Kernellength}&\textbf{$4\lambda$}&\textbf{$10\lambda$}&\textbf{$50\lambda$}\\[NEWLINE]\hline[NEWLINE]\textbf{Bias(spatialpixels)}&0.0094&0.0094&0.0074[NEWLINE]\\[NEWLINE]\hline[NEWLINE]\textbf{Bias($\lambda$)}&1/1702&1/1702&1/2162[NEWLINE]\\[NEWLINE]\hline[NEWLINE]\textbf{Jitter(ns)}&0.045&0.042&0.018[NEWLINE]\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|}[NEWLINE]\hline[NEWLINE]\textbf{Noiselevel}&\textbf{Noaddednoise}&\textbf{6dB}\\[NEWLINE]\hline[NEWLINE]\textbf{RMSerror(spatialpixels)}&0.036&0.096\\[NEWLINE]\hline[NEWLINE]\textbf{RMSerror($\lambda$)}&1/446&1/166\\[NEWLINE]\hline[NEWLINE]\textbf{Errorinpeakacceleration($\rm\%$)}&1.51&4.53[NEWLINE]\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{@{}ll@{}}[NEWLINE]\toprule[NEWLINE]parameter&measuredvalue\\\midrule[NEWLINE]systemthrow($L$)&$232.0\pm1.4$mm\\[NEWLINE]arcradius($r$)&$7.03\pm0.12$mm\\[NEWLINE]$x$-distancebetweendirectbeamandarccenter($\Deltax_{\text{dir}}$)&$2.80\pm0.05$mm\\[NEWLINE]$x$-distancebetween0$^{\text{th}}$orderandarccenter($\Deltax_0$)&$2.92\pm0.05$mm\\[NEWLINE]$y$-distancebetween0$^{\text{th}}$orderandarccenter($\Deltay_0$)&$6.33\pm0.14$mm\\\midrule[NEWLINE]coneopeninghalf-angle($\gamma$)byequation~\ref{eq:arc_radius}&$1.73\pm0.03^{\circ}$\\[NEWLINE]azimuthalincidenceangle($\alpha$)byequation~\ref{eq:exp_alpha}&$23.4\pm0.6^{\circ}$\\\midrule[NEWLINE]roll(rotationabout$z$-axis;$\phi$)byequation~\ref{eq:exp_roll}&$1.14\pm0.04^{\circ}$\\[NEWLINE]graze(rotationabout$x$-axis;$\eta$)byequation~\ref{eq:exp_eta}&$1.56\pm0.04^{\circ}$\\[NEWLINE]yaw(rotationabout$y$-axis;$\varphi$)byequation~\ref{eq:exp_yaw}&$0.69\pm0.01^{\circ}$\\\bottomrule[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|c|}[NEWLINE]\hline[NEWLINE]\rule[-1ex]{0ex}{3.5ex}[NEWLINE]\emph{Treefamily}&Growthprocess:$p(v)$\\[NEWLINE]\hline[NEWLINE]\rule[-1.5ex]{0ex}{4.5ex}[NEWLINE]Bucketrecursivetrees&$\frac{c(v)}{n}$\\[NEWLINE]\hline[NEWLINE]\rule[-2.7ex]{0ex}{6.5ex}[NEWLINE]\emph{($b,d$)-aryincreasingtrees}&$\frac{(d-1)c(v)+1-\grad^{+}(v)}{(d-1)n+1}$\\[NEWLINE]\hline[NEWLINE]\rule[-2.7ex]{0ex}{6.5ex}[NEWLINE]\emph{($b,\alpha$)-PORT}&$\frac{\grad^{+}(v)+(\alpha+1)c(v)-1}{(\alpha+1)n-1}$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{|c|c|c|}[NEWLINE]\hline[NEWLINE]\rule[-1ex]{0ex}{3.5ex}[NEWLINE]\emph{Treefamily}&\emph{Degree-weightGF$\varphi(t)$}&\emph{initialweights}$\psi_k$,$1\lek\leb-1$\\[NEWLINE]\hline[NEWLINE]\rule[-1.5ex]{0ex}{4.5ex}[NEWLINE]Bucketrecursivetrees&$(b-1)!\exp(b\cdott)$[NEWLINE]&$(k-1)!$\\[NEWLINE]\hline[NEWLINE]\rule[-2.7ex]{0ex}{6.5ex}[NEWLINE]\emph{($b,d$)-aryincreasingtrees}&$(b-1)!(d-1)^{n-1}\binom{b-1+\frac{1}{d-1}}{b-1}(1+t)^{b(d-1)+1}$&[NEWLINE]$(k-1)!(d-1)^{k-1}\binom{k-1+\frac{1}{d-1}}{k-1}$\\[NEWLINE]\hline[NEWLINE]\rule[-2.7ex]{0ex}{6.5ex}[NEWLINE]\emph{($b,\alpha$)-PORT}&$\frac{(b-1)!(\alpha+1)^{b-1}\binom{b-1-\frac{1}{\alpha+1}}{b-1}}{(1-t)^{(\alpha+1)b-1}}$&[NEWLINE]$(k-1)!(\alpha+1)^{k-1}\binom{k-1-\frac{1}{\alpha+1}}{k-1}$\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{cclllll}[NEWLINE]\hline[NEWLINE]\multicolumn{7}{c}{\cellcolor[HTML]{EFEFEF}\textsc{ChestXray-14}}\\\hline[NEWLINE]\multicolumn{7}{c}{\textsc{Fully-SupervisedMethods}}\\\hline[NEWLINE]\multicolumn{1}{c}{\textsc{Method}}&\multicolumn{6}{c}{\textsc{70\%Labelled--AUC}}\\\hline[NEWLINE]\textsc{Wang~\cite{wang2017chestx}}&\multicolumn{6}{c}{0.745}\\[NEWLINE]\textsc{Yao~\cite{yao2018weakly}}&\multicolumn{6}{c}{0.761}\\[NEWLINE]\textsc{Yan~\cite{yan2018weakly}}&\multicolumn{6}{c}{\cellcolor[HTML]{DCEDC8}0.830}\\[NEWLINE]\textsc{Baltruschat(ResNet-101)~\cite{baltruschat2019comparison}}&\multicolumn{6}{c}{\cellcolor[HTML]{F1F8E9}0.785}\\[NEWLINE]\textsc{Baltruschat(ResNet-38)~\cite{baltruschat2019comparison}}&\multicolumn{6}{c}{\cellcolor[HTML]{DCEDC8}0.806}\\[NEWLINE]\hline\hline[NEWLINE]\multicolumn{1}{c}{\textsc{Method}}&\multicolumn{6}{c}{\textsc{20\%Labelled--AUC}}\\\hline[NEWLINE]\multicolumn{1}{c}{GraphXNet~\cite{aviles2019graphx}}&\multicolumn{6}{c}{0.788}\\[NEWLINE]\multicolumn{1}{c}{\textcolor{blue}{OursW/[A1]}}&\multicolumn{6}{c}{0.770}\\[NEWLINE]\multicolumn{1}{c}{\textcolor{red}{OursW/[A1]}}&\multicolumn{6}{c}{\cellcolor[HTML]{F1F8E9}0.795}\\[NEWLINE]\multicolumn{1}{c}{\textcolor{red}{OursW/[A2]}}&\multicolumn{6}{c}{\cellcolor[HTML]{DCEDC8}0.815}\\[NEWLINE]\hline\hline[NEWLINE]\end{tabular}

\begin{tabular}{l|cccccccc}[NEWLINE]%[NEWLINE]%^.[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{Scenario1}\\[NEWLINE][NEWLINE]Model&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.039&0.062&0.038&0.062&0.165&0.186&0.061\\[NEWLINE]M2&0.045&0.056&0.0507&0.057&0.073&0.086&0.085\\[NEWLINE]M3&0.046&0.053&0.042&0.053&0.073&0.085&0.080\\[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.041&0.071&0.049&0.070&0.161&0.175&0.069\\[NEWLINE]M2&0.047&0.059&0.056&0.059&0.067&0.071&0.073\\[NEWLINE]M3&0.048&0.059&0.047&0.062&0.063&0.077&0.070\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{Scenario2}\\[NEWLINE][NEWLINE][NEWLINE]Model&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.038&0.058&0.045&0.059&0.164&0.191&0.056\\[NEWLINE]M2&0.042&0.059&0.047&0.062&0.067&0.119&0.067\\[NEWLINE]M3&0.044&0.069&0.054&0.069&0.068&0.094&0.070\\[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.045&0.058&0.041&0.056&0.148&0.170&0.065\\[NEWLINE]M2&0.036&0.065&0.048&0.065&0.063&0.099&0.066\\[NEWLINE]M3&0.044&0.055&0.046&0.055&0.067&0.089&0.075\\[NEWLINE]\hline[NEWLINE][NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{l|cccccccc}[NEWLINE]%[NEWLINE]%^.[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{Scenario1}\\[NEWLINE][NEWLINE]Model&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.047&0.058&0.031&0.058&0.077&0.087&0.110\\[NEWLINE]M2&0.049&0.058&0.031&0.057&0.086&0.062&0.116\\[NEWLINE]M3&0.051&0.049&0.034&0.049&0.070&0.064&0.109\\[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.044&0.059&0.035&0.060&0.093&0.086&0.084\\[NEWLINE]M2&0.043&0.049&0.032&0.048&0.079&0.059&0.083\\[NEWLINE]M3&0.050&0.057&0.035&0.058&0.062&0.048&0.097\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{Scenario2}\\[NEWLINE][NEWLINE][NEWLINE]Model&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.042&0.064&0.033&0.065&0.077&0.101&0.102\\[NEWLINE]M2&0.037&0.043&0.021&0.045&0.089&0.190&0.085\\[NEWLINE]M3&0.031&0.056&0.026&0.059&0.133&0.180&0.097\\[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.044&0.062&0.040&0.062&0.082&0.097&0.088\\[NEWLINE]M2&0.040&0.054&0.033&0.054&0.083&0.128&0.088\\[NEWLINE]M3&0.039&0.045&0.030&0.048&0.073&0.094&0.086\\[NEWLINE]\hline[NEWLINE][NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{lcc|*{7}{c}|*{7}{c}}[NEWLINE][NEWLINE]\hline[NEWLINE]\hline[NEWLINE]r&Model&$\delta$&\multicolumn{7}{c|}{$p=200$}&\multicolumn{7}{c}{$p=1000$}\\[NEWLINE]&&&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=n_{2}=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M4&\multirow{3}{*}{1.5}&0.252&0.166&0.136&0.173&0.059&0.042&0.3615&0.291&0.107&0.077&0.113&0.108&0.050&0.508\\[NEWLINE]&M5&&0.250&0.085&0.030&0.084&0.615&0.650&0.343&0.288&0.075&0.013&0.076&0.875&0.882&0.472\\[NEWLINE][NEWLINE][NEWLINE][NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M4&\multirow{3}{*}{1.5}&0.753&0.451&0.506&0.460&0.040&0.019&0.841&0.645&0.340&0.354&0.351&0.090&0.009&0.934\\[NEWLINE]&M5&&0.717&0.109&0.045&0.109&0.241&0.236&0.804&0.638&0.070&0.012&0.070&0.676&0.726&0.901\\[NEWLINE][NEWLINE]\hline[NEWLINE][NEWLINE][NEWLINE]\multirow{3}{*}{$3\%$}&M4&\multirow{3}{*}{1.5}&0.918&0.961&0.977&0.963&0.089&0.044&0.966&0.994&0.996&1.000&0.996&0.146&0.020&1.000\\[NEWLINE]&M5&&0.825&0.194&0.074&0.194&0.246&0.225&0.893[NEWLINE]&0.949&0.125&0.02758&0.125&0.299&0.272&0.988\\[NEWLINE][NEWLINE][NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=60\;\;n_{2}=40$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M4&\multirow{3}{*}{1.5}&0.457&0.223&0.186&0.235&0.048&0.030&0.551&0.440&0.140&0.119&0.142&0.117&0.035&0.700\\[NEWLINE]&M5&&0.467&0.083&0.028&0.083&0.519&0.549&0.543&0.430&0.073&0.013&0.075&0.868&0.872&0.680\\[NEWLINE][NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M4&\multirow{3}{*}{1.5}&0.925&0.661&0.715&0.667&0.020&0.011&0.955&0.864&0.516&0.567&0.520&0.055&0.011&0.984\\[NEWLINE]&M5&&0.895&0.106&0.041&0.111&0.210&0.199&0.936&0.793&0.072&0.014&0.071&0.542&0.591&0.977\\[NEWLINE][NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$3\%$}&M4&\multirow{3}{*}{1.5}&0.991&0.997&0.999&0.997&0.063&0.034&0.998&1.000&1.000&1.000&1.000&0.068&0.015&1.000\\[NEWLINE]&M5&&0.958&0.245&0.093&0.255&0.219&0.208&0.977&0.995&0.129&0.029&0.132&0.256&0.238&0.999\\[NEWLINE][NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccc}[NEWLINE]\hline[NEWLINE]\text{TestMethod}&normalgroup&colontumorgroup\\[NEWLINE]\hline[NEWLINE]PREPR&0.035&0.022\\[NEWLINE]BS&0.087&0.066\\[NEWLINE]SD&0.009&0.007\\[NEWLINE]CQ&0.010&0.011\\[NEWLINE]GM&0.949&0.931\\[NEWLINE]GL&0.946&0.926\\[NEWLINE]CLX&0.112&0.040\\[7pt][NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{ccc}[NEWLINE]\hline[NEWLINE]\text{TestMethod}&medulloblastomatumor&ATRTtumor\\[NEWLINE]\hline[NEWLINE]PREPR&0.045&0.040\\[NEWLINE]BS&0.058&0.056\\[NEWLINE]SD&0.010&0.006\\[NEWLINE]CQ&0.058&0.056\\[NEWLINE]GM&0.883&0.884\\[NEWLINE]GL&0.982&0.966\\[NEWLINE]CLX&1.000&0.990\\[7pt][NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{l|cccccccc}[NEWLINE]%[NEWLINE]%^.[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{Scenario1}\\[NEWLINE]&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]Model&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.051&0.049&0.023&0.049&0.069&0.067&0.142\\[NEWLINE]M2&0.046&0.048&0.020&0.047&0.172&0.057&0.133\\[NEWLINE]M3&0.050&0.056&0.020&0.055&0.150&0.064&0.131\\[NEWLINE][NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.045&0.049&0.020&0.0496&0.076&0.063&0.107\\[NEWLINE]M2&0.048&0.051&0.021&0.051&0.167&0.058&0.142\\[NEWLINE]M3&0.051&0.053&0.028&0.056&0.105&0.056&0.115\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{Scenario2}\\[NEWLINE][NEWLINE]Model&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\\[NEWLINE]\hline\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=n_2=35$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]M1&0.045&0.057&0.024&0.057&0.078&0.08&0.120\\[NEWLINE]M2&0.032&0.044&0.015&0.046&0.164&0.147&0.097\\[NEWLINE]M3&0.037&0.041&0.012&0.043&0.129&0.190&0.1107\\[NEWLINE]\hline[NEWLINE]&\multicolumn{7}{c}{$n_1=60,\;\;n_2=40$}\\[NEWLINE]\hline[NEWLINE]M1&0.041&0.049&0.020&0.049&0.051&0.060&0.100\\[NEWLINE]M2&0.044&0.052&0.023&0.053&0.165&0.186&0.107\\[NEWLINE]M3&0.042&0.047&0.021&0.048&0.114&0.116&0.106\\[NEWLINE]\hline[NEWLINE][NEWLINE]\end{tabular}

\begin{tabular}{lcc|*{7}{c}|*{7}{c}}[NEWLINE][NEWLINE]\hline[NEWLINE]\hline[NEWLINE]r&Model&$\delta$&\multicolumn{7}{c|}{$p=200$}&\multicolumn{7}{c}{$p=200$}\\[NEWLINE]&&&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M1&\multirow{3}{*}{0.6}&0.056&0.066&0.045&0.067&0.142&0.158&0.093&0.086&0.092&0.059&0.100&0.146&0.149&0.129\\[NEWLINE]&M2&&0.138&0.105&0.093&0.106&0.065&0.049&0.222&0.219&0.147&0.122&0.146&0.0645&0.053&0.294\\[NEWLINE]&M3&&0.122&0.104&0.076&0.103&0.066&0.064&0.205&0.218&0.126&0.100&0.124&0.044&0.044&0.284\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M1&\multirow{3}{*}{0.9}&0.142&0.082&0.061&0.082&0.135&0.146&0.213&0.271&0.112&0.074&0.111&0.116&0.122&0.400\\[NEWLINE]&M2&&0.475&0.221&0.191&0.221&0.056&0.039&0.569&0.731&0.313&0.289&0.314&0.046&0.033&0.788\\[NEWLINE]&M3&&0.460&0.201&0.165&0.201&0.059&0.042&0.560&0.705&0.279&0.244&0.280&0.047&0.034&0.7660\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M1&\multirow{3}{*}{0.6}&0.069&0.100&0.073&0.099&0.132&0.133&0.117&0.114&0.123&0.093&0.122&0.122&0.127&0.165\\[NEWLINE]&M2&&0.211&0.266&0.224&0.2667&0.083&0.049&0.319&0.372&0.366&0.340&00.365&0.063&0.041&0.461\\[NEWLINE]&M3&&0.186&0.217&0.179&0.219&0.060&0.041&0.2725&0.333&0.302&0.272&0.303&0.047&0.036&0.420\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M1&\multirow{3}{*}{0.9}&0.136&0.098&0.059&0.098&0.077&0.064&0.236&[NEWLINE]0.327&0.187&0.138&0.188&0.082&0.075&0.402\\[NEWLINE]&M2&&0.704&0.642&0.599&0.641&0.049&0.027&0.786&0.887&0.825&0.792&0.824&0.033&0.018&0.927\\[NEWLINE]&M3&&0.628&0.533&0.482&0.532&0.049&0.029&0.726&0.850&0.735&0.699&0.733&0.028&0.017&0.908\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE][NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$3\%$}&M1&\multirow{3}{*}{0.6}&0.101&0.190&0.145&0.190&0.121&0.119&0.168&0.171&0.260&0.208&0.258&0.126&0.113&0.229\\[NEWLINE]&M2&&0.375&0.708&0.669&0.708&0.153&0.103&0.509&0.630&0.885&0.864&0.884&0.129&0.091&0.725\\[NEWLINE]&M3&&0.360&0.654&0.607&0.654&0.139&0.089&0.4945&0.568&0.823&0.794&0.825&0.125&0.089&0.664\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$3\%$}&M1&\multirow{3}{*}{0.6}&0.334&0.400&0.332&0.400&0.127&0.107&0.436&0.519&0.565&0.494&0.561&0.147&0.128&0.598\\[NEWLINE]&M2&&0.916&0.996&0.993&0.996&0.123&0.069&0.969&0.993&0.999&0.999&0.999&0.069&0.049&0.997\\[NEWLINE]&M3&&0.901&0.992&0.986&0.992&0.109&0.074&0.944&0.985&0.999&0.999&0.999&0.089&0.067&0.993\\[NEWLINE]\hline[NEWLINE]\end{tabular}

\begin{tabular}{lcc|*{7}{c}|*{7}{c}}[NEWLINE][NEWLINE]\hline[NEWLINE]\hline[NEWLINE]r&Model&$\delta$&\multicolumn{7}{c|}{$p=200$}&\multicolumn{7}{c}{$p=200$}\\[NEWLINE]&&&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX&\DNA{PREPR}&BS&SD&CQ&GM&GL&CLX\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M1&\multirow{3}{*}{0.6}&0.050&0.077&0.060&0.077&0.157&0.178&0.088&0.083&0.079&0.059&0.078&0.135&0.153&0.127\\[NEWLINE]&M2&&0.138&0.0987&0.085&0.104&0.058&0.052&0.225&0.264&0.131&0.127&0.138&0.071&0.0507&0.335\\[NEWLINE]&M3&&0.124&0.095&0.082&0.100&0.058&0.064&0.199&0.250&0.135&0.108&0.138&0.056&0.055&0.326\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$0.5\%$}&M1&\multirow{3}{*}{0.9}&0.161&0.091&0.063&0.091&0.122&0.136&0.231&0.276&0.104&0.075&0.105&0.115&0.118&0.346\\[NEWLINE]&M2&&0.498&0.240&0.207&0.251&0.065&0.0373&0.595&0.700&0.290&0.263&0.293&0.0507&0.0287&0.782\\[NEWLINE]&M3&&0.473&0.193&0.177&0.200&0.056&0.033&0.580&0.692&0.267&0.234&0.269&0.044&0.027&0.769\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M1&\multirow{3}{*}{0.6}&0.213&0.159&0.111&0.160&0.104&0.103&0.290&0.107&0.123&0.086&0.125&0.117&0.126&0.160\\[NEWLINE]&M2&&0.192&0.251&0.222&0.263&0.0767&0.037&0.300&0.432&0.375&0.369&0.383&0.085&0.037&0.534\\[NEWLINE]&M3&&0.186&0.217&0.179&0.219&0.060&0.041&0.273&0.382&0.308&0.267&0.312&0.057&0.026&0.465\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$1\%$}&M1&\multirow{3}{*}{0.9}&0.136&0.098&0.059&0.098&0.077&0.064&0.236&0.361&0.192&0.151&0.195&0.089&0.081&0.440\\[NEWLINE]&M2&&0.674&0.611&0.591&0.619&0.043&0.0127&0.787&0.890&0.816&0.800&0.817&0.024&0.0087&0.934\\[NEWLINE]&M3&&0.624&0.537&0.513&0.545&0.044&0.014&0.753&0.869&0.757&0.728&0.756&0.025&0.011&0.912\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE][NEWLINE]&&&\multicolumn{7}{c|}{$n_{1}=n_{2}=35$}&\multicolumn{7}{c}{$n_{1}=60\;\;n_{2}=40$}\\[NEWLINE]\hline[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$3\%$}&M1&\multirow{3}{*}{0.6}&0.107&0.182&0.145&0.184&0.139&0.134&0.171&0.211&0.242&0.187&0.241&0.123&0.110&0.274\\[NEWLINE]&M2&&0.384&0.710&0.696&0.715&0.146&0.056&0.565&0.690&0.893&0.879&0.892&0.147&0.067&0.787\\[NEWLINE]&M3&&0.371&0.635&0.607&0.639&0.124&0.054&0.531&0.666&0.829&0.811&0.829&0.139&0.078&0.762\\[NEWLINE]\hline[NEWLINE]\multirow{3}{*}{$3\%$}&M1&\multirow{3}{*}{0.9}&0.327&0.388&0.320&0.390&0.122&0.090&0.443&0.545&0.557&0.488&0.557&0.146&0.123&0.634\\[NEWLINE]&M2&&0.228&0.403&0.313&0.404&0.169&0.053&0.398&0.299&0.711&0.553&0.711&0.290&0.095&0.555\\[NEWLINE]&M3&&0.922&0.993&0.995&0.994&0.115&0.039&0.968&0.993&1.000&1.000&1.000&0.061&0.033&0.998\\[NEWLINE]\hline[NEWLINE]\end{tabular}