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2210.07987v3_train__8006cbca-9955-4dd0-9b71-5b0e6721c0a5

arxiv_table_to_tex

\begin{table}[htbp]\begin{table}[htbp]\caption{Time series modeling: root mean of squared errors (RMSE) and log-likelihood (LL) values at MAP estimates by GP, Besov and Q-EP prior models.}\centering\begin{tabular}{l|lll|lll}\toprule& \multicolumn{3}{c|}{ root mean squared errors (RMSE)} & \multicolumn{3}{|c}{log-likelihood (LL)} \\\cmidrule{1-4} \cmidrule{5-7}Data Sets & GP & Besov & Q-EP & GP & Besov & Q-EP\\\midrulesimulation (jumps) & 1.2702 & 2.1603 & {\bf 1.1083} & -31.4582 & -89.8549 & -74.0590 \\simulation (turnings) & 1.4270 & 2.4556 & {\bf 0.9987} & -39.8234 & -56.7874 & -87.3124 \\\midruleTesla stocks & 180.3769 & 136.8769 & {\bf 51.2236} & -488.6458 & -281.3796 & -39.4070 \\Google stocks & 44.4236 & 39.4809 & {\bf 36.8686} & -386.1546 & -305.0058 & -265.9790 \\\bottomrule\end{tabular}\label{tab:ts_rmse}\end{table}

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Time series modeling: root mean of squared errors (RMSE) and log-likelihood (LL) values at MAP estimates by GP, Besov and Q-EP prior models.

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2210.07987v3_train__e231f49d-0a40-471f-83ba-8e6266d8b35b

arxiv_table_to_tex

\begin{table*}[htbp]\begin{table*}[htbp]\caption{MAP estimates for CT of human head and torso by GP, Besov and Q-EP prior models:relative error, $\textrm{RLE}:=\Vert \hat u-u^\dagger\Vert/\Vert u^\dagger\Vert$ of MAP ($\hat u =u^*$), log-likelihood (LL), PSNR, SSIM and HarrPSI.}\centering\begin{tabular}{l|lll|lll}\toprule\multicolumn{4}{c|}{Head} & \multicolumn{3}{|c}{Torso} \\\cmidrule{1-4} \cmidrule{5-7}& GP & Besov & Q-EP & GP & Besov & Q-EP \\\midruleRLE & 0.2999 & 0.2241 & {\bf 0.2224} & 0.2611 & 0.2177 & {\bf 0.2153} \\LL & -4.05e+5 & -1.12e+4 & -1.17e+4 & -3.30e+5 & -3.86e+3 & -4.37e+3 \\PSNR & 24.2321 & 26.7633 & {\bf 26.8281} & 23.6450 & 25.2231 & {\bf 25.3190} \\SSIM & 0.7010 & 0.7914 & {\bf 0.8096} & 0.5852 & {\bf 0.6983} & 0.6982 \\HaarPSI & 0.0525 & {\bf 0.0593} & 0.0587 & 0.0666 & {\bf 0.0732} & 0.07190 \\\bottomrule\end{tabular}\label{tab:CT_human}\end{table*}

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MAP estimates for CT of human head and torso by GP, Besov and Q-EP prior models:relative error, $\textrm{RLE

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2312.04066v2_train__aa24127c-f14d-4d8f-b39a-e4857adfc45f

arxiv_table_to_tex

\begin{table*}\begin{table*}\caption{Accuracy results on DomainNet dataset. ZS indicates zero-shot results of CLIP.}\label{tab:domainNet}\centering\resizebox{\textwidth}{!}{\begin{tabular}{c|ccccccc||c|ccccccc||c|ccccccc}\topruleMCD \cite{MCD} & clp & inf & pnt & qdr & rel & skt & Avg & CGDM \cite{CGDM} & clp & inf & pnt & qdr &rel & skt & Avg & MDD \cite{MDD} & clp & inf & pnt & qdr & rel & skt & Avg \\\midruleclp & - & 15.4 & 25.5 & 3.3 & 44.6 & 31.2 & 24.0 & clp & - & 16.9 & 35.3 & 10.8 & 53.5 & 36.9 & 30.7 & clp & - & 20.5 & 40.7 & 6.2 & 52.5 & 42.1 & 32.4 \\inf & 24.1 & - & 24.0 & 1.6 & 35.2 & 19.7 & 20.9 & inf & 27.8 & - & 28.2 & 4.4 & 48.2 & 22.5 & 26.2 & inf & 33.0 & - & 33.8 & 2.6 & 46.2 & 24.5 & 28.0 \\pnt & 31.1 & 14.8 & - & 1.7 & 48.1 & 22.8 & 23.7 & pnt & 37.7 & 14.5 & - & 4.6 & 59.4 & 33.5 & 30.0 & pnt & 43.7 & 20.4 & - & 2.8 & 51.2 & 41.7 & 32.0 \\qdr & 8.5 & 2.1 & 4.6 & - & 7.9 & 7.1 & 6.0 & qdr & 14.9 & 1.5 & 6.2 & - & 10.9 & 10.2 & 8.7 & qdr & 18.4 & 3 & 8.1 & - & 12.9 & 11.8 & 10.8 \\rel & 39.4 & 17.8 & 41.2 & 1.5 & - & 25.2 & 25.0 & rel & 49.4 & 20.8 & 47.2 & 4.8 & - & 38.2 & 32.0 & rel & 52.8 & 21.6 & 47.8 & 4.2 & - & 41.2 & 33.5 \\skt & 37.3 & 12.6 & 27.2 & 4.1 & 34.5 & - & 23.1 & skt & 50.1 & 16.5 & 43.7 & 11.1 & 55.6 & - & 35.4 & skt & 54.3 & 17.5 & 43.1 & 5.7 & 54.2 & - & 35 \\Avg & 28.1 & 12.5 & 24.5 & 2.4 & 34.1 & 21.2 & \cellcolor[gray]{0.8} 20.5 & Avg & 36 & 14 & 32.1 & 7.1 & 45.5 & 28.3 & \cellcolor[gray]{0.8} 27.2 & Avg & 40.4 & 16.6 & 34.7 & 4.3 & 43.4 & 32.3 & \cellcolor[gray]{0.8} 28.6 \\\midrule\midruleSCDA \cite{SCDA} & clp & inf & pnt & qdr & rel & skt & Avg & CDTrans \cite{CDTrans} & clp & inf & pnt & qdr & rel & skt & Avg & SSRT \cite{SSRT} & clp & inf & pnt & qdr & rel & skt & Avg \\\midruleclp & - & 18.6 & 39.3 & 5.1 & 55 & 44.1 & 32.4 & clp & - & 29.4 & 57.2 & 26 & 72.6 & 58.1 & 48.7 & clp & - & 33.8 & 60.2 & 19.4 & 75.8 & 59.8 & 49.8 \\inf & 29.6 & - & 34 & 1.4 & 46.3 & 25.4 & 27.3 & inf & 57 & - & 54.4 & 12.8 & 69.5 & 48.4 & 48.4 & inf & 55.5 & - & 54 & 9 & 68.2 & 44.7 & 46.3 \\pnt & 44.1 & 19 & - & 2.6 & 56.2 & 42 & 32.8 & pnt & 62.9 & 27.4 & - & 15.8 & 72.1 & 53.9 & 46.4 & pnt & 61.7 & 28.5 & - & 8.4 & 71.4 & 55.2 & 45 \\qdr & 30.0 & 4.9 & 15 & - & 25.4 & 19.8 & 19 & qdr & 44.6 & 8.9 & 29 & - & 42.6 & 28.5 & 30.7 & qdr & 42.5 & 8.8 & 24.2 & - & 37.6 & 33.6 & 29.3 \\rel & 54 & 22.5 & 51.9 & 2.3 & - & 42.5 & 34.6 & rel & 66.2 & 31 & 61.5 & 16.2 & - & 52.9 & 45.6 & rel & 69.9 & 37.1 & 66 & 10.1 & - & 58.9 & 48.4 \\skt & 55.6 & 18.5 & 44.7 & 6.4 & 53.2 & - & 35.7 & skt & 69 & 29.6 & 59 & 27.2 & 72.5 & - & 51.5 & skt & 70.6 & 32.8 & 62.2 & 21.7 & 73.2 & - & 52.1 \\Avg & 42.6 & 16.7 & 37 & 3.6 & 47.2 & 34.8 & \cellcolor[gray]{0.8} 30.3 & Avg & 59.9 & 25.3 & 52.2 & 19.6 & 65.9 & 48.4 & \cellcolor[gray]{0.8} 45.2 & Avg & 60 & 28.2 & 53.3 & 13.7 & 65.3 & 50.4 & \cellcolor[gray]{0.8} 45.2 \\\midrule\midrulePMTrans \cite{PMTrans} & clp & inf & pnt & qdr & rel & skt & Avg & ZS \cite{CLIP} & clp & inf & pnt & qdr & rel & skt & Avg & SKD (Ours) & clp & inf & pnt & qdr & rel & skt & Avg \\\midruleclp & - & 34.2 & 62.7 & 32.5 & 79.3 & 63.7 & 54.5 & clp & - & 48.3 & 68.5 & 14.0 & 84.6 & 65.8 & 56.3 & clp & - & 52.7 & 72.0 & 36.3 & 85.1 & 71.5 & 63.5 \\inf & 67.4 & - & 61.1 & 22.2 & 78 & 57.6 & 57.3 & inf & 73.1 & - & 68.5 & 14.0 & 84.6 & 65.8 & 61.2 & inf & 78.5 & - & 72.2 & 30.4 & 85.0 & 69.5 & 67.1 \\pnt & 69.7 & 33.5 & - & 23.9 & 79.8 & 61.2 & 53.6 & pnt & 73.1 & 48.3 & - & 14.0 & 84.6 & 65.8 & 57.2 & pnt & 78.7 & 49.8 & - & 29.6 & 84.5 & 69.7 & 62.4 \\qdr & 54.6 & 17.4 & 38.9 & - & 49.5 & 41 & 40.3 & qdr & 73.1 & 48.3 & 68.5 & - & 84.6 & 65.8 & 68.1 & qdr & 70.7 & 22.9 & 50.9 & - & 82.4 & 62.3 & 57.8 \\rel & 74.1 & 35.3 & 70 & 25.4 & - & 61.1 & 53.2 & rel & 73.1 & 48.3 & 68.5 & 14.0 & - & 65.8 & 54.0 & rel & 80.3 & 53.5 & 74.2 & 30.2 & - & 71.1 & 61.9 \\skt & 73.8 & 33.0 & 62.6 & 30.9 & 77.5 & - & 55.6 & skt & 73.1 & 48.3 & 68.5 & 14.0 & 84.6 & - & 57.7 & skt & 81.0 & 52.0 & 73.0 & 36.6 & 84.6 & - & 65.4 \\Avg & 67.9 & 30.7 & 59.1 & 27 & 72.8 & 56.9 & \cellcolor[gray]{0.8} 52.4 & Avg & 73.1 & 48.3 & 68.5 & 14.0 & 84.6 & 65.8 & \cellcolor[gray]{0.8} 59.1 & Avg & 77.9 & 46.2 & 68.5 & 32.6 & 84.3 & 68.8 & \cellcolor[gray]{0.8} \textbf{63.0} \\\bottomrule\end{tabular}}\end{table*}

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Accuracy results on DomainNet dataset. ZS indicates zero-shot results of CLIP.

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2312.04066v2_train__6b67ec37-234a-4972-a8c5-6bcec9f037b7

arxiv_table_to_tex

\begin{table*}\begin{table*}\caption{Contributions of different parts of our algorithm. Aug means using strongly augmented images alongside the weakly augmented ones, while GSDE uses only the prediction scores of the previous run, GSDE+ adds zero-shot prediction scores according to eq. \ref{eq:GSDE}.}\label{tab:losses}\centering\begin{tabular}{lllll|ll|ll}\multicolumn{5}{c|}{} & \multicolumn{2}{c|}{ResNet} & \multicolumn{2}{c}{ViT} \\$L_{AD}$ & $L_{KD}$ & Aug & GSDE & GSDE+ & VisDA & OH & VisDA & OH \\\midrule$\checkmark$ & & & & & 72.73 & 65.99 & 74.25 & 81.74 \\& $\checkmark$ & & & & 87.65 & 69.06 & 90.28 & 83.27 \\$\checkmark$ & $\checkmark$ & & & & 88.21 & 73.43 & 90.44 & 87.66 \\$\checkmark$ & $\checkmark$ & $\checkmark$ & & & 88.62 & 75.48 & 90.37 & 87.97 \\$\checkmark$ & $\checkmark$ & $\checkmark$ &$\checkmark$ & & 88.90 & 78.72 & \textbf{91.22} & 89.08 \\$\checkmark$ & $\checkmark$ & $\checkmark$ & & $\checkmark$ & \textbf{89.09} & \textbf{78.78} & 91.20 & \textbf{89.24} \\\bottomrule\end{tabular}\end{table*}

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Contributions of different parts of our algorithm. Aug means using strongly augmented images alongside the weakly augmented ones, while GSDE uses only the prediction scores of the previous run, GSDE+ adds zero-shot prediction scores according to eq. \ref{eq:GSDE

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2210.16898v1_train__8c72db1d-81f3-4e32-b471-6557d11e7acd

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\caption{Performance comparison of the proposed method against the SOTA approaches on skin lesion segmentation task.} \label{tab:quantitative}\resizebox{\textwidth}{!}{\begin{tabular}{l||cccc||cccc||cccc}\hline\multirow{2}{*}{\textbf{Methods}} & \multicolumn{4}{c||}{\textit{ISIC 2017}} & \multicolumn{4}{c||}{\textit{ISIC 2018}} & \multicolumn{4}{c}{\textit{PH$^2$}} \\ \cline{2-5} \cline{6-9} \cline{10-13}& \textbf{DSC} & \textbf{SE} & \textbf{SP}&\textbf{ACC} & \textbf{DSC} & \textbf{SE} & \textbf{SP}&\textbf{ACC} & \textbf{DSC} & \textbf{SE} & \textbf{SP}&\textbf{ACC} \\ \hlineU-Net \cite{ronneberger2015u} & 0.8159 & 0.8172 & 0.9680 & 0.9164 & 0.8545 & 0.8800 & 0.9697 & 0.9404 & 0.8936 & 0.9125 & 0.9588 & 0.9233 \\Att U-Net \cite{oktay2018attention} & 0.8082 & 0.7998 & 0.9776 & 0.9145& 0.8566 & 0.8674 & \textbf{0.9863} & 0.9376& 0.9003 & 0.9205 & 0.9640 & 0.9276 \\TransUNet \cite{chen2021transunet} &0.8123&0.8263&0.9577&0.9207 & 0.8499 & 0.8578 & 0.9653 & 0.9452 & 0.8840&0.9063&0.9427&0.9200 \\MCGU-Net \cite{asadi2020multi} & 0.8927 & 0.8502 & 0.9855 & 0.9570 & 0.895 & 0.848 & 0.986 & 0.955 & 0.9263 & 0.8322 & 0.9714 & 0.9537 \\MedT \cite{valanarasu2021medical} & 0.8037 & 0.8064 & 0.9546 & 0.9090 & 0.8389 & 0.8252 & 0.9637 & 0.9358& 0.9122 & 0.8472 & 0.9657 & 0.9416\\FAT-Net \cite{wu2022fat} &0.8500 & 0.8392 & 0.9725 & 0.9326& 0.8903 & \textbf{0.9100} & 0.9699 & 0.9578& 0.9440 & \textbf{0.9441} & 0.9741 & 0.9703 \\TMU-Net \cite{reza2022contextual} & 0.9164 & 0.9128 & 0.9789 & 0.9660 & 0.9059 & 0.9038 & 0.9746 & 0.9603 & 0.9414 & 0.9395 & 0.9756 & 0.9647 \\Swin\,U-Net \cite{cao2021swin}& 0.9183 & 0.9142 & 0.9798 & \textbf{0.9701} & 0.8946 & 0.9056 & 0.9798 & 0.9645 & 0.9449 & 0.9410 & 0.9564 & 0.9678 \\TransNorm \cite{azad2022transnorm} & 0.8933 & 0.8532 & \textbf{0.9859} & 0.9582 & 0.8951 & 0.8750 & 0.9790 & 0.9580 & 0.9437 & 0.9438 & \textbf{0.9810} & \textbf{0.9723} \\\hline\textbf{Proposed Method} & \textbf{0.9240} & \textbf{0.9246} & 0.9794 & 0.9656 & \textbf{0.9105} & 0.9089 & 0.9807 & \textbf{0.9668} & \textbf{0.9504} & 0.9439 & 0.9576 & 0.9685 \\ \hline\end{tabular}}\end{table*}

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Performance comparison of the proposed method against the SOTA approaches on skin lesion segmentation task.

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2002.11612v2_train__5fa229e4-dacc-4455-9f91-5a2c2c383919

arxiv_table_to_tex

\begin{table}\begin{table}\caption{Biological significance for predicted pathways with the best methods, GCC-10 and PathLinker-RWR.}\begin{tabular}{p{7mm}|c|c|c|c|c|c|c|c|c|c|}\cline{2-11}& \multicolumn{10}{ |c| }{k} \\ \cline{1-11}\multicolumn{1}{ |c| }{Method}& 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 &100 \\ \cline{1-11}\multicolumn{1}{ |c| }{GCC-10} & 1.00 & 1.00 & 0.94 & 0.83 & 0.84 & 0.85 & 0.88 & 0.88 & 0.84 & 0.81 \\\cline{1-11}\multicolumn{1}{ |p{1.6cm}| }{PathLinker-RWR} & 0.90& 0.88& 0.81& 0.78& 0.82& 0.73& 0.74& 0.76& 0.77 & 0.71\\\hline\end{tabular}\label{enrich}\end{table}

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Biological significance for predicted pathways with the best methods, GCC-10 and PathLinker-RWR.

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2208.02402v2_train__a33a9102-70b9-4655-974f-aec9ad4f4e89

arxiv_table_to_tex

\begin{table}[htbp]\begin{table}[htbp]% hline/vline hacks to add spacing between blocks% these commands shouldn't be visible beyond this float\newcommand{\acell}{ \cellcolor{DimGray} }\newcommand{\bcell}{ \cellcolor{Gainsboro} }\newcommand{\eol}{ \arrayrulecolor{white} \specialrule{10pt}{0pt}{0pt} }\newcommand{\eoc}{\color{white}\vline width 1pt}\resizebox{\linewidth}{!}{%\renewcommand*{\arraystretch}{0.0}\begin{tabular}{lc!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc c!\eoc}\toprule& & & \footnotesize 25\% & & & \footnotesize 50\% & & & \footnotesize 75\% & $\downarrow$ & & \footnotesize 100\% \\& Moctezuma & was & the & son & of & the & emperor & Huitzilihuitl & and & \texttt{\_\_\_} & \texttt{\_\_\_} & \texttt{\_\_\_} \\\cmidrule{2-13}Right crop 0\% & & & & & & & & & \\ \eolRight crop 25\% & \acell & \acell & \acell \\ \eolRight crop 50\% & \acell & \acell & \acell & \acell & \acell & \acell \\ \eolRight crop 75\% & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell \\ \eolRight crop 100\% & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \bcell & \bcell & \bcell \\ \eolLeft crop 0\% & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \bcell & \bcell & \bcell\\ \eolLeft crop 25\% & & & \acell & \acell & \acell & \acell & \acell & \acell & \acell & \bcell & \bcell & \bcell \\ \eolLeft crop 50\% & & & & & & \acell & \acell & \acell & \acell & \bcell & \bcell & \bcell \\ \eolLeft crop 75\% & & & & & & & & & \acell & \bcell & \bcell & \bcell \\ \eolLeft crop 100\% & & & & & & & & & & & & \bcell \\\arrayrulecolor{black} \bottomrule\end{tabular}%}\caption{Consecutive dark grey rectangles indicate substring of which sentence representation was computed and fused. The representation is not computed beyond the to-be-predicted token ( $\downarrow$ ). Light grey words are cropped because they are not in the left context. Right crop 0\% and left crop 100\% correspond to no fusion while right crop 100\% and left crop 0\% correspond to full fusion without any cropping.}\label{tab:sub_feeders}\end{table}

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Consecutive dark grey rectangles indicate substring of which sentence representation was computed and fused. The representation is not computed beyond the to-be-predicted token ( $\downarrow$ ). Light grey words are cropped because they are not in the left context. Right crop 0\% and left crop 100\% correspond to no fusion while right crop 100\% and left crop 0\% correspond to full fusion without any cropping.

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2104.13122v6_train__f2e9cc37-e727-47bd-9d7b-77b4db92301e

arxiv_table_to_tex

\begin{table}[h]\begin{table}[h]\begin{tabular}{|c|c|}\hlineFormulae to be defined & Intuitive meaning \\ \hline$\phitype{k}$ & $\anode_0$ is of type $k$ \\ \hline$\phifirst{k}$ & $\semnumber{}{\anode_0} = 0$ \\ \hline$\philast{k}$ & $\semnumber{}{\anode_0} = \tow(k+1,n)-1$ \\ \hline$\phiunique{k}$ & $\forall \anode, \anode' \ ((\anode_0 E \anode) \ \& \ (\anode_0 E \anode') \ \& \\anode \neq \anode') \ \rightarrow $ \\& $\semnumber{}{\anode} \neq \semnumber{}{\anode'}$ \\ \hline$\phipopulate{k}$ & $\forall \anode \ ((\anode_0 E \anode) \ \& \ \semnumber{}{\anode} < \tow(k,n)-1)\ \rightarrow$\\& $\exists \ \anode' \ (\anode_0 E \anode') \ \wedge \ \semnumber{}{\anode'} = \semnumber{}{\anode} + 1$ \\ \hline$\eqk{k}{\bar{\anominal}}{\bar{\anominalbis}}$ &$\semnumber{}{\anode_d} = \semnumber{}{\anode_d'}$\\ \hline$\succk{k}{\bar{\anominal}}{\bar{\anominalbis}}$ &$\semnumber{}{\anode_d'} = 1 + \semnumber{}{\anode_d}$\\ \hline$\gk{k}{\bar{\anominal}}{\bar{\anominalbis}}$ &$\semnumber{}{\anode_d} < \semnumber{}{\anode_d'}$\\ \hline\end{tabular}\caption{Family of auxiliary formulae.}\label{table-auxiliary-formulae}\end{table}

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Family of auxiliary formulae.

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2306.17181v4_train__eb938154-e6d6-4df0-9bf3-87ebdf510f3e

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\small\begin{tabular}{|l|l|l|}\hline\textbf{TESGAN (17-epoch, DailyDialog)} & \textbf{P-TESGAN (10-epoch, DailyDialog)} & \textbf{Random Noise} \\\hlineI'm so glad you finally got on the train. & Hello, Mr. Smith. I'm Mary. & Anything I have called three weeks\\I just lost my job. & I just want to tell you the truth. & Is Is Is Is Is Is Is\\Yeah. You mean the network connection? & It's the end of the world. & Left and go to go to go to go\\What happened? & What do you want to do in this company? & Mr Moon, Mr Moon\ldots Mr Moon\ldots\\So you have to wait for a while. & He just broke up with Ann. & are you have finished 6 items?\\\hline\hline\multicolumn{3}{|l|}{\textbf{TESGAN (18-epoch, IMDb)}} \\\hline\multicolumn{3}{|l|}{This is probably one of the best of the best of the series.} \\\multicolumn{3}{|l|}{I was bored to think about how stupid this movie was.} \\\multicolumn{3}{|l|}{"The Deadly Loved One" is the story of a rebellious college basketball} \\\multicolumn{3}{|l|}{I have to say, this is the worst film I have ever seen.} \\\multicolumn{3}{|l|}{I was very excited to see it, anticipating Christmas eve.} \\\multicolumn{3}{|l|}{This movie was one of the best of the year for me.} \\\hline\end{tabular}\caption{Example of unconditionally synthesized sentences. P-TESGAN denotes the perturbed TESGAN.}\label{table3}\end{table*}

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Example of unconditionally synthesized sentences. P-TESGAN denotes the perturbed TESGAN.

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2306.17181v4_train__c16fc5d5-1fea-4865-9d1c-07af62221637

arxiv_table_to_tex

\begin{table*}[htb!]\begin{table*}[htb!]\centering\begin{tabular}{cc|ccccccc}\hline\multicolumn{2}{c|}{Activation} & FBD $\downarrow$ & MSJ2 $\uparrow$ & MSJ3 $\uparrow$ & MSJ4 $\uparrow$ & MSJ5 $\uparrow$ & DSR $\uparrow$ & LM$\ast$ $\downarrow$ \\\hline\multirow{3}{*}{TESGAN} & None & 47.261 & 0.108 & 0.060 & 0.032 & 0.016 & \textbf{0.982} & - \\& Tanh & 9.780 & 0.110 & 0.057 & 0.030 & 0.015 & 0.871 & 5.402 \\& Sigmoid & \textbf{2.899} & \textbf{0.150} & \textbf{0.079} & \textbf{0.042} & \textbf{0.021} & 0.967 & \textbf{4.236} \\\hline\multirow{3}{*}{P-TESGAN} & None & 54.002 & 0.111 & 0.059 & 0.030 & \textbf{0.015} & \textbf{0.958} & - \\& Tanh & 20.158 & 0.118 & 0.061 & 0.031 & \textbf{0.015} & 0.937 & - \\& Sigmoid & \textbf{2.274} & \textbf{0.131} & \textbf{0.066} & \textbf{0.032} & 0.014 & 0.841 & \textbf{3.642} \\\hline\end{tabular}\caption{Performance according to the activation functions of the generator.$\ast$ denotes a metric not considered when selecting the best model.- denotes that the confidence of the result is low because the quality of the synthesized sentence is poor.}\label{table4}\end{table*}

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Performance according to the activation functions of the generator.$\ast$ denotes a metric not considered when selecting the best model.- denotes that the confidence of the result is low because the quality of the synthesized sentence is poor.

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2306.17181v4_train__b421e229-1208-48b2-8cd3-efdd763f26b7

arxiv_table_to_tex

\begin{table*}[htb!]\begin{table*}[htb!]\centering\begin{tabular}{|l|l|}\hline\textbf{TESGAN with Tanh} & \textbf{P-TESGAN with Tanh}\\\hlineYou are a little & You ’ re a book?\\I ’ m sorry to see you off. You ’ Ve come & You are late.\\I ’ m sorry. & I ’ m doing ’ t “ all day ’ s\\You ’ d like a tour to see the dentist. & I don't know what time it is?\\You are late. & I ’ m sorry to hear this!\\\hline\hline\textbf{TESGAN without activation} & \textbf{P-TESGAN without activation}\\\hlineI ’ d like to say it! I ’ d like to & I ’ s a big, that ’ s right.\\Yes, do you want to buy? & I like the back ones. They look like a shop.\\I ’ s right over there? & I ’, this ’, this ’! be real, \\What's the matter? & I have a problem with my English textbooks.\\I got a bite the food? & I ’ s faster, George. I ’ d like to go \\\hline\end{tabular}\caption{Synthesized sentences by tanh and non-use cases in Table~\ref{table4}. P-TESGAN denotes the perturbed TESGAN.}\label{table5}\end{table*}

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Synthesized sentences by tanh and non-use cases in Table~\ref{table4

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2003.13320v1_train__e4a883a7-32a8-45f9-a57f-86df19a390cd

arxiv_table_to_tex

\begin{table}[tp]\begin{table}[tp]\centering\caption{Split polar spectrum example for $N=16$} \label{split_polar_spectrum}\begin{tabular}{|c|c|c|}\hline index $i$ & weight $\mathbf{d}$ & $A_{16}^{(i)}(\mathbf{d})$ \\\hline 1 & \tabincell{c}{(1, 0), (1, 8), (7, 0), (7, 8)\\(0, 1), (8, 1), (0, 7), (8, 7)}& 8\\\hline 1 & \tabincell{c}{(3, 0), (3, 8), (5, 0), (5, 8)\\(0, 3), (8, 3), (0, 5), (8, 5)}& 56 \\\hline 1 & \tabincell{c}{(2, 1), (2, 7), (6, 1), (6, 7)\\(1, 2), (7, 2), (1, 6), (7, 6)}& 224\\\hline 1 & \tabincell{c}{(4, 1), (4, 7), (1, 4), (7, 4)}& 560 \\\hline 1 & \tabincell{c}{(3, 2), (3, 6), (5, 2), (5, 6)\\(2, 3), (6, 3), (2, 5), (6, 5)} & 1568 \\\hline 1 & \tabincell{c}{(4, 3), (4, 5), (3, 4), (5, 4)} & 3920 \\\hline 2 & \tabincell{c}{(2, 0), (2, 8), (6, 0), (6, 8)\\(0, 2), (8, 2), (0, 6), (8, 6)} & 16 \\\hline 2 & \tabincell{c}{(4, 0), (4, 8), (0, 4), (8, 4)} &32 \\\hline 2 & \tabincell{c}{(1, 1), (1, 7), (7, 1), (7, 7)\\} & 32 \\\hline 2 & \tabincell{c}{(3, 1), (3, 7), (5, 1), (5, 7)\\(1, 3), (7, 3), (1, 5), (7, 5)} & 224 \\\hline 2 & \tabincell{c}{(2, 2), (2, 6), (6, 2), (6, 6)} & 384 \\\hline 2 & \tabincell{c}{(4, 2), (4, 6), (2, 4), (6, 4)} & 992 \\\hline 2 & \tabincell{c}{(3, 3), (3, 5), (5, 3), (5, 5)} & 1568 \\\hline 2 & \tabincell{c}{(4, 4)} & 2432 \\\hline 3 & \tabincell{c}{(2, 0), (2, 8), (6, 0), (6, 8)\\(0, 2), (8, 2), (0, 6), (8, 6)} &8 \\\hline 3 & \tabincell{c}{(4, 0), (4, 8), (0, 4), (8, 4)} & 16 \\\hline 3 & \tabincell{c}{(1, 1), (1, 7), (7, 1), (7, 7)} & 16 \\\hline 3 & \tabincell{c}{(3, 1), (3, 7), (5, 1), (5, 7)\\(1, 3), (7, 3), (1, 5), (7, 5)} & 112 \\\hline 3 & \tabincell{c}{(2, 2), (2, 6), (6, 2), (6, 6)} & 192 \\\hline 3 & \tabincell{c}{(4, 2), (4, 6), (2, 4), (6, 4)} & 496 \\\hline 3 & \tabincell{c}{(3, 3), (3, 5), (5, 3), (5, 5)} & 784 \\\hline 3 & \tabincell{c}{(4, 4)} & 1216 \\\hline ... & ... & ... \\\hline 9 & (1, 1), (7, 7) & 8 \\\hline 9 & (3, 3), (5, 5) & 56 \\\hline 10 & (2, 2), (6, 6) & 16 \\\hline 10 & (4, 4) & 32 \\\hline 11 & (2, 2), (6, 6) & 8 \\\hline 11 & (4, 4) & 16 \\\hline 12 & (4, 4) & 16 \\\hline 13 & (2, 2), (6, 6) & 4 \\\hline 14 & (4, 4) & 4 \\\hline 15 & (4, 4) & 2 \\\hline 16 & (8, 8) & 1 \\\hline\end{tabular}\end{table}

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Split polar spectrum example for $N=16$

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2309.07330v1_train__b2813891-e7c9-424a-ad17-e48bf310aeb8

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\small\caption{Comparison of one vs.\ two-model segmentation approaches, in terms of IoU.}\begin{tabular}{|c|c|c|c|c|c|c|}\hline{\bf Approach} & Gallbladder & Liver & Cystic Duct & Cystic artery & Cystic plate & Instrument\\\hline{\bf Single model} & 0.8964 & \textbf{0.9244} & 0.4978 & 0.0& 0.4229 & \textbf{0.8989} \\\hline{\bf Two-stream} & \textbf{0.9139} & 0.8913 & \textbf{0.6833} & \textbf{0.4484} & \textbf{0.5713} & 0.8433\\\hline\end{tabular}\label{tab:twostream}\end{table*}

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Comparison of one vs.\ two-model segmentation approaches, in terms of IoU.

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2309.07330v1_train__0e39b170-c789-4c1a-86c3-a9e5c1964826

arxiv_table_to_tex

\begin{table}\begin{table}\centering\caption{Comparison of Sobel loss based segmentation and the baseline method.}\begin{tabular}{|c|c|c|c|}\hlineModel/Metric & mIoU & Acc. & Dice\\\hlineBaseline & 0.7270 & \textbf{0.9372} & 0.8247 \\\hlineBaseline+Sobel loss & \textbf{0.7454} & 0.9323 & \textbf{0.8427} \\\hline\end{tabular}\label{tab:segres}\end{table}

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Comparison of Sobel loss based segmentation and the baseline method.

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2309.07330v1_train__16486327-92f8-4d71-aa85-d6c004bf2455

arxiv_table_to_tex

\begin{table}\begin{table}\small\centering\caption{Results of CVS assessment compared to DeepCVS.}\scalebox{0.85}{\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\hline& \multicolumn{2}{|c|}{C1}& \multicolumn{2}{|c|}{C2} & \multicolumn{2}{|c|}{C3} & \multicolumn{2}{|c|}{CVS} \\\hline\multirow{4}{*}{DeepCVS}& Acc. & 0.72 & Acc. & 0.39 & Acc. & 0.54 & Acc. & 0.92 \\& Bacc. & 0.48 & Bacc. & 0.49 & Bacc. & 0.53 & Bacc. & 0.49 \\& PPV & 0.14 & PPV & 0.18 & PPV & 0.53 & PPV & NaN\footnotemark \\& NPV & 0.75 & NPV & 0.80 & NPV & 0.54 & NPV & 0.93\\% \hline% \multirow{3}{*}{CNN}% & Acc. & 0.746 & Acc. & 0.245 & Acc. & 0.482 & Acc. & \textbf{0.930} \\% & PPV & 0.204 & PPV & 0.189 & PPV & 0.468 & PPV & 0.070\\% & NPV & 0.761 & NPV & 0.854 & NPV & 0.494 & NPV & 0.938\\\hline\multirow{4}{*}{Ours}& Acc. & \textbf{0.76} & Acc.& \textbf{0.79} & Acc. & \textbf{0.69} & Acc. & 0.92 \\& Bacc. & \textbf{0.57} & Bacc. & \textbf{0.65} & Bacc. & \textbf{0.69} & Bacc. & \textbf{0.54}\\& PPV & \textbf{0.49} & PPV. & \textbf{0.43} & PPV & \textbf{0.72} & PPV & \textbf{0.23}\\& NPV & \textbf{0.79} & NPV & \textbf{0.86} & NPV & \textbf{0.67} & NPV & \textbf{0.94}\\\hline\end{tabular}}\label{cvs1}\end{table}

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Results of CVS assessment compared to DeepCVS.

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2402.01649v1_train__8f20e0f8-abc6-4ad5-8481-f147de87f6f3

arxiv_table_to_tex

\begin{table}\begin{table}\small\addtolength{\tabcolsep}{-5pt}\caption{Article Data source}\label{database}\footnotesize\begin{tabular}{l|l|l|ll}\hline\textbf{ID} & \textbf{Database} & \textbf{Link} & \textbf{Number of Articles}& \\ \hlineD1 & \cellcolor[HTML]{C0C0C0}IEEE Xplore & { http://ieeexplore.ieee.org/} & 16 & \\ \hlineD2 & \cellcolor[HTML]{C0C0C0}Scopus & { https://www.scopus.com/home.uri/} & 18 & \\ \hlineD3 & \cellcolor[HTML]{C0C0C0}Web of Science & {http://www.webofscience.com/} & 286 & \\ \hlineD4 & \cellcolor[HTML]{C0C0C0}Springer Link & { http://link.springer.com/} & 171& \\ \hline\end{tabular}\end{table}

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Article Data source

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2109.06859v1_train__99bcbefb-6af2-4bb0-94a8-4535fe2adf14

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c |c c c c}\hline& & Accuracy (\%) $\uparrow$ & NA (\%) $\uparrow$ & F1-open $\uparrow$ & AUROC $\uparrow$\\\cline{3-6} Method & Arch. & \multicolumn{4}{c}{1-shot}\\ \hlineGaussE~\cite{liu2020few} + OpenMax~\cite{bendale2016towards}$^1$ & Res18 & $57.89\pm0.59$ & - & - & $ 0.589\pm0.006$\\GaussE~\cite{liu2020few} + Counterfactual~\cite{neal2018open}$^1$ & Res18 & $57.89\pm0.59$ & - & - & $0.522\pm0.006$\\GaussE~\cite{liu2020few}$^1$ & Res18 & $57.89\pm0.59$ & - & - & $0.587\pm0.006$\\PEELER~\cite{liu2020few}$^1$ & Res18 & $58.31\pm0.58$ & - & - & $0.617\pm0.006$ \\PEELER~\cite{liu2020few} + threshold & Res18 & $56.98\pm0.88$ & $44.77\pm0.70$ & $0.357\pm0.009$ & $0.626\pm0.008$\\PEELER~\cite{liu2020few} + Entropic Loss~\cite{dhamija2018reducing} & Res18 & $56.10\pm0.86$ & $48.36\pm0.69$ & $0.367\pm0.008$ & $0.631\pm0.008$\\PEELER~\cite{liu2020few} + Objectosphere~\cite{dhamija2018reducing} & Res18 & $52.63\pm0.86$ & $27.31\pm0.37$ & $0.060\pm0.007$ & $0.548\pm0.008$\\PEELER~\cite{liu2020few} + \MetaBCE~[ours] & Res18 & $56.98\pm0.88$ & $36.94\pm0.44$ & $0.252\pm0.007$ & $0.606\pm0.008$ \\PEELER~\cite{liu2020few} + \OCML~[ours] & Res18 & $56.98\pm0.88$ & $57.60\pm0.76$ & $0.380\pm0.006$ & $0.607\pm0.007$ \\FEAT~\cite{ye2020fewshot} + threshold & Res18 & $\bf{66.42\pm0.65}$ & $56.53\pm0.89$ & $\bf{0.442\pm0.005}$ & $\bf{0.686\pm0.008}$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Res18 & $\bf{66.42\pm0.65}$ & $34.70\pm0.31$ & $0.232\pm0.006$ & $0.624\pm0.006$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Res18 & $\bf{66.42\pm0.65}$ & $\bf{59.79\pm0.54}$ & $\bf{0.440\pm0.005}$ & $0.623\pm0.006$\\ \hlinePEELER~\cite{liu2020few} + threshold & Conv64 & $51.38\pm0.81$ & $42.48\pm0.75$ & $0.310\pm0.009$ & $0.568\pm0.007$\\PEELER~\cite{liu2020few} + Entropic Loss~\cite{dhamija2018reducing} & Conv64 & $51.11\pm0.82$ & $41.81\pm0.68$ & $0.299\pm0.008$ & $0.594\pm0.008$\\PEELER~\cite{liu2020few} + Objectosphere~\cite{dhamija2018reducing} & Conv64 & $49.01\pm0.85$ & $33.79\pm0.68$ & $0.204\pm0.009$ & $0.519\pm0.009$\\PEELER~\cite{liu2020few} + \MetaBCE~[ours] & Conv64 & $51.38\pm0.81$ & $36.11\pm0.41$ & $0.233\pm0.007$ & $0.600\pm0.008$ \\PEELER~\cite{liu2020few} + \OCML~[ours] & Conv64 & $51.38\pm0.81$ & $\bf{55.80\pm0.78}$ & $0.349\pm0.006$ & $0.613\pm0.008$ \\FEAT~\cite{ye2020fewshot} + threshold & Conv64 & $\bf{55.01\pm0.62}$ & $38.80\pm0.40$ & $0.279\pm0.005$ & $0.557\pm0.006$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Conv64 & $\bf{55.01\pm0.62}$ & $33.64\pm0.30$ & $0.205\pm0.006$ & $0.616\pm0.006$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Conv64 & $\bf{55.01\pm0.62}$ & $\bf{55.81\pm0.53}$ & $\bf{0.373\pm0.005}$ & $\bf{0.626\pm0.006}$\\\hline& & \multicolumn{4}{c}{5-shot}\\ \hlineGaussE~\cite{liu2020few} + OpenMax~\cite{bendale2016towards}$^1$ & Res18 & $75.31\pm0.76$ & - & - & $0.675\pm0.007$\\GaussE~\cite{liu2020few} + Counterfactual~\cite{neal2018open}$^1$ & Res18 & $75.31\pm0.76$ & - & - & $0.533\pm0.006$\\GaussE~\cite{liu2020few}$^1$ & Res18 & $75.31\pm0.76$ & - & - & $0.665\pm0.007$\\PEELER~\cite{liu2020few}$^1$ & Res18 & $75.08\pm0.72$ & - & - & $0.699\pm0.007$\\PEELER~\cite{liu2020few} + threshold & Res18 & $73.04\pm0.68$ & $52.78\pm0.83$ & $0.472\pm0.009$ & $0.677\pm0.008$\\PEELER~\cite{liu2020few} + Entropic Loss~\cite{dhamija2018reducing} & Res18 & $70.98\pm0.64$ & $59.26\pm0.69$ & $0.491\pm0.006$ & $0.688\pm0.007$\\PEELER~\cite{liu2020few} + Objectosphere~\cite{dhamija2018reducing} & Res18 & $66.27\pm0.77$ & $26.29\pm0.19$ & $0.034\pm0.005$ & $0.564\pm0.008$\\PEELER~\cite{liu2020few} + \MetaBCE~[ours] & Res18 & $73.04\pm0.68$ & $70.98\pm0.58$ & $0.495\pm0.004$ & $0.646\pm0.005$ \\PEELER~\cite{liu2020few} + \OCML~[ours] & Res18 & $73.04\pm0.68$ & $65.64\pm0.49$ & $0.498\pm0.004$ & $0.661\pm0.006$ \\FEAT~\cite{ye2020fewshot} + threshold & Res18 & $\bf{80.26\pm0.45}$ & $63.89\pm1.02$ & $0.537\pm0.003$ & $\bf{0.727\pm0.007}$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Res18 & $\bf{80.26\pm0.45}$ & $\bf{73.32\pm0.49}$ & $\bf{0.553\pm0.003}$ & $0.667\pm0.005$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Res18 & $\bf{80.26\pm0.45}$ & $64.36\pm0.48$ & $0.544\pm0.004$ & $0.682\pm0.006$\\ \hlinePEELER~\cite{liu2020few} + threshold & Conv64 & $66.92\pm0.66$ & $47.24\pm0.83$ & $0.399\pm0.009$ & $0.608\pm0.007$\\PEELER~\cite{liu2020few} + Entropic Loss~\cite{dhamija2018reducing} & Conv64 & $65.06\pm0.71$ & $47.77\pm0.80$ & $0.386\pm0.009$ & $0.625\pm0.008$\\PEELER~\cite{liu2020few} + Objectosphere~\cite{dhamija2018reducing} & Conv64 & $62.04\pm0.71$ & $35.10\pm0.73$ & $0.219\pm0.010$ & $0.526\pm0.009$\\PEELER~\cite{liu2020few} + \MetaBCE~[ours] & Conv64 & $66.92\pm0.66$ & $\bf{68.74\pm0.56}$ & $0.460\pm0.004$ & $0.645\pm0.005$ \\PEELER~\cite{liu2020few} + \OCML~[ours] & Conv64 & $66.92\pm0.66$ & $63.57\pm0.48$ & $0.466\pm0.004$ & $0.666\pm0.006$ \\FEAT~\cite{ye2020fewshot} + threshold & Conv64 & $\bf{70.70\pm0.50}$ & $45.85\pm0.46$ & $0.389\pm0.005$ & $0.595\pm0.006$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Conv64 & $\bf{70.70\pm0.50}$ & $\bf{69.10\pm0.45}$ & $\bf{0.487\pm0.004}$ & $0.669\pm0.005$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Conv64 & $\bf{70.70\pm0.50}$ & $61.29\pm0.48$ & $\bf{0.490\pm0.004}$ & $\bf{0.680\pm0.006}$\\\hline\end{tabular}\end{center}\caption{Experimental results on miniImageNet dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold}. $^1$ Results from Liu~\etal~\cite{liu2020few}}\label{table:fsos_mini_val}\end{table}

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Experimental results on miniImageNet dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold

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2109.06859v1_train__5f881ec5-e982-4026-b8b1-13a3e3173a20

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c | c c c}\hline& & Accuracy (\%) $\uparrow$ & F1-score $\uparrow$ & AUROC $\uparrow$\\\cline{3-5} Method & Arch. & \multicolumn{3}{c}{1-shot}\\ \hlineProto Net~\cite{snell2017prototypical} + DeepSVDD~\cite{pmlr-v80-ruff18a}& Conv64 & - & - & $0.603\pm0.007$\\Proto Net~\cite{snell2017prototypical} + DeepAnomaly~\cite{golan2018deep}& Conv64 & - & - & $0.655\pm0.011$\\Proto Net~\cite{snell2017prototypical} + SVDD~\cite{tax2004support}& Conv64 & $50.00\pm0.00$ & $0.000\pm0.000$ & $0.599\pm0.030$\\Proto Net~\cite{snell2017prototypical} + OCSVM~\cite{scholkopf2000support}& Conv64 & $50.00\pm0.00$ & $0.000\pm0.000$ & $0.633\pm0.015$\\Proto Net~\cite{snell2017prototypical} + Threshold& Conv64 & $50.05\pm0.04$ & $0.002\pm0.001$ & $0.697\pm0.005$\\CLEAR~\cite{kozerawski2018clear} & Conv64 & $50.24\pm0.36$ & $0.008\pm0.012$ & $0.620\pm0.120$\\Proto Net~\cite{snell2017prototypical} + \MetaBCE~[ours]& Conv64 & $54.72\pm1.29$ & $0.169\pm0.044$ & $0.774\pm0.009$ \\Proto Net~\cite{snell2017prototypical} + \OCML~[ours]& Conv64 & $\bf{72.14\pm0.56}$ & $\bf{0.701\pm0.016}$ & $\bf{0.801\pm0.006}$ \\\hline Upper-bound (supervised FEAT~\cite{ye2020fewshot})$^1$& Conv64 & $84.25\pm0.89$ & - & -\\\hline & & \multicolumn{3}{c}{5-shot}\\ \hlineProto Net~\cite{snell2017prototypical} + DeepSVDD~\cite{pmlr-v80-ruff18a}& Conv64 & - & - & $0.656\pm0.007$ \\Proto Net~\cite{snell2017prototypical} + DeepAnomaly~\cite{golan2018deep}& Conv64 & - & - & $0.762\pm0.010$\\Proto Net~\cite{snell2017prototypical} + SVDD~\cite{tax2004support}& Conv64 & $50.61\pm0.41$ & $0.036\pm0.021$ & $0.609\pm0.036$ \\Proto Net~\cite{snell2017prototypical} + OCSVM~\cite{scholkopf2000support}& Conv64 & $52.40\pm0.45$ & $0.130\pm0.019$ & $0.656\pm0.019$ \\Proto Net~\cite{snell2017prototypical} + Threshold& Conv64 & $64.92\pm1.29$ & $0.590\pm0.063$ & $0.725\pm0.003$ \\Proto Net~\cite{snell2017prototypical} + \MetaBCE~[ours]& Conv64 & $76.16\pm0.58$ & $\bf{0.783\pm0.007}$ & $0.839\pm0.006$ \\Proto Net~\cite{snell2017prototypical} + \OCML~[ours]& Conv64 & $\bf{78.74\pm1.07}$ & $0.774\pm0.019$ & $\bf{0.874\pm0.010}$\\\hline Upper-bound (supervised FEAT~\cite{ye2020fewshot})$^1$& Conv64 & $91.26\pm0.56$ & - & -\\\hline\end{tabular}\end{center}\caption{Experimental results on CUB-200-2011 dataset for few-shot one-class classification. The best results are shown in {\bf bold}. $^1$ Supervised two-class classification.}\label{table:fsoc_cub_val}\end{table}

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Experimental results on CUB-200-2011 dataset for few-shot one-class classification. The best results are shown in {\bf bold

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2109.06859v1_train__93b7bf71-e8b0-4189-b4d4-b791ce3a81e1

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c | c c c}\hline& & Accuracy (\%) $\uparrow$ & F1-score $\uparrow$ & AUROC $\uparrow$\\\cline{3-5} Method & Arch. & \multicolumn{3}{c}{1-shot}\\ \hlineProto Net~\cite{snell2017prototypical} + DeepSVDD~\cite{pmlr-v80-ruff18a}& Conv64 & - & - & $0.656\pm0.004$\\Proto Net~\cite{snell2017prototypical} + DeepAnomaly~\cite{golan2018deep}& Conv64 & - & - & $0.603\pm0.012$\\Proto Net~\cite{snell2017prototypical} + SVDD~\cite{tax2004support}& Conv64 & $50.00\pm0.00$ & $0.000\pm0.000$ & $0.669\pm0.003$\\Proto Net~\cite{snell2017prototypical} + OCSVM~\cite{scholkopf2000support}& Conv64 & $50.00\pm0.00$ & $0.000\pm0.000$ & $0.676\pm0.003$\\Proto Net~\cite{snell2017prototypical} + Threshold& Conv64 & $50.48\pm0.11$ & $0.017\pm0.003$ & $0.704\pm0.008$\\CLEAR~\cite{kozerawski2018clear} & Conv64 & $50.53\pm0.53$ & $0.552\pm0.006$ & $0.509\pm0.008$ \\Proto Net~\cite{snell2017prototypical} + \MetaBCE~[ours]& Conv64 & $55.87\pm0.38$ & $0.208\pm0.010$ & $0.755\pm0.009$\\Proto Net~\cite{snell2017prototypical} + \OCML~[ours]& Conv64 & $\bf{72.13\pm0.33}$ & $\bf{0.724\pm0.003}$ & $\bf{0.800\pm0.004}$\\\hline Upper-bound (supervised FEAT~\cite{ye2020fewshot})$^1$& ResNet12 & $88.54\pm0.81$ & - & -\\\hline & & \multicolumn{3}{c}{5-shot}\\ \hlineProto Net~\cite{snell2017prototypical} + DeepSVDD~\cite{pmlr-v80-ruff18a}& Conv64 & - & - & $0.678\pm0.003$ \\Proto Net~\cite{snell2017prototypical} + DeepAnomaly~\cite{golan2018deep}& Conv64 & - & - & $0.719\pm0.011$\\Proto Net~\cite{snell2017prototypical} + SVDD~\cite{tax2004support}& Conv64 & $50.52\pm0.04$ & $0.021\pm0.001$ & $0.724\pm0.003$ \\Proto Net~\cite{snell2017prototypical} + OCSVM~\cite{scholkopf2000support}& Conv64 & $52.37\pm0.09$ & $0.106\pm0.003$ & $0.712\pm0.003$ \\Proto Net~\cite{snell2017prototypical} + Threshold& Conv64 & $61.90\pm0.54$ & $0.426\pm0.011$ & $0.741\pm0.008$\\Proto Net~\cite{snell2017prototypical} + \MetaBCE~[ours]& Conv64 & $75.62\pm0.65$ & $0.774\pm0.005$ & $0.831\pm0.007$\\Proto Net~\cite{snell2017prototypical} + \OCML~[ours]& Conv64 & $\bf{78.89\pm0.67}$ & $\bf{0.803\pm0.006}$ & $\bf{0.878\pm0.007}$\\\hline Upper-bound (supervised FEAT~\cite{ye2020fewshot})$^1$& ResNet12 & $94.56\pm0.51$ & - & -\\\hline\end{tabular}\end{center}\caption{Experimental results on tieredImageNet dataset for few-shot one-class classification. The best results are shown in {\bf bold}. $^1$ Supervised two-class classification.}\label{table:fsoc_tier_val}\end{table}

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Experimental results on tieredImageNet dataset for few-shot one-class classification. The best results are shown in {\bf bold

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2109.06859v1_train__003e019a-4ff8-479b-8f5d-2037e0a5d1cd

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c |c c c c}\hline& & Accuracy (\%) $\uparrow$ & NA (\%) $\uparrow$ & F1-open $\uparrow$ & AUROC $\uparrow$\\\cline{3-6} Method & Arch. & \multicolumn{4}{c}{1-shot}\\ \hlinePEELER~\cite{liu2020few} & Conv64 & $52.56\pm0.73$ & - & - & $0.549\pm0.003$\\PEELER~\cite{liu2020few} + threshold & Conv64 & $52.56\pm0.73$ & $26.51\pm1.48$ & $0.042\pm0.036$ & $0.605\pm0.007$\\Proto Nets~\cite{snell2017prototypical} + threshold & Conv64 & $41.72\pm1.03$ & $25.03\pm0.02$ & $0.001\pm0.001$ & $0.566\pm0.009$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $41.72\pm1.03$ & $35.66\pm4.85$ & $0.229\pm0.060$ & $0.613\pm0.019$\\Proto Nets~\cite{snell2017prototypical} + \OCML~[ours] & Conv64 & $41.72\pm1.03$ & $48.61\pm5.72$ & $0.371\pm0.035$ & $\bf{0.654\pm0.010}$\\FEAT~\cite{ye2020fewshot} + threshold & Conv64 & $\bf{63.16\pm0.74}$ & $32.69\pm0.29$ & $0.199\pm0.005$ & $0.537\pm0.007$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Conv64 & $\bf{63.16\pm0.74}$ & $32.70\pm0.26$ & $0.190\pm0.005$ & $0.648\pm0.006$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Conv64 & $\bf{63.16\pm0.74}$ & $\bf{60.21\pm0.80}$ & $\bf{0.414\pm0.005}$ & $0.556\pm0.005$\\\hline& & \multicolumn{4}{c}{5-shot}\\ \hlineProto Nets~\cite{snell2017prototypical} + OpenMax~\cite{bendale2016towards} & Conv64 & $70.97\pm0.99$ & $25.60\pm0.15$ & $0.02\pm0.005$ & $0.574\pm0.011$\\PEELER~\cite{liu2020few} & Conv64 & $71.65\pm0.79$ & - & - & $0.637\pm0.004$ \\PEELER~\cite{liu2020few} + threshold & Conv64 & $71.65\pm0.79$ & $42.79\pm6.17$ & $0.348\pm0.062$ & $0.665\pm0.010$\\Proto Nets~\cite{snell2017prototypical} + threshold & Conv64 & $70.97\pm0.99$ & $37.62\pm1.56$ & $0.298\pm0.022$ & $0.606\pm0.009$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $70.97\pm0.99$ & $68.59\pm2.64$ & $0.509\pm0.009$ & $0.661\pm0.031$\\Proto Nets~\cite{snell2017prototypical} + \OCML~[ours] & Conv64 & $70.97\pm0.99$ & $47.70\pm9.15$ & $0.426\pm0.103$ & $\bf{0.736\pm0.007}$\\FEAT~\cite{ye2020fewshot} + threshold & Conv64 & $\bf{77.47\pm0.55}$ & $35.31\pm0.34$ & $0.261\pm0.005$ & $0.568\pm0.007$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & Conv64 & $\bf{77.47\pm0.55}$ & $\bf{72.04\pm0.43}$ & $\bf{0.541\pm0.004}$ & $0.713\pm0.005$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & Conv64 & $\bf{77.47\pm0.55}$ & $66.95\pm0.60$ & $0.513\pm0.004$ & $0.573\pm0.005$\\\hline\end{tabular}\end{center}\caption{Experimental results on CUB-200-2011 dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold}. }\label{table:fsos_cub_val}\end{table}

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Experimental results on CUB-200-2011 dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold

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2109.06859v1_train__ccbf422f-7098-4270-815a-20ca70e45210

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c |c c c c}\hline& & Accuracy (\%) $\uparrow$ & NA (\%) $\uparrow$ & F1-open $\uparrow$ & AUROC $\uparrow$\\\cline{3-6} Method & Arch. & \multicolumn{4}{c}{1-shot}\\ \hlinePEELER~\cite{liu2020few} & Conv64 & $38.55\pm0.43$ & - & - & $0.546\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + threshold & Conv64 & $43.77\pm0.47$ & $25.38\pm0.05$ & $0.011\pm0.001$ & $0.576\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $43.77\pm0.47$ & $33.74\pm0.21$ & $0.339\pm0.004$ & $0.623\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + \OCML~[ours] & Conv64 & $43.77\pm0.47$ & $56.06\pm0.47$ & $0.299\pm0.003$ & $0.659\pm0.004$\\FEAT~\cite{ye2020fewshot} + threshold & ResNet12 & $\bf{70.88\pm0.72}$ & $50.97\pm0.06$ & $0.463\pm0.007$ & $\bf{0.697\pm0.006}$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & ResNet12 & $\bf{70.88\pm0.72}$ & $39.26\pm0.36$ & $0.308\pm0.006$ & $0.592\pm0.006$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & ResNet12 & $\bf{70.88\pm0.72}$ & $\bf{67.76\pm0.86}$ & $\bf{0.478\pm0.005}$ & $0.610\pm0.006$\\\hline& & \multicolumn{4}{c}{5-shot}\\ \hlineProto Nets~\cite{snell2017prototypical} + OpenMax~\cite{bendale2016towards} & Conv64 & $71.04\pm0.40$ & $25.73\pm0.04$ & $0.024\pm0.001$ & $0.585\pm0.003$\\PEELER~\cite{liu2020few} & Conv64 & $67.71\pm0.42$ & - & - & $0.635\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + threshold & Conv64 & $71.04\pm0.40$ & $38.08\pm0.25$ & $0.302\pm0.004$ & $0.615\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $71.04\pm0.40$ & $70.46\pm0.37$ & $0.495\pm0.003$ & $0.672\pm0.004$\\Proto Nets~\cite{snell2017prototypical} + \OCML~[ours] & Conv64 & $71.04\pm0.40$ & $72.87\pm0.36$ & $0.509\pm0.003$ & $0.727\pm0.004$\\FEAT~\cite{ye2020fewshot} + threshold & ResNet12 & $\bf{84.22\pm0.53}$ & $67.91\pm0.05$ & $0.545\pm0.005$ & $\bf{0.768\pm0.005}$\\FEAT~\cite{ye2020fewshot} + \MetaBCE~[ours] & ResNet12 & $\bf{84.22\pm0.53}$ & $76.71\pm0.73$ & $0.570\pm0.004$ & $0.636\pm0.005$\\FEAT~\cite{ye2020fewshot} + \OCML~[ours] & ResNet12 & $\bf{84.22\pm0.53}$ & $\bf{77.96\pm0.63}$ & $\bf{0.577\pm0.003}$ & $0.657\pm0.006$\\\hline\end{tabular}\end{center}\caption{Experimental results on tieredImageNet dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold}. }\label{table:fsos_tier_val}\end{table}

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Experimental results on tieredImageNet dataset for few-shot $5$-way open-set classification with $5$ open-set categories. The best results are shown in {\bf bold

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2109.06859v1_train__7dddf328-bfe6-4f14-b713-181a02ba36d1

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\begin{tabular}{|l|l|l|}\hline$g_{\theta}$ architecture name & Layer 1 & Layer 2\\ \hline1 layer & FC layer (1600, 1600) & -\\2 layers, middle dim 100 & FC layer (1600, 100) & FC layer (100, 1600)\\2 layers, middle dim 500 & FC layer (1600, 500) & FC layer (500, 1600)\\2 layers, middle dim 1000 & FC layer (1600, 1000) & FC layer (1000, 1600)\\\hline\end{tabular}\end{center}\caption{Tested architectures for the transfer learning module $g_{\theta}$ for \OCML~approach.}\label{table:ocml_architecture_table}\end{table}

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Tested architectures for the transfer learning module $g_{\theta

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2109.06859v1_train__040f4d38-1c33-496b-bdd1-17cfedd5aa1f

arxiv_table_to_tex

\begin{table}[h!]\begin{table}[h!]\begin{center}\footnotesize\begin{tabular}{l|c |c c c c}\hline& & Accuracy (\%) $\uparrow$ & NA (\%) $\uparrow$ & F1-open $\uparrow$ & AUROC $\uparrow$\\\cline{3-6} Method & Arch. & \multicolumn{4}{c}{1-shot}\\ \hlineProto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $41.72\pm1.03$ & $35.66\pm4.85$ & $0.229\pm0.060$ & $0.613\pm0.019$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE$_C$~[ours] & Conv64 & $41.72\pm1.03$ & $28.66\pm3.78$ & $0.080\pm0.077$ & $0.629\pm0.009$\\\hline& & \multicolumn{4}{c}{5-shot}\\ \hlineProto Nets~\cite{snell2017prototypical} + \MetaBCE~[ours] & Conv64 & $70.97\pm0.99$ & $68.59\pm2.64$ & $0.509\pm0.009$ & $0.661\pm0.031$\\Proto Nets~\cite{snell2017prototypical} + \MetaBCE$_C$~[ours] & Conv64 & $70.97\pm0.99$ & $37.13\pm1.53$ & $0.233\pm0.162$ & $0.684\pm0.011$\\\hline\end{tabular}\end{center}\caption{Experimental results on CUB-200-2011 dataset for few-shot $5$-way open-set classification with $5$ open-set categories.}\label{table:fsos_mbce_ablation}\end{table}

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Experimental results on CUB-200-2011 dataset for few-shot $5$-way open-set classification with $5$ open-set categories.

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2312.02428v2_train__162c6f2d-cf21-48ff-a737-e30ebcc3979c

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\footnotesize\renewcommand{\arraystretch}{1.35} % 控制行高\setlength{\tabcolsep}{4.0mm} % 控制列间距{{\begin{tabular}{l|p{80pt}|cc|cc|cc|cc}\toprule[1.5pt]\multirow{2}{*}{\textbf{\#}} & \multirow{2}{*}{\textbf{Method}} & \multicolumn{2}{c|}{Image\textbf{$\rightarrow$}Text} & \multicolumn{2}{c|}{Sketch\textbf{$\rightarrow$}Text} & \multicolumn{2}{c|}{Art\textbf{$\rightarrow$}Text} & \multicolumn{2}{c}{Low-Res\textbf{$\rightarrow$}Text} \\\cmidrule(rl){3-4}\cmidrule(rl){5-6}\cmidrule(rl){7-8}\cmidrule(rl){9-10}& & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} \\\noalign{\hrule height 1.5pt}1& CLIP$^{*}$ & 55.2 & 90.8 & 48.4 & 87.9 & 64.5 & 96.8 & 42.6 & 81.8 \\2& BLIP$^{*}$ & 71.4 & 94.9 & 55.5 & 87.0 & 81.0 & 98.8 & 49.2 & 81.8\\3& VPT & 52.2 & 91.7 & 45.2 & 87.7 & 52.7 & 94.6 & 44.3 & 84.6\\4& ImageBind & 73.5 & 96.5 & 56.1 & 88.4 & 82.7 & 99.0 & 42.4 & 73.8\\5& LanguageBind & 80.5 & 98.3 & 63.9 & 91.6 & 87.2 & 99.7 & 56.9 & 86.8\\\midrule\rowcolor{aliceblue!60} 6& FreestyleRet-CLIP & 71.6 & 98.0 & 66.7 & \textbf{96.7} & 74.4 & 99.1 & 64.1 & 94.8\\\rowcolor{aliceblue!60} 7& FreestyleRet-BLIP & \textbf{82.8} & \textbf{99.0} & \textbf{71.0} & 96.4 & \textbf{86.6} & \textbf{99.7} & \textbf{69.5} & \textbf{96.9}\\\bottomrule[1.5pt]\end{tabular}}}% \vspace{-1pt}\caption{\textbf{The Text-Retrieval performance of our FreestyleRet and baseline models.}}\label{tab:result_text}% \vspace{-1pt}\end{table*}

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\textbf{The Text-Retrieval performance of our FreestyleRet and baseline models.

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2312.02428v2_train__c534b938-3572-46de-9609-1d9829a21dec

arxiv_table_to_tex

\begin{table*}[h]\begin{table*}[h]\centering\footnotesize\renewcommand{\arraystretch}{1.35} % 控制行高\setlength{\tabcolsep}{4.0mm} % 控制列间距{{\begin{tabular}{l|p{80pt}|cc|cc|cc|cc}\toprule[1.5pt]\multirow{2}{*}{\textbf{\#}} & \multirow{2}{*}{\textbf{Method}} & \multicolumn{2}{c|}{Image\textbf{$\rightarrow$}Art} & \multicolumn{2}{c|}{Sketch\textbf{$\rightarrow$}Art} & \multicolumn{2}{c|}{Text\textbf{$\rightarrow$}Art} & \multicolumn{2}{c}{Low-Res\textbf{$\rightarrow$}Art} \\\cmidrule(rl){3-4}\cmidrule(rl){5-6}\cmidrule(rl){7-8}\cmidrule(rl){9-10}& & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} \\\noalign{\hrule height 1.5pt}1& CLIP$^{*}$ & 63.0 & 94.7 & 61.2 & 92.7 & 75.5 & 98.2 & 51.9 & 87.9 \\2& BLIP$^{*}$ & 57.1 & 88.5 & 44.8 & 82.8 & 82.8 & 98.7 & 39.4 & 79.3\\3& VPT & 67.4 & 95.5 & 60.3 & 93.1 & 61.6 & 96.5 & 44.3 & 84.6\\4& ImageBind & 46.4 & 80.5 & 28.7 & 60.8 & 82.6 & 98.9 & 57.8 & 89.6\\5& LanguageBind & 65.8 & 93.2 & 41.1 & 77.7 & 86.7 & 99.2 & 34.8 & 72.0\\\midrule\rowcolor{aliceblue!60} 6& FreestyleRet-CLIP & 72.9 & \textbf{97.8} & \textbf{66.5} & \textbf{96.2} & 85.0 & 99.6 & \textbf{62.8} & \textbf{94.1}\\\rowcolor{aliceblue!60} 7& FreestyleRet-BLIP & \textbf{73.6} & 97.4 & 63.1 & 94.4 & \textbf{90.2} & \textbf{99.7} & 60.1 & 92.2\\\bottomrule[1.5pt]\end{tabular}}}% \vspace{-1pt}\caption{\textbf{The Art-Retrieval performance of our FreestyleRet and baseline models.}}\label{tab:result_art}% \vspace{-1pt}\end{table*}

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\textbf{The Art-Retrieval performance of our FreestyleRet and baseline models.

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2312.02428v2_train__af17f515-2c25-4829-a5e8-6448ced6d85a

arxiv_table_to_tex

\begin{table*}[htb]\begin{table*}[htb]\centering\footnotesize\renewcommand{\arraystretch}{1.35} % 控制行高\setlength{\tabcolsep}{4.0mm} % 控制列间距{{\begin{tabular}{l|p{80pt}|cc|cc|cc|cc}\toprule[1.5pt]\multirow{2}{*}{\textbf{\#}} & \multirow{2}{*}{\textbf{Method}} & \multicolumn{2}{c|}{Image\textbf{$\rightarrow$}Sketch} & \multicolumn{2}{c|}{Art\textbf{$\rightarrow$}Sketch} & \multicolumn{2}{c|}{Text\textbf{$\rightarrow$}Sketch} & \multicolumn{2}{c}{Low-Res\textbf{$\rightarrow$}Sketch} \\\cmidrule(rl){3-4}\cmidrule(rl){5-6}\cmidrule(rl){7-8}\cmidrule(rl){9-10}& & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} \\\noalign{\hrule height 1.5pt}1& CLIP$^{*}$ & 70.5 & 96.1 & 60.5 & 92.9 & 55.0 & 90.8 & 60.4 & 90.9 \\2& BLIP$^{*}$ & 69.8 & 93.5 & 47.6 & 82.8 & 58.6 & 89.8 & 52.3 & 82.8\\3& VPT & 71.7 & 96.2 & 62.3 & 92.9 & 49.4 & 88.6 & 63.3 & 91.5\\4& ImageBind & 54.0 & 81.8 & 38.3 & 71.6 & 56.1 & 88.4 & 26.2 & 52.5\\5& LanguageBind & 74.6 & 96.1 & 57.5 & 87.0 & 65.7 & 94.0 & 54.5 & 83.8\\\midrule\rowcolor{aliceblue!60} 6& FreestyleRet-CLIP & 77.8 & \textbf{98.1} & 66.5 & \textbf{96.2} & 72.3 & 97.4 & 68.7 & \textbf{95.1}\\\rowcolor{aliceblue!60} 7& FreestyleRet-BLIP & \textbf{80.5} & 97.7 & \textbf{66.8} & 94.9 & \textbf{76.6} & \textbf{97.7} & \textbf{71.1} & 94.3\\\bottomrule[1.5pt]\end{tabular}}}% \vspace{-1pt}\caption{\textbf{The Sketch-Retrieval performance of our FreestyleRet and baseline models.}}\label{tab:result_sketch}% \vspace{-1pt}\end{table*}

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\textbf{The Sketch-Retrieval performance of our FreestyleRet and baseline models.

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2312.02428v2_train__dce1840f-5673-4130-832a-b7238f312557

arxiv_table_to_tex

\begin{table*}[htb]\begin{table*}[htb]\centering\footnotesize\renewcommand{\arraystretch}{1.35} % 控制行高\setlength{\tabcolsep}{4.0mm} % 控制列间距{{\begin{tabular}{l|p{80pt}|cc|cc|cc|cc}\toprule[1.5pt]\multirow{2}{*}{\textbf{\#}} & \multirow{2}{*}{\textbf{Method}} & \multicolumn{2}{c|}{Image\textbf{$\rightarrow$}Low-Res} & \multicolumn{2}{c|}{Art\textbf{$\rightarrow$}Low-Res} & \multicolumn{2}{c|}{Text\textbf{$\rightarrow$}Low-Res} & \multicolumn{2}{c}{Sketch\textbf{$\rightarrow$}Low-Res} \\\cmidrule(rl){3-4}\cmidrule(rl){5-6}\cmidrule(rl){7-8}\cmidrule(rl){9-10}& & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} & {R@1} & {R@5} \\\noalign{\hrule height 1.5pt}1& CLIP$^{*}$ & 79.3 & 97.2 & 53.0 & 89.2 & 46.0 & 82.3 & 59.5 & 92.4 \\2& BLIP$^{*}$ & \textbf{89.0} & 40.8 & 73.9 & 87.0 & 51.5 & 84.4 & 51.4 & 82.3\\3& VPT & 75.5 & 95.7 & 56.7 & 90.3 & 45.6 & 85.7 & 61.9 & 91.6\\4& ImageBind & 59.9 & 83.1 & 25.2 & 49.8 & 42.4 & 73.8 & 30.7 & 56.8\\5& LanguageBind & 81.0 & 97.6 & 47.3 & 81.2 & 58.5 & 87.9 & 55.5 & 85.6\\\midrule\rowcolor{aliceblue!60} 6& FreestyleRet-CLIP & 80.2 & 97.5 & 62.6 & \textbf{95.2} & 68.7 & 96.6 & 67.4 & \textbf{95.3}\\\rowcolor{aliceblue!60} 7& FreestyleRet-BLIP & 88.4 & \textbf{98.6} & \textbf{63.9} & 94.1 & \textbf{76.0} & \textbf{97.5} & \textbf{71.3} & 94.3\\\bottomrule[1.5pt]\end{tabular}}}% \vspace{-1pt}\caption{\textbf{The Low-Resolution Image Retrieval performance of our FreestyleRet and baseline models.}}\label{tab:result_Low_Res}% \vspace{-1pt}\end{table*}

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\textbf{The Low-Resolution Image Retrieval performance of our FreestyleRet and baseline models.

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2402.01939v1_train__8323aa04-11df-4236-8ad5-dd8c55252329

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\centering\begin{tabular}{r|c|c}\toprule\multicolumn{3}{c}{\textbf{Ablations on Scottish Gaelic-English}} \\\midrule& \textbf{Ours} & \textbf{Naive} \\\midrule5K & \textbf{13.32} & 13.05 \\5K Number & 12.76 & \textbf{13.13} \\5K Length & 12.58 & 12.28 \\5K Align & 12.14 & 12.62 \\\bottomrule\end{tabular}\caption{Ablation result of the importance of different components of our method. If we don't use one of the components, the BLEU score drops significantly.}\label{tab:abl}\end{table}

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Ablation result of the importance of different components of our method. If we don't use one of the components, the BLEU score drops significantly.

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2402.01939v1_train__037a258f-e344-472c-86f1-2205d6442d47

arxiv_table_to_tex

\begin{table*}[!t]\centering\begin{table*}[!t]\centering\small\begin{tabular}{r|c|ccc|c|ccc}\toprule& \multicolumn{4}{c|}{\textbf{Scottish Gaelic-English Ours}} & \multicolumn{4}{|c}{\textbf{Scottish Gaelic-English Naive}} \\%\cmidrule& & \multirow{1}{*}{\# ENG} & \multirow{1}{*}{\# GLA} & \multirow{1}{*}{\# seed} & & \multirow{1}{*}{\# ENG} & \multirow{1}{*}{\# GLA} & \multirow{1}{*}{\# seed}\\& BLEU & types & types & sentences & BLEU & types & types & sentences \\\midrule0K &9.08 &11077 &13826 &0 &9.08 &11077 &13836 &0 \\5K (one) &12.79 &11269 &14020 &5 &12.58 &12588 &15883 &5 \\5K &\textbf{13.32} &12763 &15847 &1511 &13.05 &12057 &15082 &1512 \\5K (half) &13.13 &12367 &15216 &1527 &12.57 &11811 &14740 &1508 \\5K (remove) &12.91 &12528 &15702 &1909 &\textbf{13.29} &12511 &15694 &1909 \\\bottomrule\end{tabular}\caption{Ablation about the number of new vocabulary introduced and the number of seed sentences used to create five thousand synthetic data. Using as little as five seed sentences boosts the 3.71 BLEU score.}\label{tab:abl_1}\end{table*}

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Ablation about the number of new vocabulary introduced and the number of seed sentences used to create five thousand synthetic data. Using as little as five seed sentences boosts the 3.71 BLEU score.

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1810.05726v3_train__32342ee0-a9b3-47b1-a9a9-af9dc10a0def

arxiv_table_to_tex

\begin{table}[h]\begin{table}[h]\setlength\aboverulesep{0pt}\setlength\belowrulesep{0pt}\centering\caption{The average test classification accuracy, recall rate, precision and false positive rate across all five cross validated folds for both Inception-v3 and ResNet-50. The statistic from the best performing network is emboldened for each species. Equations for the computation of each metric are provided below. \label{DLPrecision}}\begin{tabular}{|l|c|c|c|c|c|c|}\toprule\multicolumn{1}{|c|}{\multirow{2}[4]{*}{Species}} & \multicolumn{2}{c|}{Top-1 accuracy (\%)} & \multicolumn{2}{c|}{Precision (\%)} & \multicolumn{2}{c|}{False positive rate (\%)} \\\cmidrule{2-7} & Inception-v3 & ResNet-50 & Inception-v3 & ResNet-50 & Inception-v3 & ResNet-50 \\\midrule\textit{Chinee Apple} & 85.3 & \textbf{88.5} & \textbf{92.7} & 91.0 & \textbf{0.48} & 0.61 \\\textit{Lantana} & 94.4 & \textbf{95.0} & 90.9 & \textbf{91.7} & 0.62 & \textbf{0.55} \\\textit{Parkinsonia} & 96.8 & \textbf{97.2} & 95.6 & \textbf{97.9} & 0.29 & \textbf{0.13} \\\textit{Parthenium} & 94.9 & \textbf{95.8} & 95.8 & \textbf{96.7} & 0.26 & \textbf{0.21} \\\textit{Prickly Acacia} & 92.8 & \textbf{95.5} & \textbf{93.4} & 93.0 & \textbf{0.43} & 0.46 \\\textit{Rubber Vine} & \textbf{93.1} & 92.5 & \textbf{99.2} & 99.1 & \textbf{0.05} & 0.05 \\\textit{Siam Weed} & \textbf{97.6} & 96.5 & 94.4 & \textbf{97.2} & 0.38 & \textbf{0.18} \\\textit{Snake Weed} & 88.0 & \textbf{88.8} & 86.9 & \textbf{90.9} & 0.82 & 0.55 \\\textit{Negatives} & 97.2 & \textbf{97.6} & 96.5 & \textbf{96.7} & 3.77 & 3.59 \\\midruleWeighted average & 95.1 & \textbf{95.7} & 95.1 & \textbf{95.7} & 2.16 & \textbf{2.04} \\\bottomrule\end{tabular}%\end{table}

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The average test classification accuracy, recall rate, precision and false positive rate across all five cross validated folds for both Inception-v3 and ResNet-50. The statistic from the best performing network is emboldened for each species. Equations for the computation of each metric are provided below. \label{DLPrecision

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1810.05726v3_train__83e1b5d8-4c1b-4fa4-87bd-1ddccaa05014

arxiv_table_to_tex

\begin{table*}[h]\begin{table*}[h]\setlength\aboverulesep{0pt}\setlength\belowrulesep{0pt}\centering\caption{The confusion matrix (\%) achieved by the ResNet-50 model on the test subsets for the five cross validated folds.\label{DLConfusion}}\begin{tabular}{|c|ccccccccc|}\toprule& \multicolumn{1}{p{3em}}{\textit{Chinee apple}} & \multicolumn{1}{p{3em}}{\textit{Lantana}} & \multicolumn{1}{p{4.5em}}{\textit{Parkinsonia}} & \multicolumn{1}{p{4.5em}}{\textit{Parthenium}} & \multicolumn{1}{p{3em}}{\textit{Prickly acacia}} & \multicolumn{1}{p{3em}}{\textit{Rubber vine}} & \multicolumn{1}{p{3em}}{\textit{Siam\newline{}weed}} & \multicolumn{1}{p{3em}}{\textit{Snake weed}} & \multicolumn{1}{p{4.5em}|}{\textit{Negatives}} \\\midrule\textit{Chinee apple} & \textbf{88.5} & 1.78 & 0.00 & 0.44 & 0.18 & 0.18 & 0.27 & 3.37 & 5.33 \\\textit{Lantana} & 0.56 & \textbf{95.0} & 0.00 & 0.00 & 0.00 & 0.09 & 0.28 & 0.94 & 3.10 \\\textit{Parkinsonia} & 0.10 & 0.00 & \textbf{97.2} & 0.10 & 1.26 & 0.00 & 0.00 & 0.00 & 1.36 \\\textit{Parthenium} & 0.10 & 0.20 & 0.10 & \textbf{95.8} & 0.88 & 0.10 & 0.00 & 0.29 & 2.54 \\\textit{Prickly acacia} & 0.00 & 0.00 & 0.56 & 0.66 & \textbf{95.5} & 0.00 & 0.00 & 0.09 & 3.20 \\\textit{Rubber vine} & 0.79 & 0.50 & 0.10 & 0.10 & 0.00 & \textbf{92.5} & 0.20 & 0.40 & 5.45 \\\textit{Siam weed} & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & \textbf{96.5} & 0.09 & 3.26 \\\textit{Snake weed} & 4.13 & 1.77 & 0.00 & 0.30 & 0.20 & 0.10 & 0.30 & \textbf{88.8} & 4.43 \\\textit{Negatives} & 0.46 & 0.48 & 0.14 & 0.20 & 0.55 & 0.03 & 0.21 & 0.37 & \textbf{97.6} \\\bottomrule\end{tabular}%\end{table*}

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The confusion matrix (\%) achieved by the ResNet-50 model on the test subsets for the five cross validated folds.\label{DLConfusion

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2003.04628v1_train__eaf8f315-801c-41ef-b4aa-6b6b689e2280

arxiv_table_to_tex

\begin{table*}[ht!]\begin{table*}[ht!]\centering\resizebox{\textwidth}{!}{\begin{tabular}{r c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c | c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c | c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c c@{\hspace*{2mm}}c}~ &\multicolumn{6}{c}{\textit{Scientific articles}} &\multicolumn{6}{c}{\textit{Paper abstracts}} &\multicolumn{6}{c}{\textit{News articles}}\\\cmidrule(lr){2-7} \cmidrule(lr){8-13} \cmidrule(lr){14-19}~ &\multicolumn{2}{c}{\textbf{PubMed}} &\multicolumn{2}{c}{\textbf{ACM}} &\multicolumn{2}{c}{\textbf{SemEval}} &\multicolumn{2}{c}{\textbf{Inspec}} &\multicolumn{2}{c}{\textbf{WWW}} &\multicolumn{2}{c}{\textbf{KP20k}} &\multicolumn{2}{c}{\textbf{DUC-2001}} &\multicolumn{2}{c}{\textbf{KPCrowd}} &\multicolumn{2}{c}{\textbf{KPTimes}} \\\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}\cmidrule(lr){8-9} \cmidrule(lr){10-11} \cmidrule(lr){12-13}\cmidrule(lr){14-15} \cmidrule(lr){16-17} \cmidrule(lr){18-19}\\[-1.5em]\textbf{Model} &\small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} &\small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} &\small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} & \small{$\text{F}@10$} & \small{MAP} \\%[-.2em] % originally -.2em but for testings sake\midruleFirstPhrases &15.4 & 14.7 & 13.6 & 13.5 & 13.8 & 10.5 &29.3 & 27.9 & 10.2 & \phantom{0}9.8 & 13.5 & 12.6 &24.6 & 22.3 & 17.1 & 16.5 & \phantom{0}9.2 & \phantom{0}8.4 \\TextRank &\phantom{0}1.8 & \phantom{0}1.8 & \phantom{0}2.5 & \phantom{0}2.4 & \phantom{0}3.5 & \phantom{0}2.3 &35.8 & 31.4 & \phantom{0}8.4 & \phantom{0}5.6 & 10.2 & \phantom{0}7.4 &21.5 & 19.4 & \phantom{0}7.1 & \phantom{0}9.5 & \phantom{0}2.7 & \phantom{0}2.5 \\TF$\times$IDF &16.7 & 16.9 & 12.1 & 11.4 & 17.7 & 12.7 &\textbf{36.5} & \textbf{34.4} & \phantom{0}9.3 & 10.1 & 11.6 & 12.3 &23.3 & 21.6 & 16.9 & 15.8 & \phantom{0}9.6 & \phantom{0}9.4 \\\midrulePositionRank &\phantom{0}4.9 & \phantom{0}4.6 & \phantom{0}5.7 & \phantom{0}4.9 & \phantom{0}6.8 & \phantom{0}4.1 &34.2 & 32.2 & 11.6\da & \phantom{0}8.4 & 14.1\da & 11.2 &28.6\da & \textbf{28.0}\da & 13.4 & 12.7 & \phantom{0}8.5 & \phantom{0}6.6 \\MPRank &15.8 & 15.0 & 11.6 & 11.0 & 14.3 & 10.6 &30.5 & 29.0 & 10.8\da & 10.4 & 13.6\da & 13.3\da &25.6 & 24.9\da & \textbf{18.2} & \textbf{17.0} & 11.2\da & 10.1\da \\EmbedRank &\phantom{0}3.7 & \phantom{0}3.2 & \phantom{0}2.1 & \phantom{0}2.1 & \phantom{0}2.5 & \phantom{0}2.0 &35.6 & 32.5 & 10.7\da & \phantom{0}7.7 & 12.4 & 10.0 &\textbf{29.5}\da & 27.5\da & 12.4 & 12.4 & \phantom{0}4.0 & \phantom{0}3.3 \\\midruleKea &18.6\da & 18.6\da & 14.2\da & 13.3 & 19.5\da & \textbf{14.7}\da &34.5 & 33.2 & 11.0\da & 10.9\da & 14.0\da & 13.8\da &26.5\da & 24.5\da & 17.3 & 16.7 & 11.0\da & 10.8\da \\CopyRNN &\textbf{24.2}\da & \textbf{25.4}\da & \textbf{24.4}\da & \textbf{26.3}\da & \textbf{20.3}\da & 13.8 &28.2 & 26.4 & \textbf{22.2}\da & \textbf{24.9}\da & \textbf{25.4}\da & \textbf{28.7}\da &% Trained on KP20k% 12.7 & \phantom{0}9.7 & 15.5 & 11.1 & 11.0 & 10.6 \\% Trained on KPTimes10.5 & \phantom{0}7.2 & \phantom{0}8.4 & \phantom{0}4.2 & \textbf{39.3}\da & \textbf{50.9}\da \\CorrRNN &20.8\da & 19.4\da & 21.1\da & 20.5\da & 19.4 & 10.9 &27.9 & 23.6 & 19.9\da & 20.3\da & 21.8\da & 22.7 &% Trained on KP20k%17.0 & 11.5 & 11.5 & \phantom{0}5.7 & \phantom{0}9.7 & \phantom{0}8.0 \\% Trained on KPtimes10.5 & \phantom{0}6.5 & \phantom{0}7.8 & \phantom{0}3.2 & 20.5\da & 20.3\da \\%\midrule%Kea (KP20k) &%\sign{18.9} & \sign{18.5} &%\best[s]{13.7} & \best[s]{13.1} &%\sign{19.1} & \sign{14.1} \\%CopyRNN (extr.) &%n/a$^*$ & n/a$^*$ &%\best{30.6} & \best{28.1} &%\best{24.2} & \best{25.4} &%\best{24.8} & \best{26.6} &%n/a$^*$ & n/a$^*$ &%\best{21.0} & \best{14.2} \\%CopyRNN (extr.) &%\best[s]{24.6} & \best[s]{26.2} &%\best[s]{23.0} & \best[s]{24.3} &%\best[s]{21.7} & \best{14.7} \\\bottomrule\end{tabular}}\caption{Performance of keyphrase extraction models.$^\dagger$~indicates significance over the baselines.}\label{tab:results}\end{table*}

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Performance of keyphrase extraction models.$^\dagger$~indicates significance over the baselines.

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2103.13837v2_train__a3928166-7ccd-4bcb-b3c5-b71159c0c3b6

arxiv_table_to_tex

\begin{table}\begin{table}\centering\setlength{\tabcolsep}{8pt}\begin{tabular}{| l | l | l | l | l |}\hline$N$ & $\Rs$ & Steps & Sweeps/step & Samples \\\hline30 & $10^4$ & 3018 & 1600 & 300 \\\hline60 & $3\times10^4$ & 6056 & 800 & 110 \\\hline\end{tabular}\caption{Simulation parameters for vibrational entropy measurements using the shell method. The number of steps was different for $N=30$ and $N=60$ in order to keep the rate of shell contraction constant.}\label{table:vibrational}\end{table}

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Simulation parameters for vibrational entropy measurements using the shell method. The number of steps was different for $N=30$ and $N=60$ in order to keep the rate of shell contraction constant.

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2103.13837v2_train__0f98c1b1-95a2-42ef-be50-4c5a228b757b

arxiv_table_to_tex

\begin{table}\begin{table}\centering\setlength{\tabcolsep}{8pt}\begin{tabular}{| l | l | l | l | l | }\hline$\Svib$ & $\mu$ & $\sigma$ & skewness & kurtosis \\\hlineshell & -2.65 & 0.11 & -0.90 & 1.29 \\\hlineRTI & -2.65 & 0.09 & -0.25 & 2.76 \\\hline\end{tabular}\caption{Statistics of the probability distribution functions of the vibrational entropy measured by the shell and RTI methods for $N=30$, $\phi=0.60$.}\label{table:distributions}\end{table}

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Statistics of the probability distribution functions of the vibrational entropy measured by the shell and RTI methods for $N=30$, $\phi=0.60$.

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2312.06348v2_train__ceabffd5-b1ff-4654-b80e-82258a3c5b22

arxiv_table_to_tex

\begin{table*}[htp]\begin{table*}[htp]\centering\begin{tabular}{c|c|c|c|c}\topruleTask & Hopper & HalfCheetah & Ant & Walker2d \\\midruleExpert &3402 & 4463 & 4228 & 6717 \\BC & 2376.22 ± 754.80 & 2781.85 ± 1143.11 & 2942.24 ± 344.62 & 1091.46 ± 187.60 \\Gail & 2915.67 ± 328.12 & 4383.44 ± 62.08 & 4530.43 ± 133.30 & 1942.81 ± 957.68 \\Valuedice & 2455.25 ± 658.43 & 4734.59 ± 229.67 & 3781.56 ± 571.15 & 4606.50 ± 927.80 \\CFIL & 3234.61 ± 266.62 & 4976.73 ± 60.41 & 4222.07 ± 201.32 & 5039.77 ± 307.17 \\\midrule\textbf{DiffAIL}& \textbf{3382.03 ± 142.86} & \textbf{5362.25 ± 96.92} & \textbf{5142.60 ± 90.05} & \textbf{6292.28 ± 97.65} \\\bottomrule\end{tabular}\caption{Learned policy best performance during training for different sota imitation learning algorithms with 1 trajectory over 5 seeds in the standard state-action setting.}\label{table_1_traj}\end{table*}

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Learned policy best performance during training for different sota imitation learning algorithms with 1 trajectory over 5 seeds in the standard state-action setting.

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2312.06348v2_train__49d90938-c650-42e7-9c03-c2b7db7a9e61

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\begin{tabular}{c|c|c}\topruleEnv & Gail & DiffAIL \\\midruleHopper & 83.3\% ± 1.2\% & \textbf{92.8\% ± 2.5\%} \\HalfCheetah & 83.8\% ± 0.9\% & \textbf{94.5\% ± 0.6\%} \\Walker2d & 90.5\% ± 0.8\% & \textbf{96.1\% ± 0.6\%} \\Ant & 81.7\% ± 1.6\% & \textbf{98.8\% ± 0.1\%} \\\bottomrule\end{tabular}\caption{A comparison of the ability to distinguish expert demonstrations out of data for Gail and DiffAIL with four trajectories over five seeds. It suggests that DiffAIL has a significant improvement over Gail's discriminator. }\label{table_percent}\end{table}

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A comparison of the ability to distinguish expert demonstrations out of data for Gail and DiffAIL with four trajectories over five seeds. It suggests that DiffAIL has a significant improvement over Gail's discriminator.

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2312.06348v2_train__23487d7f-68b8-41f2-a151-8e2c61881d1b

arxiv_table_to_tex

\begin{table*}[htp]\begin{table*}[htp]\setcounter{table}{2}\centering\begin{tabular}{c|c|c|c|c}\topruleTasks & HalfCheetah & Hopper & Walker2d & Ant \\\midruleOptimizer & Adam & Adam & Adam & Adam\\Batch Size & $256$ & $256$ & $256$ & $256$ \\diffusion hidden layer & $128$ & $128$ & $128$ & $128$ \\diffusion timesteps & $10$ & $10$ & $10$ & $10$ \\noise schedule & linear & linear & linear & linear \\Diffusion learning rate & $3 \times 10^{-4}$ & $3 \times 10^{-4}$ & $3 \times 10^{-4}$ & $3 \times 10^{-4}$ \\use gradient penalty & $\textbf{True}$ & $\textbf{False}$ & $\textbf{True}$ & $\textbf{True}$ \\gradient penalty weight & $\textbf{0.1}$ & $\textbf{NAN}$ & $\textbf{0.001}$ & $\textbf{0.1}$ \\Discount factor $\gamma$ &$0.99$ & $0.99$ & $0.99$ & $0.99$ \\$Q$ learning rate & $3 \times 10^{-3}$ & $3 \times 10^{-3}$ & $3 \times 10^{-3}$ & $3 \times 10^{-3}$\\$\pi$ learning rate & $3 \times 10^{-3}$ & $3 \times 10^{-3}$ & $3 \times 10^{-3}$ & $3 \times 10^{-3}$ \\\bottomrule\end{tabular}\caption{Optimal hyperparameters of DiffAIL in both state-action and state-only settings. DiffAIL parameters change only on the gradient penalty term, indicating that it is very applicable. }\label{table_optimal_hyperparameters}\end{table*}

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Optimal hyperparameters of DiffAIL in both state-action and state-only settings. DiffAIL parameters change only on the gradient penalty term, indicating that it is very applicable.

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2312.06348v2_train__c1a1aadd-a2bf-4843-b2ea-67ca22997fdf

arxiv_table_to_tex

\begin{table*}[htp]\begin{table*}[htp]\centering\begin{tabular}{c|c|c|c|c|c}\toprulediffusion steps & Gail & DiffAIL$(2)$ & DiffAIL$(5)$ & DiffAIL$(10)$ & DiffAIL$(20)$ \\\midruleHalfCheetah $(timesteps=50)$ & 3.1h & 5.5h & 5.9h & 6.2h & 8.0h \\Ant $(timesteps=50)$ & 3.2h & 5.7h & 6.1 & 6.4 & 8.2h\\Hopper $(timesteps=75)$ &4.5h & 6.5h & 6.9h & 7.5h & 9.3h \\Walker2d $(timesteps=75)$ &4.8h & 8.4h & 8.9h & 9.5h & 11.4h \\\bottomrule\end{tabular}\caption{A comparison of running time for different diffusion stepswith DiffAIL on $4$ Mujoco Tasks, with a unit equal to $1$ hour. The first line denotes the algorithms, where the numbers in parentheses represent the diffusion steps. The first column represents the Mujoco task, where the number in parentheses represents the training steps in units of $10,000$.}\label{table_time}\end{table*}

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A comparison of running time for different diffusion stepswith DiffAIL on $4$ Mujoco Tasks, with a unit equal to $1$ hour. The first line denotes the algorithms, where the numbers in parentheses represent the diffusion steps. The first column represents the Mujoco task, where the number in parentheses represents the training steps in units of $10,000$.

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2209.14831v1_train__5569f298-ca5b-4633-a78a-52428d08bb3d

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\caption{Key space of encryption methods}\label{table:key space}\centering\begin{tabular}{|c|cc|}\hlineEncryption Method & Key space & Remark\\\hlineSHF\cite{maungmaung_kiya_2021} & $(c \times M \times M)!$ & $c =$ 3 \\CP & $c!$ & $c >$ 3 \\\hline\end{tabular}\end{table}

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Key space of encryption methods

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2209.14831v1_train__5a21ac8f-c716-468d-b43f-337497c9ff54

arxiv_table_to_tex

\begin{table}[bt]\begin{table}[bt]\caption{Detection accuracy (mAP) of proposed models (PASCAL VOC dataset)}\label{table:result}\centering\begin{tabular}{|c|ccc|}\hlineSelected feature map & Correct ($K$) & No-enc & Incorrect ($K'$) \\\hlineModel-1& 0.7244 & 0.1363 & 0.0421 \\Model-2& 0.7611 & 0.0091 & 0.0180 \\Model-3& 0.7475 & 0.0091 & 0.0078 \\Model-4& 0.7611 & 0.0023 & 0.0043 \\Model-5& 0.7587 & 0.1672 & 0.1624\\Model-6& 0.7617 & 0.1732 & 0.1672\\Model-7& 0.7695 & 0.1768 & 0.1750 \\Model-8& 0.7677 & 0.3529 & 0.3415\\Model-9& 0.7705 & 0.5767 & 0.5678 \\Model-10& 0.7705 & 0.7177 & 0.7027 \\Model-11& 0.7512 & 0.7314 & 0.7252 \\\hlineBaseline& \multicolumn{3}{c|}{0.7690}\\\hline\end{tabular}\end{table}

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Detection accuracy (mAP) of proposed models (PASCAL VOC dataset)

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2209.14831v1_train__91dc5c53-525c-49bb-a1dd-f7367306fe8a

arxiv_table_to_tex

\begin{table}[bt]\begin{table}[bt]\caption{Machine spec used for evaluating executing time}\label{table:machine info}\centering\begin{tabular}{|c|c|}\hlineProcessor & Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz\\OS & Ubuntu 18.04.6 LTS\\GPU & Quadro RTX 6000\\Memory (CPU) & 32GB\\Memory (GPU) & 24GB\\\hline\end{tabular}\end{table}

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Machine spec used for evaluating executing time

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2209.14831v1_train__a8c116f2-534d-4b2d-bbb4-ea2159575806

arxiv_table_to_tex

\begin{table}[bt]\begin{table}[bt]\caption{Learning convergence speed with and without CP (PASCAL VOC dataset)}\label{table:loss value}\centering\begin{tabular}{|c|cc|}\hline&\multicolumn{2}{c|}{Loss value} \\\cline{2-3}No. of iterations & Baseline & Model-5 \\\hline20000 & 3.5232 & 3.2191 \\40000& 2.9450 & 3.1328 \\80000& 2.3215 & 2.2475 \\120000& 1.8859 & 2.0459 \\\hline\end{tabular}\end{table}

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Learning convergence speed with and without CP (PASCAL VOC dataset)

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2204.02710v1_train__df739213-2c9d-4928-ad0a-5d9f92dcc5b4

arxiv_table_to_tex

\begin{table}\begin{table}\centering\small\caption{The Diversified-Relevance scores for ColBERT and Mix-and-Match in our human study.}\begin{tabular}{|l|l|l|}\hline& \textbf{ColBERT } & \textbf{Mix and Match~} \\\hline\multicolumn{1}{|c|}{Diversified-Relevance (DR)} & \multicolumn{1}{c|}{0.25} & \multicolumn{1}{c|}{{\bf 0.35}} \\\hline\end{tabular}\label{tab:DR-scores}\end{table}

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The Diversified-Relevance scores for ColBERT and Mix-and-Match in our human study.

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2312.00414v2_train__fb503ac5-5326-440d-a17d-a50e13a00c27

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\caption{Comparison of models. DL-DKD uses CLIP-B/32$^\ast$ only in training phase to transfer VLM knowledge into visual and textual backbone.}\scalebox{0.5}{\begin{tabular}{c|c|c|cc|c|c}\hline& Model name & Resolution & Vision backbone & Text backbone & Parameters (M) & Image-level GFLOPs \\ \hline& MS-SL & 224 & I3D (+ResNet152) & RoBERTa & 433.3 & 40.0 \\& GMMFormer & 224 & I3D (+ResNet152) & RoBERTa & 441.3 & 40.0 \\& DL-DKD & 224 & I3D (+ResNet152, CLIP-B/32$^\ast$) & RoBERTa$^\dagger$ (+CLIP-B/32$^\ast$) & 439.0 & 40.0 (+8.8$^\ast$) \\\multirow{-4}{*}{lightweight SOTA} & MS-SL (B32) & 224 & \multicolumn{2}{c|}{CLIP-B/32} & 156.3 & 8.8 \\ \hline& MS-SL (L14) & 224 & \multicolumn{2}{c|}{CLIP-L/14} & 432.6 & 162.0 \\\multirow{-2}{*}{heavyweight SOTA} & MS-SL (L14-336) & 336 & \multicolumn{2}{c|}{CLIP-L/14-336} & 432.9 & 381.9 \\ \hline& QASIR-B32 & 224 & \multicolumn{2}{c|}{CLIP-B/32} & 151.3 & 8.8 \\& QASIR-L14 & 224 & \multicolumn{2}{c|}{CLIP-L/14} & 427.6 & 162.0 \\\multirow{-3}{*}{Zero-shot} & QASIR-L14-336 & 336 & \multicolumn{2}{c|}{CLIP-L/14-336} & 427.9 & 381.9 \\ \hline& QASIR-B32 & 224 & \multicolumn{2}{c|}{CLIP-B/32} & 154.7 & 8.8 \\& QASIR-L14 & 224 & \multicolumn{2}{c|}{CLIP-L/14} & 431.0 & 162.0 \\\multirow{-3}{*}{Fine-tuned} & QASIR-L14-336 & 336 & \multicolumn{2}{c|}{CLIP-L/14-336} & 431.3 & 381.9 \\ \hline\end{tabular}}\label{tab:model_comparison}\end{table*}

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Comparison of models. DL-DKD uses CLIP-B/32$^\ast$ only in training phase to transfer VLM knowledge into visual and textual backbone.

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2312.00414v2_train__d63093c6-0831-4185-ba57-938d1f424a8b

arxiv_table_to_tex

\begin{table*}[t]\begin{table*}[t]\centering\caption{Fine-tuning QASIR performance on benchmark datasets.}\scalebox{0.57}{\begin{tabular}{lcccccccccccccccccc}\hline\rowcolor[HTML]{EFEFEF}\multicolumn{1}{l|}{\cellcolor[HTML]{EFEFEF}} & \multicolumn{6}{c|}{\cellcolor[HTML]{EFEFEF}ActivityNet Captions} & \multicolumn{6}{c|}{\cellcolor[HTML]{EFEFEF}TVR} & \multicolumn{6}{c}{\cellcolor[HTML]{EFEFEF}Charades-STA} \\ \hline\multicolumn{1}{c|}{} & GFLOPs & R@1 & R@5 & R@10 & R@100 & \multicolumn{1}{c|}{sumR} & GFLOPs & R@1 & R@5 & R@10 & R@100 & \multicolumn{1}{c|}{sumR} & GFLOPs & R@1 & R@5 & R@10 & R@100 & sumR \\ \hline\multicolumn{1}{c|}{MS-SL} & 3.4$\times$10$^3$ & 7.1 & 22.5 & 34.7 & 75.8 & \multicolumn{1}{c|}{140.1} & 4.6$\times$10$^4$ & 13.5 & 32.1 & 43.4 & 83.4 & \multicolumn{1}{c|}{172.4} & 1.3$\times$10$^3$ & 1.8 & 7.1 & 11.8 & 47.7 & 68.4 \\\multicolumn{1}{c|}{GMMFormer} & 3.4$\times$10$^3$ & 8.3 & 24.9 & 36.7 & 76.1 & \multicolumn{1}{c|}{146.0} & 4.6$\times$10$^4$ & 13.9 & 33.3 & 44.5 & 84.9 & \multicolumn{1}{c|}{176.6} & 1.3$\times$10$^3$ & 2.1 & 7.8 & 12.5 & 50.6 & 72.9 \\\multicolumn{1}{c|}{DL-DKD} & 3.4$\times$10$^3$ & 8.0 & 25.0 & 37.5 & 77.1 & \multicolumn{1}{c|}{147.6} & 4.6$\times$10$^4$ & 14.4 & 34.9 & 45.8 & 84.9 & \multicolumn{1}{c|}{179.9} & - & - & - & - & - & - \\\multicolumn{1}{c|}{MS-SL (B32)} & 5.4$\times$10$^2$ & 11.7 & 31.2 & 43.5 & 81.7 & \multicolumn{1}{c|}{168.1} & 2.0$\times$10$^3$ & 17.5 & 39.5 & 51.3 & 88.3 & \multicolumn{1}{c|}{196.6} & 2.8$\times$10$^2$ & 1.2 & 4.4 & 7.6 & 41.5 & 54.7 \\\multicolumn{1}{c|}{MS-SL (L14)} & 9.8$\times$10$^3$ & 14.8 & 36.6 & 50.3 & 84.8 & \multicolumn{1}{c|}{186.5} & 3.7$\times$10$^4$ & 22.0 & 46.2 & 58.0 & 91.1 & \multicolumn{1}{c|}{217.3} & 5.0$\times$10$^3$ & 1.7 & 7.1 & 12.0 & 54.4 & 75.2 \\\multicolumn{1}{c|}{MS-SL (L14-336)} & 2.3$\times$10$^4$ & 14.2 & 36.9 & 50.4 & 85.2 & \multicolumn{1}{c|}{186.7} & 8.7$\times$10$^4$ & 24.7 & 49.3 & 60.6 & 92.0 & \multicolumn{1}{c|}{226.6} & 1.1$\times$10$^4$ & 2.3 & 8.6 & 14.1 & 57.6 & 82.6 \\ \hline\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}QASIR-B32} \\\multicolumn{1}{c|}{$1\times1$} & 5.4$\times$10$^2$ & \textbf{14.1} & \textbf{32.9} & \textbf{44.5} & 79.9 & \multicolumn{1}{c|}{\textbf{171.4}} & 2.0$\times$10$^3$ & \textbf{19.0} & \textbf{39.9} & \textbf{50.4} & \textbf{87.2} & \multicolumn{1}{c|}{\textbf{196.5}} & 2.8$\times$10$^2$ & \textbf{1.9} & \textbf{5.8} & \textbf{10.1} & \textbf{40.0} & \textbf{57.8} \\\multicolumn{1}{c|}{$2\times2$} & 1.4$\times$10$^2$ & 13.2 & 31.7 & 43.1 & \textbf{80.0} & \multicolumn{1}{c|}{167.9} & 5.1$\times$10$^2$ & 15.8 & 34.7 & 45.5 & 84.5 & \multicolumn{1}{c|}{180.4} & 7.7$\times$10$^1$ & 1.3 & 4.9 & 8.6 & 35.5 & 50.3 \\\multicolumn{1}{c|}{$3\times3$} & 6.9$\times$10$^1$ & 10.7 & 26.8 & 36.9 & 75.0 & \multicolumn{1}{c|}{149.3} & 2.3$\times$10$^2$ & 11.6 & 28.5 & 38.5 & 80.0 & \multicolumn{1}{c|}{158.7} & 4.0$\times$10$^1$ & 0.9 & 4.1 & 6.7 & 28.3 & 40.0 \\\multicolumn{1}{c|}{$4\times4$} & 4.3$\times$10$^1$ & 8.4 & 22.5 & 32.4 & 69.7 & \multicolumn{1}{c|}{133.0} & 1.3$\times$10$^2$ & 8.6 & 22.2 & 31.5 & 74.5 & \multicolumn{1}{c|}{136.8} & 2.7$\times$10$^1$ & 0.7 & 2.9 & 4.8 & 24.6 & 32.9 \\\multicolumn{1}{c|}{$5\times5$} & 3.1$\times$10$^1$ & 6.2 & 17.7 & 25.8 & 62.1 & \multicolumn{1}{c|}{111.9} & 9.0$\times$10$^1$ & 6.3 & 17.7 & 25.6 & 68.8 & \multicolumn{1}{c|}{118.4} & 2.1$\times$10$^1$ & 0.4 & 2.0 & 3.4 & 19.8 & 25.6 \\\multicolumn{1}{c|}{$6\times6$} & 2.5$\times$10$^1$ & 4.8 & 14.0 & 20.8 & 55.2 & \multicolumn{1}{c|}{94.7} & 6.6$\times$10$^1$ & 4.8 & 13.7 & 21.0 & 63.3 & \multicolumn{1}{c|}{102.8} & 1.5$\times$10$^1$ & 0.5 & 1.8 & 3.1 & 18.3 & 23.7 \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}QASIR-L14} \\\multicolumn{1}{c|}{$1\times1$} & 9.8$\times$10$^3$ & \textbf{18.9} & \textbf{41.0} & \textbf{53.2} & \textbf{84.8} & \multicolumn{1}{c|}{\textbf{197.9}} & 3.7$\times$10$^4$ & \textbf{23.6} & \textbf{47.0} & \textbf{56.5} & \textbf{89.0} & \multicolumn{1}{c|}{\textbf{216.1}} & 5.0$\times$10$^3$ & \textbf{3.0} & \textbf{11.2} & \textbf{17.4} & \textbf{55.7} & \textbf{87.2} \\\multicolumn{1}{c|}{$2\times2$} & 2.5$\times$10$^3$ & 18.2 & 39.6 & 52.2 & \textbf{84.8} & \multicolumn{1}{c|}{194.9} & 9.2$\times$10$^3$ & 23.0 & 45.4 & 56.3 & 88.9 & \multicolumn{1}{c|}{213.6} & 1.3$\times$10$^3$ & 2.7 & 9.3 & 14.9 & 49.1 & 76.0 \\\multicolumn{1}{c|}{$3\times3$} & 1.1$\times$10$^3$ & 16.5 & 37.5 & 49.9 & 83.2 & \multicolumn{1}{c|}{187.1} & 4.1$\times$10$^3$ & 21.0 & 42.5 & 54.0 & 88.4 & \multicolumn{1}{c|}{205.8} & 6.4$\times$10$^2$ & 2.0 & 7.9 & 12.2 & 43.3 & 65.3 \\\multicolumn{1}{c|}{$4\times4$} & 7.0$\times$10$^2$ & 14.1 & 33.8 & 45.6 & 80.4 & \multicolumn{1}{c|}{174.0} & 2.3$\times$10$^3$ & 16.3 & 35.7 & 46.4 & 84.6 & \multicolumn{1}{c|}{182.9} & 4.0$\times$10$^2$ & 1.8 & 6.3 & 9.6 & 36.8 & 54.4 \\\multicolumn{1}{c|}{$5\times5$} & 4.8$\times$10$^2$ & 12.5 & 30.3 & 41.8 & 78.1 & \multicolumn{1}{c|}{162.8} & 1.5$\times$10$^3$ & 13.5 & 31.7 & 42.0 & 81.6 & \multicolumn{1}{c|}{168.9} & 3.0$\times$10$^2$ & 1.3 & 4.2 & 6.9 & 31.1 & 43.4 \\\multicolumn{1}{c|}{$6\times6$} & 3.7$\times$10$^2$ & 10.7 & 27.2 & 37.8 & 75.2 & \multicolumn{1}{c|}{150.9} & 1.1$\times$10$^3$ & 12.0 & 27.8 & 37.7 & 78.9 & \multicolumn{1}{c|}{156.4} & 1.9$\times$10$^2$ & 1.2 & 3.7 & 6.2 & 27.2 & 38.3 \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}QASIR-L14-336} \\\multicolumn{1}{c|}{$1\times1$} & 2.3$\times$10$^4$ & \textbf{19.7} & 41.4 & \textbf{53.9} & 85.1 & \multicolumn{1}{c|}{\textbf{200.1}} & 8.7$\times$10$^4$ & \textbf{26.9} & \textbf{50.6} & 60.7 & \textbf{91.4} & \multicolumn{1}{c|}{229.6} & 1.1$\times$10$^4$ & 3.1 & \textbf{10.8} & \textbf{17.3} & \textbf{57.0} & \textbf{88.2} \\\multicolumn{1}{c|}{$2\times2$} & 5.9$\times$10$^3$ & 19.3 & \textbf{41.5} & 53.8 & \textbf{85.3} & \multicolumn{1}{c|}{200.0} & 2.1$\times$10$^4$ & 26.7 & \textbf{50.6} & \textbf{61.4} & \textbf{91.4} & \multicolumn{1}{c|}{\textbf{230.1}} & 3.1$\times$10$^3$ & \textbf{3.3} & 10.6 & 17.0 & 55.2 & 86.0 \\\multicolumn{1}{c|}{$3\times3$} & 2.7$\times$10$^3$ & 18.7 & 40.6 & 52.7 & 84.4 & \multicolumn{1}{c|}{196.4} & 9.8$\times$10$^3$ & 24.2 & 47.2 & 58.3 & 89.9 & \multicolumn{1}{c|}{219.6} & 1.4$\times$10$^3$ & 2.6 & 9.0 & 15.2 & 51.3 & 78.1 \\\multicolumn{1}{c|}{$4\times4$} & 1.6$\times$10$^3$ & 16.8 & 38.1 & 50.0 & 83.4 & \multicolumn{1}{c|}{188.2} & 5.6$\times$10$^3$ & 21.6 & 43.3 & 54.3 & 88.7 & \multicolumn{1}{c|}{208.0} & 9.3$\times$10$^2$ & 2.3 & 7.1 & 11.9 & 44.3 & 65.6 \\\multicolumn{1}{c|}{$5\times5$} & 1.1$\times$10$^3$ & 15.3 & 35.6 & 47.4 & 82.0 & \multicolumn{1}{c|}{180.3} & 3.6$\times$10$^3$ & 19.0 & 39.4 & 49.7 & 86.0 & \multicolumn{1}{c|}{194.1} & 7.0$\times$10$^2$ & 2.0 & 6.5 & 10.6 & 39.7 & 58.9 \\\multicolumn{1}{c|}{$6\times6$} & 8.4$\times$10$^2$ & 13.6 & 33.0 & 44.9 & 80.0 & \multicolumn{1}{c|}{171.5} & 2.6$\times$10$^3$ & 15.9 & 35.0 & 45.2 & 83.5 & \multicolumn{1}{c|}{179.5} & 4.4$\times$10$^2$ & 1.4 & 5.1 & 8.4 & 35.4 & 50.3 \\\hline\end{tabular}}\label{tab:fine_tuned_overall}\end{table*}

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Fine-tuning QASIR performance on benchmark datasets.

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2312.00414v2_train__6721cc01-9f5a-4105-922f-14feab149784

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\caption{Comparison of super images with other reduce-then-encode methods: sparse sampling \cite{lei2021cvpr}, MGSampler \cite{Zhi_2021_ICCV}, and PMISampler \cite{Xian_2024_WACV}.}\scalebox{0.54}{\begin{tabular}{ccccccccccccccccccc}\hline\rowcolor[HTML]{EFEFEF}\multicolumn{1}{c|}{\cellcolor[HTML]{EFEFEF}} & \multicolumn{6}{c|}{\cellcolor[HTML]{EFEFEF}ActivityNet Captions} & \multicolumn{6}{c|}{\cellcolor[HTML]{EFEFEF}TVR} & \multicolumn{6}{c}{\cellcolor[HTML]{EFEFEF}Charades-STA} \\ \hline\multicolumn{1}{c|}{} & GFLOPs & R@1 & R@5 & R@10 & R@100 & \multicolumn{1}{c|}{sumR} & GFLOPs & R@1 & R@5 & R@10 & R@100 & \multicolumn{1}{c|}{sumR} & GFLOPs & R@1 & R@5 & R@10 & R@100 & sumR \\ \hline\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}2$\times$2 setting (average \#Frames: 15.5/57.7/8.1 on ActivityNet Captions/TVR/Charades-STA)} \\\multicolumn{1}{c|}{Sparse sampling} & & 18.0 & 39.4 & 51.6 & 83.7 & \multicolumn{1}{c|}{192.7} & & \textbf{27.1} & 49.6 & 60.1 & 91.3 & \multicolumn{1}{c|}{228.2} & & \textbf{3.3} & \textbf{11.0} & 16.2 & 54.0 & 84.5 \\\multicolumn{1}{c|}{MGSampler} & & 18.1 & 39.5 & 51.6 & 83.5 & \multicolumn{1}{c|}{192.7} & & 26.7 & 49.9 & 60.4 & 90.9 & \multicolumn{1}{c|}{227.9} & & 3.0 & 9.7 & 15.2 & 54.5 & 82.3 \\\multicolumn{1}{c|}{PMISampler} & & 17.9 & 39.3 & 51.5 & 83.7 & \multicolumn{1}{c|}{192.6} & & 26.9 & \textbf{50.6} & 60.7 & 91.1 & \multicolumn{1}{c|}{229.4} & & 3.0 & 10.1 & 16.0 & 53.3 & 82.4 \\\multicolumn{1}{c|}{Super images} & \multirow{-4}{*}{5.9$\times$10$^3$} & \textbf{19.3} & \textbf{41.5} & \textbf{53.8} & \textbf{85.3} & \multicolumn{1}{c|}{\textbf{200.0}} & \multirow{-4}{*}{2.1$\times$10$^4$} & 26.7 & \textbf{50.6} & \textbf{61.4} & \textbf{91.4} & \multicolumn{1}{c|}{\textbf{230.1}} & \multirow{-4}{*}{3.1$\times$10$^3$} & \textbf{3.3} & 10.6 & \textbf{17.0} & \textbf{55.2} & \textbf{86.0} \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}3$\times$3 setting (average \#Frames: 7.1/23.9/3.9 on ActivityNet Captions/TVR/Charades-STA)} \\\multicolumn{1}{c|}{Sparse sampling} & & 15.8 & 35.4 & 47.2 & 80.1 & \multicolumn{1}{c|}{178.5} & & \textbf{25.3} & \textbf{47.4} & 57.3 & 89.4 & \multicolumn{1}{c|}{219.4} & & 2.2 & 7.8 & 12.7 & 45.9 & 68.6 \\\multicolumn{1}{c|}{MGSampler} & & 15.7 & 35.7 & 47.3 & 80.4 & \multicolumn{1}{c|}{179.2} & & 23.7 & 45.7 & 56.2 & 88.1 & \multicolumn{1}{c|}{213.7} & & 2.3 & 7.7 & 12.5 & 46.9 & 69.4 \\\multicolumn{1}{c|}{PMISampler} & & 15.9 & 35.7 & 47.5 & 80.7 & \multicolumn{1}{c|}{179.8} & & 23.8 & 45.2 & 55.5 & 88.0 & \multicolumn{1}{c|}{212.6} & & 2.4 & 7.6 & 12.8 & 46.7 & 69.6 \\\multicolumn{1}{c|}{Super images} & \multirow{-4}{*}{2.7$\times$10$^3$} & \textbf{18.7} & \textbf{40.6} & \textbf{52.7} & \textbf{84.4} & \multicolumn{1}{c|}{\textbf{196.4}} & \multirow{-4}{*}{9.8$\times$10$^3$} & 24.2 & 47.2 & \textbf{58.3} & \textbf{89.9} & \multicolumn{1}{c|}{\textbf{219.6}} & \multirow{-4}{*}{1.4$\times$10$^3$} & \textbf{2.6} & \textbf{9.0} & \textbf{15.2} & \textbf{51.3} & \textbf{78.1} \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}4$\times$4 setting (average \#Frames: 4.2/14.8/2.4 on ActivityNet Captions/TVR/Charades-STA)} \\\multicolumn{1}{c|}{Sparse sampling} & & 13.2 & 30.9 & 41.8 & 74.8 & \multicolumn{1}{c|}{160.7} & & \textbf{22.8} & 43.2 & 53.5 & 86.7 & \multicolumn{1}{c|}{206.1} & & 1.8 & 6.3 & 10.9 & 40.5 & 59.6 \\\multicolumn{1}{c|}{MGSampler} & & 10.4 & 31.9 & 43.7 & 77.1 & \multicolumn{1}{c|}{166.3} & & 21.8 & 42.7 & 52.6 & 85.8 & \multicolumn{1}{c|}{202.8} & & 1.8 & 6.9 & 11.3 & 39.1 & 59.1 \\\multicolumn{1}{c|}{PMISampler} & & 13.7 & 32.0 & 43.3 & 77.0 & \multicolumn{1}{c|}{166.0} & & 22.4 & 43.1 & 53.3 & 86.7 & \multicolumn{1}{c|}{205.6} & & 1.8 & 6.6 & 10.8 & 39.4 & 58.6 \\\multicolumn{1}{c|}{Super images} & \multirow{-4}{*}{1.6$\times$10$^3$} & \textbf{16.8} & \textbf{38.1} & \textbf{50.0} & \textbf{83.4} & \multicolumn{1}{c|}{\textbf{188.2}} & \multirow{-4}{*}{5.6$\times$10$^3$} & 21.6 & \textbf{43.3} & \textbf{54.3} & \textbf{88.7} & \multicolumn{1}{c|}{\textbf{208.0}} & \multirow{-4}{*}{9.3$\times$10$^2$} & \textbf{2.3} & \textbf{7.1} & \textbf{11.9} & \textbf{44.3} & \textbf{65.6} \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}5$\times$5 setting (average \#Frames: 2.9/9.6/1.8 on ActivityNet Captions/TVR/Charades-STA)} \\\multicolumn{1}{c|}{Sparse sampling} & & 11.3 & 26.7 & 36.3 & 66.4 & \multicolumn{1}{c|}{140.7} & & \textbf{19.4} & 38.7 & 48.7 & 83.1 & \multicolumn{1}{c|}{189.9} & & 1.6 & \textbf{6.6} & 10.0 & 35.1 & 53.2 \\\multicolumn{1}{c|}{MGSampler} & & 12.2 & 28.7 & 38.8 & 70.7 & \multicolumn{1}{c|}{150.3} & & 19.1 & 38.6 & 48.7 & 83.0 & \multicolumn{1}{c|}{189.4} & & 1.9 & 6.5 & 10.0 & 34.3 & 52.6 \\\multicolumn{1}{c|}{PMISampler} & & 12.0 & 28.6 & 39.0 & 70.6 & \multicolumn{1}{c|}{150.3} & & 19.3 & 38.2 & 48.0 & 83.0 & \multicolumn{1}{c|}{188.5} & & 1.8 & 6.3 & 10.2 & 34.6 & 52.8 \\\multicolumn{1}{c|}{Super images} & \multirow{-4}{*}{1.1$\times$10$^3$} & \textbf{15.3} & \textbf{35.6} & \textbf{47.4} & \textbf{82.0} & \multicolumn{1}{c|}{\textbf{180.3}} & \multirow{-4}{*}{3.6$\times$10$^3$} & 19.0 & \textbf{39.4} & \textbf{49.7} & \textbf{86.0} & \multicolumn{1}{c|}{\textbf{194.1}} & \multirow{-4}{*}{7.0$\times$10$^2$} & \textbf{2.0} & 6.5 & \textbf{10.6} & \textbf{39.7} & \textbf{58.9} \\\rowcolor[HTML]{EFEFEF}\multicolumn{19}{l}{\cellcolor[HTML]{EFEFEF}6$\times$6 setting (average \#Frames: 2.1/6.8/1.1 on ActivityNet Captions/TVR/Charades-STA)} \\\multicolumn{1}{c|}{Sparse sampling} & & 9.6 & 22.7 & 30.7 & 57.1 & \multicolumn{1}{c|}{120.2} & & 16.2 & 33.6 & 42.8 & 79.6 & \multicolumn{1}{c|}{172.2} & & 1.8 & 5.9 & 10.1 & \textbf{34.7} & 52.6 \\\multicolumn{1}{c|}{MGSampler} & & 10.8 & 25.4 & 34.7 & 63.2 & \multicolumn{1}{c|}{134.1} & & \textbf{17.1} & 33.7 & 42.8 & 78.6 & \multicolumn{1}{c|}{172.3} & & 1.8 & \textbf{6.6} & \textbf{10.2} & 33.9 & 52.5 \\\multicolumn{1}{c|}{PMISampler} & & 10.3 & 25.1 & 34.2 & 62.9 & \multicolumn{1}{c|}{132.6} & & 16.7 & 33.9 & 42.8 & 78.4 & \multicolumn{1}{c|}{171.8} & & \textbf{1.9} & 6.3 & 9.9 & \textbf{34.7} & \textbf{52.9} \\\multicolumn{1}{c|}{Super images} & \multirow{-4}{*}{8.4$\times$10$^2$} & \textbf{13.6} & \textbf{33.0} & \textbf{44.9} & \textbf{80.0} & \multicolumn{1}{c|}{\textbf{171.5}} & \multirow{-4}{*}{2.6$\times$10$^3$} & 15.9 & \textbf{35.0} & \textbf{45.2} & \textbf{83.5} & \multicolumn{1}{c|}{\textbf{179.5}} & \multirow{-4}{*}{4.4$\times$10$^2$} & 1.4 & 5.1 & 8.4 & 35.4 & 50.3 \\ \hline\end{tabular}}\label{fig:performance_change_other_sampling}\end{table}

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Comparison of super images with other reduce-then-encode methods: sparse sampling \cite{lei2021cvpr

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2312.00414v2_train__64b26da4-b62d-478d-92e3-5edde19572ae

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\caption{Zero-shot retrieval performance on each TV show. We use the $2\times2$ QASIR-L14-336 as our base model.}\begin{tabular}{ccccccc}\hline\rowcolor[HTML]{EFEFEF}& \multicolumn{6}{c}{\cellcolor[HTML]{EFEFEF}TVR} \\ \hlineTV show title & \#Videos & R@1 & R@5 & R@10 & R@100 & sumR \\ \hlineThe Big Bang Theory & 2,155 & 22.6 & 42.6 & 53.1 & 84.4 & 202.7 \\How I Met Your Mother & 745 & 24.8 & 43.4 & 54.6 & 87.2 & 210.1 \\Friends & 2,800 & 19.5 & 36.8 & 46.4 & 81.0 & 183.8 \\Grey's Anatomy & 520 & 15.9 & 32.1 & 40.2 & 78.1 & 166.3 \\House & 2,310 & 11.9 & 24.3 & 31.6 & 66.0 & 133.9 \\Castle & 2,365 & 12.4 & 26.6 & 33.8 & 68.7 & 141.5 \\ \hlineTotal & 10,835 & 17.2 & 33.3 & 42.1 & 76.1 & 168.7 \\ \hline\end{tabular}\label{tab:tvshow_results}\end{table}

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Zero-shot retrieval performance on each TV show. We use the $2\times2$ QASIR-L14-336 as our base model.

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2401.06144v2_train__a10068fc-5361-4c00-8557-65d4c294dca4

arxiv_table_to_tex

\begin{table}[ht]\begin{table}[ht]\begin{center}\begin{tabular}{ |p{0.2\linewidth}|c c c|c c| }\hline& 32x32 & 64x64 & 96x96 & 128x128 & 160x160 \\\hline\hlinePre-trained Model & 1.47 & 2.92 & 4.96 & 7.85 & 14.8 \\\hlineVanilla fine-tune ($w_R = 1.0$) & 20.92 & 12.94 & 14.96 & 32.21 & 27.1 \\\hlineMix w/ $w_R = 0.2$ & 1.41 & \textbf{2.44} & 4.66 & 7.69 & 12.4 \\\hlineFrozen spatial conv & 1.46 & 2.85 & 4.76 & 7.62 & 11.9 \\\hlineFrozen spatial conv + $w_R = 0.2$ & \textbf{1.36} & 2.46 & \textbf{4.54} & \textbf{7.06} & \textbf{11.3} \\\hline\end{tabular}\end{center}\caption{FIDs on FFHQ across resolutions for different fine-tuning schemes. Our best result combines mixed resolution fine-tuning and parameter freezing.}\label{table:finetuned-fids}\end{table}

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FIDs on FFHQ across resolutions for different fine-tuning schemes. Our best result combines mixed resolution fine-tuning and parameter freezing.

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2203.10965v4_train__d4013423-5df4-4233-8379-b6d7f72f403f

arxiv_table_to_tex

\begin{table}[h]\begin{table}[h]\vspace{-2mm}\centering\caption{Comparison of all variants of \toolname with a triplet architecture and the baseline approach Post2Vec.}\vspace{-2mm}\label{tab:all_results}\begin{tabular}{c|ccccc}\hline\multirow{2}{*}{Model Name} & \multicolumn{5}{c}{Precision@k} \\ \cline{2-6}& \multicolumn{1}{c|}{P@1} & \multicolumn{1}{c|}{P@2} & \multicolumn{1}{c|}{P@3} & \multicolumn{1}{c|}{P@4} & P@5 \\ \hline\textbf{CodeBERT$_{ALL}$} & \multicolumn{1}{c|}{\textbf{0.848}} & \multicolumn{1}{c|}{\textbf{0.701}} & \multicolumn{1}{c|}{\textbf{0.579}} & \multicolumn{1}{c|}{\textbf{0.486}} & \textbf{0.415} \\ \hlineBERT$_{ALL}$ & \multicolumn{1}{c|}{0.845} & \multicolumn{1}{c|}{0.696} & \multicolumn{1}{c|}{0.575} & \multicolumn{1}{c|}{0.482} & 0.413 \\ \hlineRoBERTa$_{ALL}$ & \multicolumn{1}{c|}{0.843} & \multicolumn{1}{c|}{0.694} & \multicolumn{1}{c|}{0.571} & \multicolumn{1}{c|}{0.478} & 0.409 \\ \hlineBERTOverflow$_{ALL}$ & \multicolumn{1}{c|}{0.725} & \multicolumn{1}{c|}{0.592} & \multicolumn{1}{c|}{0.489} & \multicolumn{1}{c|}{0.412} & 0.354 \\ \hlineALBERT$_{ALL}$ & \multicolumn{1}{c|}{0.748} & \multicolumn{1}{c|}{0.586} & \multicolumn{1}{c|}{0.469} & \multicolumn{1}{c|}{0.386} & 0.327 \\ \hlinePost2Vec & \multicolumn{1}{c|}{0.786} & \multicolumn{1}{c|}{0.628} & \multicolumn{1}{c|}{0.507} & \multicolumn{1}{c|}{0.421} & 0.359 \\ \hline \hline\multirow{2}{*}{Model Name} & \multicolumn{5}{c}{Recall@k} \\ \cline{2-6}& \multicolumn{1}{c|}{R@1} & \multicolumn{1}{c|}{R@2} & \multicolumn{1}{c|}{R@3} & \multicolumn{1}{c|}{R@4} & R@5 \\ \hline\textbf{CodeBERT$_{ALL}$} & \multicolumn{1}{c|}{\textbf{0.848}} & \multicolumn{1}{c|}{\textbf{0.756}} & \multicolumn{1}{c|}{\textbf{0.724}} & \multicolumn{1}{c|}{\textbf{0.733}} & \textbf{0.757} \\ \hlineBERT$_{ALL}$ & \multicolumn{1}{c|}{0.845} & \multicolumn{1}{c|}{0.750} & \multicolumn{1}{c|}{0.719} & \multicolumn{1}{c|}{0.728} & 0.752 \\ \hlineRoBERTa$_{ALL}$ & \multicolumn{1}{c|}{0.843} & \multicolumn{1}{c|}{0.747} & \multicolumn{1}{c|}{0.714} & \multicolumn{1}{c|}{0.722} & 0.746 \\ \hlineBERTOverflow$_{ALL}$ & \multicolumn{1}{c|}{0.725} & \multicolumn{1}{c|}{0.635} & \multicolumn{1}{c|}{0.607} & \multicolumn{1}{c|}{0.619} & 0.644 \\ \hlineALBERT$_{ALL}$ & \multicolumn{1}{c|}{0.748} & \multicolumn{1}{c|}{0.630} & \multicolumn{1}{c|}{0.588} & \multicolumn{1}{c|}{0.588} & 0.605 \\ \hlinePost2Vec & \multicolumn{1}{c|}{0.786} & \multicolumn{1}{c|}{0.678} & \multicolumn{1}{c|}{0.636} & \multicolumn{1}{c|}{0.639} & 0.659 \\ \hline \hline\multirow{2}{*}{Model Name} & \multicolumn{5}{c}{F1-score@k} \\ \cline{2-6}& \multicolumn{1}{c|}{F@1} & \multicolumn{1}{c|}{F@2} & \multicolumn{1}{c|}{F@3} & \multicolumn{1}{c|}{F@4} & F@5 \\ \hline\textbf{CodeBERT$_{ALL}$} & \multicolumn{1}{c|}{\textbf{0.848}} & \multicolumn{1}{c|}{\textbf{0.719}} & \multicolumn{1}{c|}{\textbf{0.625}} & \multicolumn{1}{c|}{\textbf{0.561}} & \textbf{0.513} \\ \hlineBERT$_{ALL}$ & \multicolumn{1}{c|}{0.845} & \multicolumn{1}{c|}{0.714} & \multicolumn{1}{c|}{0.621} & \multicolumn{1}{c|}{0.557} & 0.510 \\ \hlineRoBERTa$_{ALL}$ & \multicolumn{1}{c|}{0.843} & \multicolumn{1}{c|}{0.711} & \multicolumn{1}{c|}{0.617} & \multicolumn{1}{c|}{0.553} & 0.505 \\ \hlineBERTOverflow$_{ALL}$ & \multicolumn{1}{c|}{0.725} & \multicolumn{1}{c|}{0.606} & \multicolumn{1}{c|}{0.527} & \multicolumn{1}{c|}{0.475} & 0.427 \\ \hlineALBERT$_{ALL}$ & \multicolumn{1}{c|}{0.748} & \multicolumn{1}{c|}{0.600} & \multicolumn{1}{c|}{0.506} & \multicolumn{1}{c|}{0.447} & 0.406 \\ \hlinePost2Vec & \multicolumn{1}{c|}{0.786} & \multicolumn{1}{c|}{0.646} & \multicolumn{1}{c|}{0.549} & \multicolumn{1}{c|}{0.488} & 0.445 \\ \hline\end{tabular}\vspace{-4mm}\end{table}

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Comparison of all variants of \toolname with a triplet architecture and the baseline approach Post2Vec.

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2210.11532v1_train__149078bb-8d39-4915-baae-7a773e0d4ad5

arxiv_table_to_tex

\begin{table*}[!th]\begin{table*}[!th]\centering\caption{List of 10 stocks randomly selected [source \url{it.finance.yahoo.com}].}\label{tab:vol_feats}\begin{tabular}{|l|l|l|}\hline\multicolumn{1}{|c|}{\textbf{Ticker}} & \multicolumn{1}{c|}{\textbf{Company}} & \multicolumn{1}{c|}{\textbf{Market}} \\ \hlineCSGKF & \multicolumn{1}{c|}{Credit Suisse Group AG} & \multicolumn{1}{c|}{Other OTC} \\ \hlineEOG & \multicolumn{1}{c|}{EOG Resources, Inc.} & \multicolumn{1}{c|}{NYSE} \\ \hlineMETA & \multicolumn{1}{c|}{Meta Platforms, Inc. } & \multicolumn{1}{c|}{Nasdaq GS} \\ \hlineNKE & \multicolumn{1}{c|}{NIKE, Inc.} & \multicolumn{1}{c|}{NYSE} \\ \hlineDIS & \multicolumn{1}{c|}{The Walt Disney Company} & \multicolumn{1}{c|}{NYSE} \\ \hlinePG & \multicolumn{1}{c|}{The Procter \& Gamble Company} & \multicolumn{1}{c|}{NYSE} \\ \hlineQQQ & \multicolumn{1}{c|}{Invesco QQQ Trust} & \multicolumn{1}{c|}{Nasdaq GM} \\ \hlineIBM & \multicolumn{1}{c|}{International Business Machines Corporation} & \multicolumn{1}{c|}{NYSE} \\ \hlineANF & \multicolumn{1}{c|}{Abercrombie \& Fitch Co.} & \multicolumn{1}{c|}{NYSE} \\ \hlineCS & \multicolumn{1}{c|}{Credit Suisse Group AG} & \multicolumn{1}{c|}{NYSE} \\ \hline\end{tabular}\end{table*}

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List of 10 stocks randomly selected [source \url{it.finance.yahoo.com

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2210.11532v1_train__30137258-4cfd-4703-8f15-b29080ecbe3e

arxiv_table_to_tex

\begin{table}[!ht]\begin{table}[!ht]\centering\caption{ADF test stationarity with AIC optimization.}\label{tab:adf-test}\begin{tabular}{l|c|c|c|c|ccc|}\cline{2-8}& \textbf{Test Statistic} & \textbf{p-value} & \textbf{Lags} & \textbf{Observations} & \multicolumn{3}{c|}{\textbf{Critical Value}} \\ \cline{6-8}& & & & & \multicolumn{1}{c|}{\textbf{1\%}} & \multicolumn{1}{c|}{\textbf{5\%}} & \textbf{10\%} \\ \hline\multicolumn{1}{|l|}{\textit{ANF}} & -2.302 & 0.171 & 5 & 2529 & \multicolumn{1}{c|}{-3.432} & \multicolumn{1}{c|}{-2.863} & -2.567 \\ \hline\multicolumn{1}{|l|}{\textit{EOG}} & -2.422 & 0.135 & 5 & 2529 & \multicolumn{1}{c|}{-3.433} & \multicolumn{1}{c|}{-2.862} & -2.567 \\ \hline\end{tabular}\end{table}

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ADF test stationarity with AIC optimization.

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2101.05806v1_train__bd3cc7a9-dd56-4fdc-b01b-36c769372a76

arxiv_table_to_tex

\begin{table*}[ht]\begin{table*}[ht]\centering\begin{tabu}{|l|c c c c|}\tabucline[1pt]{-}\hspace{1.7cm} \textbf{Features} & \textbf{B@4} & \textbf{R} & \textbf{M} & \textbf{C} \\\tabucline[1.2pt]{-}ResNet-152 & 0.473 & 0.677 & 0.329 & 77.15 \\Inception-v4 & 0.499 & 0.679 & 0.327 & 81.96 \\\hlineI3D & 0.437 & 0.678 & 0.314 & 69.24 \\R(2+1)D & 0.504 & 0.700 & 0.336 & 82.41 \\\hlineFaster-RCNN & 0.247 & 0.525 & 0.209 & 60.76 \\\hlineI3D + Faster-RCNN & 0.453 & 0.675 & 0.318 & 69.62 \\I3D + ResNet-152 & 0.478 & 0.699 & 0.337 & 81.86 \\\hlineInception-v4 + Faster-RCNN & 0.492 & 0.688 & 0.334 & 83.36 \\% Inception-v4 + C3D & 0.460 & 0.676 & 0.324 & 78.16 \\Inception-v4 + R(2+1)D & 0.510 & 0.714 & \textbf{0.345} & 88.88 \\%old% Inception-v4 + I3D & \textbf{0.502} & \textbf{0.708} & 0.330 & \textbf{85.57} \\Inception-v4 + I3D & 0.501 & \textbf{0.715} & 0.337 & 89.58 \\\hline% {'Bleu_1': 0.7736661619621461, 'Bleu_2': 0.6597869836261058, 'Bleu_3': 0.5629914922556372, 'Bleu_4': 0.46502848427303367, 'METEOR': 0.32497884042114666, 'ROUGE_L': 0.678% 0873091264125, 'CIDEr': 0.8113884523156315}Inception-v4 + I3D + Faster-RCNN & 0.465 & 0.678 & 0.325 & 81.14 \\% {'Bleu_1': 0.8130965003668075, 'Bleu_2': 0.7120395663677739, 'Bleu_3': 0.6236522919804935, 'Bleu_4': 0.5241551266873649, 'METEOR': 0.3380563761486914, 'ROUGE_L': 0.7126094288298294, 'CIDEr': 0.8626006249377787}% Inception-v4 + I3D + R(2+1)D & 0.524 & 0.713 & 0.338 & 86.26 \\Inception-v4 + R(2+1)D + Faster-RCNN & \textbf{0.511} & \textbf{0.715} & 0.344 & \textbf{90.93} \\\tabucline[1pt]{-}\end{tabu}\vspace{0.1cm}\caption{Comparison of captioning performance using different feature extractors benchmarked using WAFTM + WordPiece on the MSVD dataset.}\label{tab:comparing_features}\end{table*}

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Comparison of captioning performance using different feature extractors benchmarked using WAFTM + WordPiece on the MSVD dataset.

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2101.05806v1_train__05f401eb-c129-48c9-b0bc-6984aee7ba0f

arxiv_table_to_tex

\begin{table}[!ht]\begin{table}[!ht]\centering\begin{tabu}{|l|c|}\tabucline[1pt]{-}\hspace{0.8cm} \textbf{Architecture} & \textbf{M} \\ \tabucline[1pt]{-}% \footnotesize RecNet \cite{wang2018reconstruction} & \small \\ \hline\footnotesize Krishna et. al \cite{krishna2017dense} & \small 0.0888 \\ \hline\footnotesize Iashin et. al \cite{iashin2020better} & \small 0.0956 \\ \hline\footnotesize WAFTM + WordPiece + SCST & \small 0.0906 \\ \tabucline[1pt]{-}\end{tabu}\vspace{0.1cm}\caption{Results on ActivityNet Captions Dataset using ground-truth proposals and where each model is trained from scratch.}\label{tab:activitynet}\end{table}

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Results on ActivityNet Captions Dataset using ground-truth proposals and where each model is trained from scratch.

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2305.14427v2_train__4bee43bc-0268-485a-b187-1566a68c6889

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\begin{center}\begin{tabular}{|c|c|c|}\hline$n$ & $\langle \gamma^{(n)}_N(T)\rangle/T $ & $\langle s^{(n)}_N(T)\rangle/T$ \\\hline\hline0 & 0.0091 & 0.0434 \\1 & 0.0051 & 0.0086 \\2 & -0.0022 & -0.0165\\\hline\end{tabular}\caption{Coefficients in the momentum averaged rates at $T= 10^6$ GeV.}\label{tab:rates}\end{center}\end{table}

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Coefficients in the momentum averaged rates at $T= 10^6$ GeV.

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2305.14427v2_train__fe9ba078-2ea6-41f1-8082-7dcdaf018622

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\begin{center}\begin{tabular}{| c | c c c c c c c c |}\hlineRegime & $M/\rm{GeV}$ & $\log_{10}(y_{e})$ & $\log_{10}(y_{\mu})$ & $\log_{10}(y_{\tau})$ & $\log_{10}(y'_{\alpha})$ & $\Delta \varphi_e$ & $\Delta \varphi_\mu$ & $\Delta \varphi_\tau$ \\\hline\hline1 (wHC) & 1 & $-7.2$ & $-6$ & $-5.7$ & $-7.5$ & $\pi/2$ & $\pi/3$ & $\pi/4$ \\2 (sHC) & 100 & $-7.2$ & $-6$ & $-5.8$ & $-8$ & $\pi/2$ & $\pi/3$ & $\pi/4$ \\\hline\end{tabular}\caption{Model parameters for the comparison between the analytical and numerical solutions shown in Fig.~\ref{fig:ana_vs_num} for the regimes as labelled in Fig.~\ref{fig:regimes} and defined in Eqs.~\eqref{eq:define_regime_4}-\eqref{eq:define_regime_3}.}\label{tab:ana_vs_num_initial_condition}\end{center}\end{table}

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Model parameters for the comparison between the analytical and numerical solutions shown in Fig.~\ref{fig:ana_vs_num

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2305.14427v2_train__4445bfc9-a940-4729-b31f-37de0acb9a21

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\begin{center}\begin{tabular}{| c | c c c c | c |}\hline& $M^{\rm true}/\rm{GeV}$ & $(U_e^2)_{\rm true}$ & $(U_\mu^2)_{\rm true}$ & $(U_\tau^2)_{\rm true}$ & $\delta^{\rm true}/\rm{rad}$ \\\hline\hlineNH & $31.60$ & $2.843\times 10^{-12}$ & $ 1.087 \times 10^{-11} $ & $1.234 \times 10^{-11} $ & $ 5.396 $\\IH & $20.731$ & $3.291\times 10^{-11}$ & $ 4.823 \times 10^{-12} $ & $3.465 \times 10^{-12} $ & $5.402 $ \\\hline\end{tabular}\caption{Measurable neutrino parameters for two benchmark points that reproduce the baryon asymmetry.}\label{tab:potential_measure}\end{center}\end{table}

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Measurable neutrino parameters for two benchmark points that reproduce the baryon asymmetry.

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2105.12838v1_train__dab1d207-774e-485b-ad0d-c582f32283a5

arxiv_table_to_tex

\begin{table}[ht!]\begin{table}[ht!]\caption{The simulation-related parameters}\centering\scalebox{0.95}{\begin{tabular}{|c|c|}\hline\textbf{Parameter List} & \textbf{Values} \\ \hline{Total transmitted power at the WPT} & 10~dB\\ \hline{Total active transmit antenna at the WPT} & 64\\ \hlineThe distance of information receiver & $\rm d_{\rm info}=20$ m \\ \hlineThe distance of energy harvester & $\rm d_{\rm energy}=1$ m \\ \hlineAntenna spacing & $\lambda/2$ \\ \hlineOperation frequency & $2$ GHz \\ \hlineArray antenna gain & $15$ dBi \\ \hlinePath loss model & $128.1 + 37.6\log_{10}(d)$, d[km]\\ \hlineAngular offset’s standard deviation & $2^{\circ}$ \\ \hlineLog-normal shadowing’s standard deviation & $8$ dB \\ \hlineSubcarrier bandwidth & $15$ kHz \\ \hline{Obstacle cover ratio} & {$0-0.9$} \\ \hline{Obstacle radius} & [0.3, 0.6]\\ \hline{Obstacle height} & [5, 25]\\ \hline\end{tabular}}\label{tab:SimulationParameters}\end{table}

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The simulation-related parameters

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2012.14034v2_train__85e2a723-8d2f-447e-b1e2-e6bacfbdcf3b

arxiv_table_to_tex

\begin{table}[!htb]\begin{table}[!htb]\begin{center}%\scalebox{0.8}{\begin{tabular}{ |c|c|c|c| }\hlineObservable & BP-I & BP-II & BP-III \\\hline\hlineLightest Higgs mass & 125.0 & 125.2 & 125.6 \\\hline2nd Higgs mass & 338.2 & 322.1 & 370.4\\\hline3rd Higgs mass & 462.2 & 484.0 & 483.6 \\\hlineLightest Pseudoscalar Higgs mass & 259.0 & 256.8 & 261.7\\\hline2nd Pseudoscalar Higgs mass & 446.9 & 470.2 & 468.1 \\\hline\hlineLightest Sneutrino mass & 219.4 & 219.9 & 228.4 \\\hlineLightest CP-odd Sneutrino mass & 220.0 & 219.8 & 229.2 \\\hline\hlineLightest Chargino mass & 185.8 & 177.6 & 205.1 \\\hlineLightest Neutralino mass & 177.3 & 168.2 & 196.0 \\\hlineNext-to Lightest Neutralino mass & 200.3 & 193.2 & 218.6 \\\hline\hlineBR($h_3 \to \tilde{\nu_1} \tilde{\nu_1}$) (in \%) & 5.3 & 4.9 & 4.9 \\\hlineBR($A_3 \to \tilde{\nu_1} \tilde{\nu_1}^\prime$) (in \%) & 1.2 & 1.3 & 1.6 \\\hlineBR($\tilde{\nu_1} \to \ell \tilde{\chi^{\pm}_1}$) (in \%) & 48.2 & 48.6 & 45.3 \\\hlineBR($\tilde{\nu_1} \to \nu \tilde{\chi^{0}_1}$) (in \%)& 51.8 & 51.4 & 54.7 \\\hline$\Gamma(\tilde{\nu_1})$ (GeV) & $1.6 \times 10^{-13}$ & $8.5 \times 10^{-13}$ & $9 \times 10^{-14}$ \\\hline\end{tabular}%}\caption{Details of the BPs (all the masses are in GeV). The leptonic BRsinclude electron, muons and taus.}\label{tab:benchmark}\end{center}\end{table}

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Details of the BPs (all the masses are in GeV). The leptonic BRsinclude electron, muons and taus.

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2012.06125v1_train__4a7be948-b40b-4c2a-9c42-23715c458bae

arxiv_table_to_tex

\begin{table*}[!ht]\small\begin{table*}[!ht]\small\begin{center}\setlength\tabcolsep{4pt}\begin{tabular}{|c|l|ccccc|}\hline\multicolumn{2}{|c|}{Ablation} & Well lit & Shadows & Mixed colors & Overexposure & Low light\\ \hline\multirow{3}{*}{Loss} & No Stereo Loss & 12.80 & 12.78 & 12.78 & 12.82 & 12.81 \\& No NIR Photometric Loss & 12.64 & 12.66 & 12.64 & 12.69 & 12.75 \\& No Photometric Loss & 12.77 & 12.77 & 12.81 & 12.79 & 12.77 \\ \hlineReflectance Model & No Specular Component & 12.44 & 12.43 & 12.44 & 12.51 & 12.47 \\ \hline% No Input Segmentation & 12.51 & 12.55 & 12.45 & 12.52 & 12.54 \\\multirow{2}{*}{Inputs} & No RGB Input & 12.54 & 12.54 & 12.54 & 12.54 & 12.54 \\& No NIR Input & 13.13 & 15.19 & 16.43 & 19.82 & 19.39 \\ \hline\multicolumn{2}{|c|}{Ours (Full Method)} & \textbf{12.08} & \textbf{12.06} & \textbf{12.06} & \textbf{12.14} & \textbf{12.10} \\ \hline\end{tabular}\end{center}\vspace{-10pt}\caption{Mean absolute angular error in degrees of normal maps computed with modified versions of our full network. Results are reported for the five lighting conditions described in Section~\ref{section:Evaluation}.}\label{table:ablation}\end{table*}

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Mean absolute angular error in degrees of normal maps computed with modified versions of our full network. Results are reported for the five lighting conditions described in Section~\ref{section:Evaluation

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2012.06125v1_train__8e623a71-972e-4239-a6c6-257ed6a2f7f6

arxiv_table_to_tex

\begin{table*}[!h]\small\begin{table*}[!h]\small\begin{center}\setlength\tabcolsep{4pt}\begin{tabular}{|c|ccccc|}\hlineMethod & Well lit & Shadows & Mixed colors & Overexposure & Low light \\ \hlineSfSNet \cite{Sengupta2018SFSNet} & 14.10 & 18.32 & - & - & -\\ \hlineNestmeyer et al.\cite{Nestmeyer2020FaceRelighting} & 14.82 & 17.52 & 15.87 & 21.85 & 25.56 \\ \hlineOurs & \textbf{12.29} & \textbf{12.27} & \textbf{12.28} & \textbf{12.30} & \textbf{12.33} \\ \hline\end{tabular}\end{center}\vspace{-10pt}\caption{Mean absolute angular errors in degrees for three normal estimation methods and five different lighting scenarios. Results for SfSNet~\cite{Sengupta2018SFSNet} are omitted in some cases where they fail to generate plausible normals.}\label{table:baselines}\end{table*}

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Mean absolute angular errors in degrees for three normal estimation methods and five different lighting scenarios. Results for SfSNet~\cite{Sengupta2018SFSNet

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2202.10679v2_train__ecb4fc3d-1466-4c25-a014-2068e5b8a3fe

arxiv_table_to_tex

\begin{table*}\begin{table*}\centering\caption{Some studies of PIGL.}\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}\begin{tabular}{|p{0.4\columnwidth}|l|l|p{0.7\columnwidth}|}\hlineType &Objective& Reference& Approach\\\hline\multirow{3}{*}{\tabincell{l}{Physics-based Graph \\Data Processing} }&Sparse data enhancement& \cite{li2021physics} & Utilizing physical sparsity property of data to locate unlabelled data. \\\cline{2-4}&Filling missing data&\cite{seo2019differentiable}& Incorporating differentiable physics equations with graph learning.\\\cline{2-4}&Noisy value removal& \cite{salehi2021physgnn} & Incorporating the physical characteristics with GNNs to capture the noisy values.\\\hline\multirow{2}{*}{\tabincell{l}{Graph Representation\\ with Physical Properties}}&Precise graph visualisation&\cite{haleem2019evaluating}& Combining force-directed graph layout algorithm and deep learning algorithms.\\\cline{2-4}&Graph data structure preserving& \cite{sun2020graph} & Embedding the principles of force interaction into graph learning models. \\\hline\multirow{3}{*}{\tabincell{l}{Physics-driven Learning \\Models } } &Data dependency reduction& \cite{shah2018airsim} & Generating simulated data to pre-train the driving algorithm.\\\cline{2-4}&Reasonable parameter initialization& \cite{jia2021physics} & Generating simulated physical variables to pre-train recurrent graph network models. \\%&Accurate and explicable learning & \cite{schuetz2021combinatorial} & Physics-driven loss function \\\cline{2-4}&Accurate and explicable learning&\cite{daw2020physics}&Physics-driven loss function of LSTM model.\\\hline\end{tabular}\label{table}\end{table*}

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Some studies of PIGL.

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2201.00614v2_train__82ea7ed9-68fb-4a55-9165-57d987edf578

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\small\begin{tabular}{ccccc}\hline\multicolumn{1}{l|}{Classes} & \multicolumn{1}{c|}{Train-500} & \multicolumn{1}{c|}{Train-1000} & \multicolumn{1}{c|}{Train-1500} & Test \\ \hline\multicolumn{5}{c}{\usadata} \\ \hline\multicolumn{1}{l|}{Pro-Dem} & \multicolumn{1}{c|}{320} & \multicolumn{1}{c|}{654} & \multicolumn{1}{c|}{981} & 1543 \\\multicolumn{1}{l|}{Anti-Dem} & \multicolumn{1}{c|}{9} & \multicolumn{1}{c|}{22} & \multicolumn{1}{c|}{32} & 46 \\\multicolumn{1}{l|}{Pro-Rep} & \multicolumn{1}{c|}{133} & \multicolumn{1}{c|}{253} & \multicolumn{1}{c|}{381} & 576 \\\multicolumn{1}{l|}{Anti-Rep} & \multicolumn{1}{c|}{13} & \multicolumn{1}{c|}{17} & \multicolumn{1}{c|}{29} & 46 \\\multicolumn{1}{l|}{Other} & \multicolumn{1}{c|}{25} & \multicolumn{1}{c|}{54} & \multicolumn{1}{c|}{77} & 111 \\ \hline\multicolumn{1}{l|}{Total} & \multicolumn{1}{c|}{500} & \multicolumn{1}{c|}{1000} & \multicolumn{1}{c|}{1500} & 2322 \\ \hline\multicolumn{5}{c}{\indiadata} \\ \hline\multicolumn{1}{l|}{Pro-BJP} & \multicolumn{1}{c|}{67} & \multicolumn{1}{c|}{149} & \multicolumn{1}{c|}{208} & 360 \\\multicolumn{1}{l|}{Anti-BJP} & \multicolumn{1}{c|}{136} & \multicolumn{1}{c|}{275} & \multicolumn{1}{c|}{425} & 680 \\\multicolumn{1}{l|}{Pro-INC} & \multicolumn{1}{c|}{24} & \multicolumn{1}{c|}{60} & \multicolumn{1}{c|}{83} & 158 \\\multicolumn{1}{l|}{Anti-INC} & \multicolumn{1}{c|}{2} & \multicolumn{1}{c|}{3} & \multicolumn{1}{c|}{6} & 15 \\\multicolumn{1}{l|}{Pro-AAP} & \multicolumn{1}{c|}{35} & \multicolumn{1}{c|}{61} & \multicolumn{1}{c|}{99} & 142 \\\multicolumn{1}{l|}{Anti-AAP} & \multicolumn{1}{c|}{52} & \multicolumn{1}{c|}{101} & \multicolumn{1}{c|}{163} & 210 \\\multicolumn{1}{l|}{Other} & \multicolumn{1}{c|}{184} & \multicolumn{1}{c|}{351} & \multicolumn{1}{c|}{516} & 1120 \\ \hline\multicolumn{1}{l|}{Total} & \multicolumn{1}{c|}{500} & \multicolumn{1}{c|}{1000} & \multicolumn{1}{c|}{1500} & 2685\\\hline\end{tabular}\caption{Class-wise sample distribution in different training and testing splits of the annotated datasets.}\label{tab:dataset_class_distr}\vspace{-5mm}\end{table}

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Class-wise sample distribution in different training and testing splits of the annotated datasets.

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2201.00614v2_train__91ea8fad-9f96-4973-b7a9-048f657691f0

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\small\centering\begin{tabular}{l|c|c|c|c|c|c}\hline\multirow{2}{*}{Model} & \multicolumn{3}{c|}{\usadata} & \multicolumn{3}{c}{\indiadata} \\ \cline{2-7}& \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =0.5K\end{tabular} & \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =1K\end{tabular} & \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =1.5K\end{tabular} & \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =0.5K\end{tabular} & \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =1K\end{tabular} & \begin{tabular}[c]{@{}c@{}}$|\mathcal{D}_s|$\\ =1.5K\end{tabular} \\\hlineSiamNet & $0.39$ & $0.43$ & $0.42$ & $0.12$ & $0.14$ & $0.13$\\BICE & $0.27$ & $0.30$ & $0.33$ & $0.16$ & $0.17$ & $0.23$\\TAN & $0.38$ & $0.46$ & $0.45$ & $0.14$ & $0.14$ & $0.17$ \\SVM & $0.37$ & $0.37$ & $0.45$ & $0.13$ & $0.13$ & $0.16$\\BERT & $0.39$ & $0.50$ & $0.51$ & $0.17$ & $0.17$ & $0.21$\\ConvNet & $ 0.37 $ & $ 0.43 $ & $ 0.45 $ & $ 0.35 $ & $ 0.40 $ & $ 0.41 $\\BLSTM & $ 0.35 $ & $ 0.43 $ & $ 0.44 $ & $ 0.31 $ & $ 0.39 $ & $ 0.38 $\\\hlineLS-SVM & $0.39$ & $0.42$ & $0.44$ & $0.18$ & $0.19$ & $0.18$\\ST-ConvNet & $0.13$ & $0.15$ & $0.16$ & $0.10$ & $0.11$ & $0.11$\\ST-BLSTM & $0.13$ & $0.16$ & $0.19$ & $0.09$ & $0.12$ & $0.11$\\UST & $0.35$ & $0.42$ & $0.41$ & $0.12$ & $0.16$ & $0.16$\\GCN-ConvNet & $0.41$ & $0.45$ & $0.47$ & $0.33$ & $0.35$ & $0.40$\\GCN-BLSTM & $0.39$ & $0.42$ & $0.46$ & $0.36$ & $0.41$ & $0.42$\\\hline\name/Net.($\mathcal{C}_1$) & $ 0.32 $ & $ 0.41 $ & $ 0.42 $ & $ 0.10 $ & $ 0.12 $ & $ 0.15 $\\\name/Net.($\mathcal{C}_2$) & $ 0.36 $ & $ 0.46 $ & $ 0.46 $ & $ 0.28 $ & $ 0.31 $ & $ 0.37 $ \\\name/Cont.($\mathcal{C}_1$) & $ 0.41 $ & $ 0.47 $ & $ 0.49 $ & $ 0.36 $ & $ 0.41 $ & $ 0.43 $\\\name/Cont.($\mathcal{C}_2$) & $ 0.47 $ & $ 0.51 $ & $ 0.53 $ & $ 0.38 $ & $ 0.44 $ & $ 0.45 $ \\\hline\name ($\mathcal{C}_1$) & $\mathbf{0.46}$ & $\mathbf{0.47}$ & $\mathbf{0.49}$ & $\mathbf{0.37}$ & $\mathbf{0.42}$ & $\mathbf{0.45}$\\\name ($\mathcal{C}_2$) & $\mathbf{0.49}$ & $\mathbf{0.53}$ & $\mathbf{0.55}$ & $\mathbf{0.42}$ & $\mathbf{0.45}$ & $\mathbf{0.47}$\\\hline\end{tabular}\caption{F1 scores of all models with different sizes of labeled training data on \usadata\ and \indiadata.}\vspace{-5mm}\label{tab:overall_result}\end{table}

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F1 scores of all models with different sizes of labeled training data on \usadata\ and \indiadata.

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2201.00614v2_train__db2c08f6-874e-476b-a6de-25ea40fd9b89

arxiv_table_to_tex

\begin{table}[!t]\begin{table}[!t]\small\centering\begin{tabular}{c|c|c|c|c}\hline\multirow{2}{*}{\begin{tabular}[c]{@{}l@{}}\% unlabeled\\ data used\end{tabular}} & \multicolumn{2}{c|}{\usadata} & \multicolumn{2}{c}{\indiadata} \\ \cline{2-5}& m-F1 $\mathcal{C}_1$ & m-F1 $\mathcal{C}_2$ & m-F1 $\mathcal{C}_1$ & m-F1 $\mathcal{C}_2$ \\ \hline$100$ & 0.49 & 0.55 & 0.45 & 0.47 \\$80$ & 0.49 & 0.54 & 0.44 & 0.46 \\$50$ &0.46 & 0.51 & 0.42 & 0.43 \\$30$ & 0.45 & 0.48 & 0.42 & 0.41 \\$10$ & 0.45 & 0.45 & 0.41 & 0.39 \\ \hline\end{tabular}\caption{Macro-F1 scores of \name\ with different amount of unlabeled data used in semi-supervised phase. The size of labeled dataset used is $1500$.}\label{tab:vary_data_size}\vspace{-4mm}\end{table}

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Macro-F1 scores of \name\ with different amount of unlabeled data used in semi-supervised phase. The size of labeled dataset used is $1500$.

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2104.00178v3_train__9fb03713-b89b-4654-93a4-6667dadeb9eb

arxiv_table_to_tex

\begin{table}[]\begin{table}[]% \vspace{3mm}\renewcommand*{\arraystretch}{1.3}\centering\ttfamily\footnotesize\caption{Details of Nyx Dataset Used in Experiments}\vspace{-4mm}\input{Table/dataset}% \vspace{-4.5mm}\label{tab:DataDetail}\end{table}

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Details of Nyx Dataset Used in Experiments

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2304.11410v1_train__5a2e3e5a-07d7-4246-bb53-7b2677bf5d25

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\scalebox{0.95}{\begin{tabular}{|l|c|c|c|}\hline\textbf{Predictor} & \textbf{Estimate} & \textbf{Std-Error} & \textbf{z-value} \\ \hlineIntercept & \textbf{0.018} & 0.008 & 1.98 \\$1^{st}$ constituent's deplen & {-0.004} & 0.012 & -0.35 \\$2^{nd}$ constituent's deplen & \textbf{0.088} & 0.014 & 6.20 \\$3^{rd}$ constituent's deplen & \textbf{-0.147} & 0.015 & -10.12 \\$4^{th}$ constituent's deplen & \textbf{-0.529} & 0.016 & -32.90 \\$5^{th}$ constituent's deplen & \textbf{-2.720} & 0.023 & -118.03 \\\hline\end{tabular}}\caption{Regression model containing dependency lengths (deplen) of preverbal constituents as predictors (87143 data points); significant predictors denoted in bold with p $<$ 0.001}\label{tab:deplen-reg-only5}\end{table}

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Regression model containing dependency lengths (deplen) of preverbal constituents as predictors (87143 data points); significant predictors denoted in bold with p $<$ 0.001

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2304.11410v1_train__d22a8011-318a-4be0-ae8c-28ddaff35aa3

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\scalebox{0.95}{\begin{tabular}{|l|c|c|c|}\hline\textbf{Predictor} & \textbf{Estimate} & \textbf{Std-Error} & \textbf{z-value} \\ \hlineIntercept & -0.003 & 0.008 & -0.41 \\$1^{st}$ constituent's length & \textbf{-0.083} & 0.009 & -8.44 \\%cl2$3^{rd}$ constituent's length & \textbf{0.058} & 0.010 & 5.72 \\$4^{th}$ constituent's length & \textbf{-0.148} & 0.009 & -15.26 \\$5^{th}$ constituent's length & \textbf{-1.549} & 0.016 & -97.82 \\\hline\end{tabular}}\caption{Regression model containing preverbal constituent lengths as predictors (87143 data points); significant predictors denoted in bold with p $<$ 0.001; constituent length = word counts in the constituent}\label{tab:constlen-reg-only5}\end{table}

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Regression model containing preverbal constituent lengths as predictors (87143 data points); significant predictors denoted in bold with p $<$ 0.001; constituent length = word counts in the constituent

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2304.11410v1_train__ce7eadf2-53a8-4e37-bd7e-2c485496d962

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\scalebox{0.95}{\begin{tabular}{l|c}\hline%\textbf{Predictor} & \textbf{Brown z-value}& \textbf{WSJ z-value}\tabularnewlinePredictor(s) & Accuracy \\ \hline% \textsc{individual} & \\total dependency length & 62.69 \\2nd-last preverbal constituent's deplen & 68.48*** \\last preverbal constituent's deplen & 72.70*** \\\hline% \textsc{collective} & \\last + 2nd last preverbal constituent's deplen & 77.17*** \\% dl 2nd last phrase + dl last phrase + total dl & 76.85*** \\\hline\end{tabular}}\caption{Prediction accuracy of distinct models with dependency length as predictor on full dataset (184818 data points; deplen = dependency length; McNemar's two-tailed significance test compared to previous row: *** $p<0.001$)}\label{tab:pred-results-dl}\end{table}

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Prediction accuracy of distinct models with dependency length as predictor on full dataset (184818 data points; deplen = dependency length; McNemar's two-tailed significance test compared to previous row: *** $p<0.001$)

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2304.11410v1_train__8f939ba4-5eba-455d-990e-baaea11a417a

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\centering\scalebox{0.95}{\begin{tabular}{l|c}\hline%\textbf{Predictor} & \textbf{Brown z-value}& \textbf{WSJ z-value}\tabularnewlinePredictor(s) & Accuracy \\ \hline% total dependency length & 62.69 \\2nd-last preverbal constituent length & 54.35 \\last preverbal constituent length & 69.62*** \\\hlinelast + 2nd last preverbal constituent length & 70.28*** \\% cl 2nd last + cl last + total dl & 70.52*** \\\hline\end{tabular}}\caption{Prediction accuracy of distinct models with constituent length as predictor (184818 data points; McNemar's two-tailed test compared to previous row: *** $p<0.001$)}\label{tab:pred-results-cl}\end{table}

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Prediction accuracy of distinct models with constituent length as predictor (184818 data points; McNemar's two-tailed test compared to previous row: *** $p<0.001$)

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2112.03518v2_train__d1daa31d-1a93-428d-b80b-396595254a8a

arxiv_table_to_tex

\begin{table}[h]\begin{table}[h]\centering\label{t2}\renewcommand{\arraystretch}{1.1}\resizebox{0.8\columnwidth}{!}{\begin{tabular}{c|cc|cc}\noalign{\smallskip}\noalign{\smallskip}\hline\hline\multirow{2}{*}{} & \multicolumn{2}{c|}{$\delta\ge$0.4} & \multicolumn{2}{c}{$\delta\ge$0.6} \\\cline{2-5}& Improvement & Sucess & Improvement & Sucess \\\hlineJT-VAE & 0.84\textpm1.45 & 84\% & 0.21\textpm0.71 & 46.4\% \\GCPN & 2.49\textpm1.30 & 100\% & 0.79\textpm0.63 & 100\% \\MMPA & 3.29\textpm1.12 & - & 1.65\textpm1.44 & - \\DEFactor & 3.41\textpm1.67 & 85.9\% & 1.55\textpm1.19 & 72.6\% \\VJTNN & 3.55\textpm1.67 & - & 2.33\textpm1.17 & - \\GA-DNN & 5.93\textpm1.41 & 100\% & 3.44\textpm1.09 & 99.8\% \\\hline\textbf{Constrained GA(Ours)} & \textbf{5.53\textpm1.29} & \textbf{100\%} & \textbf{3.67\textpm1.29} & \textbf{100\%} \\\hline\hline\end{tabular}}\\\caption{Comparison on constrained improvement of penalized $Log P$ of specific molecules}\end{table}

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Comparison on constrained improvement of penalized $Log P$ of specific molecules

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2209.01604v2_train__2e9135b6-020e-4d8e-aa29-ae8db6211aef

arxiv_table_to_tex

\begin{table}[h]\begin{table}[h]\centering\small\begin{tabular}{cc|rrrrrr}\hline\multicolumn{1}{c|}{Dataset} & \multicolumn{1}{c|}{Pretraining Method} & \multicolumn{1}{c}{B-1} & \multicolumn{1}{c}{B-2} & \multicolumn{1}{c}{B-3} & \multicolumn{1}{c}{B-4} & \multicolumn{1}{c}{M} & \multicolumn{1}{c}{R-L} \\ \hline\multicolumn{1}{c|}{\multirow{7}{*}{IU X-ray}} & Scratch & 0.404 & 0.249 & 0.172 & 0.126 & 0.161 & 0.320 \\\multicolumn{1}{c|}{} & AE & 0.417 & 0.273 & 0.195 & 0.148 & \textbf{0.176} & 0.361 \\\multicolumn{1}{c|}{} & Imagenet & 0.420 & 0.256 & 0.175 & 0.127 & 0.167 & 0.326 \\\multicolumn{1}{c|}{} & MLC & 0.423 & 0.270 & 0.190 & 0.141 & \textbf{0.176} & 0.359 \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & 0.426 & 0.259 & 0.175 & 0.126 & 0.168 & 0.325 \\\multicolumn{1}{c|}{} & SimCLR & \textbf{0.456} & \textbf{0.289} & \textbf{0.202} & \textbf{0.150} & \textbf{0.176} & \textbf{0.362}\\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& 0.448 & 0.282 & 0.195 & 0.141 & \textbf{0.176} & 0.340 \\\hline\multicolumn{1}{c|}{\multirow{6}{*}{MIMIC-CXR}} & Scratch & 0.211 & 0.132 & 0.090 & 0.064 & 0.105 & 0.250 \\\multicolumn{1}{c|}{} & AE & 0.316 & 0.186 & 0.119 & 0.081 & 0.119 & 0.243 \\\multicolumn{1}{c|}{} & Imagenet & 0.270 & 0.166 & 0.109 & 0.076 & 0.114 & 0.255 \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & 0.334 & 0.203 & 0.133 & 0.091 & 0.129 & 0.261 \\\multicolumn{1}{c|}{} & SimCLR & \textbf{0.343} & \textbf{0.208} & \textbf{0.137} & \textbf{0.095} & \textbf{0.132} & 0.260 \\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& 0.325 & 0.198 & 0.130 & 0.090 & 0.129 & \textbf{0.265}\\\hline\end{tabular}\caption{Quantitative comparison among different encoders when using Transformer as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.}\label{Table:Transformer_dif_encoder}\end{table}

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Quantitative comparison among different encoders when using Transformer as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.

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2209.01604v2_train__2ba4c7b2-64b6-4290-b82f-fcceeac107a9

arxiv_table_to_tex

\begin{table}[!h]\begin{table}[!h]\centering\small\begin{tabular}{cc|rrrrrr}\hline\multicolumn{1}{c|}{Dataset} & \multicolumn{1}{c|}{Pretraining Method} & \multicolumn{1}{c}{B-1} & \multicolumn{1}{c}{B-2} & \multicolumn{1}{c}{B-3} & \multicolumn{1}{c}{B-4} & \multicolumn{1}{c}{M} & \multicolumn{1}{c}{R-L} \\ \hline\multicolumn{1}{c|}{\multirow{6}{*}{IU X-ray}} & Scratch & 0.299 & 0.185 & 0.132 & 0.100 & 0.134 & 0.324 \\\multicolumn{1}{c|}{} & AE & 0.389 & 0.233 & 0.157 & 0.111 & 0.154 & 0.317 \\\multicolumn{1}{c|}{} & Imagenet & 0.397 & 0.246 & 0.170 & 0.126 & 0.160 & \textbf{0.329} \\\multicolumn{1}{c|}{} & MLC & 0.410 & 0.250 & 0.170 & 0.123 & 0.164 & 0.325 \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & 0.425 & 0.260 & 0.177 & 0.128 & 0.169 & 0.326 \\\multicolumn{1}{c|}{} & SimCLR & 0.426 & 0.265 & 0.181 & 0.131 & 0.168 & 0.326 \\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& \textbf{0.431} & \textbf{0.268} & \textbf{0.185} & \textbf{0.137} & \textbf{0.172} & \textbf{0.332} \\\hline% \multicolumn{1}{c|}{} & SimCLR & \textbf{0.426} & \textbf{0.265} & \textbf{0.181} & \textbf{0.131} & 0.168 & 0.326 \\% \multicolumn{1}{c|}{} & MoCo & 0.425 & 0.260 & 0.177 & 0.128 & \textbf{0.169} & 0.326 \\% \hline\multicolumn{1}{c|}{\multirow{5}{*}{MIMC-CXR}} & Scratch & 0.312 & 0.193 & 0.130 & 0.092 & 0.128 & 0.272 \\\multicolumn{1}{c|}{} & AE & 0.282 & 0.174 & 0.117 & 0.083 & 0.119 & 0.264 \\\multicolumn{1}{c|}{} & Imagenet & 0.309 & 0.193 & 0.131 & 0.094 & 0.130 & 0.276 \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & 0.309 & 0.191 & 0.128 & 0.091 & 0.127 & 0.270 \\\multicolumn{1}{c|}{} & SimCLR & \textbf{0.330} & \textbf{0.206} & \textbf{0.139} & \textbf{0.099} & \textbf{0.134} & \textbf{0.278} \\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& 0.325 & 0.203 & 0.138 & 0.095 & \textbf{0.134} & \textbf{0.278} \\\hline% \multicolumn{1}{c|}{} & SimCLR & \textbf{0.330} & \textbf{0.206} & \textbf{0.139} & \textbf{0.099} & \textbf{0.134} & \textbf{0.278} \\% \multicolumn{1}{c|}{} & MoCo & 0.309 & 0.191 & 0.128 & 0.091 & 0.127 & 0.270 \\% \hline\end{tabular}\caption{Quantitative comparison among different encoders when using LSTM as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.}\label{Table:LSTM_dif_encoder}\end{table}

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Quantitative comparison among different encoders when using LSTM as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.

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2209.01604v2_train__5e0589da-540d-4429-9027-df54180f56d2

arxiv_table_to_tex

\begin{table}[!h]\begin{table}[!h]\centering\small\begin{tabular}{cc|rrrrrr}\hline\multicolumn{1}{c|}{Dataset} & \multicolumn{1}{c|}{Pretraining Method} & \multicolumn{1}{c}{B-1} & \multicolumn{1}{c}{B-2} & \multicolumn{1}{c}{B-3} & \multicolumn{1}{c}{B-4} & \multicolumn{1}{c}{M} & \multicolumn{1}{c}{R-L} \\ \hline\multicolumn{1}{c|}{\multirow{7}{*}{IU X-ray}} & Scratch & 0.351 & 0.221 & 0.156 & 0.117 & 0.153 & 0.333 \\\multicolumn{1}{c|}{} & AE & 0.389 & 0.241 & 0.166 & 0.121 & 0.161 & 0.332 \\\multicolumn{1}{c|}{} & Imagenet & 0.417 & 0.254 & 0.173 & 0.124 & 0.165 & 0.328 \\\multicolumn{1}{c|}{} & MLC & 0.412 & \textbf{0.263} & \textbf{0.189} & \textbf{0.145} & \textbf{0.169} & \textbf{0.341} \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & \textbf{0.424} & 0.259 & 0.174 & 0.124 & \textbf{0.169} & 0.331 \\\multicolumn{1}{c|}{} & SimCLR & 0.423 & 0.259 & 0.175 & 0.126 & 0.166 & 0.327 \\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& 0.415 & 0.255 & 0.174 & 0.127 & 0.165 & 0.331 \\\hline% \multicolumn{1}{c|}{} & SimCLR & 0.423 & 0.259 & 0.175 & 0.126 & 0.166 & 0.327 \\% \multicolumn{1}{c|}{} & MoCo & \textbf{0.424} & 0.259 & 0.174 & 0.124 & \textbf{0.169} & 0.331 \\% \hline\multicolumn{1}{c|}{\multirow{6}{*}{MIMC-CXR}} & Scratch & 0.309 & 0.193 & 0.130 & 0.093 & 0.128 & 0.274 \\\multicolumn{1}{c|}{} & AE & 0.299 & 0.184 & 0.124 & 0.088 & 0.123 & 0.270 \\\multicolumn{1}{c|}{} & Imagenet & 0.313 & 0.196 & 0.132 & 0.095 & 0.129 & 0.275 \\\cline{2-8}\multicolumn{1}{c|}{} & MoCo & 0.309 & 0.190 & 0.127 & 0.090 & 0.126 & 0.269 \\\multicolumn{1}{c|}{} & SimCLR & 0.327 & 0.204 & 0.137 & 0.098 & 0.134 & 0.278 \\\multicolumn{1}{c|}{} & SimCLR (w/ Lung Seg)& \textbf{0.335} & \textbf{0.209} & \textbf{0.140} & \textbf{0.100} & \textbf{0.136} & \textbf{0.279} \\\hline% \multicolumn{1}{c|}{} & SimCLR & \textbf{0.327} & \textbf{0.204} & \textbf{0.137} & \textbf{0.098} & \textbf{0.134} & \textbf{0.278} \\% \multicolumn{1}{c|}{} & MoCo & 0.309 & 0.190 & 0.127 & 0.090 & 0.126 & 0.269 \\% \hline\end{tabular}\caption{Quantitative comparison among different encoders when using GRU as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.}\label{Table:GRU_dif_encoder}\end{table}

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Quantitative comparison among different encoders when using GRU as decoder. B-n, M, and R-L are short for BLEU-n, METEOR, and ROUGE-L, respectively.

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2105.04024v3_train__40021ae1-db12-45a0-8f69-e5aa31a75b6a

arxiv_table_to_tex

\begin{table}[!ht]\begin{table}[!ht]\footnotesize\centering\renewcommand{\arraystretch}{1.5}\begin{tabular}{c | c c c c c| c c}\hline& Neighbors & Entropy Weight & Batch Size & Dropout & Epochs & Accuracy AG news & Accuracy DBPedia \\ \hlineDocSCAN & 5 & 2 & 128 & 0.1 & 5 & 83.2 \textpm 3.8 & 85.8 \textpm 3.5 \\ \hline\multirow{3}{*}{(A)} & 2 & & & & & 77.5 \textpm 6.7 & 83.1 \textpm 5.1 \\& 3 & & & & & 78.4 \textpm 5.5 & 85.3 \textpm 3.0 \\%re-run this& 10 & & & & & 82.4 \textpm 5.6 & 86.1 \textpm 3.5 \\ \hline\multirow{2}{*}{(B)} & & 1 & & & & 75.8 \textpm 5.3 & 80.3 \textpm 2.8 \\& & 4 & & & & 80.4 \textpm 3.5 & 86.7 \textpm 2.8 \\ \hline\multirow{2}{*}{(C)} & & & 64 & & & 82.4 \textpm 5.0 & 87.5 \textpm 4.2 \\& & & 256 & & & 81.3 \textpm 4.3 & 84.6 \textpm 4.1 \\ \hline\multirow{2}{*}{(D)} & & & & 0 & & 81.9 \textpm 3.7 & 86.1 \textpm 4.4 \\& & & & 0.33 & & 80.3 \textpm 3.9 & 86.8 \textpm 2.6 \\ \hline\multirow{2}{*}{(E)} & & & & & 3 & 79.4 \textpm 5.3 & 84.2 \textpm 4.4 \\& & & & & 10 & 81.5 \textpm 3.4 & 84.7 \textpm 3.7 \\ \hlinek-means & & & & & & 66.2 \textpm 8.2 & 77.1 \textpm 4.9 \\ \hline\end{tabular}\caption{Ablation Studies for DocSCAN Hyper-parameters (results reported on the AG news and DBPedia training set, cell values give the mean over 10 runs with 95\% confidence interval).}\label{tab:ablation_experiments}\end{table}

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Ablation Studies for DocSCAN Hyper-parameters (results reported on the AG news and DBPedia training set, cell values give the mean over 10 runs with 95\% confidence interval).

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2101.04017v5_train__2ae30d33-bc50-40e2-80ef-f050069d48d3

arxiv_table_to_tex

\begin{table*}\begin{table*}\caption{Reclassification results using Shaver lexicon, compared to the original NRC lexicon}\vspace{-0.2cm}\label{shaver}\footnotesize\centering\begin{tabular}{l|r r|r r|r r}\toprule%\hline\rule[-1ex]{0pt}{2.2ex} & \multicolumn{2}{p{2.2cm}|}{\textbf{ArsMeteo\newline(9171 artworks)}} & \multicolumn{2}{p{2.2cm}|}{\textbf{RaiPlay\newline(4612 media items)}} & \multicolumn{2}{p{2.2cm}}{\textbf{WikiArt Emotions\newline(4105 artworks)}} \\%\hline\midrule\rule[-1ex]{0pt}{2.2ex} \textbf{Emotion} & \textbf{NRC} & \textbf{Shaver} & \textbf{NRC} & \textbf{Shaver} & \textbf{NRC} & \textbf{Shaver} \\%\hline\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{awe (fear\_surprise)}} & $63$ & $117$ & $132$ & $7$ & $508$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{delight (joy\_surprise)}} & $52$ & $71$ & $117$ & $2$ & $1672$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{delight (surprise\_joy)}} & $52$ & $57$ & $117$ & $88$ & $1672$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{despair (fear\_sadness)}} & $19$ & $49$ & $20$ & $132$ & $0$ & $508$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{disapproval (sadness\_surprise)}} & $58$ & $83$ & $64$ & $2$ & $404$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{envy (anger\_sadness)}} & $25$ & $30$ & $21$ & $49$ & $0$ & $508$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{guilt (fear\_joy)}} & $22$ & $44$ & $73$ & $0$ & $1618$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{guilt (joy\_fear)}} & $24$ & $45$ & $73$ & $117$ & $1618$ & $1672$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{outrage (anger\_surprise)}} & $41$ & $49$ & $46$ & $20$ & $508$ & $0$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{pride (anger\_joy)}} & $20$ & $27$ & $72$ & $64$ & $1618$ & $404$ \\\midrule%\rule[-1ex]{0pt}{2.5ex} {\textbf{TOTAL}} & $324$ & $572$ & $618$ & $481$ & $7946$ & $3092$ \\%\hline\bottomrule\end{tabular}\vspace{7pt}\end{table*}

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Reclassification results using Shaver lexicon, compared to the original NRC lexicon

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2306.04127v1_train__2f85ddb8-f132-4cc3-89d9-29d3e0fb0490

arxiv_table_to_tex

\begin{table}[ht!]\begin{table}[ht!]\begin{center}\begin{tabular}{|c|c|} \hline{\bf Scalar Sector} & \\ \hline$\delta m_\phi$, $\delta Z_\phi$ ($\phi=h_1,h_2,A$) & OS \\ \hline$\delta \alpha$ & OS-pinched \\& $p_*$-pinched \\ \hline$\delta v_S$ & OSproc1 (OS $h_1 \to AA$)\\& OSproc2 (OS $h_2 \to AA$) \\& ZEMproc1 (ZEM $h_1 \to AA$) \\& ZEMproc2 (ZEM $h_2 \to AA$) \\ \hline \hline{\bf Gauge Sector} & \\ \hline$\delta m_V$, $\delta Z_V$ ($V=W^\pm,Z$) & OS \\ \hline$\delta Z_e$ & $G_\mu$ scheme \\ \hline\hline{\bf Fermion Sector} & \\ \hline$\delta m_f$, $\delta Z_f$ & OS \\ \hline\end{tabular}\caption{Summary of the renormalization schemes applied in the EWcorrections to the non-loop-induced on-shell decay widths of theCxSM Higgs boson decays. For details, see text andRefs.~\cite{Krause:2016oke,Azevedo:2021ylf,Egle:2022wmq}. \label{tab:renscheme}}\end{center}\end{table}

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Summary of the renormalization schemes applied in the EWcorrections to the non-loop-induced on-shell decay widths of theCxSM Higgs boson decays. For details, see text andRefs.~\cite{Krause:2016oke,Azevedo:2021ylf,Egle:2022wmq

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1801.07729v2_train__f9860984-59fc-47a1-955e-d58cbdab7aef

arxiv_table_to_tex

\begin{table}[tbh]\begin{table}[tbh]\caption{The effect of adding two reduced dimension layers on the representation (subspacedimensionality and variance)}\label{T:SI3}%\begin{threeparttable}[b]%\begin{adjustbox}{width=1\textwidth}\small\scalebox{0.7}{\begin{tabular}{|l|l|c|c|c|c|c|c|}\hline{Model} & {Training Strategy} & \multicolumn{3}{c|}{Original Architecture} & \multicolumn{3}{c|}{Adding two dimensionality reduction layers} \\\cline{3-8} & &number of nodes &subspace dim $^1$ &retained variance $^2$ & number of nodes &subspace dim$^1$ &retained variance$^2$ \\\hline{AlexNet}& Pre-trained & {4096} & {201} & {21.71} & {512}& {9}& {59.64}\\& \& Finetuned &&&&&& \\\hlineAlexNet&From Scratch&4096&397&35.62&512&10&62.78\\\hline{VGGNet}& Pre-trained &{4096} &{55} &{49.52} &{512}&{7}&{66.87}\\& \& Finetuned &&&&&& \\\hlineVGGNet&From Scratch&4096&36&51.16&512&7&72.52\\\hline{ResNet}& Pre-trained &{2048}$^3$ &{491} &{17.53} &{512}&{6}&{73.71}\\& \& Finetuned &&&&&& \\\hline\multicolumn{8}{|l|}{$^1$ Subspace dim: Number of principle components cumulatively retaining 95\% of variance.} \\\multicolumn{8}{|l|}{$^2$ Retained variance: Percentage of variance retained by the first two principle components. } \\\multicolumn{8}{|l|}{$^3$ ResNet does not have FC layers. This is the number of the nodes in the last pooling layer. } \\ \hline\end{tabular}}%\end{adjustbox}\end{table}

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The effect of adding two reduced dimension layers on the representation (subspacedimensionality and variance)

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1801.07729v2_train__c23eb56a-5767-4542-97db-706213288444

arxiv_table_to_tex

\begin{table}[tbh]\begin{table}[tbh]\caption{Analysis of the modes of variations of the activations on 62K paintings from the Wikiart collection in three models and their correlation with time (Pearson Correlation Coefficients) .The top two time-correlated modes are highlighted in bold.}\label{T:SI4}%\begin{adjustbox}{width=1\textwidth}\scalebox{0.77}{\small\begin{tabular}{ |l|c|c||c|c|c|c|c|c|c|c|c|c| }\hline& Subspace Dim $^1$ & Retained Variance $^2$ & \multicolumn{10}{|c|}{Correlation with time } \\% &&& \multicolumn{10}{|c|}{\hline} \\&&& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hlineAlexNet+2 & 10 & 51.13 & 0.12 & {\bf 0.66} & 0.24 & {\bf -0.43} & -0.23 & 0.04 & 0.08 & -0.05 & -0.03 & 0.00 \\\hlineVGGNet+2 & 9 & 43 & -0.15 & -0.14 & {\bf -0.46} & -0.07 & {\bf -0.59} & 0.28 & 0.02 & 0.07 & 0.02 & \\\hlineResNet+2 & 7 & 66.80 & -0.03 & {\bf -0.72} & 0.20 & 0.22 & {\bf 0.30} & -0.01 & 0.06 & & & \\\hline\multicolumn{13}{|l|}{$^1$ Subspace Dim: Number of principle components retaining 95\% of the variance} \\\multicolumn{13}{|l|}{$^2$ Retained Variance: Variance retained by first two dimensions }\\ \hline\end{tabular}}%\end{adjustbox}\end{table}

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Analysis of the modes of variations of the activations on 62K paintings from the Wikiart collection in three models and their correlation with time (Pearson Correlation Coefficients) .The top two time-correlated modes are highlighted in bold.

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2206.13365v1_train__ac8c042a-c0be-481d-a2a9-c890d0226393

arxiv_table_to_tex

\begin{table*}[tb]\begin{table*}[tb]\centering\setlength{\tabcolsep}{3pt}\caption{Comparison of the performance of the COVID-19 detection models using different signal representations on breathing and speech modalities in terms of the AUC(\%).}\vspace{-2mm}\begin{tabular}{l|cccccc||cccccc}\hline% \small\multirow{2}{*}{Representation Methods} & \multicolumn{6}{c||}{Breathing} & \multicolumn{6}{c}{Speech} \\\cline{2-13}& \multicolumn{1}{l}{Fold1} & \multicolumn{1}{l}{Fold2} & \multicolumn{1}{l}{Fold3} & \multicolumn{1}{l}{Fold4} & \multicolumn{1}{l}{Fold5} & \multicolumn{1}{l||}{Avg.}& \multicolumn{1}{l}{Fold1} & \multicolumn{1}{l}{Fold2} & \multicolumn{1}{l}{Fold3} & \multicolumn{1}{l}{Fold4} & \multicolumn{1}{l}{Fold5} & \multicolumn{1}{l}{Avg.}\\ \hlineMel-Spectrogram~\cite{sharma2021second} & 73.8 & 76.4 & 75.6 & 77.1 & 84.2 & 77.4 &74.8 & 85.1 & 79.1 & 78.6 & 80.4 & 79.6 \\SincNet~\cite{ravanelli2018interpretable} & 72.4 & 69.6 & \textbf{81.9} & 76.4 & 77.1 & 75.4& 75.0 & 84.6 & 77.4 & 76.7 & \textbf{85.2} & 79.7 \\LEAF~\cite{zeghidour2021leaf} & 71.5 & 62.9 & 66.1 & 66.6 & 73.6 & 68.2 & 60.5 & 59.1 & 63.8 & 57.4 & 62.0 & 60.6 \\%& & & & & & & \\%CosGauss-relev-2head~\cite{agrawal2020interpretable} & 76.4 & 76.3 & 79.4 & 77.9 & 81.5 & 78.3%& 77.1 & 83.3 & 81.5 & 78.4 & 85.7 & 81.2 \\\hdashline[1pt/1pt]CosGauss-relev & 75.4 & 76.0 & 79.7 & 78.1 & 82.8 & 78.4& 76.5 & \textbf{83.6} & 83.3 & \textbf{79.6} & 84.5 & \textbf{81.5}\\\hdashline[1pt/1pt]%CosGauss-relev-modFB & 72.2 & 70.4 & 79.4 & 76.7 & 81.9 & 76.1%& & & & & & \\%CosGauss-relev-modFB-relev & 73.7 & 76.0 & 81.1 & 78.3 & 82.9 & 78.4%& 75.6 & 79.4 & 80.7 & 81.2 & 82.6 & 79.9\\CosGauss-relev-pretr & 76.1 & 75.9 & 77.7 & 76.9 & 83.2 & 78.0 & 77.1 & 79.7 & \textbf{84.7} & 77.0 & 81.3 & 80.0\\CosGauss-relev-pretr-fine& \textbf{81.2} & 77.0 & 80.9 & 78.4 & \textbf{84.9} & \textbf{80.5} &78.3 & 81.5 & 83.5 & 78.0 & 81.5 & 80.6\\\hdashline[1pt/1pt]CosGauss-SSL-pretr & 77.3 & 73.9 & 79.6 & 79.3 & 81.6 & 78.3 & 78.7 & 80.5 & 81.9 & 75.8 & 81.8 & 79.7\\CosGauss-SSL-pretr-fine & 78.5 & \textbf{77.9} & 77.9 & \textbf{80.2 } & 81.3 & 79.2 & \textbf{80.7} & 81.7 & 82.7 & 76.8 & 78.3 & 80.0\\\hline\end{tabular}\label{tab:results}\end{table*}

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Comparison of the performance of the COVID-19 detection models using different signal representations on breathing and speech modalities in terms of the AUC(\%).

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2306.16466v2_train__729297a2-d27c-449f-af1a-aa35c7f526b6

arxiv_table_to_tex

\begin{table}\begin{table}\caption{For different $t_1$, mean-field parameters $\chi_1$ and $\chi_2$ along upper phase boundary of CSL in Fig.\ref{spinmodeldiag}.}\label{tab:chi1chi2}%\centering\begin{tabular}{|c|c|c||c|c|c|}\hline$t_1$ & $\chi_1$ & $\chi_2$ &$t_1$ & $\chi_1$ & $\chi_2$\\\hline$0.05$& $0.3917e^{i\frac{\pi}{4}}$& $2.7796$& $0.7$& $0.4534e^{i\frac{\pi}{4}}$& $0.1958$\\\hline$0.1$& $0.3933e^{i\frac{\pi}{4}}$& $1.3887$&$0.711$& $0.4562e^{i\frac{\pi}{4}}$& $0.1866$ \\\hline$0.2$& $0.3986e^{i\frac{\pi}{4}}$& $0.6913$&$0.75$& $0.4465e^{i\frac{\pi}{4}}$& $0.2154$ \\\hline$0.3$& $0.4071e^{i\frac{\pi}{4}}$& $0.4546$&$0.8$& $0.4384e^{i\frac{\pi}{4}}$& $0.2345$ \\\hline$0.4$& $0.42e^{i\frac{\pi}{4}}$& $0.3266$&$0.85$& $0.4321e^{i\frac{\pi}{4}}$& $0.2473$ \\\hline$0.5$& $0.4416e^{i\frac{\pi}{4}}$& $0.2306$&$0.9$& $0.4266e^{i\frac{\pi}{4}}$& $0.2574$ \\\hline$0.6$& $0.4503e^{i\frac{\pi}{4}}$& $0.2052$&$0.95$& $0.4215e^{i\frac{\pi}{4}}$& $0.2661$ \\\hline$0.65$& $0.4493e^{i\frac{\pi}{4}}$& $0.2078$&$1$& $0.4163e^{i\frac{\pi}{4}}$& $0.274$ \\\hline\end{tabular}\end{table}

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For different $t_1$, mean-field parameters $\chi_1$ and $\chi_2$ along upper phase boundary of CSL in Fig.\ref{spinmodeldiag

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2211.08939v3_train__2d64e176-6c1e-4f6d-8688-57934b088e9a

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Results for the Wave equation.}\label{tab:wave}\begin{tabular}{|c|c|c|c|c|}\hlineModel & PINN & XPINNv2 & APINN-X & APINN-M\\ \hlineRel. $L_2$ & 1.900E-3$\pm$3.375E-4 & 1.378E-3$\pm$2.424E-4 & {1.492E-3$\pm$7.041E-4} & \textbf{1.299E-3$\pm$2.941E-4} \\ \hline\end{tabular}\end{table}

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Results for the Wave equation.

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2211.08939v3_train__82ef9209-e97d-4254-99bf-74f8a0a6a3cd

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Results for the Helmholtz equation.}\label{tab:helmholtz}\begin{tabular}{|c|c|c|c|c|}\hlineModel & PINN & XPINNv1 & XPINNv2 & -\\ \hlineRel. $L_2$ & 2.438E-3$\pm$5.196E-4 & 5.222E-2$\pm$4.001E-3 & 1.297E-3$\pm$1.786E-4 & - \\ \hlineModel & APINN-X-F & APINN-X & APINN-M-F & APINN-M \\ \hlineRel. $L_2$ & 1.554E-3$\pm$3.203E-4 & \textbf{1.275E-3$\pm$4.710E-4} & 1.911E-3$\pm$3.850E-4 & 1.477E-3$\pm$5.679E-4\\ \hline\end{tabular}\end{table}

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Results for the Helmholtz equation.

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2211.08939v3_train__0808672e-64d6-424e-afca-a910f327ab5f

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Results for the Klein-Gordon equation.}\label{tab:KG}\begin{tabular}{|c|c|c|c|c|}\hlineModel & PINN & XPINNv1 & XPINNv2 & -\\ \hlineRel. $L_2$ & 3.565E-3$\pm$9.412E-4 & 5.980E-1$\pm$7.601E-2 & 3.700E-3$\pm$2.741E-4 & - \\ \hlineModel & APINN-X-F & APINN-X & APINN-M-F & APINN-M\\ \hlineRel. $L_2$ & 3.195E-3$\pm$8.112E-4 & {3.030E-3$\pm$1.474E-3} & 3.197E-2$\pm$6.253E-3 & \textbf{2.846E-3$\pm$8.568E-4}\\ \hline\end{tabular}\end{table}

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Results for the Klein-Gordon equation.

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2211.08939v3_train__3d744c3a-0fab-4184-a31e-8b5fa89892ce

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Results for the Poisson's equation.}\label{tab:poisson}\begin{tabular}{|c|c|c|c|}\hlineModel & PINN & XPINNv1 & XPINNv2\\ \hlineRel. $L_2$ & 4.436E-2$\pm$ 2.721E-2 & 4.022E-1$\pm$ 1.005E-3 & 8.578E-2$\pm$ 9.856E-3 \\ \hlineModel & APINN-F & APINN & APINN-O\\ \hlineRel. $L_2$& 4.263E-2 $\pm$ 1.189E-2 & \textbf{3.978E-2 $\pm$ 2.061E-2} & \textcolor{red}{2.749E-2 $\pm$ 1.432E-2}\\\hline\end{tabular}\end{table}

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Results for the Poisson's equation.

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2211.08939v3_train__abcb2e52-54c4-4c35-af50-f69f8548bf35

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Relative $L_2$ error for the function $u$ in the Boussinesq-Burger equation.}\label{tab:BB_u}\begin{tabular}{|c|c|c|c|c|}\hlineModel & PINN & XPINN & XPINN4 & / \\ \hlineRel. $L_2$ & 1.470E-02$\pm$6.297E-03 & 1.456E-02$\pm$6.391E-03&3.254E-02$\pm$1.025E-02& / \\ \hlineModel & APINN-M & APINN-X & APINN4-M & APINN4-X \\ \hlineRel. $L_2$ & \bf1.091E-02$\pm$4.588E-03 & 1.388E-02$\pm$4.310E-03 & 1.328E-02$\pm$8.099E-03& 2.559E-02$\pm$6.554E-03\\ \hline\end{tabular}\end{table}

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Relative $L_2$ error for the function $u$ in the Boussinesq-Burger equation.

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2211.08939v3_train__15a3b2d1-994a-4517-b523-0df9bbd69c54

arxiv_table_to_tex

\begin{table}[]\begin{table}[]\centering\caption{Relative $L_2$ error for the function $v$ in the Boussinesq-Burger equation.}\label{tab:BB_v}\begin{tabular}{|c|c|c|c|c|}\hlineModel & PINN & XPINN & XPINN4 & / \\ \hlineRel. $L_2$ & 1.106E-01$\pm$4.498E-02 & 9.786E-02$\pm$3.485E-02& 2.706E-01$\pm$9.078E-02& / \\ \hlineModel & APINN-M & APINN-X & APINN4-M & APINN4-X \\ \hlineRel. $L_2$ & \bf8.185E-02$\pm$2.973E-02 &9.623E-02$\pm$2.446E-02 &9.616E-02$\pm$5.397E-02& 1.676E-01$\pm$4.946E-02\\ \hline\end{tabular}\end{table}

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Relative $L_2$ error for the function $v$ in the Boussinesq-Burger equation.

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2310.03542v3_train__0828b61b-9718-457f-8693-6373f3942d47

arxiv_table_to_tex

\begin{table}[t]\begin{table}[t]\begin{tabular}[t]{|l|l|l|}\hline\multicolumn{3}{|c|}{$(\beta=1.9, \kappa=1.0)$} \\\hline$N_s$ & \#configurations & \#eigenvalues \\ \hline16 & 3000 & 33 \\ \hline20 & 1500 & 63 \\ \hline\end{tabular}\mbox{}\begin{tabular}[t]{|l|l|l|}\hline\multicolumn{3}{|c|}{$(\beta=2.1, \kappa=1.0)$ and $(\beta=2.6, \kappa=0.3)$} \\\hline$N_s$ & \#configurations & \#eigenvalues \\ \hline20 & 8970 & 63 \\ \hline24 & 8000 & 110 \\ \hline28 & 3000 & 174 \\ \hline32 & 1150 & 260 \\ \hline\end{tabular}\caption{Configuration statistics and number of (non-degenerate)eigenvalues used to study the volume scaling of the localizationproperties of staggered eigenmodes in the confined phase (top table)and in the deconfined and Higgs phases (bottom table).}\label{table:2}\end{table}

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Configuration statistics and number of (non-degenerate)eigenvalues used to study the volume scaling of the localizationproperties of staggered eigenmodes in the confined phase (top table)and in the deconfined and Higgs phases (bottom table).

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2310.03542v3_train__6984c70c-3128-4525-b78a-03fa04b3280f

arxiv_table_to_tex

\begin{table}[b]\begin{table}[b]\centering\begin{tabular}{c|c}\hline\hline$\kappa_{\mathrm{loc}}$ & 0.7303(56)\\$a$ & 0.24915(13)\\$b$ & 0.1185(53)\\$c$ & 0.1874(52)\\$d$ & 26.4(2.0) \\\hline$\chi^2/\mathrm{dof}$& 2.05\end{tabular}\caption{Parameters of a best fit of the $\kappa$ dependence of themobility edge in the deconfined and Higgs phases at $\beta=2.6$,with the fitting function in Eq.~\eqref{eq:sigmo}. Onlystatistical errors are reported.}\label{tab:kc}\end{table}

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Parameters of a best fit of the $\kappa$ dependence of themobility edge in the deconfined and Higgs phases at $\beta=2.6$,with the fitting function in Eq.~\eqref{eq:sigmo

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2209.01217v3_train__94bfb8b4-552a-46ac-8c76-0620fd989ea7

arxiv_table_to_tex

\begin{table}[tb]\begin{table}[tb]\caption{performance of TabularNCD on the unknown classes.}\begin{center}\setlength{\tabcolsep}{3pt}\begin{tabular}{l l c c c c}\hlineDataset & Method & BACC & ACC & NMI & ARI \\\hline\multirow{4}{*}{MNIST} & Baseline & 57.7$\pm$4.7 & 57.6$\pm$4.5 & 0.37$\pm$0.2 & 0.31$\pm$0.3 \\& Spect. clust & - & - & - & - \\& \textit{k}-means & 60.1$\pm$0.0 & 61.1$\pm$0.0 & 0.48$\pm$0.0 & 0.38$\pm$0.0 \\& TabularNCD & \textbf{91.5$\pm$4.1} & \textbf{91.4$\pm$4.2} & \textbf{0.82$\pm$0.06} & \textbf{0.81$\pm$0.04} \\\hline\multirow{4}{*}{Forest} & Baseline & 55.6$\pm$2.0 & 68.5$\pm$1.4 & 0.27$\pm$0.02 & 0.15$\pm$0.01 \\& Spect. clust & 32.1$\pm$1.4 & 85.8$\pm$4.0 & 0.01$\pm$0.01 & 0.09$\pm$0.01 \\& \textit{k}-means & 32.9$\pm$0.0 & 62.0$\pm$0.0 & 0.04$\pm$0.00 & 0.05$\pm$0.00 \\& TabularNCD & \textbf{66.8$\pm$0.6} & \textbf{92.2$\pm$0.2} & \textbf{0.37$\pm$0.09} & \textbf{0.56$\pm$0.09} \\\hline\multirow{4}{*}{Letter} & Baseline & 55.7$\pm$3.6 & 55.9$\pm$3.6 & 0.49$\pm$0.04 & 0.33$\pm$0.04 \\& Spect. clust & 45.3$\pm$4.0 & 45.3$\pm$4.0 & 0.48$\pm$0.03 & 0.18$\pm$0.03 \\& \textit{k}-means & 50.2$\pm$0.6 & 49.9$\pm$0.6 & 0.40$\pm$0.01 & 0.28$\pm$0.01 \\& TabularNCD & \textbf{71.8$\pm$4.5} & \textbf{71.8$\pm$4.5} & \textbf{0.60$\pm$0.04} & \textbf{0.54$\pm$0.04} \\\hline\multirow{4}{*}{Human} & Baseline & 80.0$\pm$0.5 & 78.0$\pm$0.6 & 0.64$\pm$0.01 & 0.62$\pm$0.01 \\& Spect. clust & 70.2$\pm$0.0 & 69.4$\pm$0.0 & 0.72$\pm$0.00 & 0.60$\pm$0.00 \\& \textit{k}-means & 75.3$\pm$0.0 & 77.0$\pm$0.0 & 0.62$\pm$0.00 & 0.59$\pm$0.00 \\& TabularNCD & \textbf{98.9$\pm$0.2} & \textbf{99.0$\pm$0.2} & \textbf{0.95$\pm$0.01} & \textbf{0.97$\pm$0.01} \\\hline\multirow{4}{*}{Satimage} & Baseline & 53.8$\pm$3.4 & 53.9$\pm$4.2 & 0.25$\pm$0.03 & 0.22$\pm$0.03 \\& Spect. clust & 82.2$\pm$0.1 & 77.8$\pm$0.1 & 0.51$\pm$0.00 & 0.46$\pm$0.00 \\& \textit{k}-means & 73.7$\pm$0.3 & 69.2$\pm$0.2 & 0.30$\pm$0.00 & 0.28$\pm$0.00 \\& TabularNCD & \textbf{90.8$\pm$4.0} & \textbf{91.4$\pm$5.0} & \textbf{0.71$\pm$0.11} & \textbf{0.79$\pm$0.07} \\\hline\multirow{4}{*}{Pendigits} & Baseline & 72.8$\pm$5.5 & 72.8$\pm$5.4 & 0.62$\pm$0.06 & 0.54$\pm$0.07 \\& Spect. clust & {84.0$\pm$0.0} & {84.0$\pm$0.0} & \textbf{0.78$\pm$0.00} & 0.67$\pm$0.00 \\& \textit{k}-means & 82.5$\pm$0.0 & 82.5$\pm$0.0 & 0.72$\pm$0.00 & 0.63$\pm$0.00 \\& TabularNCD & \textbf{85.5$\pm$0.7} & \textbf{85.6$\pm$0.8} & 0.76$\pm$0.02 & \textbf{0.71$\pm$0.02} \\\hline\multirow{4}{*}{Census} & Baseline & 53.0$\pm$3.5 & \textbf{55.0$\pm$6.5} & 0.49$\pm$0.02 & 0.30$\pm$0.03 \\& Spect. clust & 23.6$\pm$3.3 & 51.3$\pm$5.5 & 0.24$\pm$0.11 & 0.18$\pm$0.09 \\& \textit{k}-means & 38.5$\pm$2.6 & 49.8$\pm$3.6 & 0.41$\pm$0.05 & 0.28$\pm$0.03 \\& TabularNCD & \textbf{61.9$\pm$0.6} & 50.1$\pm$0.9 & 0.48$\pm$0.01 & 0.30$\pm$0.00 \\\hline\end{tabular}\label{table:tabularncd_results}\end{center}\footnotesize{The standard deviation is computed over 10 executions. The 2 unsupervised clustering methods (Spect. clust and $k$-means) are only fitted to the test instances belonging to the unknown classes.}\end{table}

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performance of TabularNCD on the unknown classes.

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2209.01217v3_train__7aaed380-002e-40f3-ba4b-582946aa3fbd

arxiv_table_to_tex

\begin{table}[!hbt]\begin{table}[!hbt]\caption{Ablation study of the proposed method.}\begin{center}\begin{tabular}{ l | c | c | c | c }\hlineMethod / Metrics & BACC & ACC & NMI & ARI \\\hlineTabularNCD & 90.8$\pm$4.0 & 91.4$\pm$5.0 & 0.71$\pm$0.11 & 0.79$\pm$0.07 \\\hline- w/o SSL & 88.4$\pm$5.3 & 88.6$\pm$7.0 & 0.67$\pm$0.15 & 0.67$\pm$0.10 \\- w/o CE & 72.0$\pm$6.1 & 69.5$\pm$6.0 & 0.44$\pm$0.12 & 0.49$\pm$0.08 \\- w/o BCE & 33.3$\pm$0.0 & 51.7$\pm$0.0 & 0.00$\pm$0.00 & 0.00$\pm$0.00 \\- w/o MSE & 66.7$\pm$5.7 & 63.9$\pm$4.4 & 0.44$\pm$0.02 & 0.37$\pm$0.02 \\ \hline\end{tabular}\label{table:ablation_study}\end{center}\footnotesize{\textbf{SSL:} Self-Supervised Learning, \textbf{CE:} Cross Entropy loss of the classification network, \textbf{BCE:} Binary Cross Entropy loss of the clustering network, \textbf{MSE:} Mean Squared Error consistency loss. The dataset is Satimage \cite{uci}.}\end{table}

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Ablation study of the proposed method.

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2209.01217v3_train__62e53aed-07e4-4798-827e-4ebcf6df3871

arxiv_table_to_tex

\begin{table}[!h]\begin{table}[!h]\caption{Clustering performance on new classes of $k$-means on different data representations.}\begin{center}\begin{tabular}{l | c c c c}\hlineDataset & \multicolumn{4}{c}{MNIST} \\\hlineMethod / Metrics & BACC & ACC & NMI & ARI \\\hline(1) $k$-means & 61.0 & 61.1 & 0.476 & 0.378 \\(2) $k$-means w/ SSL & 63.8 & 63.9 & 0.501 & 0.414 \\(3) $k$-means w/ joint & 84.9 & 85.4 & 0.748 & 0.728 \\\hline\end{tabular}\label{table:k_means_different_latent}\end{center}\footnotesize{(1) corresponds to the input data, (2) to the latent space after Self-Supervised Learning on all the available data (Sec. \ref{sec:ssl}), and (3) after the joint training of the proposed method (Sec. \ref{sec:joint})}\end{table}

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Clustering performance on new classes of $k$-means on different data representations.

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2307.06524v1_train__c059d00b-9e90-43ed-b75c-e2c7e364fdf3

arxiv_table_to_tex

\begin{table*}[ht]\begin{table*}[ht]\centering\label{tab:sample-dialogue}\begin{tabular}{l|l|l}\multicolumn{1}{c|}{\textbf{Hyperparameter}} & \multicolumn{1}{c}{\textbf{Sweep Range}} & \textbf{Best Value} \\\topruleLearning Rate & 1 $\times 10^{-4}, 1 \times 10^{-5}, 1 \times 10^{-3}, 6 \times 10^{-4}$ & $6 \times 10^{-4}$ \\\hlineBatch Size & 32, 64, 128 & 32 \\\hlineEarly Stopping (Min Delta) & 0, 0.001, 0.005, 0.1, 0.5 & 0 \\\hlineEarly Stopping (Patience) & 0, 1, 2, 3, 4 & 4 \\\hlineGradient Clip Norm & 1.0 & 1.0 \\\hlinePrecision & 16, 32 & 32 \\\hlineContext Window Size & 1, 2, 3, 4 & 3 \\\hline\end{tabular}\caption{Hyperparameter values for all experiments.\label{tab:hyperparams}}\end{table*}

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Hyperparameter values for all experiments.\label{tab:hyperparams

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2111.03237v3_train__da32d273-d5d8-48fc-a1dc-3ba72b36c935

arxiv_table_to_tex

\begin{table}[htbp]\begin{table}[htbp]\centering\begin{tabular}{| c| c c c c c c c c |}\hline$\delta$ & $1.5$ & $2$ & $2.5$ & $3$ & $3.5$ & $4$& $4.5$& $5$ \\[0.5ex]\hline$\beta=0$ & 0.27 & 0.20 & 0.16 & 0.12 & 0.10 & 0.08 &0.07 & 0.06 \\\hline$\beta=5$ & 0.45 & 0.38 & 0.33 & 0.29 & 0.26 & 0.23 & 0.20 & 0.18 \\\hline$\beta=10$ & 0.62 & 0.58 & 0.55 & 0.52 & 0.50 & 0.48 & 0.45 & 0.44 \\\hline\end{tabular} \\[0.5ex]\caption{MSE of GLM-EP for the 1-bit CS problem. $n=10^5$. The MSE is averaged over 100 independent runs. The number of iterations is 20.}\label{Tab:1-bit}\end{table}

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MSE of GLM-EP for the 1-bit CS problem. $n=10^5$. The MSE is averaged over 100 independent runs. The number of iterations is 20.

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2111.03237v3_train__e1a365a4-3ec9-4b01-98b4-41cd2d274e6e

arxiv_table_to_tex

\begin{table}[htbp]\begin{table}[htbp]\centering\begin{tabular}{| c | c c c c c |}\hlineSNR & 30dB& 35dB & 40dB & 45dB & 50dB \\[0.2ex]\hlineMSE &1.28e-01 & 5.92e-02 & 2.18e-02 & 6.94e-03 & 2.14e-03\\\hline\end{tabular} \\[0.5ex]\caption{MSE of GLM-EP for noisy phase retrieval. $\delta=1.1$. $n=10^5$. $\beta=10$. The MSE is averaged over 100 independent runs. The number of iterations is 10.} \label{Tab:PR_noisy}\end{table}

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MSE of GLM-EP for noisy phase retrieval. $\delta=1.1$. $n=10^5$. $\beta=10$. The MSE is averaged over 100 independent runs. The number of iterations is 10.

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2203.13503v1_train__07c4e820-515d-4fae-bb54-0edbb5b2ca25

arxiv_table_to_tex

\begin{table*}[h]\begin{table*}[h]\vspace{-5pt}\tiny\centering\begin{tabular}{c|ccccc|ccccc|ccccc}\toprule\multirow{2}{*}{Criteria} & \multicolumn{5}{c|}{SL}& \multicolumn{5}{c|}{SSMI}&\multicolumn{5}{c}{PSNR}\\& BE & LGM & DEGM & DEGM-2& CN-DPM*& BE & LGM & DEGM & DEGM-2& CN-DPM*& BE & LGM & DEGM & DEGM-2& CN-DPM*\\\midruleMNIST &26.3&685.3&22.3 &22.3&21.9&0.88&0.19&0.90 &0.90&0.90&21.0&7.0&21.8 &21.8&21.8\\SVHN &47.0&941.7&30.1 &29.0&39.3&0.58&0.20&0.66 &0.67&0.61&13.7&5.0&15.5 &15.7&14.3\\Fashion&43.8&663.4&37.7 &27.4&36.6&0.68&0.15&0.72 &0.79&0.73&18.4&3.7&19.0 &20.6&19.2\\IFashion &45.9&1148.4&35.6 &27.4&38.4&0.72&0.11&0.76 &0.81&0.76&18.2&5.0&19.4 &20.6&19.1\\RMNIST &27.9&704.2&20.2 &22.1&25.3&0.87&0.20&0.91 &0.90&0.89&16.5&7.0&22.2 &21.8&21.2\\Cifar10 &994.4&1241.1&615.3 &608.1&892.1&0.29&0.23&0.49 &0.50&0.34&16.5&15.4&18.9 &18.9&17.0\\Average &197.5&897.4&126.9 &122.7&175.6&0.67&0.18&0.74 &0.76&0.70&18.1&7.2&19.5 &19.9&18.8\\\bottomrule\end{tabular}\caption{The performance of various models under the MSFIRC learning setting.}\label{Unsupervised1}\end{table*}

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The performance of various models under the MSFIRC learning setting.

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2203.13503v1_train__a246b93f-4c7f-4579-be51-b4101df5d275

arxiv_table_to_tex

\begin{table*}[h]\begin{table*}[h]\vspace{-5pt}\tiny\centering\begin{tabular}{c|ccccc|ccccc|ccccc}\toprule\multirow{2}{*}{Criteria} & \multicolumn{5}{c|}{SL}& \multicolumn{5}{c|}{SSMI}&\multicolumn{5}{c}{PSNR}\\& BE & LGM & DEGM & DEGM-2& CN-DPM*& BE & LGM & DEGM & DEGM-2& CN-DPM*& BE & LGM & DEGM & DEGM-2& CN-DPM*\\\midruleCelebA &213.9&535.6&229.2&217.0&215.4&0.69&0.48&0.66&0.69&0.69&23.5&19.3&23.2&23.4&23.5\\CACD &414.9&814.3&368.3&281.95&347.3&0.57&0.47&0.62&0.68&0.63&20.6&17.33&21.2&22.4&21.4\\3D-Chair &649.1&2705.9&324.0&291.46&513.8&0.73&0.42&0.84&0.86&0.79&19.0&13.54&22.4&23.1&20.5\\Omniglot &875.1&5958.9&225.6&195.7&343.2&0.73&0.22&0.92&0.93&0.89&17.9&9.2&24.0&24.6&22.1\\Sub-ImageNet &758.4&683.1&689.6&652.8&769.1&0.37&0.42&0.41&0.43&0.37&18.5&18.9&19.0&19.2&18.5\\Car &745.1&583.7&588.8&565.9&709.8&0.39&0.48&0.47&0.49&0.42&18.0&19.0&19.0&19.2&18.2\\Zappos &451.1&431.2&263.4&275.8&280.7&0.68&0.60&0.75&0.74&0.73&20.0&20.2&22.4&22.3&22.1\\CUB &492.0&330.2&461.3&569.6&638.6&0.35&0.48&0.45&0.43&0.35&19.0&20.9&19.3&18.6&18.0\\Average &575.0&1505.4&393.8&381.3&477.2&0.60&0.45&0.64&0.66&0.61&19.6&17.3&21.3&21.6&20.5\\\bottomrule\end{tabular}\caption{The performance of various models under the CCCOSCZC learning setting.}\label{Unsupervised2}\end{table*}

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The performance of various models under the CCCOSCZC learning setting.

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2203.13503v1_train__cd26e0e8-a883-4da0-b806-ef8388345c98

arxiv_table_to_tex

\begin{table}[ht]\begin{table}[ht]\centering\begin{tabular}{l|cccccc}\hlineModel & LGM &BE & DEGM& DEGM-2&CN-DPM* &LIMix \\\hlineN &${1.9 \times 10^9}$ &${3.9 \times 10^9}$&${3.2 \times 10^8}$ &${1.3 \times 10^9}$&${9.4 \times 10^9}$&${9.4 \times 10^9}$ \\\hline\end{tabular}\caption{The number of parameters of various models under CCCOSCZC learning setting.}\label{Unsupervised_2}\end{table}

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The number of parameters of various models under CCCOSCZC learning setting.

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2311.10091v1_train__532b93ad-b829-45d6-bbc4-041e300f30e5

arxiv_table_to_tex

\begin{table}[t!]\begin{table}[t!]\setlength{\tabcolsep}{2pt}\centering\small\caption{Quantitative results on the \MipNerfDataset~ data set. We report the PSNR, LPIPS and SSIM results for each object and compare them to baselines. Our method achieves a performance comparable to the baselines while being significantly faster during inference\revAdded{~(see \tabref{perf_comparison})}.\revAdded{In our comparison, we exclude the two scenes with license issues: Flowers, Treehill.}}\label{tab:outdoor_scenes}\vspace{-1em}\resizebox{1\columnwidth}{!}{\begin{tabular}{cc|lll|lll}\toprule& & \multicolumn{3}{c}{Outdoor scenes} & \multicolumn{3}{c}{Indoor scenes} \\& & PSNR~$\uparrow$ & SSIM~$\uparrow$ & LPIPS~$\downarrow$ & PSNR~$\uparrow$ & SSIM~$\uparrow$ & LPIPS~$\downarrow$ \\\midrule\multirow{4}{*}{\rotatebox[origin=c]{90}{\emph{offline}}} & NeRF~\cite{mildenhall2020nerf} & 22.20 & 0.485 & 0.501 & 26.84 & 0.790 & 0.370 \\& Mip-NeRF~\cite{barron2021mipnerf} & 22.02 & 0.505 & 0.484 & 26.98 & 0.798 & 0.361 \\& Mip-NeRF 360~\cite{barron2022mipnerf360} & 25.92~\tikzcircle[gold,fill=gold]{2pt} & 0.747~\tikzcircle[gold,fill=gold]{2pt} & 0.244~\tikzcircle[gold,fill=gold]{2pt} & 31.72~\tikzcircle[gold,fill=gold]{2pt} & 0.917~\tikzcircle[gold,fill=gold]{2pt} & 0.179~\tikzcircle[gold,fill=gold]{2pt} \\& Ours (full ray) & 24.30~\tikzcircle[silver,fill=silver]{2pt} & 0.703~\tikzcircle[silver,fill=silver]{2pt} & 0.316~\tikzcircle[silver,fill=silver]{2pt} & 29.04 & 0.900~\tikzcircle[silver,fill=silver]{2pt} & 0.239~\tikzcircle[silver,fill=silver]{2pt} \\\midrule\midrule\multirow{4}{*}{\rotatebox[origin=c]{90}{\emph{interactive}}}& I-NGP~\cite{mueller2022ingp} & 23.90~\tikzcircle[bronze,fill=bronze]{2pt} & 0.648~\tikzcircle[bronze,fill=bronze]{2pt} & 0.369 & 29.47~\tikzcircle[silver,fill=silver]{2pt} & 0.877~\tikzcircle[bronze,fill=bronze]{2pt} & 0.273~\tikzcircle[bronze,fill=bronze]{2pt} \\& MobileNeRF~\cite{chen2022mobilenerf} & 22.90 & 0.524 & 0.463 & 25.74 & 0.757 & 0.453 \\& BakedSDF~\cite{yariv2023bakedsdf} & 23.40 & 0.577 & 0.351~\tikzcircle[bronze,fill=bronze]{2pt} & 27.20 & 0.845 & 0.300 \\& Ours & 23.17 & 0.606 & 0.389 & 29.19~\tikzcircle[bronze,fill=bronze]{2pt} & 0.872 & 0.285 \\\bottomrule\end{tabular}}\end{table}

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Quantitative results on the \MipNerfDataset~ data set. We report the PSNR, LPIPS and SSIM results for each object and compare them to baselines. Our method achieves a performance comparable to the baselines while being significantly faster during inference\revAdded{~(see \tabref{perf_comparison

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2311.10091v1_train__d52d8d03-64a6-4897-ae6f-0b53a378c553

arxiv_table_to_tex

\begin{table*}[!thbp]\begin{table*}[!thbp]\centering\small\caption{\revAdded{Per-scene quantitative LPIPS comparison on \ShellyDataset{} data set. }}\label{tab:shelly_details_lpips}\vspace{-1em}\begin{tabular}{c|c|c|c|c|c|c|c}\topruleLPIPS~$\downarrow$ & \tabincell{c}{NeRF\\~\cite{mildenhall2020nerf}} & \tabincell{c}{MipNeRF\\\cite{barron2021mipnerf}} & \tabincell{c}{NeuS\\\cite{wang2021neus}} & \tabincell{c}{I-NGP\\\cite{mueller2022ingp}} & \tabincell{c}{MobileNeRF\\\cite{chen2022mobilenerf}} & \tabincell{c}{Ours\\(full ray)} & {Ours} \\\midruleFernvase & 0.093 & 0.088 & 0.094 & 0.068 & 0.074 & 0.065 & 0.046 \\Pug & 0.198 & 0.190 & 0.209 & 0.156 & 0.167 & 0.132 & 0.093 \\Woolly & 0.241 & 0.217 & 0.232 & 0.181 & 0.163 & 0.139 & 0.089 \\Horse & 0.071 & 0.064 & 0.067 & 0.049 & 0.057 & 0.036 & 0.029 \\Khady & 0.246 & 0.239 & 0.251 & 0.215 & 0.218 & 0.185 & 0.160 \\Kitten & 0.094 & 0.092 & 0.097 & 0.079 & 0.094 & 0.066 & 0.056 \\\midruleAverage & 0.157 & 0.148 & 0.158 & 0.125 & 0.129 & 0.104 & 0.079 \\\bottomrule\end{tabular}\end{table*}

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\revAdded{Per-scene quantitative LPIPS comparison on \ShellyDataset{

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2311.10091v1_train__185c076a-ec1d-477f-8070-7d752efe67d4

arxiv_table_to_tex

\begin{table*}[!thbp]\begin{table*}[!thbp]\centering\small\caption{\revAdded{Per-scene quantitative SSIM comparison on \ShellyDataset{} dataset. }}\label{tab:shelly_details_ssim}\vspace{-1em}\begin{tabular}{c|c|c|c|c|c|c|c}\topruleSSIM~$\uparrow$ & \tabincell{c}{NeRF\\~\cite{mildenhall2020nerf}} & \tabincell{c}{MipNeRF\\\cite{barron2021mipnerf}} & \tabincell{c}{NeuS\\\cite{wang2021neus}} & \tabincell{c}{I-NGP\\\cite{mueller2022ingp}} & \tabincell{c}{MobileNeRF\\\cite{chen2022mobilenerf}} & \tabincell{c}{Ours\\(full ray)} & {Ours} \\\midruleFernvase & 0.937 & 0.940 & 0.932 & 0.955 & 0.944 & 0.964 & 0.976 \\Pug & 0.863 & 0.868 & 0.865 & 0.896 & 0.885 & 0.910 & 0.947 \\Woolly & 0.805 & 0.822 & 0.803 & 0.876 & 0.891 & 0.896 & 0.950 \\Horse & 0.975 & 0.980 & 0.973 & 0.985 & 0.980 & 0.988 & 0.992 \\Khady & 0.831 & 0.835 & 0.833 & 0.852 & 0.823 & 0.862 & 0.881 \\Kitten & 0.949 & 0.954 & 0.949 & 0.967 & 0.942 & 0.969 & 0.979 \\\midruleAverage & 0.893 & 0.899 & 0.893 & 0.922 & 0.911 & 0.932 & 0.954 \\\bottomrule\end{tabular}\end{table*}

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\revAdded{Per-scene quantitative SSIM comparison on \ShellyDataset{

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