## 4 Tt-Vfd-Sim
### TT-VFDL-SIM for Classification
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **FM Structure** \\ \end{tabular} } & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Compression**} & \multicolumn{3}{c}{**SIM Partial Training (RD) *} & \multicolumn{3}{c}{**Merging Task Training**} \\ \cline{5-8}  & & & **Ratio** & & \(R^{2}\) & MSE & \(R^{2}\) & \begin{tabular}{c} **Best Learning Rate** \\ \end{tabular} \\ \hline \multirow{8}{*}{\begin{tabular}{c} MFCMLFM \\ \end{tabular} } & \multirow{8}{*}{AIRQUAL} & **1.20** & **0.00765** & **0.47** & **0.00372** & **0.75** & **0.01** \\ \cline{3-8}  & & 2.00 & 0.00645 & 0.56 & **0.00376** & **0.75** & 0.0005 \\ \cline{3-8}  & & 3.00 & 0.00745 & 0.49 & **0.00389** & **0.74** & 0.0001 \\ \cline{3-8}  & & **1.20** & **0.00338** & **–0.60** & **0.00129** & **0.37** & **0.001** \\ \cline{3-8}  & & 2.00 & 0.00346 & \(-0.80\) & **0.00148** & **0.27** & 0.01 \\ \cline{3-8}  & & 3.00 & 0.00257 & \(-0.35\) & **0.00133** & **0.35** & 0.01 \\ \cline{3-8}  & & **1.25** & **0.00520** & **0.97** & **0.00373** & **0.98** & **0.01** \\ \cline{3-8}  & & 1.67 & 0.00547 & 0.97 & **0.00378** & **0.98** & 0.01 \\ \cline{3-8}  & & 5.00 & 0.00569 & 0.97 & **0.00396** & **0.98** & 0.01 \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} MLFM \\ \end{tabular} } & \multirow{8}{*}{AIRQUAL} & **1.20** & **0.00760** & **0.47** & **0.00385** & **0.74** & **0.0005** \\ \cline{3-8}  & & 2.00 & 0.00528 & 0.63 & **0.00406** & **0.72** & 0.001 \\ \cline{3-8}  & & 3.00 & 0.00814 & 0.45 & **0.00410** & **0.72** & 0.001 \\ \cline{3-8}  & & **1.20** & **0.00265** & **–0.28** & **0.00106** & **0.48** & **0.0005** \\ \cline{3-8}  & & 2.00 & 0.00284 & \(-0.46\) & **0.00108** & **0.47** & 0.01 \\ \cline{3-8}  & & 3.00 & 0.00293 & \(-0.52\) & **0.00137** & **0.33** & 0.01 \\ \cline{3-8}  & & **1.25** & **0.00484** & **0.97** & **0.00395** & **0.98** & **0.001** \\ \cline{3-8}  & & 1.67 & 0.00475 & 0.97 & **0.00420** & **0.98** & 0.01 \\ \cline{3-8}  & & 5.00 & 0.00476 & 0.97 & **0.00441** & **0.97** & 0.01 \\ \hline \multirow{8}{*}{
\begin{tabular}{c} SLFM \\ \end{tabular} } & \multirow{8}{*}{AIRQUAL} & **1.20** & **0.00862** & **0.40** & **0.00375** & **0.75** & **0.0005** \\ \cline{3-8}  & & 2.00 & 0.00517 & 0.64 & **0.00379** & **0.74** & 0.001 \\ \cline{3-8}  & & 3.00 & 0.00762 & 0.48 & **0.00386** & **0.74** & 0.0005 \\ \cline{3-8}  & & **1.20** & **0.00287** & **-0.37** & **0.00182** & **0.11** & **0.0005** \\ \cline{3-8}  & & 2.00 & 0.00264 & \(-0.37\) & **0.00192** & **0.06** & 0.001 \\ \cline{3-8}  & & 3.00 & 0.00253 & \(-0.33\) & **0.00212** & **–0.04** & 0.01 \\ \cline{3-8}  & & **1.25** & **0.00531** & **0.97** & **0.00428** & **0.98** & **0.01** \\ \cline{3-8}  & & 1.67 & 0.00465 & 0.97 & **0.00431** & **0.98** & 0.01 \\ \cline{3-8}  & & 5.00 & 0.00618 & 0.97 & **0.00444** & **0.97** & 0.001 \\ \hline \hline \end{tabular}

* MSE and \(R^{2}\) values of the SIM Partial Training are the averaged values of all guest parties which are participating in the TT-VFDL-SIM (for regression).

\end{table} 
Table 11: Performance of the TT-VFDL-SIM with method option as RD (for regression) under various conditions. As described in Section 5.1.5, we experimented by changing the learning rate of merging task training to 0.01, 0.001, and 0.0005 for each experimental unit, and the learning rate that achieved the highest performance was organized in the Best Learning Rate column. The experimental results for (FM Structure, Dataset, Compression Ratio) showing the highest performance for each (FM Structure, Dataset) are shown in red. These are summarized as main performance for each (FM Structure, Dataset) in Table 8. In addition, the merging task training performance, which is higher than that of CNTR for the same experimental unit, is indicated in bold. Meanwhile, for Method option DD, there are three feature options for extracting task-driven features.