## 5 Results and Analysis  
We conduct experiments on all datasets with weights of the central task \(\in\) {1, 3, 6, 9, 12, 15}, which are specified in the experiment setting. The validation performance of MTDNN-SIWLM is depicted in Table 2. Each row of the table represents the weight of the central task, and the weights of the auxiliary tasks are all set to 1. In the case of MNLI, the validation and test datasets had matched or mismatched versions, and the weight settings for the highest performance in each version differed, at 1 and 6. We use accuracy/F1 and Pearson/Spearman for the evaluation metrics of QQP and STS-B, respectively. STS-B performed best in different weights for each metric. MNLI, QQP, QNLI, and SST-2 with large data sizes generally exhibit higher performance when the weight of the central task is less than 6. For CoLA, STS-B, MRPC, and RTE, which have a small data size, it was found that when a weight of 9 or more was applied, the performance was enhanced more in most cases. Consequently, applying equal weights when performing MTL on a small dataset may increase performance improvement. Figure 3a illustrates the accuracy variance of each dataset according to the task weight change. The \(x\)-axis indicates the weight of the central task, as used in Table 2. The \(y\)-axis indicates the difference between the minimum accuracy and the accuracy for each weight setting in one dataset. We use the same evaluation index for all datasets by expressing accuracy in this graph. Moreover, STS-B, which does not use the accuracy metric, is excluded from the graph. Furthermore, in Figure 3b, only pairwise text classification tasks (MNLI-m, QQP, MRPC and RTE) are represented to exclude performance differences caused by the differences in the task type. The value indicated by each axis is the same as in Figure 3a. As depicted in Figure 3b, for RTE and MRPC with small data sizes, the accuracy variance according to the task weight is relatively large. In contrast, MNLI-m and QQP with large data sizes have low accuracy variance. The smaller the data size, the more performance change is affected by the task weight. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Task Weight**} & **MNLI-m/mm** & **QQP** & **QNLI** & **SST-2** & **CoLA** & **STS-B** & \multirow{2}{*}{**MRPC Acc/F1**} & \multirow{2}{*}{**RTE Acc**} \\  & **Acc** & **Acc/F1** & **Acc** & **Acc** & **Acc/Mcc** & & **P/S Corr** & \\ \hline
1 & **84.65**/84.30 & 90.61/87.36 & 91.01 & 92.54 & 80.92/52.65 & 88.01/87.97 & 87.00/90.20 & 76.17 \\
3 & 84.52/84.35 & 90.76/87.56 & 91.23 & 92.54 & 81.20/53.39 & **88.05**/88.16 & 86.76/90.14 & 75.81 \\
6 & 84.34/**84.60** & **90.80**/87.61 & 91.14 & **92.88** & 81.11/53.18 & 87.83/87.90 & 86.76/90.21 & 77.25 \\
9 & 84.51/84.55 & 90.73/87.49 & **91.36** & 92.66 & 80.72/52.06 & 88.02/**88.20** & 87.99/90.90 & 77.61 \\
12 & 84.37/84.46 & 90.79/87.61 & 91.06 & 92.77 & **81.30/53.64** & 87.91/87.99 & **87.99/91.04** & 77.25 \\
15 & 84.52/84.54 & 90.59/**87.70** & 91.15 & 92.20 & 80.92/52.69 & 87.83/87.98 & 87.01/90.31 & **77.98** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Validation performance of MTDNN-SIWLM are reported; highest results are in bold font. Figure 3: Accuracy variance according to the task weight change. (**a**) amount of change in accuracy for each dataset except STS-B; (**b**) amount of change in accuracy for four datasets belonging to the Pairwise Text Classification. Accuracy difference = (accuracy at each weight \(-\) minimum accuracy). We fine-tune the model with the highest performance in Table 2. We achieve the highest performing model by averaging the performance of MNLI-m and MNLI-mm. For two metrics among QQP, STS-B, and MRPC, we attain the highest performance model by averaging performance. We demonstrate that our model is superior to other MTL-based models by comparing the validation performance the validation performance to three representative MTL models and the BERT model. As shown in Table 3, models using MTL outperform BERT.