## 4 Materials and Methods
### Proto-MAML
#### 4.3.2 Proto-MAML Training Within a BERT-Enhanced QA Framework
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Metric** & **Description** & **Mathematical Definition** \\ \hline \multirow{6}{*}{\(\mathbf{Precision}_{[\text{START}]}\)} & \multicolumn{2}{p{113.8 pt}}{Represents the precision for the start index, measuring the proportion of true positives} \\  & \((TP_{A^{\prime}_{[\text{START}]}})\) to the total of true positives & \multirow{2}{*}{\(\mathbf{Precision}_{[\text{START}]}=\frac{TP_{A^{\prime}_{[\text{START}]}}}{TP_{A^{\prime}_{[\text{START}]}}+FP_{A^{\prime}_{[\text{START}]}}}\)} \\  & \((TP_{A^{\prime}_{[\text{START}]}})\) and false positives (\(FP_{A^{\ \begin{table}
\begin{tabular}{l l l l l} \hline \hline \(i\) & **PE PHP** & **PE Java** & **PE C** & **PE C++** \\ \hline
5 & 0.0576 & 0.0291 & 0.0140 & 0.0191 \\ \hline
6 & 0.5731 & 0.2690 & 0.5018 & 0.4388 \\ \hline
7 & 0.3622 & 0.1672 & 0.2225 & 0.2630 \\ \hline
8 & 0.0643 & 0.0349 & 0.1835 & 0.0585 \\ \hline
9 & 0.0013 & 0.2236 & 0.1934 & 0.2525 \\ \hline
10 & 0.0163 & 0.0160 & 0.0173 & 0.0219 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Prediction Error (PE) for different configurations of 5-shot-\(i\)-way tasks across programming languages during Proto-MAML training. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \(i\) & **F1 combined PHP** & **F1 combined Java** & **F1 combined C** & **F1 combined C++** \\ \hline
5 & 96.90\% & 98.41\% & 99.23\% & 98.95\% \\ \hline
6 & 75.85\% & 87.00\% & 78.20\% & 80.40\% \\ \hline
7 & 83.25\% & 91.50\% & 89.00\% & 87.25\% \\ \hline
8 & 96.55\% & 98.10\% & 90.75\% & 96.85\% \\ \hline
9 & 99.93\% & 88.95\% & 90.30\% & 87.70\% \\ \hline
10 & 99.10\% & 99.12\% & 99.05\% & 98.80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: F1 combined values for PHP, Java, C, and C++ in 5-shot-\(i\)-way tasks during the training of Proto-MAML. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \(i\) & **PHP** & **Java** & **C** & **C++** \\ \hline
5 & 0.0753 & 0.0501 & 0.0273 & 0.0283 \\ \hline
6 & 0.6501 & 0.3888 & 0.6173 & 0.5833 \\ \hline
7 & 0.5985 & 0.2399 & 0.3171 & 0.3329 \\ \hline
8 & 0.0884 & 0.0581 & 0.2612 & 0.0852 \\ \hline
9 & 0.0017 & 0.3095 & 0.2999 & 0.3636 \\ \hline
10 & 0.0222 & 0.0281 & 0.0290 & 0.0342 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average meta-loss values \(\mathcal{L}^{(2)}_{\text{meta}}\) for different programming languages and configurations during 5-shot-\(i\)-way training of Proto-MAML. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \(i\) & **Entropy PHP** & **Entropy Java** & **Entropy C** & **Entropy C++** \\ \hline
5 & 0.182 & 0.160 & 0.140 & 0.145 \\ \hline
6 & 0.275 & 0.210 & 0.260 & 0.250 \\ \hline
7 & 0.240 & 0.195 & 0.210 & 0.220 \\ \hline
8 & 0.185 & 0.170 & 0.190 & 0.180 \\ \hline
9 & 0.140 & 0.230 & 0.210 & 0.225 \\ \hline
10 & 0.16 To determine the optimal values of the 5-shot-\(i\)-way models and maintain clarity regarding the performance metrics of Proto-MAML for QA with respect to each programming language, a statistical analysis was conducted using the Wilcoxon Signed-Rank (WSR) test. This test is an alternative to the paired t-test for related samples but does not require the assumption of normality [57]. The procedure to calculate the test statistic \(\mathcal{W}\) in the WSR test is as follows:

1. Calculation of the Differences (\(\mathcal{D}_{i}\)): Compute the differences between each pair of observations from the resulting 5-shot-\(i\)-way models as \(\mathcal{D}_{i}=X_{i,f}-X_{i,g}\), where \(X_{i,f}\) and \(X_{i,g}\) represent the observations from the two related samples in the \(i^{\text{th}}\) model for the observation pair \(\{f,g\}\). 2. Ranking of the Absolute Differences: Order the differences by their absolute values, excluding any differences equal to zero, and assign ranks to them. If there are differences with the same absolute value, assign them an average rank. 3.