## 4 Materials and Methods
### Proto-MAML
#### 4.3.2 Proto-MAML Training Within a BERT-Enhanced QA Framework
Sum of Positive and Negative Ranks: Sum the ranks corresponding to the positive differences \(\mathcal{W}^{+}\) and the ranks corresponding to the negative differences \(\mathcal{W}^{-}\) as follows: \(\mathcal{W}^{+}=\sum_{\mathcal{D}_{i}>0}R_{i}\) and \(\mathcal{W}^{-}=\sum_{\mathcal{D}_{i}<0}R_{i}\), where \(R_{i}\) is the rank assigned to the absolute value of \(D_{i}\). 4. Test Statistic: The test statistic of the Wilcoxon test is the smaller of \(\mathcal{W}^{+}\) and \(\mathcal{W}^{-}\); namely \(\mathcal{W}=\min(\mathcal{W}^{+},\mathcal{W}^{-})\). 5. Determination of the \(p\)-Value: The value of \(\mathcal{W}\) is compared to a Wilcoxon distribution table to determine the corresponding \(p\)-value. The commonly used significance level is \(\alpha=0.05\). If \(p<\alpha\), the null hypothesis is rejected, concluding that there is a significant difference between the two samples. Figure 6: Evolution of the meta-loss \(\mathcal{L}^{(2)}_{\text{meta}}\) for different programming languages and values of \(i\), visualized every 10 epochs. The steps and results of the analysis for each programming language concerning the WSR test are detailed below. The metrics \(\mathrm{Precision}_{\mathrm{combined}}\), \(\mathrm{Recall}_{\mathrm{combined}}\), and \(F1_{\mathrm{combined}}\) were obtained for different values of \(i\) with respect to each language. These values were used to evaluate the effectiveness of each model. For each language \(l\in L\):

* For each pair of models \((f,g)\), where \(f,g\in i\) and \(f>g\): 1. Difference in \(\mathrm{Precision}\): \(\mathcal{D}_{f,g,l}^{\mathrm{Precision}_{\mathrm{combined}}}=\mathrm{ Precision}_{\mathrm{combined}}^{g,l}-\mathrm{Precision}_{\mathrm{combined}}^{f,l}\); 2. Difference in \(\mathrm{Recall}\): \(\mathcal{D}_{f,g,l}^{\mathrm{Recall}_{\mathrm{combined}}}=\mathrm{Recall}_{ \mathrm{combined}}^{g,l}-\mathrm{Recall}_{\mathrm{combined}}^{f,l}\); 3. Difference in \(\mathrm{F1}\): \(\mathcal{D}_{f,g,l}^{\mathrm{F1}_{\mathrm{combined}}}=F1_{\mathrm{combined}}^{g,l}-F1 _{\mathrm{combined}}^{f,l}\); 4. Classification and Sign of the Differences: 1. If \(\mathcal{D}_{f,g,l}^{\mathrm{Metric}}>0\), then model \(g\) is better than model \(f\) in language \(l\), 2. If \(\mathcal{D}_{f,g,l}^{\mathrm{Metric}}<0\), then model \(g\) is worse than model \(f\) in language \(l\). The differences are ordered by their absolute value, and ranks are assigned to the differences, where smaller absolute values receive lower ranks. In the case of differences with equal absolute values, an average rank is assigned. The statistic \(\mathcal{W}\) is calculated by summing the ranks of the positive differences, as follows: \(\mathcal{W}=\sum_{\mathcal{D}_{i}>0}R_{i}\), where \(\mathcal{D}_{i}>0\) represents the positive differences and \(R_{i}\) are the corresponding ranks. With the obtained value of \(\mathcal{W}\), a Wilcoxon distribution table is used to calculate the \(p\)-value. A significance level of \(\alpha=0.05\) is established. If \(p<\alpha\), it is concluded that there is a significant difference between the models. For each language, the WSR results are listed in Table 8.

As demonstrated by Tables 4-6, optimal values for \(F1_{\mathrm{combined}}\), Entropy, and PE, alongside the superior meta-loss \(\mathcal{L}_{\mathrm{meta}}\) presented in Table 7, were identified under the following configurations: 5-shot-9-way for PHP, 5-shot-10-way for Java, 5-shot-5-way for C, and 5-shot-8-way for C++. These findings, derived through rigorous application of the Wilcoxon