## 4 Materials and Methods
### Proto-MAML
#### 4.3.2 Proto-MAML Training Within a BERT-Enhanced QA Framework
Previous studies, such as those cited in [55], have demonstrated that this range is effective for ensuring generalization without overfitting, thus avoiding degradation in meta-learning updates. Compared to alternative configurations, such as \(i>10\), which increase task complexity, the range \(5\leq i\leq 10\) has been shown to achieve a favorable trade-off between training efficiency and performance. Configurations with \(i<5\), on the other hand, may oversimplify the learning task, leading to insufficient representation of real-world complexities [56]. When setting \(i\) within this intermediate range, FSL tasks provide a more realistic and generalizable benchmark for model evaluation. Metrics such as Precision, Recall, F1-score, and EM have been widely adopted in the context of QA tasks due to their ability to evaluate both the accuracy and completeness of predictions. Precision and Recall focus on correctness and coverage, while the F1-score integrates both of these measures, providing a balanced perspective. Exact Match (EM) complements these metrics by quantifying the exact alignment between predicted and ground truth indices, making it indispensable for QA models predicting \(A^{\prime}_{V_{\text{ISTART}}}\) and \(A^{\prime}_{V_{\text{IEND}}}\) spans. These metrics have been validated as effective evaluation tools across various QA benchmarks, demonstrating their robustness in capturing nuanced performance in Answer Extraction (AE) and Recommender Systems (RS) contexts. During training, metrics such as Entropy \(H(p)\) and Prediction Error (PE) are integral to Proto-MAML. The Entropy quantifies the uncertainty in softmax predictions, with lower values reflecting greater confidence. This metric ensures the adaptability of the model to new tasks by identifying areas that require fine-tuning or data augmentation. The PE measures the alignment between predicted and actual indices, directly influencing positional accuracy. Reducing the PE improves the reliability of predictions, enhances the ability of the model to generalize to unseen data, and optimizes its performance across diverse scenarios. Table 2 summarizes the performance metrics obtained during and after training. The configurations for the support and query sets under the 5-shot-\(i\)-way with \(n=100\) epochs are described in \[\min_{\theta}\sum_{\forall i\in\mathcal{T}}\mathcal{L}_{\mathcal{T}_{i}}( \mathcal{Q},\theta^{\prime}_{\mathcal{T}_{i}}), \tag{12}\]9

Table 4 summarizes the \(F1_{\text{combined}}\) results for different values of \(i\) during training. Based on this, Table 5 expands the analysis by presenting the entropy (\(H(p)\)) values, which reflect the uncertainty in predictions across different programming languages and configurations, considering the distributions of true positives (\(TP_{A^{\prime}_{V_{\text{ISTART}}}}\) and \(TP_{A^{\prime}_{V_{\text{IEND}}}}\)), false positives (\(FP_{A^{\prime}_{V_{\text{ISTART}}}}\) and \(FP_{A^{\prime}_{V_{\text{IEND}}}}\)), and false negatives (\(FN_{A^{\prime}_{V_{\text{ISTART}}}}\) and \(FN_{A^{\prime}_{V_{\text{IEND}}}}\)). Complementing these data, Table 6 provides the PE obtained for the same configurations. Table 7 presents the average meta-loss values \(\mathcal{L}^{(2)}_{\text{meta}}\) across different programming languages and configurations during 5-shot-\(i\)-way training, highlighting the general differences in performance over \(n=100\) epochs. Figure 6 complements this table by illustrating the evolution of meta-loss values (recorded every 10 epochs), providing a comprehensive view of the training progress for various programming languages under their respective configurations.