## 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} p{113.8 pt}} \hline \hline
**Model** & **Complexity** & **Technical Reasoning** & **Comparative Performance (vs. Proto-MAML)** \\ \hline Proto-MAML & \(O(n\log n)\) & 1. Attention mechanism (\(O(n^{2})\)): Each token interacts with every other token, resulting in \(n\times n\) operations. 2. Logarithmic reduction: Meta-learning adjusts parameters incrementally, scaling with the logarithm of task size (7 \(\sim\log n\)). 3. Combined complexity: Meta-learning reduces \(O(n^{2})\) operations to \(O(n\log n)\), optimizing for dynamic scenarios. & Performance: Achieves an average F1-score of 98.78\% across all tasks. Specific results: PHP (99.3\%), Java (99.12\%), C/C++ (97.23\%), with an overall Exact Match (EM) score of 98.78\%. \\ \hline SySeVR [27] & \(O(n^{3})\) & 1. Abstract Syntax Tree (AST, \(O(n^{2})\)): Evaluates relationships between nodes, requiring \(n\times n=n^{2}\) operations. 2. Program Dependency Graph (PDG, \(O(n^{3})\)): Captures semantic dependencies, generating \(n^{3}\) combinations for multi-level relationships. 3. Integration bottleneck: Combined AST and PDG operations elevate complexity to \(O(n^{3})\). & Performance: F1 of 95.42\% in C/C++. Proto-MAML achieves a higher F1-score, with lower computational complexity. \\ \hline BBVD [29] & \(O(n^{2})\) & 1. Token-level analysis (\(O(n^{2})\)): PET evaluates \(n\times n=n^{2}\) relationships between tokens. 2. Absence of meta-learning: No iterative parameter optimization, unlike Proto-MAML. & Performance: F1 of 95.42\% in C/C++. Proto-MAML achieves a higher F1-score of 97.23\%, with lower computational complexity. \\ \hline VulDefend [30] & \(O(n^{2})\) & 1. AST (\(O(n^{2})\)): Encodes syntactic relationships, requiring \(n\times n=n^{2}\). 2. SSA (\(O(n^{2})\)): Tracks control flow across nodes, increasing complexity with data flow dependencies. 3. Combined iteration: Sequential RNN and LSTM processes add \(O(n^{2})\) layers, resulting in \(O(n^{4})\) overall. & Performance: Fl of 98.8\% in C/C++, while that of Proto-MAML is 97.23\%, significantly outperforming VulDefend by +7.33\%. \\ \hline SeqTrans [31] & \(O(n^{2})\) & 1. BSN (\(O(n)\)): Iteratively evaluates \(O(n)\) candidates for each token. 2. Pairwise comparisons (\(O(n^{2})\)): Evaluates token relationships across sequences, resulting in \(n\times n=n^{2}\). +74.2\%. \\ \hline VRepair [32] & \(O(n^{4})\) & 1. SNN (\(O(n^{2})\)): Processes tokens linearly with \(n\times n=n^{2}\) operations. 2. SSA (\(O(n^{2})\)): Adds flow analysis complexity. 3. Cross-propagation: SNN and SSA integration results in \(O(n^{2})\times O(n^{2})=O(n^{4})\). & Performance: Research metric of 27.59\% in C. Proto-MAML achieves an exact match of 98.2\%, significantly outperforming VRepair. \\ \hline DB-CBIL [33] & \(O(n^{4})\) & 1. CNN (\(O(n^{2})\)): Performers filtering and dimensionality reduction over \(n\times n=n^{2}\) operations. 2. BiLSTM (\(O(n^{2})\)): Captures forward and backward dependencies sequentially. 3. Joint iterations: Combined CNN and BiLSTM layers result in \(O(n^{2})\times O(n^{2})=O(n^{4})\). & Performance: Reconstruction rate of 99.51\% in C/C++. Proto-MAML achieves 98.78\% overall accuracy, with significantly lower computational demands. \\ \hline VuRLE [34] & \(O(n^{5})\) & 1. AST (\(O(n^{2})\)): Captures hierarchical relationships between nodes. 2. DBSCAN (\(O(n^{3})\)): Clustering compares each token with all others, resulting in \(O(n^{3})\). 3. Combined processes: \(O(n^{2})\times O(n^{3})=O(n^{5})\). & Performance: Replacement prediction rate of 65.59\% in Java. Proto-MAML achieves a rate of 99.5\%, outperforming VReL by +33.91\%. \\ \hline VulD-Transformer [35] & \(O(n^{4})\) & 1. TPG (\(O(n^{2})\)): Builds semantic graphs for tokens. 2. Transformer attention (\(O(n^{2})\)): Token-to-token relationships generate \(n^{2}\) interactions. 3. Combined iterations: \(O(n^{2})\times O(n^{2})=O(n^{4})\). & Performance: Accuracy ranging from 59.34\% to 80.44\% in C/C++. Proto-MAML surpasses \\ \hline GPT Survey [36] & \(O(n^{2})\)\(\sim O(n^{3})\) & 1. Pre-trained database search (\(O(n^{2})\)): Each input of size \(n\) is compared with internal data sets, scaling quadratically. 2. Answer calibration (\(O(n^{3})\)): Complex queries require iterative re-evaluations, elevating costs. & Performance: Accuracy of 88\%. Proto-MAML achieves an average F1-score of 97.5\%, with lower complexity. \\ \hline \hline \end{tabular}
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