# Dynamic Relevance-Weighting-Based Width-Adaptive Auto-Encoder
## 3 Width-Adaptive Autoencoder
### Adding and Pruning Nodes
This demonstrates its strong classification ability, especially on complex and imbalanced datasets like Epilepsy. Furthermore, it achieves the lowest training and testing loss values (0.7044 and 0.7899, respectively), indicating better learning stability and generalization. In contrast, other models such as DEVDAN, SAQN, and NDL perform significantly worse, with accuracies ranging between 25-31% and notably lower F1-scores, suggesting they struggle to capture meaningful patterns in the data. Although the WAAE has the largest model width (2032), this increased capacity enables it to represent complex temporal patterns more effectively, reinforcing the idea that adaptive width contributes significantly to its superior performance. * Computational complexity and time for Epilepsy

Table 14 presents a comparative analysis of the computational complexity and runtime performance of the WAAE against several state-of-the-art models using the Epilepsy dataset. Although the WAAE exhibits the highest test FLOPs (3.335 G) and model FLOPs (0.00145 G), it maintains competitive training time (176.62 s) and moderate training FLOPs (174.02 G). In contrast, DEVDAN, while having the lowest model FLOPs (0.00048 G), shows an exceptionally high training FLOPs (837742.70 G), suggesting inefficiency. SAQN variants achieve low model and test FLOPs but vary significantly in training time depending on epochs. NDL stands out with the shortest training and testing time and the lowest model FLOPs, but at the cost of slightly higher test FLOPs than SAQN. Overall, the WAAE strikes a balance between adaptability and computational efficiency, offering a favorable trade-off for real-time epilepsy data processing. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Accuracy** & **F1-Score** & **Train Loss** & **Test Loss** & **Width** \\ \hline DEVDAN & 25.48\% & 16\% & 0.8749 & 0.9535 & 1323 \\ SAQN & 26.52\% & 26.35\% & 1.0313 & 1.1628 & 257 \\ SAQN with epochs & 27.04\% & 26.80\% & 0.8729 & 0.937 & 254 \\ NDL & 31.04\% & 24.60\% & 1.0201 & 0.9543 & 226 \\ WAAE & 65.32\% & 65.21\% & 0.7044 & 0.7899 & 2032 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Performance measure comparison on the Epilepsy dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Train Time** & **Test Time** & \begin{tabular}{c} **Training** \\ **FLOPs (G)** \\ \end{tabular} & \
\begin{tabular}{c} **Testing** \\ **FLOPs (G)** \\ \end{tabular} &
\begin{tabular}{c} **Model’s** \\ **FLOPs (G)** \\ \end{tabular} \\ \hline DEVDAN & 10.8530 & 0.3858 & 1.0896 & 0.04792 & 0.00016 \\ SAQN & 80.2866 & 0.1774 & 1.12255 & 0.11704 & 0.00077 \\ SAQN with epochs & 79.7202 & 0.1691 & 1.71629 & 0.11704 & 0.00077 \\ NDL & 2.3384 & 0.007 & 1.321611 & 0.091686 & 0.00030 \\ WAAE & 175.0063 & 0.109 & 281.31 & 1.1248 & 0.00740 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Computational complexity and runtime comparison of Width-Adaptive AE and state-of-the-art approaches on [PERSON]’s dataset. * Comparative evaluation with existing state-of-the-art models

These results further highlight the advantage of using the proposed inner-product-based relevance weighting mechanism compared to the simpler heuristics used in DEVDAN, SAQN, and NDL. Although these baseline models incorporate basic node evaluation methods, they fall short in adapting to data complexity as efficiently as our approach. This provides indirect but strong evidence of the contribution and necessity of our more structured weighting criterion. Figure 12 displays a bar chart comparing the accuracy or F1-score of five models, DEVDAN, SAQN, SAQN with epochs, NDL, and WAAE, across four datasets: MNIST, CIFAR-10, Parkinson, and Epilepsy. Since the real datasets are unbalanced, the F1-score is used for comparison rather than accuracy. WAAE consistently outperforms or matches other models in terms of accuracy or F1-score across all datasets. For MNIST, all models perform similarly with high accuracy (~90-100%), with WAAE slightly leading.