# Dynamic Relevance-Weighting-Based Width-Adaptive Auto-Encoder
## 3 Width-Adaptive Autoencoder
### Adding and Pruning Nodes
The model's large width of 1896 further enhances its capacity to learn complex \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Accuracy** & **Train Loss** & **Test Loss** & **Width** \\ \hline DEVDAN & 41\% & 0.5660 & 0.5583 & 262 \\ SAQN & 33.89\% & 0.2428 & 0.2560 & 257 \\ SAQN with epochs & 32.99\% & 0.0604 & 0.0623 & 257 \\ NDL & 37.47\% & 0.6468 & 0.6469 & 798 \\ WAAE & 44.66\% & 0.5526 & 0.5538 & 1896 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance measure comparison on CIFAR-10 dataset. patterns in the CIFAR-10 dataset. The consistency between its low train and test losses (0.5526 and 0.5538, respectively) also reflects strong generalization. Therefore, the WAAE demonstrates the advantages of automated architecture tuning and the use of suitable loss functions, which together result in more reliable and higher classification performance than models like NDL that depend on manually selected, dataset-specific parameters. * Computational complexity and time for CIFAR-10

Table 10 presents a comparison of computational complexity and runtime performance for several models on the CIFAR-10 dataset, highlighting the trade-offs between training cost, inference efficiency, and model complexity. The WAAE, while more computationally intensive than some alternatives, demonstrates a balanced trade-off between performance and resource usage. It achieves a training time of 413.14 s, which is significantly faster than models like NDL (965.32 s) and SAQN with epochs (1258.41 s), despite having higher training FLOPs at 8246.78 gigaflops. This suggests that the WAAE is computationally heavier but more optimized. At test time, it maintains a competitive speed (0.698 s), similar to DEVDAN (0.6918 s) and SAQN (0.6849 s), although it incurs the highest testing FLOPs at 233.03 gigaflops, reflecting its increased model complexity. The model's FLOPs per inference (0.0233 G) are also the highest among all compared approaches, corresponding to its larger width and adaptive architecture. In contrast, models like SAQN and DEVDAN are computationally lighter but offer lower accuracy, while NDL exhibits extremely high training FLOPs (131,579.84 G) without delivering superior predictive performance. Consequently, the WAAE achieves the best balance between training efficiency, inference speed, and classification accuracy, making it a robust choice when moderate computational resources are available. It is important to note that the compared models, DEVDAN [18], SAQN [21], and NDL [17], employ simpler node selection or importance heuristics such as activation frequency and threshold-based pruning. These models therefore serve as effective baselines to isolate the impact of the inner-product-based relevance weighting used in our approach. The consistently superior performance of the WAAE across both accuracy and computational cost demonstrates the effectiveness of our more principled node relevance strategy. #### 4.2.4 Performance Comparison of the Proposed Approach with State-of-the-Art Models on Real Datasets

A comprehensive performance comparison was performed between the proposed WAAE and several state-of-the-art models across the two considered real-world datasets. The evaluation focuses on key performance metrics such as accuracy, F1-score, loss values, computational complexity, and model width. * Learned width dynamics and performance metrics for Parkinson's \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Model**} & **Train Time** & **Test Time** & **Training** & **Testing** & **Model’s** \\  & **(s)** & **(s)** & **FLOPs (G)** & **FLOPs (G)** & **FLOPs (G)** \\ \hline DEVDAN & 471.3421 & 0.6918 & 877.0574 & 32.3301 & 0.00483 \\ SAQN & 198.0413 & 0.6849 & 379.3614 & 31.6 & 0.00316 \\ SAQN with epochs & 1258.4149 & 0.4738 & 3034.2842 & 31.6 & 0.00316 \\ NDL & 965.3241 & 2.9983 & 131,579.845 & 99.287 & 0.00490 \\ WAAE & 413.1391 & 0.698 & 8246.7779 & 233.0302 & 0.0233 \\ \hline \end{tabular}
\end{table}