# Dynamic Relevance-Weighting-Based Width-Adaptive Auto-Encoder
## 3 Width-Adaptive Autoencoder
### Adding and Pruning Nodes
Similarly, SAQN (Self-Adaptive Quasi-Autoencoder Network) adopts the same structural framework as DEVDAN but updates its network parameters using generative training exclusively. Neurons are added or removed based on the estimated NS value, allowing the model to adaptively reshape its architecture without engaging in discriminative learning phases. In contrast, NDL (Neurogenesis Deep Learning) is a dynamic deep learning approach that adds neurons only when the model fails to adequately reconstruct the input, as indicated by reconstruction error. While effective, NDL is memory-intensive due to its reliance on storing past samples for retraining and its progressively expanding architecture. Moreover, it requires frequent retraining and multiple forward passes to stabilize the updated network, making it computationally expensive. To assess the effectiveness of the proposed approach, experiments are conducted on the MNIST [36] and CIFAR-10 [37] benchmark datasets. A SoftMax classifier is used in all cases to evaluate classification performance after the final AE model is learned. DEVDAN [18], SAQN [21], and SAQN with epochs adopt the MSE loss function as specified by their approaches, while NDL [17] and Width-Adaptive AE adopt Binary Cross-Entropy. * Learned width dynamics and performance metrics for MNIST

Table 7 presents a comprehensive comparison of performance metrics across several models on the MNIST dataset. The proposed WAAE achieves the highest accuracy at 95.97%, outperforming all baselines, including NDL (95.03%), DEVDAN (90.60%), SAQN with epochs (89.61%), and standard SAQN (86.37%). In terms of training and testing loss, the WAAE also records the lowest values (0.0627 and 0.0629, respectively), indicating effective optimization. This contrasts with the higher loss values observed in DEVDAN and SAQN, which correlates with their lower classification performance. A key distinction lies in the learned network width: the WAAE dynamically expands to 1593 neurons, significantly wider than NDL (560), SAQN (258), and DEVDAN (14). This flexibility enables the proposed model to better capture the underlying complexity of the data, contributing to its superior accuracy and lower loss. These results highlight the effectiveness of the WAAE. The superior performance of the WAAE can be attributed not only to its ability \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & \multicolumn{2}{c}{**Parkinson**} & \multicolumn{2}{c}{**Epilepsy**} \\ \hline Learning Type & Manual & Dynamic & Manual & Dynamic \\ Learned parameter & 457,948,938 & 3,703,840 & 74,522,760 & 725,602 \\ Train time (s) & 10866.75 & 175.01 & 6192.44 & 176.62 \\ Test time (s) & 32.51 & 0.11 & 54.44 & 0.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between the manual tuning and dynamic learning approaches in terms of learned parameters, training time, and testing time for the two real datasets. to dynamically learn an optimal network width but also to its robustness against the limitations inherent in competing models. For instance, while NDL achieves high accuracy, its architecture heavily depends on user-defined parameters such as the reconstruction threshold and MaxOutlier. These parameters require manual tuning through a trial-and-error process, as there is no standardized approach for their selection. As a result, NDL's performance is sensitive to configuration choices, which can lead to inconsistent convergence and suboptimal generalization if not thoroughly optimized. The model's behavior demonstrates that varying the MaxOutlier percentage affects node expansion in unintuitive ways, further complicating its tuning. In contrast, the WAAE eliminates this dependency by autonomously adjusting its width based on learning dynamics, achieving better convergence as evidenced by its significantly lower training and testing losses. Additionally, models like DEVDAN and SAQN suffer from structural limitations.