# Dynamic Relevance-Weighting-Based Width-Adaptive Auto-Encoder
## 3 Width-Adaptive Autoencoder
### Adding and Pruning Nodes
This suggests that the model's architecture is not only scalable but also optimized for real-time deployment. Thus, although the WAAE entails higher training cost, its design allows it to balance complexity and performance more effectively than its peers, justifying the resource investment with its superior learning capacity and generalization. Figure 11 provides a visual comparison of the reconstruction quality of 10 random MNIST digit instances using five different models: DEVDAN, SAQN, SAQN,

Figure 11: Reconstruction of 10 random MNIST instances using (**a**) DEVDAN model; (**b**) SAQN; (**c**) SAQN without epochs; (**d**) NDL model; and (**e**) Width-Adaptive AE. epochs, NDL, and WAAE. The top row in each subfigure shows the original digit images, while the bottom row displays the corresponding reconstructions. Among the models, WAAE clearly produces the most accurate and visually faithful reconstructions, with digits that are crisp, well-formed, and closely match the original inputs in both shape and structure. The NDL model also performs well, producing generally recognizable digits with minor blurring, indicating a solid capacity to capture data representations. In contrast, the DEVDAN model yields reconstructions that are blurred and less distinct, though some digit structures remain identifiable. Both SAQN and SAQN without epochs perform poorly, with reconstructions that resemble random noise rather than digit shapes, reflecting a failure to learn meaningful latent representations. These visual results align with earlier quantitative findings and underscore the effectiveness of WAAE's adaptive architecture and appropriate loss function in achieving superior reconstruction and representational quality. * Learned width dynamics and performance metrics for CIFAR-10

Table 9 presents a performance comparison of several models on the CIFAR-10 dataset using various evaluation metrics, including accuracy, train and test loss, and model width. Among the models, the WAAE achieves the highest accuracy at 44.66%, which can be attributed to its large width (1896). DEVDAN also shows reasonable performance with 41% accuracy and balanced train and test losses, indicating good generalization despite its relatively small width of 262. In contrast, the SAQN models, both with and without epoch-based training, report the lowest accuracies (33.89% and 32.99%, respectively) even though they achieve very low loss values. This suggests a misalignment between the MSE loss function used and the classification nature of the task, leading to poor predictive performance. The NDL model, with a wider architecture (width of 798) achieves moderate accuracy (37.47%) but does not outperform DEVDAN, underscoring that higher width alone does not guarantee better performance. The superior performance of the WAAE in Table 9 can be further understood in light of how model width is determined in comparison to other models such as NDL. Notably, NDL relies on user-defined thresholds. Specifically, the MaxOutlier percentage is used to determine its width. This approach introduces variability and a degree of uncertainty into the model configuration, as the width is highly sensitive to this parameter. For example, when the MaxOutlier threshold is decreased to 10% of the data, the NDL model reaches its maximum width, with a corresponding loss of 0.63. Conversely, increasing the threshold to 30% reduces the width significantly to 308, yet the loss remains nearly unchanged. This demonstrates that the NDL model's performance does not scale linearly with its width, and that finding an optimal configuration requires trial and error that may not generalize well across datasets. In contrast, the WAAE employs a more systematic and data-driven method for determining width, enabling it to dynamically adjust its architecture in response to the data characteristics without requiring manual threshold tuning. This adaptability likely contributes to its ability to achieve the highest accuracy (44.66%) among all models in the comparison.