## 4 Results and Discussion
### Network Architecture
In modeling based on RGB components, using a \(1\times 1\) kernel means examining the relationships between individual color components, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer (Type)** & **Output Shape** & **Number of Parameters** \\ \hline Input layer & (None, 50, 50, 3) & 0 \\ \hline Conv2D & (None, 50, 50,3 2) & 128 \\ \hline Activation & (None, 50, 50, 32) & 0 \\ \hline Conv2D & (None, 50, 50, 64) & 2112 \\ \hline Activation & (None, 50, 50, 64) & 0 \\ \hline AveragePooling2D & (None, 46, 46, 64) & 0 \\ \hline LayerNormalization & (None, 46, 46, 64) & 128 \\ \hline Conv2D & (None, 46, 46, 64) & 4160 \\ \hline Activation & (None, 46, 46, 64) & 0 \\ \hline AveragePooling2D & (None, 44, 44, 64) & 0 \\ \hline GlobalMaxPooling2D & (None, 64) & 0 \\ \hline Flatten & (None, 64) & 0 \\ \hline Dense & (None, 150) & 9750 \\ \hline Dropout & (None, 150) & 0 \\ \hline Dense & (None, 50) & 7550 \\ \hline Dense & (None, 1) & 51 \\ \hline \hline \end{tabular}  
* Total params: 23,879 (93.28 KB) Trainable params: 23,879 (93.28 KB) Non-trainable params: 0 (0.00 Byte)  
\end{table} 
Table 2: Neural network architecture and parameters used in this study. rather than the neighborhood of each pixel. In our task, there was no need to detect small and then larger details, as is the case in shape recognition. The GELU activation function [47], applied as an alternative to ReLU (Rectified Linear Unit) and other activation functions in neural networks, ensures better gradient behavior and more efficient learning in deep neural networks (Figure 10). Its continuity, differentiability, and ability to preserve nonlinear data characteristics make it a valuable tool in the design of deep learning models. Unlike ReLU, which can suffer from gradient flow issues during training (known as the vanishing gradient problem), GELU provides better gradient throughput due to its structure. GELU preserves nonlinear features that are crucial for learning data representations, helping models better capture complex dependencies in training data. Figure 10: ReLU and GELU activation functions. Figure 9: Neural network architecture used in this study. In the LayerNormalization layer, normalization is performed along the feature axis for each sample, meaning that normalization is independent of other samples in the batch. Each feature vector (e.g., channels in an image) was normalized separately, considering only the values within that vector, not the entire batch. Unlike BatchNormalization, which operates depending on batch size, LayerNormalization remains stable even with small batches or a batch size of one. Normalization can help prevent issues like vanishing or exploding gradients and accelerate convergence. Normalizing the activations helps maintain values within a reasonable range, stabilizing the learning process. When activations are normalized, the optimizer (learning algorithm) finds it easier to adjust network weights, speeding up convergence to optimal weight values. GlobalMaxPool2D is a layer used in neural networks to reduce spatial data dimensions after applying convolutional layers or other layers processing spatial data, such as pooling layers [48; 49]. GlobalMaxPool2D operates by selecting the maximum value of each feature channel across the entire spatial area (all points) of the input feature tensor. GlobalMaxPool2D is an effective tool for spatial dimensionality reduction, retaining only the most significant features (highest values) from each feature channel. This reduces the number of model parameters, which can help reduce overfitting and computational complexity. GlobalMaxPool2D has no trainable parameters; its sole purpose is to select the maximum value from each feature channel throughout the feature map. For each feature channel, the GlobalMaxPool2D layer selects the highest value across the entire spatial area (height and width). The result of GlobalMaxPool2D is a tensor with reduced dimensions, containing only the maximum values for each feature channel.