## 4 Results and Discussions
As the parameters were elevated to 200,000 and 350,000, the BER climbed marginally to 6.0 \(\times\) 10\({}^{-3}\) and 6.3 \(\times\) 10\({}^{-3}\), respectively, indicating a tendency of minor performance deterioration. The training and validation loss curves at 8 dBm optical power for various parameter configurations in Figure 7a-d indicate that the losses for all four groups consistently decreased with the increase in epochs, while the disparity between training and validation losses remained minimal. The training and validation loss graphs for the four sets of parameters show that there was no sign of overfitting; all graphs show a steady decrease during training, with the final values staying close together and no major splits observed. This result was mostly due to the weight-decay regularization technique used by the AdamW optimizer, which substantially reduced the danger of overfitting as the parameter scale expanded. When the quantity of trainable parameters surpassed 150,000, the decline in  
Figure 5: Comparison of signal constellation diagrams for various neural networks and VNE (optical power: 8 dBm). Figure 6: BER performance curve of 2D-CNN with varying quantities of trainable parameters. BER optimization performance was not due to overfitting; rather, it was likely a consequence of redundant feature representation or the introduction of extraneous noise from an excess of trainable parameters, which increased the model's sensitivity to dynamic channel fluctuations. Experimental results showed that the 150,000-parameter setup struck the best balance between being complex enough and being able to generalize well: it reduced the chance of underfitting by effectively extracting features (which was shown by the higher BER in the 100,000-parameter setup) while avoiding issues of wasted computing power and increased noise that come with having too many parameters. Figure 8 compares CNN BER with different activation functions. The figure shows that the 2D-CNN with ReLU activation function had the lowest BER of \(5.5\times 10^{-3}\), suggesting higher performance. The main reasons ReLU works are ReLU has an easy mathematical expression. This function saves computational power and speeds model training. Second, the ReLU function handles gradient vanishing well. Vanishing gradients hamper deep neural network model training. When x > 0, the ReLU function gradient was 1, avoiding gradient vanishing and improving model convergence. The Sigmoid function outputted 0-1. The gradient approached zero when the input value was extremely high or low, increasing BER and preventing parameter updates. The Tanh function reduced gradient vanishing, but its output was limited to \(-1\) and 1; thus, minor gradients still affected training. Mish had a greater BER than ReLU since its properties did not match the 2D-CNN model's tasks, leading to lower performance. Therefore, in this experiment, the ReLU function outperformed Mish as an activation function. Figure 9 illustrates the BER curves of the 2D-CNN using MSE and cross-entropy (CE) loss functions. We regulated variables and maintained other factors at a steady level. Utilizing MSE as the loss function, the 2D-CNN achieved a minimal BER of \(5.9\times 10^{-3}\), signifying outstanding performance. Regression problems were addressed with MSE. The signal-processing environment of this experiment rendered signal prediction a regression problem. The MSE quantified deviation by averaging the squared discrepancies between expected and actual values. BER was significantly reduced during training since it emphasized absolute error and systematically adjusted parameters to align predicted values with actual values. The cross-entropy loss function meas  
Figure 7: Training and validation loss curves for different numbers of trainable parameters at 8 dBm. (**a**) 100,000 parameters; (**b**) 150,000 parameters; (**c**) 200,000 parameters; (**d**) 350,000 parameters. across probability distributions in classification tasks.