## 4 Discussion
### Ablation Study  
In this ablation study, we conducted an in-depth exploration of the roles of various model components and analyzed their inter-relationships and impact on overall performance, as shown in Figure 9. These experiments reveal the critical importance and interdependence of each component in handling the complex problem of nonlinear fiber pulse propagation. Firstly, residual blocks and the self-attention mechanism play pivotal roles in the entire model. Removing the residual blocks led to a significant increase in MSE, reaching 1.45 times the baseline model. This indicates that residual blocks are crucial for extracting  
Figure 8: The variation in RMSE with distance within and beyond the training scope. It shows that within the training scope (indicated by the vertical black line at 12 m), RMSE remains very low and almost constant. Figure 7: Training and validation loss rates over epochs for different model configurations of DeepONet. The figure shows the performance of models with different widths (\(n=1\) and \(n=2\)) and training conditions (single variable vs. multiple variables). The loss rates demonstrate an improvement in model accuracy and generalization as the model width increases, with a significant reduction in validation loss observed for the \(n=2\) configuration, calculated in RMSE. and processing multi-level features. Similar to \"skip connections\" in deep neural networks, residual blocks effectively mitigate the vanishing gradient problem and enhance the model's ability to represent complex signals. The self-attention mechanism further amplifies this effect by capturing the interdependencies among input features, significantly improving the model's predictive accuracy. When the self-attention mechanism was removed, the MSE soared to 1.81 times the baseline, marking the most substantial impact among all configurations. This underscores the indispensability of the self-attention mechanism in handling the highly intricate task of nonlinear fiber transmission. The FLOPs (Floating Point Operations per Second) and model parameter count provide additional insight into the computational efficiency and complexity of the model. Removing the residual blocks drastically reduced the FLOPs from 4.859 G to 1.629 G, highlighting the computational load associated with these blocks. This reduction in computational cost, however, comes at the expense of model accuracy, as evidenced by the increase in MSE. Similarly, while the self-attention mechanism has no impact on the FLOPs, it slightly decreases the model parameter count from 9.473 M to 9.204 M. This indicates that the self-attention mechanism, although not computationally expensive, is crucial for the model's performance due to its ability to efficiently manage dependencies within the data. Secondly, the dropout layer and the learning rate scheduler also demonstrate important roles in enhancing the model's generalization ability and stability, although their impact is not as pronounced as that of the residual blocks and the self-attention mechanism. The MSE increased by 18% when the dropout layer was removed, indicating that dropout contributes to preventing overfitting and maintaining generalization. Dropout achieves this by randomly dropping out certain neurons during training, preventing the model from over-relying on specific pathways, thereby improving its performance on unseen data. Notably, neither the FLOPs nor the model parameter count were affected by the removal of dropout, confirming that its contribution lies primarily in regularization rather than computational efficiency. The learning rate scheduler plays a critical role in dynamically adjusting the learning rate during training, ensuring the model converges smoothly to the optimal solution. When  
Figure 9: This chart compares the minimum training MSE, FLOPs (Floating Point Operations per Second), and model parameter count (in millions) across different configurations in the ablation study.