# Kolmogorov-Arnold Finance-Informed Neural Network in Option Pricing
## 7 Discussion
### Computational Resources  
The computational cost analysis between KAFIN and the baseline models, as outlined in Table 7, provides significant insights into both the runtime efficiency and resource utilization associated with each method. This analysis is crucial for understanding the trade-offs between model complexity and computational feasibility, especially in real-world applications where time and memory resources are often constrained. The runtime for completing 2300 epochs across the models demonstrates the inherent efficiency differences in terms of computational demands. Specifically, KAFIN, which is based on a decomposition of the Kolmogorov-Arnold representation (KAR) approach, completes 2300 epochs in 312.34 s, resulting in an average epoch time of 0.1358 s. This is substantially faster than the other models, particularly the FINN REG, which requires 1185.42 s for the same task, or an average of 0.5154 s per epoch. This stark contrast in epoch time can be attributed to the architectural optimizations in KAFIN, particularly the advanced training techniques employed, which allow it to process data more efficiently. The decomposition of KAR into separate attention-based components is designed to capture complex financial data relationships with fewer training iterations, ultimately leading to faster convergence. In comparison, the other baseline models, such as FINN DNN and FINN FFN, take 1555.49 and 160.31 s, respectively, to complete 2300 epochs, with corresponding average times per epoch of 0.6763 and 0.0697 s. These differences suggest that KAFIN's efficient convergence process, aided by its advanced regularization \begin{table}
\begin{tabular}{l r r r r r} \hline \hline
**Method** & **KAFIN** & **FINN REG** & **FINN FNN** & **FINN DNN** & **FINN MLP** \\ \hline Runtime (s) & 312.34 & 1185.42 & 160.31 & 1555.49 & 46.23 \\ Sec/Epoch & 0.1358 & 0.5154 & 0.0697 & 0.6763 & 0.0201 \\ Avg GPU MB & 25.7246 & 4.4531 & 4.8423 & 10.3193 & 1.7456 \\ Model Size (KB) & 7 & 11 & 13 & 1375 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Runtime and resource consumption for 2300 epochs. and optimization techniques, enables it to achieve high performance with significantly less computational overhead. The computational efficiency of KAFIN can also be linked to its ability to achieve faster stabilization during training. The system's architecture allows for a streamlined training process, which requires fewer epochs to reach an optimal solution, as evidenced by its performance in minimizing residual errors during financial modeling tasks. In terms of memory consumption, KAFIN demonstrates a moderate average GPU memory usage of 25.7246 MB, which is higher than FINN REG (4.4531 MB) and FINN FNN (4.8423 MB), but still relatively low compared to the FINN DNN (10.3193 MB) and FINN MLP (1.7456 MB). While KAFIN requires slightly more memory due to the increased architectural complexity introduced by the decomposition of KAR, its memory usage is justified by its enhanced ability to capture intricate patterns in financial data. The decomposition of KAR in KAFIN introduces additional layers and model components that are likely to require more memory. These components involve attention mechanisms and advanced regularization terms, which contribute to a higher memory footprint. However, this increased memory usage is a trade-off for the model's ability to learn complex relationships more effectively, which in turn leads to faster convergence and better predictive accuracy, particularly for tasks such as American put option pricing. Comparatively, the baseline models like FINN REG and FINN FNN consume less memory, with FINN REG having the lowest average GPU memory usage (4.4531 MB). However, their lower memory consumption correlates with their slower convergence and higher residual errors, as they may not be as well-equipped to handle the complexity of financial data without additional model parameters and sophisticated regularization strategies.