# How Resilient Are Kolmogorov-Arnold Networks in Classification Tasks? A Robustness Investigation
## 5 Results and Discussion
### Visualization Results  
The visualizations presented in this section provide a comprehensive view of the latent space movements for various models--KAN, MLP, KAN-Mixer, MLP-Mixer, and hybrid models (KANConv_KAN, ConvNet_MLP, ConvNet_KAN, and KANConv_MLP)--when subjected to different adversarial attacks (FGSM, BIM, PGD, and CW) at varying \(\epsilon\) val  
Figure 9: Comparison of loss trends for ConvNet_KAN, ConvNet_MLP, KANC_KAN, and KANC_MLP models under standard and randomized smoothing training across the BTSRD dataset (best viewed in color).  
ues. These t-SNE plots enable a direct comparison of model robustness across diverse training approaches, including standard, adversarial training, and randomized smoothing, providing insights into their behavior under attack. Due to space limitations, only a few representative figures are included in this paper to highlight key performance differences between the models. However, the full set of figures, showcasing all latent space movements under different attack scenarios and parameter settings, is available on ([[https://sie-lab-kr.github.io/Is-KAN-Robustness/](https://sie-lab-kr.github.io/Is-KAN-Robustness/)]([https://sie-lab-kr.github.io/Is-KAN-Robustness/](https://sie-lab-kr.github.io/Is-KAN-Robustness/)), accessed on 6 September 2024). In these visualizations, green bounding boxes represent correct classifications, while red bounding boxes indicate misclassifications. Blue dashed lines illustrate the latent space trajectory of samples misclassified due to adversarial perturbations, while green dashed lines mark samples that remain correctly classified despite the attack.  
For instance, under an FGSM attack with \(\epsilon=0.01\), the MLP-Mixer trained under standard conditions (Figure 10a) exhibited significant latent space shifts, resulting in numerous disrupted correct classifications. Conversely, the KAN-Mixer trained using standard settings (Figure 10b) showed less movement, reflecting better robustness even under the same attack conditions. Furthermore, when trained, the KAN-Mixer (Figure 10d) demonstrated even less movement in the latent space compared to the MLP-Mixer under adversarial training (Figure 10c), emphasizing its greater resilience to adversarial perturbations. Similarly, the KAN-Mixer model trained with randomized smoothing (Figure 10f) showed the most constrained latent space movement, underscoring its robustness, whereas the MLP-Mixer trained with randomized smoothing (Figure 10e) still exhibited more substantial latent space shifts. These visualizations emphasize the superior stability of KAN-Mixer models under adversarial conditions across different training strategies.  
Figure 10: Latent space movement visualizations for MLP-Mixer, KAN-Mixer, KAN, and MLP models under FGSM attack (\(\epsilon=0.01\)) across different training strategies. Each subfigure represents a different model and training approach, showing how the latent space shifts under adversarial attack.  
Additionally, visualizations comparing the KAN and MLP models under different settings (Figure 10) reveal distinct latent space movements. For example, adversarially trained KAN models exhibits more stability in the latent space compared to standard training (Figure 10h vs. Figure 10g). Similarly, the MLP models show more substantial latent shifts under standard training (Figure 10j vs. Figure 10k), and randomized smoothing results in more constrained movements for both KAN and MLP (Figure 10i,j), suggesting enhanced robustness against adversarial attacks.