# How Resilient Are Kolmogorov-Arnold Networks in Classification Tasks? A Robustness Investigation
## 5 Results and Discussion
### KAN-Mixer vs. MLP-Mixer Models
The training performance outcomes of the KAN_Mixer and MLP_Mixer models are depicted in Figure 8, which showed loss during the training phase, respectively, over 100 epochs. \begin{table}
\begin{tabular}{c c c|c c c|c c|c c|c c|c c|c c|c c} \hline \hline \multirow{2}{*}{**TT**} & \multirow{2}{*}{**AT**} & \multirow{2}{*}{\(\epsilon\)} & \multicolumn{8}{c}{**GTSRB**} & \multicolumn{8}{c}{**BTSRB**} & \multicolumn{8}{c}{**CTSRD**} \\  & & & \multicolumn{3}{c}{**KAN-Mixer**} & \multicolumn{3}{c}{**MLP-Mixer**} & \multicolumn{3}{c}{**KAN-Mixer**} & \multicolumn{3}{c}{**MLP-Mixer**} & \multicolumn{3}{c}{**KAN-Mixer**} & \multicolumn{3}{c}{**MLP-Mixer**} \\ \cline{3-19}  & & & **Acc** & **SAR** & **DoC** & **Acc** & **SAR** & **DoC** & **Acc** & **SAR** & **DoC** & **Acc** & **SAR** & **DoC** & **Acc** & **SAR** & **DoC** \\ \hline \multirow{9}{*}{**T-Mixer**} & none & - & 0.715 & 0 & 0 & 0.74 & 0 & 0 & 0.97 & 0 & 0 & 0.985 & 0 & 0 & 0.88 & 0 & 0 & 0.925 & 0 & 0 \\  & FGSM & 0.01 & 0.285 & 0.445 & 26.97 & 0.405 & 0.34 & 26.97 & 0.295 & 0.675 & 21.47 & 0.395 & 0.59 & 21.47 & 0.265 & 0.62 & 29.63 & 0.355 & 0.58 & 29.63 \\  & FGSM & 0.1 & 0.045 & 0.67 & 27.13 & 0.035 & 0.705 & 27.13 & 0.07 & 0.9 & 21.87 & 0.005 & 0.98 & 21.87 & 0.15 & 0.765 & 29.81 & 0.11 & 0.815 & 29.81 \\  & FGSM & 1 & 0.005 & 0.71 & 0.256 & 0 & 0.74 & 42.56 & 0.1 & 0.96 & 39.79 & 0 & 0.985 & 39.82 & 0.02 & 0.86 & 43.79 & 0 & 0.925 & 43.81 \\  & BIM & 0.01 & 0.585 & 0.13 & 0.55 & 0.68 & 0.06 & 0.55 & 0.855 & 0.115 & 0.55 & 0.97 & 0.015 & 0.55 & 0.825 & 0.06 & 0.55 & 0.92 & 0.05 & 0.55 \\  & BIM & 0.1 & 0.235 & 0.48 & 4.88 & 0.295 & 0.445 & 5.02 & 0.21 & 0.76 & 4.43 & 0.305 & 0.68 & 4.67 & 0.545 & 0.34 & 5.02 & 0.645 & 0.28 & 5.07 \\  & BIM & 1 & 0 & 0.715 & 27.69 & 0 & 0.74 & 28.01 & 0 & 0.97 & 22.11 & 0 & 0.985 & 22.29 & 0.015 & 0.865 & 30.53 & 0.03 & 0.895 & 30.58 \\  & PGD & 0.01 & 0.095 & 0.625 & 26.97 & 0.315 & 0.43 & 26.97 & 0.135 & 0.835 & 21.47 & 0.255 & 0.73 & 21.47 & 0.2 & 0.68 & 29.63 & 0.285 & 0.64 & 29.63 \\  & PGD & 0.1 & 0 & 0.715 & 27.04 & 0.005 & 0.735 & 27.05 & 0.015 & 0.955 & 21.63 & 0.005 & 0.98 & 21.66 & 0.035 & 0.845 & 29.72 & 0.06 & 0.865 & 29.72 \\  & PGD & 1 & 0 & 0.715 & 33.05 & 0 & 0.74 & 33.32 & 0 & 0.97 & 29.91 & 0 & 0.985 & 30.04 & 0 & 0.88 & 35.31 & 0 & 0.925 & 35.48 \\  & CW & - & 0.28 & 0.435 & 19.46 & 0.395 & 0.345 & 16.87 & 0.27 & 0.7 & 16.95 & 0.385 & 0.6 & 14.64 & 0.3 & 0.58 & 22.39 & 0.32 & 0.605 & 22.39 \\ \hline \multirow{9}{*}{**T-Mixer**} & none & - & 0.31 & 0 & 0 & 0.36 & 0 & 0 & 0.305 & 0 & 0 & 0.205 & 0 & 0 & 0.315 & 0 & 0 & 0.2 & 0 & 0 \\  & FGSM & 0.01 & 0.56 & 0.035 & 26.97 & 0.63 & 0.04 & 26.97 & 0.83 & 0.035 & 21.47 & 0.895 & 0 & 21.47 & 0.5 & 0.03 & 29.63 & 0.47 & 0.02 & 29.63 \\  & FGSM & 0.1 & 0.53 & 0.06 & 27.13 & 0.558 & 0.08 & 27.13 & 0.945 & 0.11 & 28.77 & 0.905 & 0 & 21.87 & 0.49 & 0.77 & 29.81 & 0.475 & 0.035 & 29.81 \\  & FGSM & 1 & 0.02 & 0.3 & 42.33 & 0.05 & 0.33 & 42.45 & 0.15 & 0.28 & 39.57 & 0.11 & 0.19 & 39.58 & 0.09 & 0.3 & 43.48 & 0.045 & 0.19 & 43.82 \\  & BIM & 0.01 & 0.28 & 0  
Figure 8 illustrates the loss values during the training of the KAN-Mixer and MLP-Mixer models across the BTSD, GTSRB, and CTSRD datasets using different training strategies: standard, adversarial training, and randomized smoothing. The x axis represents the training epochs, while the y axis shows the loss values. In standard training, both models showed a steady decrease in loss. The MLP-Mixer converged faster, particularly in the early epochs of the GTSRB and CTSRD datasets, while the KAN-Mixer achieved comparable stability after more epochs. Under adversarial training, the KAN-Mixer significantly reduced loss, particularly in the BTSD and CTSRD datasets, indicating better resilience to adversarial perturbations. The MLP-Mixer initially reduce loss rapidly but plateaued at a higher level. However, with randomized smoothing, the KAN-Mixer maintained consistently lower loss values than the MLP-Mixer, especially in the GTSRB dataset, suggesting an advantage from the smoothing technique.