# Simplified Routing Mechanism for Capsule Networks
## 6 Results
Figure 17: Classification test accuracy on SVHN dataset. Figure 18: Classification test accuracy on GTSRB dataset. Figure 15: Classification test accuracy on SmallINORB dataset. Figure 25 shows the processing times for the three capsule-based networks. It can be seen that for all six datasets, the capsule network was faster with our proposed routing algorithm than with the dynamic routing algorithm introduced by [PERSON] et al. The smallest increase was achieved for the Fashion-MNIST and MNIST datasets, but this still represents an 18.60% and a 19.33% speedup. For more complex datasets, much higher speed increases were achieved. A running time reduction of 25.55% was achieved for SVHN and 26.54% for CIFAR10. The best results were observed for the SmallNORB and GTSRB datasets. For SmallNORB it was 35.28%, while for GTSRB, it was 48.30%. Compared to [PERSON]'s solution, our proposed algorithm performed worse, but the difference in efficiency between the two solutions is significant. Figure 24: Classification test loss on GTSRB dataset. Figure 23: Classification test loss on SVHN dataset. Figure 22: Classification test loss on CIFAR10 dataset. The test errors during the training process are shown in Table 2, where the capsule-based solutions were compared with the recently released neural network-based approaches. It can be clearly seen that our proposed modifications to the routing algorithm have led to efficiency gains. It is important to note that our capsule-based solution does not always approach the effectiveness of the state-of-the-art solutions, however, the capsule network used consists of only three layers with a very minimal number of parameters (<5.4 M). Its architecture is quite simple, but with further improvements, a higher efficiency can be achieved. Prior to this, we felt it necessary to improve the efficiency of the routing algorithm. Experience has shown that designing deep network architecture in the area of capsule networks is too resource-intensive. For this reason, it is necessary to increase the processing speed of the routing algorithm. Figure 26 shows the confusion matrices for the capsule network-based approaches in the case of the six datasets used. It can be seen that for simpler datasets, such as MNIST, the difference between the three optimization algorithms is minimal. For more complex datasets, the differences are more pronounced. Tables 3-8 show the efficiencies achieved by capsule networks for each class, separately. This table also shows that our proposed method is in most cases able to provide a more effective solution than the other solutions tested. However, there are cases where our solution falls short compared with solutions by [PERSON] et al. and [PERSON]. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **MNIST** & **F-MNIST** & **S.NORB** & **CIFAR10** & **SVHN** & **GTSRB** \\ \hline [PERSON] et al. [25] & 0.58\% & - & - & **10\%** & 13.6\% & 9.29\% \\ [PERSON] et al. [26] & 2.09\% & 10.95\% & - & - & - & - \\ [PERSON] et al. [27] & - & - & **5.57\%** & - & - & - \\ [PERSON] et al. [28] & - & - & - & 26.5\% & - & - \\ [PERSON] et al. [29] & 1.8\% & - & - & 39.4\% & 16.5\% & - \\ [PERSON] et al. [30] & 0.6\% & - & - & 31.7\% & - & - \\ [PERSON] et al. [11] & 0.45\% & **8.35\%** & 9.15\% & 29.36\% & 8.05\% & 2.67\% \\ [PERSON] [20] & 0.7\% & 9.25\% & 10.18\% & 41.18\% & 11.36\% & 9.79\% \\ Ours & **0.41\%** & **8.35\%** & 8.54\% & 28.26\% & **6.90\%** & **2.22\%** \\ \hline \end{tabular}
\end{table} 
Table 2: Classification test errors on the different datasets, compared with other methods. Figure 25: Comparison of training time on the same hardware (Nvidia Quadro RTX4000 series). Figure 26: Confusion matrices for the capsule-based networks.