Efficient and Accurate Capsule Networks with B-Spline-Based Activation Functions

This paper introduces Capsule Kolmogorov-Arnold Networks (CapsuleKAN), a novel capsule network architecture. It advances traditional capsule networks by enhancing convolutional and fully connected layers through Conv KAN and Linear-KAN. ConvKAN employs B-spline-based convolutions to generate superior feature maps and higher quality capsules. In contrast, LinearKAN utilizes B-splines as activation functions to capture complex nonlinearities with fewer parameters, optimizing the network's efficiency. Evaluations on the MNIST dataset revealed that CapsuleConvKAN, CapsuleLinearKAN, and CapsuleConv-LinearKAN achieved accuracy rates of 99.72%, 99.71 %, and 99.75%, respectively, with significant parameter reductions of 30K, 1.42M, and 1.44M. On the FashionMNIST dataset, the models attained accuracy rates of 93.22 %, 93.25 %, and 93.34 %, respectively. These results clearly demonstrate that CapsuleKAN models significantly enhance both accuracy and parameter efficiency compared to traditional capsule networks.