A novel capsule network based on Multi-Order Descartes Extension Transformation

In recent years, the capsule network has significantly impacted deep learning with its unique structure that robustly handles spatial relationships and image deformations like rotation and scaling. While previous research has primarily focused on enhancing the structural network of capsule networks to process complex images, little attention has been given to the rich semantic information contained within the capsules themselves. We recognize this gap and propose the Multi-Order Descartes Expansion Capsule Network (MODE-CapsNet). By introducing the Multi-Order Descartes Expansion Transformation (MODET), this innovative architecture enhances the expressiveness of a single capsule by enabling its projection into a higher-dimensional space. As far as we know, this is the first significant enhancement at the single-capsule granularity level, providing a new perspective for improving capsule networks. Additionally, we proposed a hierarchical routing algorithm designed explicitly for the MODE capsules, significantly optimizing computational efficiency and performance. Experimental results on datasets (MNIST, Fashion-MNIST, SVHN, CIFAR-10, tiny-ImageNet) showed that MODE capsules exhibited improved separability and expressiveness, contributing to overall network accuracy, robustness, and computational efficiency.