Capsule Networks based on Cross Product

In Capsule Networks(CapsNets), the dynamic routing mechanism is used to generate the digital capsules, the lengths of which represent the probabilities that the entities exist. However, the dynamic routing has high computational complexity, which makes CapsNets not efficent than other modern deep networks. Inspired by the geometry meaning of cross product, we calculate the cross product of the feature and weight capsules, whose length is used as a measure of the probability of the input sample belonging to different classes. It is shown in the simulation that the resulting capsules tend to be more sparse with the increase of the dimension of the feature capsule, besides, some subcapsules have greater effects on the classification. The represented model improves the performace of the ResNet backbones by 23% on CIFAR-10 dataset and that of tht CNN by 17% on MNIST dataset.