No routing needed between capsules

Most capsule network designs rely on traditional matrix multiplication between capsule layers and computationally expensive routing mechanisms to deal with the capsule dimensional entanglement that the matrix multiplication introduces. By using Homogeneous Vector Capsules (HVCs), which use element wise multiplication rather than matrix multiplication, the dimensions of the capsules remain unentangled. In this work, we study HVCs as applied to the highly structured MNIST dataset in order to produce a direct comparison to the capsule research direction of Geoffrey Hinton, et al. In our study, we show that a simple convolutional neural network using HVCs performs as well as the prior best performing capsule network on MNIST using 5.5x fewer parameters, 4x fewer training epochs, no reconstruction subnetwork, and requiring no routing mechanism. The addition of multiple classification branches to the network establishes a new state of the art for the MNIST dataset with an accuracy of 99.87% for an ensemble of these models, as well as establishing a new state of the art for a single model (99.83% accurate). (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Automated summary

The study demonstrates that a simple convolutional neural network using Homogeneous Vector Capsules (HVCs) performs as well as previous capsule networks on the MNIST dataset, but with fewer parameters, fewer training epochs, and no routing mechanism required.