Exploring dynamic routing as a pooling layer

Dynamic routing is a routing-by-agreement mechanism which is important for achieving the equivariance and invariance properties for capsule network (CapsNet). It is valuable to explore the nature of dynamic routing for better understanding of the capsule idea and further improving the performance of neural networks. This paper explores the dynamic routing from the pooling perspective. We modify the original dynamic routing algorithm for better applying it in traditional Convolutional Neural Networks (CNNs) as a pooling layer. We also use a parameter λ in softmax to smoothly adjust the sparsity in the routing, which leads to lower cost compared to the original dynamic routing. We experimentally show that the dynamic routing can be applied to beyond the capsule network to improve the performance of CNNs, and the coupling coefficients generated by the routing can be used to generate heatmaps which provide visual explanations to some extent. Further, the proposed dynamic routing method, combining a CNN backbone, achieves better results with much fewer parameters than the baselines on aff-NIST and multi-MNIST tasks.