Neural Network Encapsulation

A capsule is a collection of neurons which represents different variants of a pattern in the network. The routing scheme ensures only certain capsules which resemble lower counterparts in the higher layer should be activated. However, the computational complexity becomes a bottleneck for scaling up to larger networks, as lower capsules need to correspond to each and every higher capsule. To resolve this limitation, we approximate the routing process with two branches: a master branch which collects primary information from its direct contact in the lower layer and an aide branch that replenishes master based on pattern variants encoded in other lower capsules. Compared with previous iterative and unsupervised routing scheme, these two branches are communicated in a fast, supervised and one-time pass fashion. The complexity and runtime of the model are therefore decreased by a large margin. Motivated by the routing to make higher capsule have agreement with lower capsule, we extend the mechanism as a compensation for the rapid loss of information in nearby layers. We devise a feedback agreement unit to send back higher capsules as feedback. It could be regarded as an additional regularization to the network. The feedback agreement is achieved by comparing the optimal transport divergence between two distributions (lower and higher capsules). Such an add-on witnesses a unanimous gain in both capsule and vanilla networks. Our proposed EncapNet performs favorably better against previous state-of-the-arts on CIFAR10/100, SVHN and a subset of ImageNet.