  Capsule network (CapsNet) was introduced as an enhancement over convolutional
neural networks, supplementing the latter's invariance properties with
equivariance through pose estimation. CapsNet achieved a very decent
performance with a shallow architecture and a significant reduction in
parameters count. However, the width of the first layer in CapsNet is still
contributing to a significant number of its parameters and the shallowness may
be limiting the representational power of the capsules. To address these
limitations, we introduce Path Capsule Network (PathCapsNet), a deep parallel
multi-path version of CapsNet. We show that a judicious coordination of depth,
max-pooling, regularization by DropCircuit and a new fan-in routing by
agreement technique can achieve better or comparable results to CapsNet, while
further reducing the parameter count significantly.
