  Capsule Network is powerful at defining the positional relationship between
features in deep neural networks for visual recognition tasks, but it is
computationally expensive and not suitable for running on mobile devices. The
bottleneck is in the computational complexity of the Dynamic Routing mechanism
used between the capsules. On the other hand, XNOR-Net is fast and
computationally efficient, though it suffers from low accuracy due to
information loss in the binarization process. To address the computational
burdens of the Dynamic Routing mechanism, this paper proposes new Fully
Connected (FC) layers by xnorizing the linear projection outside or inside the
Dynamic Routing within the CapsFC layer. Specifically, our proposed FC layers
have two versions, XnODR (Xnorize the Linear Projection Outside Dynamic
Routing) and XnIDR (Xnorize the Linear Projection Inside Dynamic Routing). To
test the generalization of both XnODR and XnIDR, we insert them into two
different networks, MobileNetV2 and ResNet-50. Our experiments on three
datasets, MNIST, CIFAR-10, and MultiMNIST validate their effectiveness. The
results demonstrate that both XnODR and XnIDR help networks to have high
accuracy with lower FLOPs and fewer parameters (e.g., 96.14% correctness with
2.99M parameters and 311.74M FLOPs on CIFAR-10).
