  Capsules as well as dynamic routing between them are most recently proposed
structures for deep neural networks. A capsule groups data into vectors or
matrices as poses rather than conventional scalars to represent specific
properties of target instance. Besides of pose, a capsule should be attached
with a probability (often denoted as activation) for its presence. The dynamic
routing helps capsules achieve more generalization capacity with many fewer
model parameters. However, the bottleneck that prevents widespread applications
of capsule is the expense of computation during routing. To address this
problem, we generalize existing routing methods within the framework of
weighted kernel density estimation, and propose two fast routing methods with
different optimization strategies. Our methods prompt the time efficiency of
routing by nearly 40\% with negligible performance degradation. By stacking a
hybrid of convolutional layers and capsule layers, we construct a network
architecture to handle inputs at a resolution of $64\times{64}$ pixels. The
proposed models achieve a parallel performance with other leading methods in
multiple benchmarks.
