  Capsule Networks have emerged as a powerful class of deep learning
architectures, known for robust performance with relatively few parameters
compared to Convolutional Neural Networks (CNNs). However, their inherent
efficiency is often overshadowed by their slow, iterative routing mechanisms
which establish connections between Capsule layers, posing computational
challenges resulting in an inability to scale. In this paper, we introduce a
novel, non-iterative routing mechanism, inspired by trainable prototype
clustering. This innovative approach aims to mitigate computational complexity,
while retaining, if not enhancing, performance efficacy. Furthermore, we
harness a shared Capsule subspace, negating the need to project each
lower-level Capsule to each higher-level Capsule, thereby significantly
reducing memory requisites during training. Our approach demonstrates superior
results compared to the current best non-iterative Capsule Network and tests on
the Imagewoof dataset, which is too computationally demanding to handle
efficiently by iterative approaches. Our findings underscore the potential of
our proposed methodology in enhancing the operational efficiency and
performance of Capsule Networks, paving the way for their application in
increasingly complex computational scenarios. Code is available at
https://github.com/mileseverett/ProtoCaps.
