  Capsule networks were proposed as an alternative approach to Convolutional
Neural Networks (CNNs) for learning object-centric representations, which can
be leveraged for improved generalization and sample complexity. Unlike CNNs,
capsule networks are designed to explicitly model part-whole hierarchical
relationships by using groups of neurons to encode visual entities, and learn
the relationships between those entities. Promising early results achieved by
capsule networks have motivated the deep learning community to continue trying
to improve their performance and scalability across several application areas.
However, a major hurdle for capsule network research has been the lack of a
reliable point of reference for understanding their foundational ideas and
motivations. The aim of this survey is to provide a comprehensive overview of
the capsule network research landscape, which will serve as a valuable resource
for the community going forward. To that end, we start with an introduction to
the fundamental concepts and motivations behind capsule networks, such as
equivariant inference in computer vision. We then cover the technical advances
in the capsule routing mechanisms and the various formulations of capsule
networks, e.g. generative and geometric. Additionally, we provide a detailed
explanation of how capsule networks relate to the popular attention mechanism
in Transformers, and highlight non-trivial conceptual similarities between them
in the context of representation learning. Afterwards, we explore the extensive
applications of capsule networks in computer vision, video and motion, graph
representation learning, natural language processing, medical imaging and many
others. To conclude, we provide an in-depth discussion regarding the main
hurdles in capsule network research, and highlight promising research
directions for future work.
