  A recently proposed method in deep learning groups multiple neurons to
capsules such that each capsule represents an object or part of an object.
Routing algorithms route the output of capsules from lower-level layers to
upper-level layers. In this paper, we prove that state-of-the-art routing
procedures decrease the expressivity of capsule networks. More precisely, it is
shown that EM-routing and routing-by-agreement prevent capsule networks from
distinguishing inputs and their negative counterpart. Therefore, only symmetric
functions can be expressed by capsule networks, and it can be concluded that
they are not universal approximators. We also theoretically motivate and
empirically show that this limitation affects the training of deep capsule
networks negatively. Therefore, we present an incremental improvement for
state-of-the-art routing algorithms that solves the aforementioned limitation
and stabilizes the training of capsule networks.
