Capsule Routing via Variational Bayes

TL;DR

This paper introduces a Bayesian capsule routing algorithm based on Variational Bayes, improving uncertainty modeling and performance in shape recognition tasks, and transforming capsule networks into Capsule-VAEs.

Contribution

It proposes a novel Variational Bayes routing method for capsule networks, enhancing uncertainty handling and reducing the number of capsules needed for high performance.

Findings

Outperforms state-of-the-art on smallNORB with 50% fewer capsules

Achieves competitive results on CIFAR-10, Fashion-MNIST, SVHN

Significantly improves MNIST to affNIST generalization

Abstract

Capsule networks are a recently proposed type of neural network shown to outperform alternatives in challenging shape recognition tasks. In capsule networks, scalar neurons are replaced with capsule vectors or matrices, whose entries represent different properties of objects. The relationships between objects and their parts are learned via trainable viewpoint-invariant transformation matrices, and the presence of a given object is decided by the level of agreement among votes from its parts. This interaction occurs between capsule layers and is a process called routing-by-agreement. In this paper, we propose a new capsule routing algorithm derived from Variational Bayes for fitting a mixture of transforming gaussians, and show it is possible transform our capsule network into a Capsule-VAE. Our Bayesian approach addresses some of the inherent weaknesses of MLE based models such as the variance-collapse by modelling uncertainty over capsule pose parameters. We outperform the state-of-the-art on smallNORB using 50% fewer capsules than previously reported, achieve competitive performances on CIFAR-10, Fashion-MNIST, SVHN, and demonstrate significant improvement in MNIST to affNIST generalisation over previous works.