Iterative Collaborative Routing among Equivariant Capsules for Transformation-Robust Capsule Networks

Transformation-robustness is an important feature for machine learning models that perform image classification. Many methods aim to bestow this property to models by the use of data augmentation strategies, while more formal guarantees are obtained via the use of equivariant models. We recognise that compositional, or part-whole structure is also an important aspect of images that has to be considered for building transformation-robust models. Thus, we propose a capsule network model that is, at once, equivariant and compositionality aware. Equivariance of our capsule network model comes from the use of equivariant convolutions in a carefully-chosen novel architecture. The awareness of compositionality comes from the use of our proposed novel, iterative, graph-based routing algorithm, termed Iterative collaborative routing (ICR). ICR, the core of our contribution, weights the predictions made for capsules based on an iteratively averaged score of the degree-centralities of its nearest neighbours. Experiments on transformed image classification on FashionMNIST, CIFAR-10, and CIFAR-100 show that our model that uses ICR outperforms convolutional and capsule baselines to achieve state-of-the-art performance.