Group Equivariant Capsule Networks
This work addresses the problem of building more robust and interpretable neural networks for researchers in machine learning, particularly in computer vision, by integrating insights from group convolutional networks into capsule networks, though it is incremental as it builds on existing capsule and group convolution ideas.
The paper tackles the challenge of ensuring equivariance and invariance in capsule networks by introducing a framework that combines group theory with capsule networks, resulting in a method that provides guaranteed equivariance and invariance properties, interpretable output capsules, and sparse evaluation of group convolutions.
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by agreement algorithm defined on elements of a group and prove that equivariance of output pose vectors, as well as invariance of output activations, hold under certain conditions. Second, we connect the resulting equivariant capsule networks with work from the field of group convolutional networks. Through this connection, we provide intuitions of how both methods relate and are able to combine the strengths of both approaches in one deep neural network architecture. The resulting framework allows sparse evaluation of the group convolution operator, provides control over specific equivariance and invariance properties, and can use routing by agreement instead of pooling operations. In addition, it is able to provide interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose.