Cohen Welling bases & SO(2)-Equivariant classifiers using Tensor nonlinearity.

Muthuvel Murugan, K Venkata Subrahmanyam

Abstract:

In this paper we propose autoencoder architectures for learning a Cohen-Welling
(CW)-basis for images and their rotations. We use the learned CW-basis to build
a rotation equivariant classifier to classify images. The autoencoder and classi-
fier architectures use only tensor product nonlinearity. The model proposed by
Cohen & Welling (2014) uses ideas from group representation theory, and extracts
a basis exposing irreducible representations for images and their rotations. We
give several architectures to learn CW-bases including a novel coupling AE archi-
tecture to learn a coupled CW-bases for images in different scales simultaneously.
Our use of tensor product nonlinearity is inspired from recent work of Kondor
(2018a). Our classifier has very good accuracy and we use fewer parameters.
Even when the sample complexity to learn a good CW-basis is low we learn clas-
sifiers which perform impressively. We show that a coupled CW-bases in one scale
can be deployed to classify images in a classifier trained and tested on images in
a different scale with only a marginal dip in performance.

Keywords: group representations, group equivariant networks, tensor product nonlinearity

Data: [Fashion-MNIST](https://paperswithcode.com/dataset/fashion-mnist)