  Weight sharing in convolutional neural networks (CNNs) ensures that their
feature maps will be translation-equivariant. However, although conventional
convolutions are equivariant to translation, they are not equivariant to other
isometries of the input image data, such as rotation and reflection. For the
classification of astronomical objects such as radio galaxies, which are
expected statistically to be globally orientation invariant, this lack of
dihedral equivariance means that a conventional CNN must learn explicitly to
classify all rotated versions of a particular type of object individually. In
this work we present the first application of group-equivariant convolutional
neural networks to radio galaxy classification and explore their potential for
reducing intra-class variability by preserving equivariance for the Euclidean
group E(2), containing translations, rotations and reflections. For the radio
galaxy classification problem considered here, we find that classification
performance is modestly improved by the use of both cyclic and dihedral models
without additional hyper-parameter tuning, and that a D16 equivariant model
provides the best test performance. We use the Monte Carlo Dropout method as a
Bayesian approximation to recover epistemic uncertainty as a function of image
orientation and show that E(2)-equivariant models are able to reduce variations
in model confidence as a function of rotation.
