  Many classes of images exhibit rotational symmetry. Convolutional neural
networks are sometimes trained using data augmentation to exploit this, but
they are still required to learn the rotation equivariance properties from the
data. Encoding these properties into the network architecture, as we are
already used to doing for translation equivariance by using convolutional
layers, could result in a more efficient use of the parameter budget by
relieving the model from learning them. We introduce four operations which can
be inserted into neural network models as layers, and which can be combined to
make these models partially equivariant to rotations. They also enable
parameter sharing across different orientations. We evaluate the effect of
these architectural modifications on three datasets which exhibit rotational
symmetry and demonstrate improved performance with smaller models.
