  We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a
natural generalization of convolutional neural networks that reduces sample
complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of
layer that enjoys a substantially higher degree of weight sharing than regular
convolution layers. G-convolutions increase the expressive capacity of the
network without increasing the number of parameters. Group convolution layers
are easy to use and can be implemented with negligible computational overhead
for discrete groups generated by translations, reflections and rotations.
G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.
