  Recent improvements in generative adversarial visual synthesis incorporate
real and fake image transformation in a self-supervised setting, leading to
increased stability and perceptual fidelity. However, these approaches
typically involve image augmentations via additional regularizers in the GAN
objective and thus spend valuable network capacity towards approximating
transformation equivariance instead of their desired task. In this work, we
explicitly incorporate inductive symmetry priors into the network architectures
via group-equivariant convolutional networks. Group-convolutions have higher
expressive power with fewer samples and lead to better gradient feedback
between generator and discriminator. We show that group-equivariance integrates
seamlessly with recent techniques for GAN training across regularizers,
architectures, and loss functions. We demonstrate the utility of our methods
for conditional synthesis by improving generation in the limited data regime
across symmetric imaging datasets and even find benefits for natural images
with preferred orientation.
