  Latest Generative Adversarial Networks (GANs) are gathering outstanding
results through a large-scale training, thus employing models composed of
millions of parameters requiring extensive computational capabilities. Building
such huge models undermines their replicability and increases the training
instability. Moreover, multi-channel data, such as images or audio, are usually
processed by realvalued convolutional networks that flatten and concatenate the
input, often losing intra-channel spatial relations. To address these issues
related to complexity and information loss, we propose a family of
quaternion-valued generative adversarial networks (QGANs). QGANs exploit the
properties of quaternion algebra, e.g., the Hamilton product, that allows to
process channels as a single entity and capture internal latent relations,
while reducing by a factor of 4 the overall number of parameters. We show how
to design QGANs and to extend the proposed approach even to advanced models.We
compare the proposed QGANs with real-valued counterparts on several image
generation benchmarks. Results show that QGANs are able to obtain better FID
scores than real-valued GANs and to generate visually pleasing images.
Furthermore, QGANs save up to 75% of the training parameters. We believe these
results may pave the way to novel, more accessible, GANs capable of improving
performance and saving computational resources.
