  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 real-valued convolutional networks that flatten and concatenate
the input, losing any intra-channel spatial relation. To address these issues,
here we propose a family of quaternion-valued generative adversarial networks
(QGANs). QGANs exploit the properties of quaternion algebra, e.g., the Hamilton
product for convolutions. This 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 multiple image generation benchmarks. Results show
that QGANs are able to generate visually pleasing images and to obtain better
FID scores with respect to their real-valued GANs. 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.
