Quaternion Generative Adversarial Networks

Abstract

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.

PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions

“…Moreover, when processing multidimensional data with correlated channels, such as color images, rather than mulichannel audio or multisensor signals, PHC layers bring benefits due to the weight sharing among different channels. This allows to capture latent intra-channels relations that standard convolutional networks ignore because of the rigid structure of the weights (Grassucci et al, 2021a;Parcollet et al, 2019b).…”

“…Recent state-of-the-art convolutional models achieved astonishing results in various fields of application by large-scaling the overall parameters amount (Karras et al, 2020;d'Ascoli et al, 2021;Dosovitskiy et al, 2021). Simultaneously, quaternion neural networks (QNNs) demonstrated to significantly reduce the number of parameters while still gaining comparable performances (Parcollet et al, 2019c;Grassucci et al, 2021a;Tay et al, 2019). Quaternion models exploit hypercomplex algebra properties, including the Hamilton product, to painstakingly design interactions among the imaginary units, thus involving 1/4 of free parameters with respect to real-valued models.…”