Quaternion Generative Adversarial Networks

Official PyTorch repository for:

Eleonora Grassucci, Edoardo Cicero, Danilo Comminiello, "Quaternion Generative Adversarial Networks", Generative Adversarial Learning: Architectures and Applications, editors: Dr Roozbeh Razavi-Far, Dr Ariel Ruiz-Garcia, Professor Vasile Palade, Professor Jürgen Schmidhuber, Springer, Sept. 2021.

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.

Results

Summary parameters and memory results for SNGAN and QSNGAN.

Model	# Total parameters	Disk Memory^
SNGAN	61,173,000	115 GB
QSNGAN	16,896,105	35 GB

^ Memory required by the generator checkpoint for inference.

Samples generated from the real-valued SNGAN on the left and from the proposed Quaternion-valued QSNGAN on the right on the CelebA-HQ dataset and 102 Oxford Flowers dataset.

Training

The files SNGAN_128.txt and QSNGAN_128.txt contain the configurations and options for training.

Please install the requirements.txt file. Download the dataset and set the name and the path in the .txt configuration file. Images are resized by default to 128x128 if not set differently. Default Dataloaders are set up for CelebA-HQ, 102 Oxford Flowers and CIFAR10. For the latter set image_size=32 and the model either SNGAN_32 or QSNGAN_QSN_32.

Training can be performed through:

python Qmain_FromText.py --TextArgs=*choose-the-txt-file*

Quaternion convolution visualized

Quaternion convolutions adjust the kernels of the convolution to reproduce the Hamilton product. The figure above shows real-valued filters and wuaternion-valued filters for a generic layer with 4 channels in input and 8 channels in output. In the figure you can see how the real-valued convolution needs a different filter for each input channel, while quaternion convolution share the filters among inputs. You can found a detailed description in the paper.

Cite

Please cite our work if you found it useful:

@article{grassucci2021quaternion,
      title={Quaternion Generative Adversarial Networks}, 
      author={Grassucci, Eleonora and Cicero, Edoardo and Comminiello, Danilo},
      year={2021},
      eprint={2104.09630},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

Interested in Quaternion Generative Models?

Check also:

• Lightweight Convolutional Neural Network by Hypercomplex Parameterization, Under Review at ICLR2021, 2021 [Paper] [GitHub].
• Quaternion-Valued Variational Autoencoder, ICASSP, 2021 [Paper] [GitHub].
• An Information-Theoretic Perspective on Proper Quaternion Variational Autoencoders, Entropy, 2021 [Paper] [GitHub].
• Hypercomplex Image-to-Image Translation, under review, 2022 [GitHub].