# Quaternion Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2104.09630 · HTML: https://mlsanity.com/paper/2104.09630/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 27 of 27)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [Consistency Regularization for Generative Adversarial Networks](https://mlsanity.com/paper/1910.12027/) (2019)
- [A U-Net Based Discriminator for Generative Adversarial Networks](https://mlsanity.com/paper/2002.12655/) (2020)
- [Self-Supervised GANs via Auxiliary Rotation Loss](https://mlsanity.com/paper/1811.11212/) (2018)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [Quaternion Convolutional Neural Networks for Heterogeneous Image Processing](https://mlsanity.com/paper/1811.02656/) (2018)
- [Lipschitz Generative Adversarial Nets](https://mlsanity.com/paper/1902.05687/) (2019)
- [Quaternion Convolutional Neural Networks for Detection and Localization of 3D Sound Events](https://mlsanity.com/paper/1812.06811/) (2018)
- [Generative Adversarial Networks are Special Cases of Artificial Curiosity (1990) and also Closely Related to Predictability Minimization (1991)](https://mlsanity.com/paper/1906.04493/) (2019)
- [A Quaternion-Valued Variational Autoencoder](https://mlsanity.com/paper/2010.11647/) (2020)
- [AlgebraNets](https://mlsanity.com/paper/2006.07360/) (2020)
- [Compressing deep quaternion neural networks with targeted regularization](https://mlsanity.com/paper/1907.11546/) (2019)

## Built on by (most cited first, 17 of 17)

- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2305.07283/) (2023)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss](https://mlsanity.com/paper/2202.02063/) (2022)
- [Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representation](https://mlsanity.com/paper/2204.01851/) (2022)
- [Learning Speech Emotion Representations in the Quaternion Domain](https://mlsanity.com/paper/2204.02385/) (2022)
- [Multi-View Hypercomplex Learning for Breast Cancer Screening](https://mlsanity.com/paper/2204.05798/) (2022)
- [Generalizing Medical Image Representations via Quaternion Wavelet Networks](https://mlsanity.com/paper/2310.10224/) (2023)
- [Hypercomplex Image-to-Image Translation](https://mlsanity.com/paper/2205.02087/) (2022)
- [Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling](https://mlsanity.com/paper/2310.07623/) (2023)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation](https://mlsanity.com/paper/2403.11722/) (2024)
- [3D GANs and Latent Space: A comprehensive survey](https://mlsanity.com/paper/2304.03932/) (2023)
- [Enhancing Semantic Communication with Deep Generative Models -- An ICASSP Special Session Overview](https://mlsanity.com/paper/2309.02478/) (2023)
- [Demystifying the Hypercomplex: Inductive Biases in Hypercomplex Deep Learning](https://mlsanity.com/paper/2405.07024/) (2024)
- [KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorch](https://mlsanity.com/paper/2407.00452/) (2024)
- [A Novel Wasserstein Quaternion Generative Adversarial Network for Color Image Generation](https://mlsanity.com/paper/2512.08542/) (2025)

## Abstract (arXiv)

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.