# A Quaternion-Valued Variational Autoencoder

arXiv: https://arxiv.org/abs/2010.11647 · HTML: https://mlsanity.com/paper/2010.11647/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Quaternion Generative Adversarial Networks](https://mlsanity.com/paper/2104.09630/) (2021)
- [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)
- [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)
- [Demystifying the Hypercomplex: Inductive Biases in Hypercomplex Deep Learning](https://mlsanity.com/paper/2405.07024/) (2024)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detection](https://mlsanity.com/paper/2509.05512/) (2025)

## Abstract (arXiv)

Deep probabilistic generative models have achieved incredible success in many fields of application. Among such models, variational autoencoders (VAEs) have proved their ability in modeling a generative process by learning a latent representation of the input. In this paper, we propose a novel VAE defined in the quaternion domain, which exploits the properties of quaternion algebra to improve performance while significantly reducing the number of parameters required by the network. The success of the proposed quaternion VAE with respect to traditional VAEs relies on the ability to leverage the internal relations between quaternion-valued input features and on the properties of second-order statistics which allow to define the latent variables in the augmented quaternion domain. In order to show the advantages due to such properties, we define a plain convolutional VAE in the quaternion domain and we evaluate its performance with respect to its real-valued counterpart on the CelebA face dataset.