A Quaternion-Valued Variational Autoencoder

TL;DR

This paper introduces a novel quaternion-valued variational autoencoder that leverages quaternion algebra to enhance performance and reduce parameters, demonstrating advantages over traditional VAEs on face image data.

Contribution

The paper presents the first quaternion-valued VAE, exploiting quaternion algebra to improve modeling efficiency and parameter reduction compared to real-valued VAEs.

Findings

Quaternion VAE outperforms real-valued VAE on CelebA dataset

Significant reduction in network parameters achieved

Leveraging quaternion properties enhances feature relations

Abstract

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.