Quaternion Backpropagation

TL;DR

This paper introduces a novel quaternion backpropagation method based on GHRCalculus, addressing the limitations of previous derivative calculations in quaternion neural networks, and validates its effectiveness through experiments.

Contribution

It develops a new quaternion backpropagation approach using GHRCalculus, correcting previous derivative calculation issues in quaternion neural networks.

Findings

Successfully derived quaternion backpropagation using GHRCalculus

Demonstrated the correctness of the method through experiments

Addresses limitations of previous derivative approaches in quaternion networks

Abstract

Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial derivatives with respect to the real and imaginary parts. However, we can show that product- and chain-rule does not hold with this approach. We solve this by employing the GHRCalculus and derive quaternion backpropagation based on this. Furthermore, we experimentally prove the functionality of the derived quaternion backpropagation.