# Quaternion Backpropagation

arXiv: https://arxiv.org/abs/2212.13082 · HTML: https://mlsanity.com/paper/2212.13082/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 26 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [Quaternion Gradient and Hessian](https://mlsanity.com/paper/1406.3587/) (2014)
- [Speech recognition with quaternion neural networks](https://mlsanity.com/paper/1811.09678/) (2018)

## Abstract (arXiv)

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.