# Quaternion Capsule Networks

arXiv: https://arxiv.org/abs/2007.04389 · HTML: https://mlsanity.com/paper/2007.04389/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [Iterative collaborative routing among equivariant capsules for transformation-robust capsule networks](https://mlsanity.com/paper/2210.11095/) (2022)

## Abstract (arXiv)

Capsules are grouping of neurons that allow to represent sophisticated information of a visual entity such as pose and features. In the view of this property, Capsule Networks outperform CNNs in challenging tasks like object recognition in unseen viewpoints, and this is achieved by learning the transformations between the object and its parts with the help of high dimensional representation of pose information. In this paper, we present Quaternion Capsules (QCN) where pose information of capsules and their transformations are represented by quaternions. Quaternions are immune to the gimbal lock, have straightforward regularization of the rotation representation for capsules, and require less number of parameters than matrices. The experimental results show that QCNs generalize better to novel viewpoints with fewer parameters, and also achieve on-par or better performances with the state-of-the-art Capsule architectures on well-known benchmarking datasets.