# Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterion

arXiv: https://arxiv.org/abs/2402.14227 · HTML: https://mlsanity.com/paper/2402.14227/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [Quaternion Convolutional Neural Networks for Heterogeneous Image Processing](https://mlsanity.com/paper/1811.02656/) (2018)
- [Quaternion Convolutional Neural Networks for Detection and Localization of 3D Sound Events](https://mlsanity.com/paper/1812.06811/) (2018)
- [Quaternion Gradient and Hessian](https://mlsanity.com/paper/1406.3587/) (2014)
- [Predicting respiratory motion for real-time tumour tracking in radiotherapy](https://mlsanity.com/paper/1508.00749/) (2015)
- [Prediction of the Position of External Markers Using a Recurrent Neural Network Trained With Unbiased Online Recurrent Optimization for Safe Lung Cancer Radiotherapy](https://mlsanity.com/paper/2106.01100/) (2021)
- [Prediction of the motion of chest internal points using a recurrent neural network trained with real-time recurrent learning for latency compensation in lung cancer radiotherapy](https://mlsanity.com/paper/2207.05951/) (2022)

## Built on by (most cited first, 1 of 1)

- [Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules](https://mlsanity.com/paper/2510.16607/) (2025)

## Abstract (arXiv)

We develop a robust quaternion recurrent neural network (QRNN) for real-time processing of 3D and 4D data with outliers. This is achieved by combining the real-time recurrent learning (RTRL) algorithm and the maximum correntropy criterion (MCC) as a loss function. While both the mean square error and maximum correntropy criterion are viable cost functions, it is shown that the non-quadratic maximum correntropy loss function is less sensitive to outliers, making it suitable for applications with multidimensional noisy or uncertain data. Both algorithms are derived based on the novel generalised HR (GHR) calculus, which allows for the differentiation of real functions of quaternion variables and offers the product and chain rules, thus enabling elegant and compact derivations. Simulation results in the context of motion prediction of chest internal markers for lung cancer radiotherapy, which includes regular and irregular breathing sequences, support the analysis.