# Hypercomplex-Valued Recurrent Correlation Neural Networks

arXiv: https://arxiv.org/abs/2002.00027 · HTML: https://mlsanity.com/paper/2002.00027/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 6 of 6)

- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Multi-View Hypercomplex Learning for Breast Cancer Screening](https://mlsanity.com/paper/2204.05798/) (2022)
- [Hypercomplex Image-to-Image Translation](https://mlsanity.com/paper/2205.02087/) (2022)
- [Towards Explaining Hypercomplex Neural Networks](https://mlsanity.com/paper/2403.17929/) (2024)
- [Fully tensorial approach to hypercomplex-valued neural networks](https://mlsanity.com/paper/2407.00449/) (2024)
- [Dynamics of Structured Complex-Valued Hopfield Neural Networks](https://mlsanity.com/paper/2503.19885/) (2025)

## Abstract (arXiv)

Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, can be used to implement high-capacity associative memories. In this paper, we extend the bipolar RCNNs for processing hypercomplex-valued data. Precisely, we present the mathematical background for a broad class of hypercomplex-valued RCNNs. Then, we provide the necessary conditions which ensure that a hypercomplex-valued RCNN always settles at an equilibrium using either synchronous or asynchronous update modes. Examples with bipolar, complex, hyperbolic, quaternion, and octonion-valued RCNNs are given to illustrate the theoretical results. Finally, computational experiments confirm the potential application of hypercomplex-valued RCNNs as associative memories designed for the storage and recall of gray-scale images.