# KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorch

arXiv: https://arxiv.org/abs/2407.00452 · HTML: https://mlsanity.com/paper/2407.00452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks for Heterogeneous Image Processing](https://mlsanity.com/paper/1811.02656/) (2018)
- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Quaternion Generative Adversarial Networks](https://mlsanity.com/paper/2104.09630/) (2021)
- [Deep Octonion Networks](https://mlsanity.com/paper/1903.08478/) (2019)
- [Hypercomplex neural network in time series forecasting of stock data](https://mlsanity.com/paper/2401.04632/) (2024)
- [Bidirectional Quaternion Long-Short Term Memory Recurrent Neural Networks for Speech Recognition](https://mlsanity.com/paper/1811.02566/) (2018)

## Abstract (arXiv)

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated with Keras that can do computations within TensorFlow and PyTorch. It provides Dense and Convolutional 1D, 2D, and 3D layers architectures.