# Selected aspects of complex, hypercomplex and fuzzy neural networks

arXiv: https://arxiv.org/abs/2301.00007 · HTML: https://mlsanity.com/paper/2301.00007/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 95 references that are in the map.
- First posted on arXiv 29 Dec 2022.

## Builds on (most cited first, 23 of 23)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [Shake-Shake regularization](https://mlsanity.com/paper/1705.07485/) (2017)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [Approximation Capabilities of Neural ODEs and Invertible Residual Networks](https://mlsanity.com/paper/1907.12998/) (2019)
- [Machine Learning from a Continuous Viewpoint](https://mlsanity.com/paper/1912.12777/) (2019)
- [The universal approximation theorem for complex-valued neural networks](https://mlsanity.com/paper/2012.03351/) (2020)
- [A General Framework for Hypercomplex-valued Extreme Learning Machines](https://mlsanity.com/paper/2101.06166/) (2021)
- [Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks](https://mlsanity.com/paper/2205.13273/) (2022)
- [Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2209.02456/) (2022)
- [A Deep Neuro-Fuzzy Network for Image Classification](https://mlsanity.com/paper/2001.01686/) (2019)
- [Universal Function Approximation on Graphs](https://mlsanity.com/paper/2003.06706/) (2020)

## Abstract (arXiv)

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.