3 research outputs found
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time
hypercomplex-valued Hopfield-type neural networks. To ensure the neural
networks belonging to this class always settle down at a stationary state, we
introduce novel hypercomplex number systems referred to as real-part
associative hypercomplex number systems. Real-part associative hypercomplex
number systems generalize the well-known Cayley-Dickson algebras and real
Clifford algebras and include the systems of real numbers, complex numbers,
dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as
particular instances. Apart from the novel hypercomplex number systems, we
introduce a family of hypercomplex-valued activation functions called
-projection functions. Broadly speaking, a
-projection function projects the activation potential onto the
set of all possible states of a hypercomplex-valued neuron. Using the theory
presented in this paper, we confirm the stability analysis of several
discrete-time hypercomplex-valued Hopfield-type neural networks from the
literature. Moreover, we introduce and provide the stability analysis of a
general class of Hopfield-type neural networks on Cayley-Dickson algebras
Selected aspects of complex, hypercomplex and fuzzy neural networks
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.Comment: 46 page