Series of Semihypergroups of Time-Varying Artificial Neurons and Related Hyperstructures

Abstract

Detailed analysis of the function of multilayer perceptron (MLP) and its neurons together with the use of time-varying neurons allowed the authors to find an analogy with the use of structures of linear differential operators. This procedure allowed the construction of a group and a hypergroup of artificial neurons. In this article, focusing on semihyperstructures and using the above described procedure, the authors bring new insights into structures and hyperstructures of artificial neurons and their possible symmetric relations.

Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

“…In this section, we will include several examples of the above reasoning. We will apply the theoretical results in the area of artificial neurons, i.e., in a way, continue with the paper [11] which focuses on artificial neurons. For notation, recall [11].…”

“…We will apply the theoretical results in the area of artificial neurons, i.e., in a way, continue with the paper [11] which focuses on artificial neurons. For notation, recall [11]. Further on we consider a generalization of the usual concept of artificial neurons.…”

“…Therefore, in this present paper we continue in the direction of [2,4] presenting results parallel to [11]. Our constructions, no matter how theoretical they may seem, are motivated by various practical issues of signal processing [12][13][14][15][16].…”

“…Moreover, series of groups motivated by the Galois theory of solvability of algebraic equations and the modern theory of extensions of fields, are often discussed in literature. Notice also paper [11] where the theory of artificial neurons, used further on in some examples, has been studied.…”

n-Ary Cartesian Composition of Multiautomata with Internal Link for Autonomous Control of Lane Shifting

“…By extensive hypergroup in the sense of hypercompositional structures we mean a hypergroup that {a, b} ⊆ a * b for all a, b ∈ H, i.e., that the elements are included in its "resalt of hyperoperation". For the same application on this theory in other science or real-life problems see, for example, [3][4][5][6][7].…”