Model of a Neural Network for Solving Systems of Inequalities with Three Real Unknowns

J. Pierre, Sakodi Mjanaheri and Luz, Mpemba Ngoma and Camile, Likotelo Binene and Andre, Boleli Nkanga and Telesphore, Nsumbu Lukamba and Cedric, Kabeya Tshiseba and Boniface, Engombe Wedi (2023) Model of a Neural Network for Solving Systems of Inequalities with Three Real Unknowns. Journal of Advances in Mathematics and Computer Science, 38 (9). pp. 51-64. ISSN 2456-9968

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Abstract

Apart from all other machine learning models, neural networks are much more complex models in the sense
that they represent mathematical functions with millions of coefficients (parameters).
In this article, it is about designing and implementing a network of artificial neurons by applying the
Heaviside activation function on each neuron of the first layer of the network and finally on the single output neuron, we apply the logical "and". To solve a system of linear inequalities with three real unknowns, it is to
represent graphically in frame system of the three-dimensional plane, the set of points M of whose coordinates () simultaneously verify all the inequalities of the system. Where are coefficients of with 1≤ i ≤ 3 and the independent terms. The set of solutions of this system is a part of whose points satisfy these three inequalities simultaneously. In a neural network, the are variables, the are weights associated with these variables and the are biases. This model has been implemented in python with the keras easy library for solve systems of linear inequalities with three real unknowns by graphically representing elemental solutions in R3.

Item Type: Article
Subjects: Apsci Archives > Mathematical Science
Depositing User: Unnamed user with email support@apsciarchives.com
Date Deposited: 21 Sep 2023 08:37
Last Modified: 21 Sep 2023 08:37
URI: http://eprints.go2submission.com/id/eprint/1696

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