Hechth–Nielsen theorem for a modified neural network with diagonal synaptic connections

2019;
: pp. 101-108
https://doi.org/10.23939/mmc2019.01.101
Received: September 24, 2018
Revised: December 31, 2018
Accepted: December 31, 2018
1
Ivan Franko Drogobych State Pedagogical University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Ivan Franko Drogobych State Pedagogical University
5
Lviv Polytechnic National University

The work suggests a modified three-layer neural network with architecture that has only the diagonal synaptic connections between neurons; as a result we obtain the transformed Hecht-Nielsen theorem.  This architecture of a three-layer neural network ($m=2n+1$ is the number of neurons in the hidden layer of the neural network; $n$ is the number of input signals) allows us to approximate the function of $n$ variables, with the given accuracy $\varepsilon>0$, using one aggregation operation, whereas a three-layer neural network that has both diagonal and non-diagonal synaptic connections between neurons approximates the function of $n$ variables by means of two aggregation operations. In addition, the matrix diagonalization of the synaptic    connections leads to a decrease of computing resources and reduces the time of adjustment of the weight coefficients during the training of a neural network.

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Math. Model. Comput. Vol.6, No.1, pp.101-108 (2019)