Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Formalism of the General Mathematical Expression of Multilayer Perceptron Neural Networks

Version 1 : Received: 17 May 2021 / Approved: 18 May 2021 / Online: 18 May 2021 (10:26:19 CEST)

How to cite: Hounmenou, C.G.; Gneyou, K.E.; GLELE KAKAÏ, R.L. A Formalism of the General Mathematical Expression of Multilayer Perceptron Neural Networks. Preprints 2021, 2021050412 (doi: 10.20944/preprints202105.0412.v1). Hounmenou, C.G.; Gneyou, K.E.; GLELE KAKAÏ, R.L. A Formalism of the General Mathematical Expression of Multilayer Perceptron Neural Networks. Preprints 2021, 2021050412 (doi: 10.20944/preprints202105.0412.v1).

Abstract

Neural networks models are mostly represented by oriented graphs where only the components, constitutive elements of the graph, are transcribed into mathematical xpression. Indeed, accurate knowledge of the full expression of the model is required in certain situations such as selecting among several reference models, the one that best fits the available data or comparing the explanatory and predictive performance of an established model with respect to some reference models. In this paper, we establish a formalism of the mathematical expression for multilayer perceptron neural network in a general framework, MLP-p-n-q, with p, n and q natural integers and show its restriction to cases where one has a hidden layer and multivariate outputs (MLP-p-1-q), and then a single output (MLP-p-1-1). Then, we give some specific cases of the most commonly used models. An application case is presented in the context of solving a nonlinear regression problem.

Subject Areas

Expression of multilayer network models, oriented graph, multivariate model, nonlinear regression

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