Towards a mathematical framework to inform neural network modelling via polynomial regression

Even when neural networks are widely used in a large number of applications, they still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing interest the overlapping area between more traditional statistical methods, which can help overcome those problems. In this article, mathematical framework relating polynomial regression is explored by building explicit expression coefficients from weights given network, using Taylor expansion approach. achieved single hidden layer The validity proposed method depends on different factors like distribution synaptic potentials chosen activation function. performance empirically tested via simulation synthetic data generated polynomials train with structures hyperparameters, showing that almost identical predictions be obtained certain conditions met. Lastly, learning data, produces approximate correctly locally.