A discussion about the mathematics underlying artificial neural networks (ANN) and some examples of ANNs applications

The report will consider the mathematical model of ANN as a multiparametric function of a special kind approximating a target function. The ANN learning process is considered as the task of selecting the ANN parameters that provide the best approximation of the target function. The feature of the ANN structure as a function of a set of parameters is analyzed, which makes it possible to relatively quickly calculate the derivatives of the discrepancy with the target function according to the ANN parameters and, thus, minimize this discrepancy using gradient methods. The report also examines some examples of the ANNs application.