  Deep learning of the Artificial Neural Networks (ANN) can be treated as a
particular class of interpolation problems. The goal is to find a neural
network whose input-output map approximates well the desired map on a finite or
an infinite training set. Our idea consists of taking as an approximant the
input-output map, which arises from a nonlinear continuous-time control system.
In the limit such control system can be seen as a network with a continuum of
layers, each one labelled by the time variable. The values of the controls at
each instant of time are the parameters of the layer.
