About of synthesis of neural networks
The use of neural networks for solving problems of various orientations, to which classification problems (in particular, image recognition problems on images), tasks of segmentation, forecasting and dynamic programming, etc., have become quite popular at the present time. But, it is worth noting that the proposed solutions to all these problems are based on the use of neural network training methods using gradient descent or its modifications, which entails a set of shortcomings: uncertainty in setting initial values, lack of well-founded recommendations on the choice of parameters of algorithms training (step of training and others) and others. The method of constructing a neural network is based on the successive addition of neurons for the connection of new "nearest" points from the learning set using the function of activating the rectifier (relu), and in the neuron of the output layer it is a linear function. In this paper, this method is applied to the approximation of a parabola function. As a result, a neural network approximating the parabola function is obtained. The structure of a neural network is a single-layer perceptron with a set of neurons in a hidden layer with one neuron in the input and output layers. The method proposed in the article allows us to approximate not only the parabola function, but also any other function of one variable with a given accuracy. The graphs of comparison of the original function and approximated for the purpose of demonstrating the obtained results are given, as well as a part of the structure of the obtained neural network.