On the synthesis and complexity of feedforward networks

A method for synthesis of one hidden layer feedforward neural networks approximating functions of several variables to the desired degree of accuracy is presented. The method fully determines the network architecture including the values of all weights. In the first step, the inverse Radon transform is used to decompose a problem of of approximating a function of several variables into several problems of approximating a function of one variable. In the second step, each of the obtained one-dimensional functions is approximated by a sub-network. Then sub-networks are combined to construct the network approximating the original function. The upper bound of the final approximation error ε and errors at each step are estimated. The complexity of the network, or the number of neurons in the hidden layer, is O_ε (1/εⁿ), where n is the dimension of the space