Using parity-N problems as a way to compare abilities of shallow, very shallow and very deep architectures

Abstract

This paper presents a new concept of a dual neural network which is hybrid of linear and nonlinear network. This approach allows for solving the problem of Parity-3 with only one sigmoid neuron or Parity-7 with 2 sigmoid neurons that is shown in the analytical and experimental manner. The paper describes the architecture of ANN, presents an analytical way of choosing the weights and the number of neurons, and provides the results of network training for different ANN architectures solving the Parity-N problem.