N-bit parity neural networks: new solutions based on linear programming

Abstract

In this paper, the N-bit parity problem is solved with a neural network that allows direct connections between the input layer and the output layer. The activation function used in the hidden and output layer neurons is the threshold function. It is shown that this choice of activation function and network structure leads to several solutions for the 3-bit parity problem using linear programming. One of the solutions for the 3-bit parity problem is then generalized to obtain a solution for the N-bit parity problem using ⌊ N/2⌋ hidden layer neurons. Compared to other existing solutions in the literature, the present solution is more systematic and simpler. Furthermore, the present solution can be simplified by using a single hidden layer neuron with a “staircase” type activation function instead of ⌊ N/2⌋ hidden layer neurons. The present activation function is easier to implement in hardware than those in the literature for N-bit parity networks. We also review similarities and differences between the present results and those obtained in the literature.