On the solution of the parity problem by a single hidden layer feedforward neural network

It is known that the N-bit parity problem is solvable by a standard feed-forward neural network having a single hidden layer consisting of (N/2) + 1 hidden units if N is even and (N+1)/2 hidden units if N is odd. The network does not allow a direct connection between the input layer and the output layer and the transfer function used in all hidden units and the output unit is the usual sigmoidal function (x) = 1=(1 + exp(?x)). We show that such a solution can be easily obtained by solving a system of linear equations.