Explicit synthesis of multilayer perceptrons using Walsh expansion

A synthetic method for explicitly designing multilayer perceptrons is addressed in this paper. The basic idea of the present method is to use the hidden units of perceptrons to form the basis functions of a truncated Walsh series expansion. The synthesis of a multilayer perceptron is therefore transformed to Walsh expansion of the desired mapping, leading to the desired weights of the perceptrons being explicitly solvable. As compared with conventional backpropagation training, the present approach can provide a special advantage that the generalization errors are bounded and easily controllable. Applications of the present synthetic method are illustrated