Explicit solution of the optimum weights of multilayer perceptron: the binary input case

Explicit solutions of multilayer feedforward networks have previously been discussed by Yu (1992). This paper extends the similar idea to binary input case. We show that the hidden units can be used to form the basis functions of the binary Walsh transform and the network training can therefore be treated as finding the coefficients of the binary Walsh expansion of the desired mapping, thus making the optimum weights explicitly solvable. For the incomplete training set case, a useful approach is presented to assure the resultant network having smooth generalization performance. Noise rejection performance of the obtained network is also illustrated.