Necessary Conditions for Multilayer Nets having Solutions and Convergent Superiority of Bipolar Nets

Abstract

Abstract This paper formulates a necessary condition for multilayer nets to have solutions by a set of normal vectors orthogonal to separation hyperplanes. Comparing the necessary condition to the distributions of normal vectors with the weights and biases initialized ordinarily by random numbers with zero mean, it is derived that bipolar nets are superior to unipolar nets in convergence of the back propagation learning initialized in such an ordinary manner.