Uniqueness logic represented via decimal numbers with WASD neural network

Abstract

A novel concept, uniqueness logic represented via decimal numbers (UL-D), is proposed and defined in this paper. Aiming at achieving the UL-D, we construct a neural network (i.e., NN) based on weights-and-structure-determination algorithm (i.e., the resultant WASD-NN). Differing from the back-propagation neural network (BP-NN) adjusting weights by lengthy iterative process and being unable to acquire the optimal structure adaptively, the WASD-NN can determine the optimal weights directly and the optimal structure automatically. Note that the UL-D is a nonlinear discontinuous mapping, of which the approximation has rarely been investigated before. In this paper, we firstly investigate the WASD-NN activated by commonly used continuous power functions, with corresponding numerical experiment results less satisfactory. By understanding the nature of the UL-D, the WASD-NN activated by discontinuous signum function is thus creatively built up, and the numerical experiment studies demonstrate well the efficient and superior approximating ability of the signum-function activated WASD-NN in achieving the UL-D.