Novel methods and results in training universal multi-nested neurons

Abstract

This paper presents state of the art methods for training compact universal CNN cells (or neurons) to represent arbitrary local Boolean functions. The design tools are analyzed and optimized such that they are capable to provide fast solutions for cells with more than 4 inputs. In particular, it is proved statistically that any arbitrary Boolean function with n=5 inputs (corresponding to a von Neumann CNN neighborhood) admits multinested cell realizations thus confirming a conjecture that was previously proven only for n<5. Several hints are also provided regarding the choice and the influence of various parameters of the design algorithms on the quality of the solution and the speed of finding it.