Novel law discovery perceptrons with improved efficiency of the network learning

The issue of effective learning specific neural networks capable of creating symbolic description of rules governing a set of empirical data is considered. In the field of our interests are atypical perceptrons suitable for implementing partial-rational or polynomial functions that describe the data set. A novel factor of the presented approach is an attempt to improve effectiveness of the perceptron learning by making proper transformations of the partial-rational or polynomial functions. These transformations enable to eliminate from the learning process operations on complex numbers as well as time consuming operations connected with using activation functions of the ln(.) and exp(.) type. Such an approach has proved to be a successful way to improve efficiency of the network training in the sense of increasing the learning speed and robustness. The paper presents the proposed transformations used to modify one-dimensional partial-rational as well as one-dimensional polynomial expressions. Perceptron schemes resulting from these expressions are also shown. Moreover, we discuss the applied method suitable for learning the networks and demonstrate the achieved training effects.