ABSTRACT
This chapter deals with hidden-layer neurons activated by a group of Euler polynomials. It focuses on the activation functionactivation function and the structure improvements. The chapter explores the single-input-single-outputsingle-input-single-output Euler-polynomial neurone Euler-polynomial neuronet model with a three-layer structure. It presents the simple theoretical basis on the approximation abilityapproximation ability of Euler-polynomial neuronetEuler-polynomial neuronet. The chapter examines the numerical studies which verify and substantiate the efficacy and superior performance of the proposed weights-and-structure-determination (WASD) algorithm for Euler-polynomial neuronetEuler-polynomial neuronet. Numerical studies including comparisons substantiate the efficacy and superiority of Euler-polynomial neuronet with the proposed WASD algorithm. According to the observed relation between the performance of Euler-polynomial neuronetEuler-polynomial neuronet and the number of its hidden-layer neurons, the structure automatic determination is also considered, and thus leads to the weights-and-structure-determination WASD algorithm. Based on the weights-direct-determination subalgorithm, a WASD algorithm has been further proposed for Euler-polynomial neuronetEuler-polynomial neuronet to find the optimal number of hidden-layer neurons in an automatic, effective and deterministic manner.
