Foundations of Nonconventional Neural Units and their Classification

This article introduces basic types of nonconventional neural units and focuses on their notation and classification. Namely, the notation and classification of higher order nonlinear neural units, time-delay dynamic neural units, and time-delay higher order nonlinear neural units are introduced. Brief introduction into the simplified parallels of the higher order nonlinear aggregating function of higher order neural units with both the synaptic and somatic neural operation of biological neurons is made. Based on the mathematical notation of neural input intercorrelations of higher order neural units, it is shown that the higher order polynomial aggregating function of neural inputs can be understood as a single-equation representation of synaptic neural operation plus partial somatic neural operation. Thus, it unravels new simplified yet universal mathematical insight into understanding the higher computational power of neurons that also conforms to biological neuronal morphology. The classification of nonconventional neural units is founded first according to the nonlinearity of the aggregating function; second, according to the dynamic order; and third, according to time-delay implementation within neural units.