A general nonlinear neuron model

Abstract

An accepted conclusion for modeling a physiological neuron is its divisibility into two mathematical processes. These are the digital process and the analog process. In a 1943 paper McCulloch and Pitts presented a neural model performing switching logic (an IT digital process). Their model represents the basis of the model used in the well-known Perceptron, devised by Rosenblatt in 1957. The Perceptron is a neural network of models that included varying weights, which corresponds to a neuron’s analog process. This talk will define the digital and the analog processes. These processes will be associated with a physiological neuron’s anatomy. The Perceptron’s neuron model continues to be used in current neural networks despite a serious limitation of only realizing linearly separable switching functions. Linearly separable switching functions will also be defined. The currently used “linear” neuron model will be shown to have severely limited switching logic realizations. Linear separability will also be defined. A general non-linear neuron model will be defined, which is capable of performing all possible switching logic realizations. Examples of both a linear neuron model’s and nonlinear neuron models’ switching logic realizations will be included. The proposed nonlinear neuron model, which more accurately takes into account actual neurophysiologic mechanisms, can form the basis of modeling network processes at all levels of the nervous system, including the brain.