A unit paradox for artificial neuronal networks

In formal or artificial neuronal networks (FNN; ANN) built of threshold logic gates, a unit step function is used. Recently the step function has been replaced by an S-shaped curve. This replacement is common and many studies are based on this substitution, often combined rarely not with some adaptive or learning procedure. However, the dynamical consequences e. g. in the time course of single unit discharges have not been sufficiently examined. The concepts of unit (neuron) and network in these models of engineering and neurobiology correspond to each other only partially: model units may behave similarly to real nets of real units. This is called here a unit paradox. Propositions are presented to eliminate this apparent contradiction. A further paradox is also mentioned (Section 3). It seems necessary to reconsider the relationship of the various trends of neural network theory.