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Formal neuron structure-functional scheme “complexity” improvement evolutionary aspects


G. M. Alakoz

It is shown: 1. Real neuron realizable logical function enumeration task (set from withdout) dimensionality is determined by: quantity and meaning of input variables, setting at the stage of “formalization”, which is determined by predominant motivation, readjusting central nervous system to biological and social organism’s needs satisfaction, in accordance with P.K. Anokhin theory of functional systems; completeness degree of its structure-functional scheme against logical functions class on which tasks allocation between neuronet and (sub)neuronal control levels depends; logical function setting presentation form: the more abstract presentation form is the greater enumeration task dimensionality is and vice versa: the more presentation form focuses on setting logical function realization mechanism, the simpler its values indirect enumeration task is. At the same time enumeration abstract form “complexity” does not decrease, and only is reallocated across efferent presentation form and context, implicating by “default” setting logical function real realization mechanism. 2. The variety of the same functions realization by the same real neuron modes is immense and their functioning presupposes not only structural parameters selection, but possibility of maladjustment of both class itself and its functions separately. It is stipulated by: full functions class “coverage” redundancy by set of functions, realizable by real neuron or neuronal ensemble. Such a redundancy either lacks or minimized in hardware at the engineering stage; structural redundancy, which obtains in all (multi)threshold systems, setting up the same (logical) function by model’s parameters variation such as weight and threshold vectors components; neurochemical and molecular-biological processes variety, allowing to implement the same function. This reveals through the one group-theoretical model notations variety. 3. Transition to group-theoretical formal neurons models is getting imminent when computing elemental basis jumps to nanometer range. As a result: computing control tasks part automatically extends to the level of physicochemical processes, exploiting as computing “material basis”; the relation “initial-derivative” between combinative and finite state machines, which results in necessity of logical functions expression through arithmetical ones. Mentioned above facts give reasons to consider that real neuron structure-functional schemes evolution coursed from commutating functions support-oriented finite state machines to combinative logic ones realizable in arithmetic operation basis.
May 29, 2020

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