Prerequisites for the analysis of the neural networks functioning in terms of projective geometry

Abstract

Abstract It is shown that during training an artificial neural network built on elements with a threshold activation function, the weighting coefficients of each neuron can be selected from a certain discrete set, the nature of which depends on the number of neurons inputs. An example of a neuron with three inputs is considered in detail. It is shown that there are only 8 non-trivial combinations of weight coefficients that specify the work of neurons of this variety: any other combination of weight coefficients that describe the work of a non-degenerate neuron with this number of inputs can be replaced by one of the above 8 combinations without changing the character of the neuron functioning in the network. A method has been developed that allows one to determine relevant combinations of weights for neurons with an arbitrary number of inputs. It is shown that the proposed approach creates the prerequisites for assessing the “information power” of neural networks based on data on the nature of the connections between the neurons that form it.