Network connectivity of neurons-feature detectors

Abstract

Studies the logical modelling of neural networks. The principles of feature representation and the mechanisms of the features' interaction in the following layers under the feature space formation have not previously been elucidated. Approaches connected with the syntactic theory of pattern recognition are suggested, in the sense that the symbolic manipulations are realized in our model of the network's actions. The layer of neuron-detectors is the first layer in the information processing pathway, where the transformation from quantitative to qualitative form, from the field of stimulus intensity to the layer distribution of neuron responses is accomplished. Each response encodes the presence of a revealed stimulus feature. In other words, if the receptive field of the primary feature detectors correspond to the physical field of the percepting value, encoded by a membrane potential or spike, then the receptive fields of the following layers represent the mutual location emerged at the previous layers. This paper addresses the question of how more complex features could be formed by the neurons of the following layers, coming from the primary features of the cell-detectors. The paper is based on the ultraproduct theory, the formalism of algebra and mathematical logic. The neuron network investigated accomplishes transformations according to the analogue-symbolic scheme, realizing a specific syntax of grammar, operating with such symbols, by the physical laws of the system described. The symbol representation of a signal cannot be reduced to its quantization in the general situation.<>