Some system considerations of neuron pools with feedback

Abstract

This paper describes an approach to the analysis of the inputoutput relationships present in a neuron pool that receives a number of inputs. These inputs consist of primary inputs to the neuron pool and inputs resulting from feedback of information from the neuron pool as well. Multiple input-output relationships are obtained in terms of the synaptic weightings of the inputs, the membrane response characteristics of the neurons and the conduction delays on the feedback pathways. y=(I+MHD) -1 ·MFx is the explicit representation of the cell pool behavior assuming quasi-linear conditions, where y is the output vector of cell responses, I is the identity matrix, M is the response matrix of the cells, H is the feedback synaptic weighting matrix, D is the delay matrix, F is the input weighting matrix, and x is the input vector. It is shown that a solution to this formulation exists, is unique, is stable, and can be computed by specified algorithms. An insight gained from this formulation suggests that the output of each cell in the pool is related to virtually all of the inputs to the pool and the outputs of all cells in the pool.