POPULATION CODING BY SIMULTANEOUS ACTIVITIES OF NEURONS IN INTRINSIC COORDINATE SYSTEMS DEFINED BY THEIR RECEPTIVE-FIELD WEIGHTING FUNCTIONS

In this paper we address the problem of how external stimuli from the outside world, which can be represented as vectors by a set of numbers , might be expressed, transformed, and possibly reconstructed in neuro nal networks of sensory brain areas. Our work is based on the approach of modeling the firing rate responses of simple linear sensory neuron s. As characteristic functions, the receptive field weighting profiles can be determined from the firing rate responses of linear neurons to external stimuli in electrophysiological experiments. The responses o f such neurons to arbitrary stimuli can be described as a linear funct ion of the dot product of the stimulus vector and a special vector, th e receptive field weighting function. The stimulus vector can be recon structed in the coordinate system whose basis vectors are the receptiv e field weighting functions of linear neurons as a linear combination of the basis vectors and some weighting coefficients calculated from t he firing rates of the neurons. Georgopoulos, Kettner, and Schwartz de veloped a scheme of population coding to reconstruct a simple three-di mensional vector, the direction of an arm movement from results of ele ctrophysiological observations in primate motor cortex. Daugman introd uced an iterative algorithm to compress and reconstruct image vectors in a network of neural elements whose receptive field weighting functi ons were similar to receptive field weighting functions of orientation -selective neurons in cat visual cortex. Pellionisz and Llinas showed in their tensor network theory how sensorimotor transformations of vec tors might take place in neuronal networks. We show how these seemingl y different approaches are related and compare their advantages and di sadvantages. We adopted the iterative algorithm of Daugman to code ima ge vectors and calculated the weights of neural elements taking place in the reconstruction of the stimuli in different layers of the networ k. Then we determined what the receptive field profiles of neurons in higher layers look like at different stages of the iteration process a nd at equilibrium. Finally, we provide theoretical predictions that mi ght be verified in electrophysiological experiments to reveal which po pulation coding scheme is applied by the particular neuronal network i n sensory areas of the brain.