Population Coding by Neurons in Intrinsic Coordinate Systems 501 tions and to exploit the parallels of this machine vision approach and the tensor network theory of the central nervous system

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 neuronal networks of sensory brain areas. Our work is based on the approach of modeling the firing rate responses of simple linear sensory neurons. 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 of such neurons to arbitrary stimuli can be described as a linear function of the dot product of the stimulus vector and a special vector, the receptive field weighting function. The stimulus vector can be reconstructed in the coordinate system whose basis vectors are the receptive field weighting functions of linear neurons as a linear combination of the basis vectors and some weighting coefficients calculated from the firing rates of the neurons. Georgopoulos, Kettner, and Schwartz developed a scheme of population coding to reconstruct a simple three-dimensional vector, the direction of an arm movement from results of electrophysiological observations in primate motor cortex. Daugman introduced an iterative algorithm to compress and reconstruct image vectors in a network of neural elements whose receptive field weighting functions 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 vectors might take place in neuronal networks. We show how these seemingly different approaches are related and compare their advantages and disadvantages. We adopted the iterative algorithm of Daugman to code image vectors and calculated the weights of neural elements taking place in the reconstruction of the stimuli in different layers of the network. Then we determined what the receptive field profiles of neurons in higher layers look like at different stages of the iteration process and at equilibrium. Finally, we provide theoretical predictions that might be verified in electrophysiological experiments to reveal which population coding scheme is applied by the particular neuronal network in sensory areas of the brain.