Emergence of radial orientation selectivity: Effect of cell density changes and eccentricity in a layered network

Abstract

Previous work by Linsker revealed how simple cells can emerge in the absence of structured environmental input, via a self-organisation learning process. He empirically showed the development of spatial-opponent cells driven only by input noise, emerging as a result of structure in the initial synaptic connectivity distribution. To date, a complete set of radial eigenfunctions have not been provided for this multi-layer network. In this paper, the complete set of eigenfunctions and eigenvalues for a three-layered network is for the first time analytically derived. Initially a simplified learning equation is considered for which the homeostatic parameters are set to zero. To extend the eigenfunction analysis to the full learning equation, including non-zero homeostatic parameters, a perturbation analysis is used.