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

TL;DR

This paper analytically derives the eigenfunctions and eigenvalues for a three-layered neural network, revealing how radial orientation selectivity can emerge through self-organization driven by input noise.

Contribution

It provides the first complete analytical derivation of eigenfunctions for a multi-layer network, extending previous work on simple cells and self-organization.

Findings

Eigenfunctions and eigenvalues for the three-layer network are derived analytically.

Perturbation analysis extends results to include homeostatic parameters.

Results elucidate mechanisms of radial orientation selectivity emergence.

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.