Note on Development of Modularity in Simple Cortical Models

Abstract

The existence of modularity in the organization of nervous systems (e.g. cortical columns and olfactory glomeruli) is well known. We show that localized activity patterns in a layer of cells, collective excitations, can induce the formation of modular structures in the anatomical connections via a Hebbian learning mechanism. The networks are spatially homogeneous before learning, but the spon(cid:173) taneous emergence of localized collective excitations and subse(cid:173) quently modularity in the connection patterns breaks translational symmetry. This spontaneous symmetry breaking phenomenon is similar to those which drive pattern formation in reaction-diffusion systems. We have identified requirements on the patterns of lateral connections and on the gains of internal units which are essential for the development of modularity. These essential requirements will most likely remain operative when more complicated (and bi(cid:173) ologically realistic) models are considered.