Breaking Rotational Symmetry in a Self&hyphenOrganizing Map Model for Orientation Map Development

We analyze the pattern formation behavior of a high&hyphendimensional self&hyphenorganizing map (SOM) model for the competitive projection of ON&hyphencenter&hyphentype and OFF&hyphencenter&hyphentype inputs to a common map layer. We mathematically show, and numerically confirm, that even isotropic stimuli can drive the development of oriented receptive fields and an orientation map in this model. This result provides an important missing link in the spectrum of pattern formation behaviors observed in SOM models. Extending the model by including further layers for binocular inputs, we also investigate the combined development of orientation and ocular dominance maps. A parameter region for combined patterns exists; corresponding maps show a preference for perpendicular intersection angles between iso&hyphenorientation lines and ocularity domain boundaries, consistent with experimental observations.