Spontaneous symmetry breaking in self-organizing neural fields

We extend the theory of self-organizing neural fields in order to analyze the joint emergence of topography and feature selectivity in primary visual cortex through spontaneous symmetry breaking. We first show how a binocular one-dimensional topographic map can undergo a pattern forming instability that breaks the underlying symmetry between left and right eyes. This leads to the spatial segregation of eye specific activity bumps consistent with the emergence of ocular dominance columns. We then show how a 2-dimensional isotropic topographic map can undergo a pattern forming instability that breaks the underlying rotation symmetry. This leads to the formation of elongated activity bumps consistent with the emergence of orientation preference columns. A particularly interesting property of the latter symmetry breaking mechanism is that the linear equations describing the growth of the orientation columns exhibits a rotational shift-twist symmetry, in which there is a coupling between orientation and topography. Such coupling has been found in experimentally generated orientation preference maps.