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For the brain to recognize local orientations within images, neurons mustspontaneously break the translation and rotation symmetry of their responsefunctions -- an archetypal example of unsupervised learning. The dominantframework for unsupervised learning in biology is Hebb's principle, but howHebbian learning could break such symmetries is a longstanding biophysicalriddle. Theoretical studies agree that this should require inputs to visualcortex to invert the relative magnitude of their correlations at longdistances. Empirical measurements have searched in vain for such an inversion,and report the opposite to be true. We formally approach the question throughthe hermitianization of a multi-layer model, which maps it into a problem ofzero-temperature phase transitions. In the emerging phase diagram, bothsymmetries break spontaneously as long as (1) recurrent interactions aresufficiently long-range and (2) Hebbian competition is duly accounted for. Therelevant mechanism for symmetry breaking is competition among connectionssprouting from the same afferent cell. Such competition, and not the structureof the inputs, is capable of triggering the broken-symmetry phase required byimage processing. We provide analytic predictions on the relative magnitudes ofthe relevant length-scales needed for this novel mechanism to occur. Theseresults reconcile experimental observations to the Hebbian paradigm, shed lighton a new mechanism for visual cortex development, and contribute to our growingunderstanding of the relationship between learning and symmetry breaking.

Mechanisms for spontaneous symmetry breaking in developing visual cortex