  For the brain to recognize local orientations within images, neurons must
spontaneously break the translation and rotation symmetry of their response
functions -- an archetypal example of unsupervised learning. The dominant
framework for unsupervised learning in biology is Hebb's principle, but how
Hebbian learning could break such symmetries is a longstanding biophysical
riddle. Theoretical studies agree that this should require inputs to visual
cortex to invert the relative magnitude of their correlations at long
distances. Empirical measurements have searched in vain for such an inversion,
and report the opposite to be true. We formally approach the question through
the hermitianization of a multi-layer model, which maps it into a problem of
zero-temperature phase transitions. In the emerging phase diagram, both
symmetries break spontaneously as long as (1) recurrent interactions are
sufficiently long-range and (2) Hebbian competition is duly accounted for. The
relevant mechanism for symmetry breaking is competition among connections
sprouting from the same afferent cell. Such competition, and not the structure
of the inputs, is capable of triggering the broken-symmetry phase required by
image processing. We provide analytic predictions on the relative magnitudes of
the relevant length-scales needed for this novel mechanism to occur. These
results reconcile experimental observations to the Hebbian paradigm, shed light
on a new mechanism for visual cortex development, and contribute to our growing
understanding of the relationship between learning and symmetry breaking.
