  The architecture of iso-orientation domains in the primary visual cortex of
placental carnivores and primates apparently follows species invariant
quantitative laws. Dynamical optimization models assuming that neurons
coordinate their stimulus preferences throughout cortical circuits linking
millions of cells specifically predict these invariants. This might indicate
that V1's intrinsic connectome and its functional architecture adhere to a
single optimization principle with high precision and robustness. To validate
this hypothesis, it is critical to closely examine the quantitative predictions
of alternative candidate theories. Random feedforward wiring within the
retino-cortical pathway represents a conceptually appealing alternative to
dynamical circuit optimization because random dimension-expanding projections
are believed to generically exhibit computationally favorable properties for
stimulus representations.
  Here, we ask whether the quantitative invariants of V1 architecture can be
explained as a generic emergent property of random wiring. We generalize and
examine the stochastic wiring model proposed by Ringach and coworkers, in which
iso-orientation domains in the visual cortex arise through random feedforward
connections between semi-regular mosaics of retinal ganglion cells (RGCs) and
visual cortical neurons. We derive closed-form expressions for cortical
receptive fields and domain layouts predicted by the model for perfectly
hexagonal RGC mosaics [...] We conclude that V1 layout invariants are specific
quantitative signatures of visual cortical optimization, which cannot be
explained by generic random feedforward-wiring models.
  *See pdf for the full abstract.*
