Topological maps are for robust and wiring-efficient dimensionality reduction

Most mammalian species present topological maps of preference for the ori-
entation of edges in their early visual cortex. However, despite the evidence
that evolution has favoured topological map organisation in most species, a
clear explanation for the functional role of such maps is lacking. Traditional
approaches based on wiring minimisation are incomplete, showing how topology
can reduce metabolic costs, but only after assuming a functional role of short-
ranged like-tuned connectivity. In this work, we claim that topological maps
are for reducing the complexity of the propagated information in a robust and
wiring-efficient way through dimensionality reduction. In particular, we use com-
putational approaches based on activity dependant synaptic plasticity to show
that topological maps reflect the wiring minimisation of a component of lateral
connectivity, short-range excitation, that reduces the effective dimensionality and
increases the noise-robustness of neural codes, in line with expectations from effi-
cient coding and the free energy principle. We also show how this idea can explain
phenomena observed in the visual cortex of animal species