Coverage, Continuity and Visual Cortical Architecture

TL;DR

This paper analytically investigates the elastic net model's ability to replicate the common design of orientation preference maps in the visual cortex, revealing conditions for periodic and aperiodic patterns that align with experimental observations.

Contribution

It provides the first analytical calculation of cortical representations predicted by the elastic net model, identifying regimes that produce realistic aperiodic maps with lower pinwheel densities.

Findings

Predicted OPM layouts are mostly perfectly periodic.

A novel regime of aperiodic OPMs with lower pinwheel densities was found.

Extreme limits produce OPMs resembling experimental data.

Abstract

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.