Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

TL;DR

This paper investigates whether the functional architecture of visual cortical maps can be explained as optimal solutions of energy functionals, introducing a dynamical systems approach to analyze their coordinated organization.

Contribution

It develops a rigorous, general method to analyze the optimization principles underlying the organization of multiple cortical maps in visual cortex.

Findings

Identifies ground states of candidate energy functionals for cortical maps.

Analyzes how different optimization principles influence map structures.

Provides a framework to infer optimization principles from observed map patterns.

Abstract

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.