Pinwheel Stability in a Non-Euclidean Model of Pattern Formation in the Visual Cortex

다국어 초록 (Multilingual Abstract)

The structure of neural maps in the primary visual cortex arises from the problem of representing
a high-dimensional stimulus manifold on an essentially two-dimensional piece of cortical tissue. In
order to treat the problem theoretically, stimuli are usually represented by a set of features, such
as centroid position, orientation, spatial frequency, phase etc. Inputs to the cortex are, however,
activity distributions over aerent nerve .bers; i.e., they require, in principle, a description as high-
dimensional vectors. We study the relation between high-dimensional maps, which can be assumed
to rely on a Euclidean geometry, and low-dimensional feature maps, which need to be formulated
in Riemannian space in order to represent high-dimensional maps to a good accuracy. We show
numerically that the Riemannian framework allows for a suggestive explanation of the abundance
of typical structural units (\pinwheels") in feature maps emerging in the course of the adaptation
process from an initially unstructured state.0

참고문헌 (Reference)

1 S. Tanaka, "NeuroIm-age" 30 : 462-, 2006

2 R. Miikkulainen, "Computational Maps in the Visual Cortex" Springer 2005