Orientation column

About: Orientation column is a research topic. Over the lifetime, 1142 publications have been published within this topic receiving 130169 citations.

Hebbian learning of recurrent connections: a geometrical perspective

Abstract: We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics derives from an energy function and therefore always converges to equilibrium points. The equilibria reflect the correlation structure of the inputs, a global object extracted through local recurrent interactions only. Second, we use numerical methods to illustrate how learning extracts the hidden geometrical structure of the inputs. Indeed, multidimensional scaling methods make it possible to project the final connectivity matrix on to a distance matrix in a high-dimensional space, with the neurons labelled by spatial position within this space. The resulting network structure turns out to be roughly convolutional. The residual of the projection defines the non-convolutional part of the connectivity which is minimized in the process. Finally, we show how restricting the dimension of the space where the neurons live gives rise to patterns similar to cortical maps. We motivate this using an energy efficiency argument based on wire length minimization. Finally, we show how this approach leads to the emergence of ocular dominance or orientation columns in primary visual cortex. In addition, we establish that the non-convolutional (or long-range) connectivity is patchy, and is co-aligned in the case of orientation learning.

Spatial resolution and nonlinearities of simple cells in the cat visual cortex measured with parallel line pairs

Abstract: The spatial resolution of simple cells in cat visual cortex was measured by stimulation with pairs of 6? wide parallel light bars of various spacings. These double lines were moved across the receptive field and were taken as resolved if there was a 10% deflection between the double peak responses of cells. As a control, recordings were also made from several geniculate fibers. The smallest bar separations resolved by simple cells were larger than those which have been found for cells of the lateral geniculate nucleus (LGN), although the smallest cortical receptive field centers were as small as those of LGN-cells. The correlation between optimal resolving power of a cell and the width of its excitatory receptive field was much weaker in cortical simple cells than in LGN cells. In contrast to the LGN, the double line responses of most simple cells differ markedly from an additive superposition of two single line responses spaced according to the actual interline distance. As possible mechanisms underlying these nonlinearities three different connectivity schemes were investigated. Two of these models were based on receptive field concepts; the third one used intracortical circuits. Only the latter model could explain all the nonlinear effects seen in the neurophysiological experiments.