Topological ordering in neural nets with weak nearest neighbour interactions

We show that topological order can be developed in networks with weak nearest neighbour interactions through the controlled smoothing of their energy landscapes. The energy landscape deformations are modelled by deterministic annealing. In cortical mappings, we use a combination of elastic and nearest neighbour lateral interactions, which helps to control the cortex pattern. Utilizing only nearest neighbour lateral interactions in the visual cortex mappings, one obtains the simultaneous formation of retinotopy and ocular dominance stripes where regular clusters of cortical cells are associated with either left or right eyes