Scaling self-organizing maps to model large cortical networks

Self-organizing computational models with specific intracortical connections can explain many functional features of visual cortex, such as topographic orientation and ocular dominance maps. However, due to their computational requirements, it is difficult to use such detailed models to study large-scale phenomenal like object segmentation and binding, object recognition, tilt illusions, optic flow, and fovea-periphery differences. This article introduces two techniques that make large simulations practical. First, we show how parameter scaling equations can be derived for laterally connected self-organizing models. These equations result in quantitatively equivalent maps over a wide range of simulation sizes, making it possible to debug small simulations and then scale them up only when needed. Parameter scaling also allows detailed comparison of biological maps and parameters between individuals and species with different brain region sizes. Second, we use parameter scaling to implement a new growing map method called GLISSOM, which dramatically reduces the memory and computational requirements of large self-organizing networks. With GLISSOM, it should be possible to simulate all of human VI at the single-column level using current desktop workstations. We are using these techniques to develop a new simulator Topographica, which will help make it practical to perform detailed studies of large-scale phenomena in topographic maps.