Competition and Arbors in Ocular Dominance

Hebbian and competitive Hebbian algorithms are almost ubiquitous in modeling pattern formation in cortical development. We analyse in theoretical detaila particular model (adapted from Piepenbrock & Obermayer, 1999) for the development of Id stripe-like patterns, which places competitive and interactive cortical influences, and free and restricted initial arborisationonto a common footing. 1 Introduction Cats, many species of monkeys, and humans exibit ocular dominance stripes, which are alternating areas of primary visual cortex devoted to input from (the thalamic relay associated with)just one or the other eye (see Erwin et aI, 1995; Miller, 1996; Swindale, 1996 for reviews of theory and data). These well-known fingerprint patterns have been a seductive targetfor models of cortical pattern formation because of the mix of competition and cooperation they suggest. A wealth of synaptic adaptation algorithms has been suggested to account for them (and also the concomitant refinement of the topography of the map between the eyes and the cortex), many of which are based on forms of Hebbian learning. Critical issues for the models are the degree of correlation between inputs from the eyes, the nature of the initial arborisation of the axonal inputs, the degree and form of cortical competition, and the nature of synaptic saturation (preventing weights from changing sign or getting too large) and normalisation (allowing cortical and/or thalamic cells to support only a certain total synaptic weight).