Can Hebbian volume learning explain discontinuities in cortical maps?

It has recently been shown that orientation and retinotopic position, both of which are mapped in primary visual cortex, can show correlated jumps (Das & Gilbert, 1997). This is not consistent with maps generated by Kohonen's algorithm (Kohonen, 1982), where changes in mapped variables tend to be anticorrelated. We show that it is possible to obtain correlated jumps by introducing a Hebbian component (Hebb, 1949) into Kohonen's algorithm. This correspondents to a volume learning mechanism where synaptic facilitation depends not only on the spread of a signal from a maximally active neuron but also requires postsynaptic activity at a synapse. The maps generated by this algorithm show discontinuities across which both orientation and retinotopic position change rapidly, but these regions, which include the orientation singularities, are also aligned with the edges of ocular dominance columns, and this is not a realistic feature of cortical maps. We conclude that cortical maps are better modeled by standard, non-Hebbian volume learning, perhaps coupled with some other mechanism (e.g., that of Ernst, Pawelzik, Tsodyks, & Sejnowski, 1999) to produce receptive field shifts.