A simple model of correlation-based synaptic plasticity via axonal sprouting and retraction (Elliott, Howarth, & Shadbolt, 1996a) is shown to be equivalent to the class of correlation-based models (Miller, Keller, & Stryker, 1989), although these were formulated in terms of weight modification of anatomically fixed synapses. Both models maximize the same measure of synaptic correlation, subject to certain constraints on connectivity. Thus, the analyses of the correlation-based models suffice to characterize the behavior of the sprouting-and-retraction model. More detailed models are needed for theoretical distinctions to be drawn between plasticity via sprouting and retraction, weight modification, or a combination.
The model of Elliott et al. involves stochastic search through allowed weight patterns for those that improve correlations. That of Miller et alinstead follows dynamical equations that determine continuous changes of the weights that improve correlations. The identity of these two approaches is shown to depend on the use of subtractive constraint enforcement in the models of Miller et al. More generally, to model the idea that neural development acts to maximize some measure of correlation subject to a constraint on the summed synaptic weight, the constraint must be enforced subtractively in a dynamical model.