An analysis of synaptic normalisation in a general class of Hebbian models.

Abstract

In standard Hebb models of developmental synaptic plasticity, synaptic normalisation must be introduced in order to constrain synaptic growth and ensure the presence of activity-dependent, competitive dynamics. In such models, multiplicative normalisation cannot segregate afferents whose patterns of electrical activity are positively correlated, while subtractive normalisation can. It is now widely believed that multiplicative normalisation cannot segregate positively correlated afferents in any Hebb model. However, we recently provided a counter-example to this belief by demonstrating that our own neurotrophic model of synaptic plasticity, which can segregate positively correlated afferents, can be reformulated as a non-linear Hebb model with competition implemented through multiplicative normalisation. We now perform an analysis of a general class of Hebb models under general forms of synaptic normalisation. In particular, we extract conditions on the forms of these rules that guarantee that such models possess a fixed point structure permitting the segregation of all but perfectly correlated afferents. We find that the failure of multiplicative normalisation to segregate positively correlated afferents in a standard Hebb model is quite atypical.

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