Multiplicative synaptic normalisation and a non-linear Hebb rule underlie a neurotrophic model of competitive synaptic plasticity

Abstract

Synaptic normalisation is used to enforce competitive dynamics is many models of developmental synaptic plasticity. In linear and semi-linear Hebbian models, multiplicative synaptic normalisation fails to segregate afferents whose activity patterns are positively correlated. To achieve this, the biologically problematic device of subtractive synaptic normalisation must be used instead. Our own model of competition for neurotrophic support, which can segregate positively correlated afferents, was developed in part in an attempt to overcome these problems by removing the need for synaptic normalisation altogether. However, we now show that the dynamics of our model decompose into two decoupled subspaces, with competitive dynamics being implemented in one of them through a non-linear Hebb rule and multiplicative synaptic normalisation. This normalisation is "emergent" rather than imposed. We argue that these observations permit biologically plausible forms of synaptic normalisation to be viewed as abstract and general descriptions of the underlying biology in certain, scaleless models of synaptic plasticity.

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