Specialisation in Recurrent Neural Networks with Spike-timing-dependent Plasticity

We examine how Spike-Timing-Dependent Plasticity (STDP) can strengthen recurrent excitatory connections in a network of Poisson neurons stimulated by two pools of external inputs, where only one pool has spike-time correlation. We derive conditions on the STDP and network parameters such that the network exhibits a stable activity in terms of spiking-rates and show how the evolution of the recurrent weights is determined by the interplay between STDP, the synaptic mechanisms and the input correlation structure. The results indicate that STDP induces competition that causes the emergence of a bimodal distribution of the weights, while the mean of the weights rapidly reaches a stable equilibrium. This behaviour can be related to the emergence of functional areas in recurrently connected networks, such as self-organising maps inspired by the evolution of the visual cortex in the first weeks of new-born mammalian animals.