Distributed synaptic weights in a LIF neural network and learning rules

摘要

Abstract Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connectivity parameter (strengths of the synaptic weights) with the effect of processing the input current with different intensities. We first study the properties of the network activity depending on the distribution of synaptic weights and in particular its discrimination capacity. Then, we consider simple learning rules and determine the synaptic weight distribution it generates. We outline the role of noise as a selection principle and the capacity to memorize a learned signal. Highlights ? Learning rules are introduced in the seminal integrate-and-fire neural network model. ? Several important properties are proved mathematically including the capacity of such networks to produce any given si