Quantitative study of attractor neural network retrieving at low spike rates: I. substrate—spikes, rates and neuronal gain

Abstract

We discuss the conversion of the description of the dynamics of a neural network from a temporal variation of synaptic currents driven by point spikes and modulated by a synaptic structure to a description of the current dynamics driven by spike rates. The conditions for the validity of such a conversion are discussed in detail and are shown to be quite realistic in cortical conditions. This is done in preparation for a discussion of a scenario of an attractor neural network, based on the interaction of synaptic currents and neural spike rates.The spike rates are then expressed in terms of the currents themselves to provide a closed set of dynamical equations for the currents. The current-rate relation is expressed as a neuronal gain function, converting currents into spike rates. It describes an integrate-and-fire element with noisy inputs, under explicit quaniitatve conditions which we argue to be plausible in a cortical situation In particular, it is shown that the gain of the current to rate transduction function, deduced from realistic parameters, does not exclude the possibility of a stable operation of the prospectrve ANN at low spike rates The actual integration into an associative memory network is left for the consecutive article.