QUANTITATIVE STUDY OF ATTRACTOR NEURAL NETWORK RETRIEVING AT LOW SPIKE RATES .1. SUBSTRATE SPIKES, RATES AND NEURONAL GAIN

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 quantitative 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 prospective ANN at low spike rates. The actual integration into an associative memory network is left for the consecutive article.