Dynamics of an attractor neural network converting temporal into spatial correlations

The dynamics of a model attractor neural network, dominated by collateral feedback, composed of excitatory and inhibitory neurons described by afferent currents and spike rates, is studied analytically. The network stores stimuli learned in a temporal sequence. The statistical properties of the delay activities are investigated analytically under the approximation that no neuron is activated by more than one of the learned stimuli, and that inhibitory reaction is instantaneous. The analytic results reproduce the details of simulations of the model in which the stored memories are uncorrelated, and neurons can be shared, with low probability, by different stimuli. As such, the approximate analytic results account for a delayed match to sample experiments of Miyashita in the inferotemporal cortex of monkeys. If the stimuli used in the experiment are uncorrelated, the analysis deduces the mean coding level f in a stimulus (i.e. the mean fraction of neurons activated by a given stimulus) from the fraction of selective neurons which have a high correlation coefficient, of f approximately 0.0125. It also predicts the structure of the distribution of the correlation coefficients among neurons.