Retrieval properties of attractor neural networks that obey Dale's law using a self-consistent signal-to-noise analysis

The recently proposed self-consistent signal-to-noise analysis is applied to a current--rate dynamics attractor network of excitatory neurons with a Hebbian synaptic matrix. The effect of inhibitory interneurons is included by a term modeling their effective inhibition that depends upon both the level of activity of the excitatory neurons and the stored patterns. The low rate attractor structure is identified, and at low loading the network retrieves single patterns with uniform low rates without errors, and is stable to the admixture of additional patterns. The self-consistent signal-to-noise method enables the analysis of the network properties with an extensive number of patterns, and the results are compared with simulations. The method allows the identification of the fixed point structure of networks for which there is no Lyapanov function, and hence for which mean-field techniques cannot be used. This analysis is shown to provide a powerful and straightforward way to analyse the properties of networks with neuronal specificity, low spike rates and synaptic noise, as well as incorporating the effects of random asymmetric synaptic dilution and limited analog synaptic depth in a natural way. The simulations show that the network properties are very robust both to errors in the stimulus and to the stimulus strength and duration