RETRIEVAL PROPERTIES OF ATTRACTOR NEURAL NETWORKS THAT OBEY DALES LAWUSING A SELF-CONSISTENT SIGNAL-TO-NOISE ANALYSIS

The recently proposed self-consistent signal-to-noise analysis is appl ied 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 modelling their effective inhibition that depen ds upon both the level of activity of the excitatory neurons and the s tored patterns. The low rate attractor structure is identified, and at low loading the network retrieves single patterns with uniform low ra tes without errors, and is stable to the admixture of additional patte rns. The self-consistent signal-to-noise method enables the analysis o f the network properties with an extensive number of patterns, and the results are compared with simulations. The method allows the identifi cation 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 straightforwar d way of analysing the properties of networks with neuronal specificit y, low spike rates and synaptic noise, as well as incorporating the ef fects of random asymmetric synaptic dilution and limited analogue syna ptic depth in a natural way. The simulations show that the network pro perties are very robust both to errors in the stimulus and to the stim ulus strength and duration.