Threshold-linear formal neurons in auto-associative nets

Most analytical results concerning the long-time behaviour of associative memory networks have been obtained by using binary elementary units. The use of alternative types of neuron-like processing elements is considered as a way of testing the generality of those results and of approaching biological realism. In particular, threshold-linear units are proposed as appropriate in models designed to reproduce low firing rates, in which long-time stability does not rely on single unit saturation. Such units are simple enough to allow detailed analytical understanding of the properties of the network. This is demonstrated by analysing the attractor states of a network operating at low rates. It is shown that while the interesting retrieval behaviour persists, the roles of the different parameters as well as the nature of the stable states change completely with respect to the binary implementation.