Categorization ability in a biologically motivated neural network

In this work, we study the categorization properties of an extreme and asymmetrically diluted version of the Hopfield model for associative memory when the effect of the refractory period of the neurons is taken into account in the dynamics of the system. The simplest way of modeling these refractory periods is by means of a time-dependent threshold that acts only on those neurons that emit a signal and favors them to be at rest during a given time interval. The dynamic equations are derived in the limit of extreme dilution, using an approach, that explicitly preserves the dependence of the system on its whole history. The categorization error is analyzed for different values of the parameters. In particular, we confront our analytical results with numerical simulations for the noiseless case T=0. When the number of examples or their correlations increases, the system always categorizes independently of the amplitude of the potential that mimics the effect of the refractory period.