Categorization in the pseudo-inverse neural network

We investigate analytically the emergence of the categorization ability in the pseudo-inverse attractor neural network. More pointedly, we consider the problem of learning an extensive number of concepts alpha N by storing a finite number of examples s of each concept. We find that there is a critical value s(c) = 1/alpha beyond which the categorization error, as measured by the average fraction of unstable sites in the concepts, decreases monotonically with s.