  The categorization ability of fully connected neural network models, with
either discrete or continuous Q-state units, is studied in this work in replica
symmetric mean-field theory. Hierarchically correlated multi-state patterns in
a two level structure of ancestors and descendents (examples) are embedded in
the network and the categorization task consists in recognizing the ancestors
when the network is trained exclusively with their descendents. Explicit
results for the dependence of the equilibrium properties of a Q=3-state model
and a $Q=\infty$-state model are obtained in the form of phase diagrams and
categorization curves. A strong improvement of the categorization ability is
found when the network is trained with examples of low activity. The
categorization ability is found to be robust to finite threshold and synaptic
noise. The Almeida-Thouless lines that limit the validity of the
replica-symmetric results, are also obtained.
