Layered feed-forward neural network with exactly soluble dynamics

A model layered feed-forward neural network is studied and solved exactly in the thermodynamic limit. Layer-to-layer recursion relations are found and analyzed as a function of the relevant external parameters. Stochasticity is introduced by a ``temperature'' variable. A region of good recall is found, separated from a region of no recall by a first-order line terminating at a critical point. The exact time evolution of mixtures of patterns is given as well.