  We perform a stationary state replica analysis for a layered network of Ising
spin neurons, with recurrent Hebbian interactions within each layer, in
combination with strictly feed-forward Hebbian interactions between successive
layers. This model interpolates between the fully recurrent and symmetric
attractor network studied by Amit el al, and the strictly feed-forward
attractor network studied by Domany et al. Due to the absence of detailed
balance, it is as yet solvable only in the zero temperature limit. The built-in
competition between two qualitatively different modes of operation,
feed-forward (ergodic within layers) versus recurrent (non- ergodic within
layers), is found to induce interesting phase transitions.
