Layered neural networks

Exact solutions for the dynamics of layered feedforward neural networks are presented. These networks are expected to respond to an input by going through a sequence of preassigned states on the various layers. The family of networks considered has a variety of interlayer couplings: linear and non-linear Hebbian, Hebbian with Gaussian synaptic noise and with various kinds of dilution. In addition, the authors also solve the problem of layered networks with the pseudoinverse (projector) matrix of couplings. In all cases the solutions take the form of layer-to-layer recursions for the mean overlap with a (random) key pattern and for the width of the embedding field distribution. The dynamics is governed by the fixed points of these recursions. For all cases, non-trivial domains of attraction of the memory states are found and graphically displayed.