EXACT DYNAMICS IN FEEDFORWARD NEURAL NETWORKS

I consider layered neural networks in which the weights are trained by optimizing an arbitrary performance function with respect to a set of examples. Using the cavity method and many-body diagrammatic techniqu es, the evolution in the network can be described by an overlap and a noise parameter. Parameter pairs corresponding to various input condit ions are found to collapse on a universal curve. Simulations with the maximally stable network confirm the theory.