Generalization and chaos in a layered neural network
David Domínguez, W. K. Theumann · Journal of Physics A Mathematical and General · 1997
The generalization performance of a multi-state and a graded response layered attractor neural network trained with examples of low activity is established exactly for monotonic and non-monotonic input/output functions. Complex behaviour is found which goes from fixed-point attractors to chaos through a cascade of bifurcations, depending on an appropriate threshold or cut-off parameter. The effect of the irregular behaviour on the generalization curves is explicitly demonstrated and phase diagrams for the recognition ratio of concepts in terms of the threshold/cut-off exhibit ordered (generalization), disordered (paramagnetic or self-sustained activity) and chaotic phases.