Inference and Chaos by a Network of Non-monotonic Neurons

The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the activity of the neurons, are obtained and searched for through its numerical behavior. Complex behavior leading from fixed points to chaos through a cascade of bifurcation are found, when we increase the correlation between samples or decrease the activity of the samples and the load of concepts, or tune the threshold of fatigue of the neurons. Both the information dimension and the Liapunov exponent are given, and a phase diagram is built.