Inference and Chaos by a Network of Non-monotonic Neurons

TL;DR

This paper investigates the dynamics of a network of non-monotonic neurons, revealing how it transitions from fixed points to chaos, and provides a phase diagram illustrating these behaviors.

Contribution

It introduces a detailed analysis of the macroscopic dynamics of non-monotonic neuron networks, including chaos and bifurcation phenomena, with quantitative measures and phase diagrams.

Findings

Complex behavior from fixed points to chaos observed

Bifurcation cascade triggered by parameter changes

Information dimension and Lyapunov exponent calculated

Abstract

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.