Chaotic Dynamics of High Order Neural Networks

TL;DR

This paper explores the complex chaotic behaviors in highly diluted neural networks with high order synapses, revealing how these connections can enhance storage capacity and induce new chaotic phases depending on various parameters.

Contribution

It introduces a detailed analysis of chaotic dynamics in high order neural networks, highlighting the emergence of a new chaotic phase influenced by network parameters.

Findings

High order synapses improve storage capacity.

A new chaotic phase depends on parameters $psilon$, $T$, and $lpha$.

Rich dynamic behaviors are observed in the system.

Abstract

The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the system. The dynamics displays a very rich behavior, and in particular a new chaotic phase emerges depending on the weight of the high order connections $\epsilon$, the noise level $T$ and the network load defined as the rate between the number of stored patterns and the mean connectivity per neuron $\alpha =P/C$.