The attractors in sequence processing neural networks

TL;DR

This paper investigates the properties of attractors in sequence processing neural networks, revealing a critical loading ratio and exponential growth in attractor length, with implications for network robustness.

Contribution

It introduces a detailed analysis of attractor length and relaxation time in neural networks, identifying a critical point and exponential growth behavior.

Findings

Critical loading ratio identified

Attractor length grows exponentially with loading ratio

Relaxation time linearly related to loading ratio

Abstract

The average length and average relaxation time of attractors in sequence processing neural networks are investigated. The simulation results show that a critical point of $\alpha $, the loading ratio, is found. Below the turning point, the average length is equal to the number of stored patterns; conversely, the ratio of length and numbers of stored patterns, grow with an exponential dependence $\exp (A\alpha) $. Moreover, we find that the logarithm of average relaxation time is only linearly associated with $\alpha $ and the turning point of coupling degree is located for examining robustness of networks.