Topology and Dynamics of Attractor Neural Networks: The Role of Loopiness

TL;DR

This paper introduces the loopiness coefficient to quantify how network topology influences neural network dynamics, revealing that higher loopiness increases state correlations and can impair network performance.

Contribution

It provides an exact topological analysis framework for sequence processing neural networks, highlighting the impact of loopiness on dynamics and performance.

Findings

Higher loopiness correlates with increased state correlations.

Large loopiness reduces neural network performance.

The theory applies to various network topologies.

Abstract

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. The large loopiness coefficient means the large probability of finding loops in the networks. We develop the recursive equations for the overlap parameters of neural networks in the term of the loopiness. It was found that the large loopiness increases the correlations among the network states at different times, and eventually it reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular, and densely-connected small-world, where encouraging results are obtained.