Optimal sequence memory in driven random networks

TL;DR

This paper investigates how time-varying inputs influence chaos and memory in randomly coupled neural networks, revealing conditions for stability and optimal information storage.

Contribution

It provides an exact analytical condition for the transition to chaos and demonstrates how input suppresses chaos, enhancing sequential memory capacity.

Findings

Input shifts the chaos transition to higher coupling strengths.

A regime of coexistent expansive, non-chaotic dynamics optimizes memory.

Dynamic mean-field theory accurately predicts activity and stability.

Abstract

Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information processing. Dynamic mean-field theory yields the statistics of the activity, the maximum Lyapunov exponent, and the memory capacity of the network. We find an exact condition that determines the transition from stable to chaotic dynamics and the sequential memory capacity in closed form. The input suppresses chaos by a dynamic mechanism, shifting the transition to significantly larger coupling strengths than predicted by local stability analysis. Beyond linear stability, a regime of coexistent locally expansive, but non-chaotic dynamics emerges that optimizes the capacity of the network to store sequential input.