Optimal short-term memory before the edge of chaos in driven random recurrent networks

TL;DR

This paper uses mean-field theory to analyze how driven recurrent neural networks optimally store short-term memory, finding peak performance just before the edge of chaos where dynamics are stable with input but unstable without.

Contribution

It derives analytical expressions for short-term memory measures in driven recurrent networks and clarifies their relationships, highlighting peak memory capacity near the edge of chaos.

Findings

Memory measures peak before the edge of chaos.

Input-driven networks are stable while their undriven counterparts are unstable.

Analytical formulas for memory capacity, mutual information, and Fisher information are provided.

Abstract

The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to derive an approximate expression for the conditional probability density of the state of a neuron given a past input signal. From this conditional probability density, we can analytically calculate short-term memory measures, such as memory capacity, mutual information, and Fisher information, and determine the relationships among these measures, which have not been clarified to date to the best of our knowledge. We show that the network contribution of these short-term memory measures peaks before the edge of chaos, where the dynamics of input-driven networks is stable but corresponding systems without input signals are unstable.