A characterization of the Edge of Criticality in Binary Echo State Networks

TL;DR

This paper introduces binary Echo State Networks, deriving a closed-form expression for their Edge of Criticality and analyzing how input variance influences their critical behavior.

Contribution

It presents a novel binary ESN model and provides a theoretical derivation of the EoC, enhancing understanding of their dynamics under noise and input signals.

Findings

Derived a closed-form expression for EoC in binary ESNs

Input variance significantly affects the EoC

Binary ESNs behave similarly to standard ESNs in critical regimes

Abstract

Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to be effective in solving tasks when configured on a region in (hyper-)parameter space called \emph{Edge of Criticality} (EoC), where the system is maximally sensitive to perturbations hence affecting its behaviour. In this paper, we propose binary ESNs, which are architecturally equivalent to standard ESNs but consider binary activation functions and binary recurrent weights. For these networks, we derive a closed-form expression for the EoC in the autonomous case and perform simulations in order to assess their behavior in the case of noisy neurons and in the presence of a signal. We propose a theoretical explanation for the fact that the variance of the input plays a major role in characterizing the EoC.