A characterization of the Edge of Criticality in Binary Echo State Networks
This work provides a theoretical characterization of critical behavior in binary ESNs, which is incremental as it extends existing EoC concepts to a specific binary variant.
The authors tackled the problem of characterizing the Edge of Criticality (EoC) in Echo State Networks by proposing binary ESNs with binary activations and weights, deriving a closed-form expression for the EoC in the autonomous case and analyzing the role of input variance through simulations.
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.