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

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.

References in corpus (6)

• Stimulus-Dependent Suppression of Chaos in Recurrent Neural Networks
• Local Dynamics in Trained Recurrent Neural Networks
• Determination of the edge of criticality in echo state networks through Fisher information maximization
• Criticality in Random Threshold Networks: Annealed Approximation and Beyond
• Learning may need only a few bits of synaptic precision
• A complete mean-field theory for dynamics of binary recurrent neural networks

Cited by in corpus (1)

• Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere