Edge of stability echo state networks
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In this paper, we propose a new Reservoir Computing (RC) architecture, called the Edge of Stability Echo State Network (ES^2N). The introduced ES^2N model is based on defining the reservoir layer as a convex combination of a nonlinear reservoir (as in the standard ESN), and a linear reservoir that implements an orthogonal transformation. We provide a thorough mathematical analysis of the introduced model, proving that the whole eigenspectrum of the Jacobian of the ES2N map can be contained in an annular neighbourhood of a complex circle of controllable radius, and exploit this property to demonstrate that the ES^2N's forward dynamics evolves close to the edge-of-chaos regime by design. Remarkably, our experimental analysis shows that the newly introduced reservoir model is able to reach the theoretical maximum short-term memory capacity. At the same time, in comparison to standard ESN, ES^2N is shown to offer a favorable trade-off between memory and nonlinearity, as well as a significant improvement of performance in autoregressive nonlinear modeling.
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