Reservoir Computing — Echo State Networks

A fixed random recurrent network (reservoir) projects input into a high-dimensional space. Only the readout weights are trained. The reservoir must operate near the edge of chaos for optimal memory and nonlinearity.

Spectral radius: — | MSE: — | Nodes active: —%

Reservoir size N30

Spectral radius0.95

Input scale0.50

Sparsity0.20

Leak rate α0.80

Target signal

Echo state networks (Jaeger 2001): x(t+1) = (1−α)x(t) + α·tanh(Wx(t) + W_in·u(t)). Only W_out is trained via ridge regression. The echo state property holds when the spectral radius ρ < 1 — but optimal performance often occurs near ρ ≈ 1, the edge of chaos. Larger ρ → more memory, less stability.