The Asymptotic Performance of Linear Echo State Neural Networks
This work offers theoretical insights into the performance of echo-state networks, which is incremental for researchers in neural network theory and reservoir computing.
The authors studied the mean-square error performance of linear echo-state neural networks under noise, deriving deterministic equivalents for MSE as data and network size grow large, and obtained simple formulas for specific random connectivity settings to provide new insights.
In this article, a study of the mean-square error (MSE) performance of linear echo-state neural networks is performed, both for training and testing tasks. Considering the realistic setting of noise present at the network nodes, we derive deterministic equivalents for the aforementioned MSE in the limit where the number of input data $T$ and network size $n$ both grow large. Specializing then the network connectivity matrix to specific random settings, we further obtain simple formulas that provide new insights on the performance of such networks.