Tailoring Echo State Networks for Optimal Learning

As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigmis its reservoir-a directed and weighted network of neurons that projects the input time series into a high-dimensional space where linear regression or classification can be applied. By analyzing the dynamics of the reservoir we show that the ensemble of eigenvalues of the network contributes to the ESN memory capacity. Moreover, we find that adding short loops to the reservoir network can tailor ESN for specific tasks and optimize learning. We validate our findings by applying ESN to forecast both synthetic and real benchmark time series. Our results provide a simple way to design task-specific ESN and offer deep insights for other recurrent neural networks.