Tailoring Artificial Neural 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 to finance, and language processing. A key feature of the ESN paradigm is its reservoir ---a directed and weighted network--- that represents the connections between neurons and projects the input signals into a high dimensional space. Despite extensive studies, the impact of the reservoir network on the ESN performance remains unclear. Here we systematically address this fundamental question. Through spectral analysis of the reservoir network we reveal a key factor that largely determines the ESN memory capacity and hence affects its performance. Moreover, we find that adding short loops to the reservoir network can tailor ESN for specific tasks and optimal learning. We validate our findings by applying ESN to forecast both synthetic and real benchmark time series. Our results provide a new way to design task-specific recurrent neural networks, as well as new insights in understanding complex networked systems.