Network structure effects in reservoir computers

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition, or control of robotic systems. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network, driving the nodes with an input signal and using the node outputs to fit a training signal. In this work, we set up reservoirs where the edges (or connections) between all the network nodes are either +1 or 0 and proceed to alter the network structure by flipping some of these edges from +1 to -1. We use this simple network because it turns out to be easy to characterize; we may use the fraction of edges flipped as a measure of how much we have altered the network. In some cases, the network can be rearranged in a finite number of ways without changing its structure; these rearrangements are symmetries of the network, and the number of symmetries is also useful for characterizing the network. We find that changing the number of edges flipped in the network changes the rank of the covariance of a matrix consisting of the time series from the different nodes in the network and speculate that this rank is important for understanding the reservoir computer performance.