Network Structure Effects in Reservoir Computers

Abstract

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.

arXiv commentaccepted for Chaos

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• A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning
• Breaking Symmetries of the Reservoir Equations in Echo State Networks
• Catch-22s of reservoir computing
• Dimension of Reservoir Computers
• Reducing network size and improving prediction stability of reservoir computing
• Time Shifts to Reduce the Size of Reservoir Computers
• Machine Learning Potential of a Single Pendulum
• Criticality in Reservoir Computer of Coupled Phase Oscillators
• Transfer learning of chaotic systems
• Cluster-based Input Weight Initialization for Echo State Networks
• Stability Analysis of Reservoir Computers Dynamics via Lyapunov Functions
• Reservoir Computers with Random and Optimized Time-Shifts
• Adding Filters to Improve Reservoir Computer Performance
• Role of assortativity in predicting burst synchronization using echo state network
• Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach
• Time-shift selection for reservoir computing using a rank-revealing QR algorithm
• Asymmetrically connected reservoir networks learn better
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Artificial Intelligence for Dynamical Systems in Wireless Communications: Modeling for the Future
• Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data
• Prediction performance of random reservoirs with different topology for nonlinear dynamical systems with different number of degrees of freedom