Spectral Bounds for Graph Echo State Network Stability

Graph echo state networks (GESN) are a class of reservoir computing models for the efficient and effective processing of graphs. They compute graph embeddings by the convergence to a fixed point of a dynamical system, randomly initialized according to a generalization of the echo state property, called the graph embedding stability (GES) property. In this paper, we prove new and more accurate bounds for necessary and sufficient GES conditions. Experiments demonstrate how these bounds allow an easier parameter selection and better quality reservoirs.