Centrality-Based Pruning for Efficient Echo State Networks

Abstract

Echo State Networks (ESNs) are a reservoir computing framework widely used for nonlinear time-series prediction. However, despite their effectiveness, the randomly initialized reservoir often contains redundant nodes, leading to unnecessary computational overhead and reduced efficiency. In this work, we propose a graph centrality-based pruning approach that interprets the reservoir as a weighted directed graph and removes structurally less important nodes using centrality measures. Experiments on Mackey-Glass time-series prediction and electric load forecasting demonstrate that the proposed method can significantly reduce reservoir size while maintaining, and in some cases improving, prediction accuracy, while preserving the essential reservoir dynamics.

Figures (3)

• Figure 1: Echo State Network (ESN) architecture. The input is mapped into a recurrent reservoir through $W^{in}$, where the internal connections $W$ generate dynamic states. The output is computed using trained weights $W^{out}$, while the reservoir remains fixed after initialization.
• Figure 2: Test RMSE versus pruned nodes for Mackey-Glass prediction across reservoir sizes $N=200$ (top left), $N=300$ (top right), $N=500$ (bottom left), and $N=700$ (bottom right). The curves show different centrality measures, and the dashed line indicates the initial error. In general, moderate pruning improves performance before it degrades.
• Figure 3: Performance of centrality-based pruning on electricity load forecasting, shown as test RMSE versus pruned nodes for reservoir sizes $N=200$ (top left), $N=300$ (top right), $N=500$ (bottom left), and $N=700$ (bottom right). Different centrality measures are compared, and the dashed line shows the initial error.