Node pruning reveals compact and optimal substructures within large networks

Abstract

The structural complexity of reservoir networks poses a significant challenge, often leading to excessive computational costs and suboptimal performance. In this study, we introduce a systematic, task specific node pruning framework that enhances both the efficiency and adaptability of reservoir networks. By identifying and eliminating redundant nodes, we demonstrate that large networks can be compressed while preserving or even improving performance on key computational tasks. Our findings reveal the emergence of optimal subnetwork structures from larger Erdos Renyi random networks, indicating that efficiency is governed not merely by size but by topological organization. A detailed analysis of network structure at both global and node levels uncovers the role of density distributions, special-radius and asymmetric input-output node distributions, among other graph-theoretic measures that enhance the computational capacity of pruned compact networks. We show that pruning leads to non-uniform network refinements, where specific nodes and connectivity patterns become critical for information flow and memory retention. This work offers fundamental insights into how structural optimization influences reservoir dynamics, providing a pathway toward designing more efficient, scalable, and interpretable machine learning architectures.