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arXiv · 2508.21172

Deep Residual Echo State Networks: exploring residual orthogonal connections in untrained Recurrent Neural Networks

Matteo Pinna·Andrea Ceni·Claudio Gallicchio
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Abstract

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with long-term information processing. In this paper, we introduce a novel class of deep untrained RNNs based on temporal residual connections, called Deep Residual Echo State Networks (DeepResESNs). We show that leveraging a hierarchy of untrained residual recurrent layers significantly boosts memory capacity and long-term temporal modeling. For the temporal residual connections, we consider different orthogonal configurations, including randomly generated and fixed-structure, and study their effect on network dynamics. A thorough mathematical analysis outlines necessary and sufficient conditions to ensure stable dynamics within DeepResESN. Empirically, the proposed approach consistently outperforms traditional shallow and deep RC on a variety of time series tasks. Overall, DeepResESN offers a promising approach for designing hierarchical ESNs with better prediction accuracy on long sequences, without sacrificing the computational advantages that make RC attractive.

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Matteo Pinna, Andrea Ceni, Claudio Gallicchio. 2025-08-28. Deep Residual Echo State Networks: exploring residual orthogonal connections in untrained Recurrent Neural Networks. https://doi.org/10.1109/tnnls.2026.3718377

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