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

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.