Code will be released (approx.) around Oct./Nov. 2025.

This repository contains the official code for the paper:

Deep Residual Echo State Networks: exploring residual orthogonal connections in untrained Recurrent Neural Networks,
Matteo Pinna, Andrea Ceni, Claudio Gallicchio,
arxiv:2508.21172, 2025.

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 configurations, and we study their effect on network dynamics. A thorough mathematical analysis outlines necessary and sufficient conditions to ensure stable dynamics within DeepResESN. Our experiments on a variety of time series tasks showcase the advantages of the proposed approach over traditional shallow and deep RC.

To install the required dependencies:

conda create -n deepresesn python=3.12
conda activate deepresesn
pip install -e .

If you use the model or code in this repository, consider citing our paper:

@article{pinna2025deep,
  title={Deep Residual Echo State Networks: exploring residual orthogonal connections in untrained Recurrent Neural Networks},
  author={Pinna, Matteo and Ceni, Andrea and Gallicchio, Claudio},
  journal={arXiv preprint arXiv:2508.21172},
  year={2025}
}