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

arXiv: https://arxiv.org/abs/2508.21172 · HTML: https://mlsanity.com/paper/2508.21172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Dynamical Systems as Temporal Feature Spaces](https://mlsanity.com/paper/1907.06382/) (2019)
- [Random orthogonal additive filters: a solution to the vanishing/exploding gradient of deep neural networks](https://mlsanity.com/paper/2210.01245/) (2022)
- [Edge of stability echo state networks](https://mlsanity.com/paper/2308.02902/) (2023)
- [Residual Reservoir Memory Networks](https://mlsanity.com/paper/2508.09925/) (2025)

## Abstract (arXiv)

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.