# Hierarchical Architectures in Reservoir Computing Systems

arXiv: https://arxiv.org/abs/2105.06923 · HTML: https://mlsanity.com/paper/2105.06923/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 14 May 2021.

## Builds on (most cited first, 2 of 2)

- [Optimal modularity and memory capacity of neural reservoirs](https://mlsanity.com/paper/1706.06511/) (2017)
- [Reservoir Topology in Deep Echo State Networks](https://mlsanity.com/paper/1909.11022/) (2019)

## Built on by (most cited first, 5 of 5)

- [RN-Net: Reservoir Nodes-Enabled Neuromorphic Vision Sensing Network](https://mlsanity.com/paper/2303.10770/) (2023)
- [Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence](https://mlsanity.com/paper/2305.00100/) (2023)
- [Deterministic Reservoir Computing for Chaotic Time Series Prediction](https://mlsanity.com/paper/2501.15615/) (2025)
- [Temporal Convolution Derived Multi-Layered Reservoir Computing](https://mlsanity.com/paper/2407.06771/) (2024)
- [Local learning for stable backpropagation-free neural network training towards physical learning](https://mlsanity.com/paper/2603.24790/) (2026)

## Abstract (arXiv)

Reservoir computing (RC) offers efficient temporal data processing with a low training cost by separating recurrent neural networks into a fixed network with recurrent connections and a trainable linear network. The quality of the fixed network, called reservoir, is the most important factor that determines the performance of the RC system. In this paper, we investigate the influence of the hierarchical reservoir structure on the properties of the reservoir and the performance of the RC system. Analogous to deep neural networks, stacking sub-reservoirs in series is an efficient way to enhance the nonlinearity of data transformation to high-dimensional space and expand the diversity of temporal information captured by the reservoir. These deep reservoir systems offer better performance when compared to simply increasing the size of the reservoir or the number of sub-reservoirs. Low frequency components are mainly captured by the sub-reservoirs in later stage of the deep reservoir structure, similar to observations that more abstract information can be extracted by layers in the late stage of deep neural networks. When the total size of the reservoir is fixed, tradeoff between the number of sub-reservoirs and the size of each sub-reservoir needs to be carefully considered, due to the degraded ability of individual sub-reservoirs at small sizes. Improved performance of the deep reservoir structure alleviates the difficulty of implementing the RC system on hardware systems.