# Symmetry-Aware Reservoir Computing

arXiv: https://arxiv.org/abs/2102.00310 · HTML: https://mlsanity.com/paper/2102.00310/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 39 references that are in the map.
- First posted on arXiv 30 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Rapid Time Series Prediction with a Hardware-Based Reservoir Computer](https://mlsanity.com/paper/1807.07627/) (2018)

## Built on by (most cited first, 7 of 7)

- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Learning unseen coexisting attractors](https://mlsanity.com/paper/2207.14133/) (2022)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks](https://mlsanity.com/paper/2111.03706/) (2021)
- [On the emergence of numerical instabilities in Next Generation Reservoir Computing](https://mlsanity.com/paper/2505.00846/) (2025)

## Abstract (arXiv)

We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that highlights inversion and permutation symmetries, and to a chaotic system inference task that presents an inversion symmetry rule. For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced neural network and training data, greatly speeding up the time to result and outperforming hand crafted artificial neural networks. When both symmetries are respected, we find that the network size N necessary to obtain zero error for 50 different RC instances scales linearly with the parity-order n. Moreover, some symmetry-aware RC instances perform a zero error classification with only N=1 for n≤7. Furthermore, we show that a symmetry-aware RC only needs a training data set with size on the order of (n+n/2) to obtain such performance, an exponential reduction in comparison to a regular RC which requires a training data set with size on the order of n2n to contain all 2n possible n-bit-long sequences. For the inference task, we show that a symmetry-aware RC presents a normalized root-mean-square error three orders-of-magnitude smaller than regular RCs. For both tasks, our RC approach respects the symmetries by adjusting only the input and the output layers, and not by problem-based modifications to the neural network. We anticipate that generalizations of our procedure can be applied in information processing for problems with known symmetries.