# Time Shifts to Reduce the Size of Reservoir Computers

arXiv: https://arxiv.org/abs/2205.02267 · HTML: https://mlsanity.com/paper/2205.02267/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 3 May 2022.

## Builds on (most cited first, 7 of 7)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Do Reservoir Computers Work Best at the Edge of Chaos?](https://mlsanity.com/paper/2012.01409/) (2020)
- [Rapid Time Series Prediction with a Hardware-Based Reservoir Computer](https://mlsanity.com/paper/1807.07627/) (2018)
- [Optimizing Memory in Reservoir Computers](https://mlsanity.com/paper/2201.01605/) (2022)
- [Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Links](https://mlsanity.com/paper/1912.02721/) (2019)
- [Fundamental aspects of noise in analog-hardware neural networks](https://mlsanity.com/paper/1907.09002/) (2019)
- [Reservoir Computers with Random and Optimized Time-Shifts](https://mlsanity.com/paper/2108.12765/) (2021)

## Built on by (most cited first, 3 of 3)

- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing](https://mlsanity.com/paper/2307.07195/) (2023)
- [Time-shift selection for reservoir computing using a rank-revealing QR algorithm](https://mlsanity.com/paper/2211.17095/) (2022)

## Abstract (arXiv)

A reservoir computer is a type of dynamical system arranged to do computation. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network that includes recurrent connections. In order to achieve accurate results, the reservoir usually contains hundreds to thousands of nodes. This high dimensionality makes it difficult to analyze the reservoir computer using tools from dynamical systems theory. Additionally, the need to create and connect large numbers of nonlinear nodes makes it difficult to design and build analog reservoir computers that can be faster and consume less power than digital reservoir computers. We demonstrate here that a reservoir computer may be divided into two parts; a small set of nonlinear nodes (the reservoir), and a separate set of time-shifted reservoir output signals. The time-shifted output signals serve to increase the rank and memory of the reservoir computer, and the set of nonlinear nodes may create an embedding of the input dynamical system. We use this time-shifting technique to obtain excellent performance from an opto-electronic delay-based reservoir computer with only a small number of virtual nodes. Because only a few nonlinear nodes are required, construction of a reservoir computer becomes much easier, and delay-based reservoir computers can operate at much higher speeds.