# Master memory function for delay-based reservoir computers with single-variable dynamics

arXiv: https://arxiv.org/abs/2108.12643 · HTML: https://mlsanity.com/paper/2108.12643/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 91 references that are in the map.
- First posted on arXiv 28 Aug 2021.

## Builds on (most cited first, 18 of 18)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Reinforcement Learning in a large scale photonic Recurrent Neural Network](https://mlsanity.com/paper/1711.05133/) (2017)
- [Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems](https://mlsanity.com/paper/2002.05514/) (2020)
- [Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing](https://mlsanity.com/paper/2108.04074/) (2021)
- [Human action recognition with a large-scale brain-inspired photonic computer](https://mlsanity.com/paper/2004.02545/) (2020)
- [Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacity](https://mlsanity.com/paper/2006.06322/) (2020)
- [Deep Neural Networks using a Single Neuron: Folded-in-Time Architecture using Feedback-Modulated Delay Loops](https://mlsanity.com/paper/2011.10115/) (2020)
- [Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalisation](https://mlsanity.com/paper/1610.06268/) (2016)
- [Performance boost of time-delay reservoir computing by non-resonant clock cycle](https://mlsanity.com/paper/1905.02534/) (2019)
- [A complete, parallel and autonomous photonic neural network in a semiconductor multimode laser](https://mlsanity.com/paper/2012.11153/) (2020)
- [Performance and Complexity Analysis of bi-directional Recurrent Neural Network Models vs. Volterra Nonlinear Equalizers in Digital Coherent Systems](https://mlsanity.com/paper/2103.03832/) (2021)
- [Photonic machine learning implementation for signal recovery in optical communications](https://mlsanity.com/paper/1710.01107/) (2017)
- [Reservoir computing with simple oscillators: Virtual and real networks](https://mlsanity.com/paper/1802.08590/) (2018)
- [Richness of Deep Echo State Network Dynamics](https://mlsanity.com/paper/1903.05174/) (2019)
- [Takens-inspired neuromorphic processor: a downsizing tool for random recurrent neural networks via feature extraction](https://mlsanity.com/paper/1907.03122/) (2019)
- [Limitations of the recall capabilities in delay based reservoir computing systems](https://mlsanity.com/paper/2010.15562/) (2020)

## Built on by (most cited first, 4 of 4)

- [Adaptive Sensing of Continuous Physical Systems for Machine Learning](https://mlsanity.com/paper/2603.03650/) (2026)
- [Information Processing Capacity of Stationary Physical Systems: Theory, Data-efficient Estimation Methods, and Photonic Demonstration](https://mlsanity.com/paper/2605.19152/) (2026)
- [A Single Atom in Front of a Mirror is a Universal Reservoir Computer](https://mlsanity.com/paper/2608.10382/) (2026)
- [Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Data](https://mlsanity.com/paper/2609.24754/) (2026)

## Abstract (arXiv)

We show that many delay-based reservoir computers considered in the literature can be characterized by a universal master memory function (MMF). Once computed for two independent parameters, this function provides linear memory capacity for any delay-based single-variable reservoir with small inputs. Moreover, we propose an analytical description of the MMF that enables its efficient and fast computation. Our approach can be applied not only to reservoirs governed by known dynamical rules such as Mackey-Glass or Ikeda-like systems but also to reservoirs whose dynamical model is not available. We also present results comparing the performance of the reservoir computer and the memory capacity given by the MMF.