mlsanityData to 7 Oct 2026

Echo state networks are universal

arXiv 1806.00797 ↗First posted 3 Jun 2018cs.NE cs.AIcited by 86

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Abstract (arXiv)

This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times. This result guarantees that any fading memory input/output system in discrete time can be realized as a simple finite-dimensional neural network-type state-space model with a static linear readout map. This approximation is valid for infinite time intervals. The proof of this statement is based on fundamental results, also presented in this work, about the topological nature of the fading memory property and about reservoir computing systems generated by continuous reservoir maps.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 10; 2023: 12; 2024: 20; 2025: 22; 2026: 14.

86 papers.

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  1. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  2. 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
  3. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  4. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  5. 2021Learning strange attractors with reservoir systemscited by 16
  6. 2023Neural Oscillators are Universalcited by 16
  7. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  8. 2023Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirscited by 15
  9. 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
  10. 2022Chaotic Hedging with Iterated Integrals and Neural Networkscited by 10
  11. 2022Applications of Signature Methods to Market Anomaly Detectioncited by 9
  12. 2024Infinite-dimensional next-generation reservoir computingcited by 9
38 more
  1. 2022Reservoir kernels and Volterra seriescited by 8
  2. 2024Recurrent Natural Policy Gradient for POMDPscited by 8
  3. 2023Infinite-dimensional reservoir computingcited by 7
  4. 2024Stability analysis of chaotic systems in latent spacescited by 7
  5. 2022Data-driven prediction and control of extreme events in a chaotic flowcited by 6
  6. 2021Embedding Information onto a Dynamical Systemcited by 5
  7. 2022Universality and approximation bounds for echo state networks with random weightscited by 5
  8. 2023Memory of recurrent networks: Do we compute it right?cited by 5
  9. 2023Learning noise-induced transitions by multi-scaling reservoir computingcited by 5
  10. 2024Positional Encoding Helps Recurrent Neural Networks Handle a Large Vocabularycited by 5
  11. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  12. 2025Feedback-driven recurrent quantum neural network universalitycited by 5
  13. 2022Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state networkcited by 4
  14. 2024Stochastic Reservoir Computerscited by 4
  15. 2024Universal randomised signatures for generative time series modellingcited by 4
  16. 2021Nonlinear Autoregression with Convergent Dynamics on Novel Computational Platformscited by 3
  17. 2022Delay Embedded Echo-State Network: A Predictor for Partially Observed Systemscited by 3
  18. 2024State-space systems as dynamic generative modelscited by 3
  19. 2024Neural networks in non-metric spacescited by 3
  20. 2024Universality of Real Minimal Complexity Reservoircited by 3
  21. 2025Asymptotic evaluation of the information processing capacity in reservoir computingcited by 3
  22. 2025Role of scrambling and noise in temporal information processing with quantum systemscited by 3
  23. 2025Stochastic dynamics learning with state-space systemscited by 3
  24. 2025ResCP: Reservoir Conformal Prediction for Time Series Forecastingcited by 3
  25. 2022Quantum-Classical Hybrid Information Processing via a Single Quantum Systemcited by 2
  26. 2023Improving the Performance of Echo State Networks Through State Feedbackcited by 2
  27. 2024On the choice of the non-trainable internal weights in random feature mapscited by 2
  28. 2024Fading memory and the convolution theoremcited by 2
  29. 2025Quantum Reservoir Computing and Risk Boundscited by 2
  30. 2025Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamicscited by 2
  31. 2025Echoes of the Past: A Unified Perspective on Fading memory and Echo Statescited by 2
  32. 2025Echo State Networks as State-Space Models: A Systems Perspectivecited by 2
  33. 2021Universal set of Observables for Forecasting Physical Systems through Causal Embeddingcited by 1
  34. 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
  35. 2023Ensemble Reservoir Computing for Dynamical Systems: Prediction of Phase-Space Stable Region for Hadron Storage Ringscited by 1
  36. 2023Sequential Learning from Noisy Data: Data-Assimilation Meets Echo-State Networkcited by 1
  37. 2023Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networkscited by 1
  38. 2024Universality of reservoir systems with recurrent neural networkscited by 1

50 most cited of 86 All 86 (JSON)