mlsanityData to 7 Oct 2026

Reservoir Computing Universality With Stochastic Inputs

arXiv 1807.02621 ↗First posted 7 Jul 2018cs.ET cs.NE math.DScited by 48

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Abstract (arXiv)

The universal approximation properties with respect to L p -type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown. First, it is proved that linear reservoir systems with either polynomial or neural network readout maps are universal. More importantly, it is proved that the same property holds for two families with linear readouts, namely, trigonometric state-affine systems and echo state networks, which are the most widely used reservoir systems in applications. The linearity in the readouts is a key feature in supervised machine learning applications. It guarantees that these systems can be used in high-dimensional situations and in the presence of large datasets. The L p criteria used in this paper allow the formulation of universality results that do not necessarily impose almost sure uniform boundedness in the inputs or the fading memory property in the filter that needs to be approximated.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jul 2018.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 10; 2024: 12; 2025: 7; 2026: 6.

48 papers.

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  1. 2021Next Generation Reservoir Computingcited by 160
  2. 2021Optimal Stopping via Randomized Neural Networkscited by 26
  3. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  4. 2022Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysiscited by 22
  5. 2023A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learningcited by 22
  6. 2021Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computingcited by 21
  7. 2021Learning strange attractors with reservoir systemscited by 16
  8. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  9. 2023Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirscited by 15
  10. 2022Learning unseen coexisting attractorscited by 12
  11. 2022Catch-22s of reservoir computingcited by 11
  12. 2024Controlling Chaos Using Edge Computing Hardwarecited by 11
36 more
  1. 2023Inverse Approximation Theory for Nonlinear Recurrent Neural Networkscited by 10
  2. 2024Infinite-dimensional next-generation reservoir computingcited by 9
  3. 2022Reservoir kernels and Volterra seriescited by 8
  4. 2023Infinite-dimensional reservoir computingcited by 7
  5. 2022Universality and approximation bounds for echo state networks with random weightscited by 5
  6. 2023Memory of recurrent networks: Do we compute it right?cited by 5
  7. 2024Positional Encoding Helps Recurrent Neural Networks Handle a Large Vocabularycited by 5
  8. 2025Feedback-driven recurrent quantum neural network universalitycited by 5
  9. 2024Stochastic Reservoir Computerscited by 4
  10. 2024Universal randomised signatures for generative time series modellingcited by 4
  11. 2021Nonlinear Autoregression with Convergent Dynamics on Novel Computational Platformscited by 3
  12. 2021Master memory function for delay-based reservoir computers with single-variable dynamicscited by 3
  13. 2024State-space systems as dynamic generative modelscited by 3
  14. 2024Universality of Real Minimal Complexity Reservoircited by 3
  15. 2024RandNet-Parareal: a time-parallel PDE solver using Random Neural Networkscited by 3
  16. 2025Asymptotic evaluation of the information processing capacity in reservoir computingcited by 3
  17. 2023Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computingcited by 2
  18. 2023Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemscited by 2
  19. 2023Improving the Performance of Echo State Networks Through State Feedbackcited by 2
  20. 2025Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Seriescited by 2
  21. 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
  22. 2023Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networkscited by 1
  23. 2024Universality of reservoir systems with recurrent neural networkscited by 1
  24. 2024Separation capacity of linear reservoirs with random connectivity matrixcited by 1
  25. 2025Frozen in Time: Parameter-Efficient Time Series Transformers via Reservoir-Induced Feature Expansion and Fixed Random Dynamicscited by 1
  26. 2024Estimation of AMOC transition probabilities using a machine learning based rare-event algorithmcited by 0
  27. 2024Unsupervised Reservoir Computing for Multivariate Denoising of Severely Contaminated Signalscited by 0
  28. 2025A tensor network approach for chaotic time series predictioncited by 0
  29. 2025A Solvable Molecular Switch Model for Stable Temporal Information Processingcited by 0
  30. 2025Symplectic Representation of Legendre Dynamicscited by 0
  31. 2026ParalESN: Enabling parallel information processing in Reservoir Computingcited by 0
  32. 2026Recurrent Quantum Feature Maps for Reservoir Computingcited by 0
  33. 2026Data-Specific Hyper-Parameter Design: A Paradigm Shift in Reservoir Computingcited by 0
  34. 2026Kolmogorov-Arnold Reservoir Computingcited by 0
  35. 2026NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processescited by 0
  36. 2026Free-Probability Kernels for Zero-Rollout Hyperparameter Selection in Reservoir Computingcited by 0