mlsanityData to 14 Oct 2026

Fading memory echo state networks are universal

arXiv 2010.12047 ↗First posted 22 Oct 2020cs.NEcited by 32

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Abstract (arXiv)

Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various L p-type criteria. When 1≤ p< ∞, only p-integrability hypotheses need to be imposed, while in the case p=∞ a uniform boundedness hypotheses on the inputs is required. This note shows that, in the last case, a universal family of ESNs can be constructed that contains exclusively elements that have the echo state and the fading memory properties. This conclusion could not be drawn with the results and methods available so far in the literature.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Oct 2020.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 8; 2024: 6; 2025: 6; 2026: 5.

32 papers.

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  1. 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
  2. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  3. 2022Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysiscited by 22
  4. 2021Learning strange attractors with reservoir systemscited by 17
  5. 2023Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirscited by 16
  6. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  7. 2023Inverse Approximation Theory for Nonlinear Recurrent Neural Networkscited by 11
  8. 2024Infinite-dimensional next-generation reservoir computingcited by 9
  9. 2022Reservoir kernels and Volterra seriescited by 8
  10. 2023Infinite-dimensional reservoir computingcited by 7
  11. 2023Memory of recurrent networks: Do we compute it right?cited by 6
  12. 2022Universality and approximation bounds for echo state networks with random weightscited by 5
20 more
  1. 2025Feedback-driven recurrent quantum neural network universalitycited by 5
  2. 2024State-space systems as dynamic generative modelscited by 3
  3. 2025Role of scrambling and noise in temporal information processing with quantum systemscited by 3
  4. 2025Stochastic dynamics learning with state-space systemscited by 3
  5. 2023Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemscited by 2
  6. 2024Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Expertscited by 2
  7. 2024On the choice of the non-trainable internal weights in random feature mapscited by 2
  8. 2024Fading memory and the convolution theoremcited by 2
  9. 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
  10. 2023Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networkscited by 1
  11. 2024Universality of reservoir systems with recurrent neural networkscited by 1
  12. 2026On Dominant Manifolds in Reservoir Computing Networkscited by 1
  13. 2023Change Point Detection with Conceptorscited by 0
  14. 2025On the dimension of pullback attractors in recurrent neural networkscited by 0
  15. 2025A tensor network approach for chaotic time series predictioncited by 0
  16. 2025Fractal and Chaotic Activation Functions in Echo State Networks: Preprocessing Topology Governs the Echo State Propertycited by 0
  17. 2026Data-Specific Hyper-Parameter Design: A Paradigm Shift in Reservoir Computingcited by 0
  18. 2026Kolmogorov-Arnold Reservoir Computingcited by 0
  19. 2026NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processescited by 0
  20. 2026A KKL Observer Perspective on Reservoir Computingcited by 0