mlsanityData to 14 Oct 2026

Universality of reservoir systems with recurrent neural networks

arXiv 2403.01900 ↗First posted 4 Mar 2024cs.NE cs.LGcited by 1

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Abstract (arXiv)

Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means that, given an approximation error to be achieved, one can construct an RNN reservoir system that approximates each target dynamical system in the class just via adjusting its linear readout. To show the universality, we construct an RNN reservoir system via parallel concatenation that has an upper bound of approximation error independent of each target in the class.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 32 references that are in the map. First posted on arXiv 4 Mar 2024.

Builds on

15 of 32 references.

References · 15

  1. 2018Echo state networks are universalcited by 87
  2. 2016Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with ℓ1 and ℓ0 Controlscited by 84
  3. 2020Approximation Bounds for Random Neural Networks and Reservoir Systemscited by 52
  4. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
  5. 2019On Generalization Bounds of a Family of Recurrent Neural Networkscited by 42
  6. 2017Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systemscited by 39
  7. 2020Fading memory echo state networks are universalcited by 32
  8. 2022Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activationscited by 29
  9. 2020Neural network approximation and estimation of classifiers with classification boundary in a Barron classcited by 28
  10. 2021Neural Estimation of Statistical Divergencescited by 25
  11. 2020Discrete-time signatures and randomness in reservoir computingcited by 23
  12. 2021Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergencescited by 15
3 more
  1. 2023Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networkscited by 11
  2. 2023Infinite-dimensional reservoir computingcited by 7
  3. 2022Universality and approximation bounds for echo state networks with random weightscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Upper Generalization Bounds for Neural Oscillatorscited by 0