mlsanityData to 7 Oct 2026

Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

arXiv 1712.00754 ↗First posted 3 Dec 2017cs.NEcited by 39

Not on the map. Why?

Abstract (arXiv)

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Dec 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 5; 2024: 12; 2025: 10; 2026: 4.

39 papers.

Sort:

By area:

  1. 2021Universal Approximation Under Constraints is Possible with Transformerscited by 32
  2. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  3. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  4. 2023Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirscited by 15
  5. 2024Infinite-dimensional next-generation reservoir computingcited by 9
  6. 2022Reservoir kernels and Volterra seriescited by 8
  7. 2023Infinite-dimensional reservoir computingcited by 7
  8. 2023Gated recurrent neural networks discover attentioncited by 7
  9. 2021Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Ito Diffusionscited by 5
  10. 2022Universality and approximation bounds for echo state networks with random weightscited by 5
  11. 2025Feedback-driven recurrent quantum neural network universalitycited by 5
  12. 2024Stochastic Reservoir Computerscited by 4
27 more
  1. 2024Universal randomised signatures for generative time series modellingcited by 4
  2. 2025Random Feature Representation Boostingcited by 4
  3. 2024State-space systems as dynamic generative modelscited by 3
  4. 2024Low-dimensional approximations of the conditional law of Volterra processes: a non-positive curvature approachcited by 3
  5. 2024Universality of Real Minimal Complexity Reservoircited by 3
  6. 2024RandNet-Parareal: a time-parallel PDE solver using Random Neural Networkscited by 3
  7. 2025Stochastic dynamics learning with state-space systemscited by 3
  8. 2025ResCP: Reservoir Conformal Prediction for Time Series Forecastingcited by 3
  9. 2024Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Expertscited by 2
  10. 2024Fading memory and the convolution theoremcited by 2
  11. 2025Quantum Reservoir Computing and Risk Boundscited by 2
  12. 2021Interpretable Design of Reservoir Computing Networks using Realization Theorycited by 1
  13. 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
  14. 2023Refined Kolmogorov Complexity of Analog, Evolving and Stochastic Recurrent Neural Networkscited by 1
  15. 2024Universality of reservoir systems with recurrent neural networkscited by 1
  16. 2024Separation capacity of linear reservoirs with random connectivity matrixcited by 1
  17. 2025Upper Approximation Bounds for Neural Oscillatorscited by 1
  18. 2021Reservoir Computers Modal Decomposition and Optimizationcited by 0
  19. 2024A finite-sample generalization bound for stable LPV systemscited by 0
  20. 2025A tensor network approach for chaotic time series predictioncited by 0
  21. 2025A Solvable Molecular Switch Model for Stable Temporal Information Processingcited by 0
  22. 2025A Unified Representation of Neural Networks Architecturescited by 0
  23. 2025Symplectic Representation of Legendre Dynamicscited by 0
  24. 2026ParalESN: Enabling parallel information processing in Reservoir Computingcited by 0
  25. 2026Upper Generalization Bounds for Neural Oscillatorscited by 0
  26. 2026Kolmogorov-Arnold Reservoir Computingcited by 0
  27. 2026LoRA-RC: Reservoir Computing with Low-Rank Adaptationcited by 0