mlsanityData to 7 Oct 2026

Infinite-dimensional reservoir computing

arXiv 2304.00490 ↗First posted 2 Apr 2023cs.LG math.PR stat.MLcited by 7

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Abstract (arXiv)

Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the readouts with a certain integral representation built on infinite-dimensional state-space systems. It is shown that this class is very rich and possesses useful features and universal approximation properties. The reservoir architectures used for the approximation and estimation of elements in the new class are randomly generated echo state networks with either linear or ReLU activation functions. Their readouts are built using randomly generated neural networks in which only the output layer is trained (extreme learning machines or random feature neural networks). The results in the paper yield a fully implementable recurrent neural network-based learning algorithm with provable convergence guarantees that do not suffer from the curse of dimensionality.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 34 of its 73 references that are in the map. First posted on arXiv 2 Apr 2023.

Builds on

34 of 73 references.

References · 34

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  3. 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 94
  4. 2018Echo state networks are universalcited by 86
  5. 2016Kernels for sequentially ordered datacited by 83
  6. 2018A Priori Estimates of the Population Risk for Two-layer Neural Networkscited by 76
  7. 2020Representation formulas and pointwise properties for Barron functionscited by 62
  8. 2020Approximation Bounds for Random Neural Networks and Reservoir Systemscited by 52
  9. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
  10. 2021Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamicscited by 46
  11. 2017Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systemscited by 39
  12. 2020On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamicscited by 39
22 more
  1. 2021Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionalitycited by 34
  2. 2020Fading memory echo state networks are universalcited by 31
  3. 2020Non-Euclidean Universal Approximationcited by 29
  4. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  5. 2020Temporal Information Processing on Noisy Quantum Computerscited by 23
  6. 2020Discrete-time signatures and randomness in reservoir computingcited by 23
  7. 2019Risk bounds for reservoir computingcited by 22
  8. 2022Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysiscited by 22
  9. 2019Differentiable reservoir computingcited by 20
  10. 2021Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Componentscited by 18
  11. 2021Learning strange attractors with reservoir systemscited by 16
  12. 2019Learning Nonlinear Input-Output Maps with Dissipative Quantum Systemscited by 13
  13. 2019Dynamical Systems as Temporal Feature Spacescited by 12
  14. 2020Memory and forecasting capacities of nonlinear recurrent networkscited by 11
  15. 2020Dimension reduction in recurrent networks by canonicalizationcited by 11
  16. 2022Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEscited by 11
  17. 2020Higher-Order Quantum Reservoir Computingcited by 10
  18. 2022Chaotic Hedging with Iterated Integrals and Neural Networkscited by 10
  19. 2021Learning Temporal Quantum Tomographycited by 9
  20. 2016The Asymptotic Performance of Linear Echo State Neural Networkscited by 6
  21. 2021Embedding Information onto a Dynamical Systemcited by 5
  22. 2022Transport in reservoir computingcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 1; 2026: 1.

7 papers.

  1. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  2. 2023A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regressioncited by 8
  3. 2025Random Feature Representation Boostingcited by 4
  4. 2024RandNet-Parareal: a time-parallel PDE solver using Random Neural Networkscited by 3
  5. 2024Fading memory and the convolution theoremcited by 2
  6. 2024Universality of reservoir systems with recurrent neural networkscited by 1
  7. 2026Vestibular reservoir computingcited by 0