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Kolmogorov-Arnold Reservoir Computing

arXiv 2606.19984 ↗First posted 18 Jun 2026cs.LGcited by 0

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Abstract (arXiv)

Reservoir computing offers a lightweight framework for forecasting dynamical systems but may struggle to capture long-range dependencies due to limited representational capacity. Conventional reservoir computing recurrently uses fixed reservoirs with hyperparameter sensitivity, while the next generation reservoir computing removes recurrence at the cost of rapidly growing feature dimensions. Here, we develop Kolmogorov-Arnold Reservoir Computing (KARC), which replaces reservoirs with explicit basis-function expansions inspired by the Kolmogorov-Arnold representation theorem. We rigorously show that KARC is a lightweight design of Kolmogorov-Arnold networks (KANs), preserving the potential expressive capacity of KANs while admitting efficient closed-form training of reservoir computing. At comparable cost, KARC outperforms existing reservoir computing methods on challenging benchmarks including partial differential equations. It can also be integrated with generative diffusion models for facilitating text-to-image generation. This work thus establishes a principled bridge between reservoir computing and KANs, yielding a unified framework for efficient dynamical forecasting and generative modeling.

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References · 23

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
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  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  5. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  7. 2020Time Series Forecasting With Deep Learning: A Surveycited by 457
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  11. 2022Physics-Informed Deep Neural Operator Networkscited by 110
  12. 2018Echo state networks are universalcited by 86
11 more
  1. 2024Operator Learning: Algorithms and Analysiscited by 84
  2. 2024Latent Neural Operator for Solving Forward and Inverse PDE Problemscited by 76
  3. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
  4. 2017Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systemscited by 39
  5. 2025MesaNet: Sequence Modeling by Locally Optimal Test-Time Trainingcited by 37
  6. 2020Fading memory echo state networks are universalcited by 31
  7. 2024Infinite-dimensional next-generation reservoir computingcited by 9
  8. 2022Reservoir kernels and Volterra seriescited by 8
  9. 2023Learning noise-induced transitions by multi-scaling reservoir computingcited by 5
  10. 2026Adaptive Spectral Feature Forecasting for Diffusion Sampling Accelerationcited by 5
  11. 2025Next-Generation Reservoir Computing for Dynamical Inferencecited by 1

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