# Kolmogorov-Arnold Reservoir Computing

arXiv: https://arxiv.org/abs/2606.19984 · HTML: https://mlsanity.com/paper/2606.19984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [Latent Neural Operator for Solving Forward and Inverse PDE Problems](https://mlsanity.com/paper/2406.03923/) (2024)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [MesaNet: Sequence Modeling by Locally Optimal Test-Time Training](https://mlsanity.com/paper/2506.05233/) (2025)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Fading memory echo state networks are universal](https://mlsanity.com/paper/2010.12047/) (2020)
- [Infinite-dimensional next-generation reservoir computing](https://mlsanity.com/paper/2412.09800/) (2024)
- [Reservoir kernels and Volterra series](https://mlsanity.com/paper/2212.14641/) (2022)
- [Adaptive Spectral Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2603.01623/) (2026)
- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [Next-Generation Reservoir Computing for Dynamical Inference](https://mlsanity.com/paper/2509.11338/) (2025)

## 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.