Kolmogorov-Arnold Reservoir Computing
This work provides a principled bridge between reservoir computing and Kolmogorov-Arnold networks, enabling efficient and high-fidelity dynamical system forecasting for researchers in time-series prediction and dynamical systems.
KARC replaces traditional reservoirs with explicit basis-function expansions, achieving superior performance on challenging benchmarks including partial differential equations while maintaining efficient closed-form training. It also integrates with generative diffusion models for text-to-image generation.
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 trainable 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 text-to-image generation. This work thus establishes a principled bridge between reservoir computing and KANs, enabling efficient and high-fidelity dynamical system forecasting.