Kolmogorov-Arnold Reservoir Computing

We present an adaptive reservoir computing framework for the CTF-4-Science Lorenz benchmark, which evaluates machine learning models across twelve distinct tasks spanning five qualitatively different scenarios: baseline forecasting, noisy signal reconstruction, forecasting under noise, few-shot learning, and parametric generalization. Rather than applying a uniform inference strategy, we tailor the training and prediction procedure of Echo State Networks (ESNs) to the specific demands of each evaluation scenario. Our key contributions are fourfold: (1) exact reservoir state synchronization that eliminates warmup approximation error in short-time prediction; (2) histogram-guided candidate selection that directly optimizes the long-time ergodic evaluation metric; (3) multi-seed reservoir search for few-shot regimes with severely limited training data; and (4) sequential multi-sequence training that resolves state-distribution mismatch in parametric generalization tasks. The proposed framework achieves a score of 74.91 on the public benchmark leaderboard, demonstrating that carefully adapted reservoir computing constitutes a competitive and computationally efficient approach for diverse chaotic system modeling challenges.

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a general linear continuous-time reservoir in the infinite-data limit, we show that the training data generate an invariant subspace of the trained reservoir, whose dimension equals the number of dominant modes. We then specialize to a simplified diagonal linear reservoir, where we link the dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, which yields a finite-dimensional approximation of the backward-time Koopman operator of the system generating the training data. We illustrate the emergence of these dominant modes during training in simulation, and discuss how the analysis may be extended to nonlinear RC via tangent dynamics and differential p-dominance.

Quantum reservoir computing uses a fixed quantum circuit as a feature generator and trains only a simple linear readout on top of it. This makes it cheap to train and free of the optimisation problems that affect many quantum machine-learning models. A natural worry is that the very large feature space the circuit produces might inflate apparent performance without adding anything real. This paper provides two things. First, it gives a complete, reproducible recipe for one such reservoir applied to forecasting chaotic systems, including how data is fed in, how the circuit is built, and how the readout is trained. Second, it gives a way to tell whether the reservoir's high dimension is actually doing useful work. We grow the size of the prediction problem and the size of the quantum reservoir together, so that extra capacity cannot be the explanation for any improvement, and we track a single stability number that measures how well behaved the readout fit is. On two chaotic test systems, a spatiotemporal chain and a shallow-water fluid model, the quantum reservoir keeps a flat, stable error as both sizes grow, while a matched classical reservoir does not. We report where the classical baseline is in fact stronger, so the comparison is honest. The result is a clean specification plus a diagnostic that other groups can apply to any reservoir whose features have a known scale.