A K–R Parameter Framework for Explicit Control of Nonlinear Excitation and Regularization in Reservoir Computing

Reservoir computing provides an efficient paradigm for nonlinear temporal processing; however, its practical performance and stability are often governed by implicitly coupled hyperparameters that simultaneously influence nonlinear excitation and readout regularization. This coupling obscures the interpretation of reservoir dynamics and leads to high sensitivity with respect to parameter variations, particularly in chaotic and memory-dominated systems. To address this limitation, this work introduces a unified K–R parameter framework that explicitly decouples nonlinear excitation and readout stabilization, enabling principled and interpretable control of reservoir behavior. The proposed framework incorporates a nonlinear excitation parameter directly into the reservoir state update equation and a regularization parameter into the readout learning process, without altering reservoir topology or increasing model complexity. Extensive experiments are conducted on the canonical Mackey–Glass chaotic time-series prediction benchmark using identical data splits, prediction horizons, and evaluation protocols. A baseline echo state network achieves an NRMSE of 0.00331, confirming that the benchmark operates in a near-saturated accuracy regime. Within this context, the K–R framework attains stable performance with a best NRMSE of 0.00583 at and , while exhibiting markedly improved robustness across a broad range of parameter settings. Comprehensive K–R parameter sweeps, supplementary NORMA evaluations, and sensitivity analyses demonstrate that the proposed framework enlarges the region of stable operating configurations and reduces sensitivity to random reservoir initialization and regularization choices. Rather than pursuing marginal accuracy gains on saturated benchmarks, the K–R framework provides structural insight into stability–accuracy trade-offs and enables reproducible control of reservoir dynamics. These properties make the framework particularly relevant for physical, delay-based, and real-world reservoir computing systems, where robustness, interpretability, and reliable operation are essential.