Noise-Robust conceptors for physical reservoir computing: adaptation to perturbations

Abstract

Conceptors are a powerful extension of reservoir computing (RC) that enable the selective recall and stabilization of internal dynamics. However, their application to physical RC remains challenging because measured reservoir states are inevitably affected by noise and physical perturbations. In this work, we propose a noise-robust cross-trial-correlation-based (CTC) method for computing conceptors in noisy reservoir systems. By exploiting the consistency of the reservoir response across repeated trials, the method suppresses noise contributions that are uncorrelated between measurements. Numerical simulations of leaky echo state networks under additive state noise and parameter drift show that CTC-based conceptors preserve the relevant internal dynamics and extend the operational range of the reservoir compared with standard conceptors and unconstrained reservoirs. In an autonomous-generation task, the CTC-based conceptor maintains predictive capability beyond 50% noise, where the other configurations fail to sustain autonomous generation. Under combined noise and parameter drift, the CTC approach maintains normalized root mean square error values below 0.3, while the alternative approaches considered exceed this error level in the tested conditions. These numerical results establish a concrete step towards adapting conceptor-based control to physical RC platforms.