Numerical Evaluation of a Weakly Supervised Filtering Method Based on Echo State Networks

Noise filtering, the task of recovering clean signals from noisy data, is central to many fields but becomes challenging when the generative model is unknown and clean reference signals are unavailable. We propose a weakly supervised method based on Echo State Networks that filters noise using only relative information about noise levels, without requiring ground-truth signals. This study analyzes the properties of the proposed method and evaluates how its performance depends on a key Echo State Network’s hyperparameter: the spectral radius of the recurrent weight matrix. We also investigate the effectiveness of ensemble averaging in reducing performance variability and identify the network components that contribute most to this effect.