Covariance-based information processing in reservoir computing systems

Abstract

In biological neuronal networks, information representation and processing are achieved through plasticity learning rules that have been empirically characterized as sensitive to second and higher-order statistics in spike trains. However, most models in both computational neuroscience and machine learning aim to convert diverse statistical properties in inputs into first-order statistics in outputs, like in modern deep learning networks. In the context of classification, such schemes have merit for inputs like static images, but they are not well suited to capture the temporal structure in time series. In contrast, the recently developed covariance perceptron uses second-order statistics by mapping input covariances to output covariances in a consistent fashion. Here, we explore the applicability of covariance-based perceptron readouts in reservoir computing networks to classify synthetic multivariate time series structured at different statistical orders (first and second). We show that the second-order framework outperforms or matches the classical mean paradigm in terms of accuracy. Our results highlight a nontrivial relationship between input and reservoir properties in generating the output reservoir activity, which suggests an important role for recurrent connectivity in transforming information representations in biologically inspired architectures. Finally, we solve a speech recognition task for the classification of spoken digits to further demonstrate the potential of covariance-based decoding for real data.