Statistical temporal pattern extraction by neuronal architecture

Neuronal systems need to process temporal signals. Here, we show how higher-order temporal (co)fluctuations can be employed to represent and process information. Concretely, we demonstrate that a simple biologically inspired feedforward neuronal model can extract information from up to the third-order cumulant to perform time series classification. This model relies on a weighted linear summation of synaptic inputs followed by a nonlinear gain function. Training both the synaptic weights and the nonlinear gain function exposes how the nonlinearity allows for the transfer of higher-order correlations to the mean, which in turn enables the synergistic use of information encoded in multiple cumulants to maximize the classification accuracy. The approach is demonstrated both on synthetic and real-world datasets of multivariate time series. Moreover, we show that the biologically inspired architecture makes better use of the number of trainable parameters than a classical machine-learning scheme. Our findings emphasize the benefit of biological neuronal architectures, paired with dedicated learning algorithms, for the processing of information embedded in higher-order statistical cumulants of temporal (co)fluctuations.