Response of the parameters of a neural network to pseudoperiodic time series

We propose a representation plane constructed from parameters of a multilayer neural network, with the aim of characterizing the dynamical character of a learned time series. We find that fluctuation of this plane reveals distinct features of the time series. Specifically, a periodic representation plane corresponds to a periodic time series, even when contaminated with strong observational noise or dynamical noise. We present a theoretical explanation for how the neural network training algorithm adjusts parameters of this representation plane and thereby encodes the specific characteristics of the underlying system. This ability, which is intrinsic to the architecture of the neural network, can be employed to distinguish the chaotic time series from periodic counterparts. It provides a new path toward identifying the dynamics of pseudoperiodic time series. Furthermore, we extract statistics from the representation plane to quantify its character. We then validate this idea with various numerical data generated by the known periodic and chaotic dynamics and experimentally recorded human electrocardiogram data.