Shared hidden state and network representations of interconnected dynamical systems

This paper demonstrates that the signal structure of an interconnected dynamical system, such as that represented by various dynamical graphical models, can be very different from the interconnection structure of its subsystems. These differences are revealed by considering the network semantics of each representation, characterized by the set of realizations consistent with each network structure. The reason these system networks can be so different is that subsystems never share hidden state, and thus subsystem structures partition the entire system state, while signal structures remain agnostic towards the presence of shared hidden state. Remaining agnostic towards the presence of shared hidden state make signal structures a weaker description of the underlying system structure, but it also gives signal structures a lower information cost for identification. Identifying a system´s subsystem structure demands the identification of the correct partition of system states, which can be very expensive.