Intrinsic units: identifying a system's causal grain

Integrated information theory (IIT) aims to account for the quality and quantity of consciousness in physical terms. According to IIT, a substrate of consciousness must be a system of units (e.g. synapses, neurons, minicolumns, etc.) that is a maximum of intrinsic, specific, unitary cause-effect power, quantified by integrated information ([Formula: see text]). The grain of each unit must be the one-from micro (finer) to macro (coarser)-that maximizes the system's integrated information. Here we provide a framework for computing the integrated information of systems whose constituents include macro units, and in doing so provide the means to identify a system's intrinsic units-those that constitute the system from its intrinsic perspective, and directly account for its experience. First, we formalize what it means for these units, as part of a substrate of consciousness, to satisfy IIT's postulates of physical existence. Next, we extend the mathematical framework of IIT 4.0 to assess cause-effect power across grains. Then, using simple, simulated systems, we show that the integrated information of systems containing macro units can be higher than that of corresponding systems of micro units. Three examples highlight specific kinds of macro units, and how each kind can increase cause-effect power. The implications of the framework are discussed in the broader context of IIT, including how it provides a foundation for tests and inferences about consciousness.