Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data

Abstract

The broad concept of emergence is instrumental in various key open scientific questions – yet, few quantitative theories of what constitutes emergent phenomena have been proposed. We introduce a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour, which we refer to as causal decoupling. Moreover, we provide criteria that can be efficiently calculated in large systems, making the theory applicable in a range of practical scenarios. We illustrate our framework in a number of case studies, including Conway’s Game of Life and ECoG data from macaques during a reaching task, which suggest that the neural representation of motor behaviour may be causally decoupled from cortical activity.