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The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces 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, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conways Game of Life, Reynolds flocking model, and neural activity as measured by electrocorticography.
Exploiting recent developments in information theory, we propose, illustrate, and validate a principled information-theoretic algorithm for module discovery and resulting measure of network modularity. This measure is an order parameter (a dimensionl
We show that dynamical gain modulation of neurons stimulus response is described as an information-theoretic cycle that generates entropy associated with the stimulus-related activity from entropy produced by the modulation. To articulate this theory
In the realm of motor control, artificial agents cannot match the performance of their biological counterparts. We thus explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. The architect
The information content of symbolic sequences (such as nucleic- or amino acid sequences, but also neuronal firings or strings of letters) can be calculated from an ensemble of such sequences, but because information cannot be assigned to single seque
Safely deploying machine learning models to the real world is often a challenging process. Models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a simulation ca