Learning diverse causally emergent representations from time series data

Cognitive processes usually take place at a macroscopic scale in systems characterised by emergent properties that make the whole ‘more than the sum of its parts.’ While recent proposals have provided quantitative, information-theoretic metrics to detect emergence in time series data, it is often highly non-trivial to identify the relevant macroscopic variables a priori. In this paper we leverage recent advances in representation learning and differentiable information estimators to put forward a data-driven method to find variables with emergent properties. The proposed method successfully detects variables that exhibit emergent behaviour and recovers the ground-truth emergence values in a synthetic dataset. Furthermore, we show the method can be extended to learn multiple independent features, extracting a diverse set of emergent quantities. We finally show that a modified method scales to real experimental data from several brain activity datasets, paving the ground for future analyses uncovering the emergent structure of cognitive representations in biological and artificial intelligence systems.