Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of individual properties. On the other hand, causality can exhibit emergence, meaning that new causal laws may arise as we increase the level of abstraction. Causal emergence theory aims to bridge these two concepts and even employs measures of causality to quantify emergence. This paper provides a comprehensive review of recent advancements in quantitative theories and applications of causal emergence. Two key problems are addressed: quantifying causal emergence and identifying it in data. Addressing the latter requires the use of machine learning techniques, thus establishing a connection between causal emergence and artificial intelligence. We highlighted that the architectures used for identifying causal emergence are shared by causal representation learning, causal model abstraction, and world model-based reinforcement learning. Consequently, progress in any of these areas can benefit the others. Potential applications and future perspectives are also discussed in the final section of the review.

Finding emergence in data: causal emergence inspired dynamics learning

Modelling complex dynamical systems in a data-driven manner is challenging due to the presence of emergent behaviors and properties that cannot be directly captured by micro-level observational data. Therefore, it is crucial to develop a model that can effectively capture emergent dynamics at the macro-level and quantify emergence based on the available data. Drawing inspiration from the theory of causal emergence, this paper introduces a machine learning framework aimed at learning macro-dynamics within an emergent latent space. The framework achieves this by maximizing the effective information (EI) to obtain a macro-dynamics model with stronger causal effects. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed framework. Not only does it successfully capture emergent patterns, but it also learns the coarse-graining strategy and quantifies the degree of causal emergence in the data. Furthermore, experiments conducted on environments different from the training dataset highlight the superior generalization ability of our model.