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Emergence and causality are two fundamental concepts for understandingcomplex systems. They are interconnected. On one hand, emergence refers to thephenomenon where macroscopic properties cannot be solely attributed to thecause of individual properties. On the other hand, causality can exhibitemergence, meaning that new causal laws may arise as we increase the level ofabstraction. Causal emergence theory aims to bridge these two concepts and evenemploys measures of causality to quantify emergence. This paper provides acomprehensive review of recent advancements in quantitative theories andapplications of causal emergence. Two key problems are addressed: quantifyingcausal emergence and identifying it in data. Addressing the latter requires theuse of machine learning techniques, thus establishing a connection betweencausal emergence and artificial intelligence. We highlighted that thearchitectures used for identifying causal emergence are shared by causalrepresentation learning, causal model abstraction, and world model-basedreinforcement learning. Consequently, progress in any of these areas canbenefit the others. Potential applications and future perspectives are alsodiscussed in the final section of the review.

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