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.

翻译：涌现与因果关系是理解复杂系统的两个基本概念，二者相互关联。一方面，涌现指宏观性质不能完全归因于个体性质之因的现象；另一方面，因果关系也可能呈现涌现性，即随着抽象层次的提升，可能产生新的因果规律。因果涌现理论旨在弥合这两个概念，甚至运用因果度量来量化涌现现象。本文系统综述了因果涌现量化理论及应用的最新进展，重点解决两个关键问题：量化涌现现象及其在数据中的识别。后者需借助机器学习技术，从而建立因果涌现与人工智能之间的联系。我们强调，用于识别因果涌现的架构与因果表征学习、因果模型抽象及基于世界模型的强化学习具有共性。因此，任一领域的进展都能促进其他领域的发展。本文最后部分还探讨了潜在应用及未来展望。