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：涌现与因果是理解复杂系统的两个基本概念，且二者相互关联。一方面，涌现是指宏观属性不能完全归因于微观属性之因果的现象；另一方面，因果性本身也可能涌现，即随着抽象层次的提升，新的因果律可能产生。因果涌现理论旨在衔接这两个概念，甚至利用因果度量来量化涌现。本文全面梳理了因果涌现定量理论及应用的最新进展，重点解决两个关键问题：量化涌现现象以及从数据中识别涌现。解决后一问题需要借助机器学习技术，从而建立了因果涌现与人工智能之间的联系。我们强调，用于识别涌现的架构与因果表征学习、因果模型抽象以及基于世界模型的强化学习所采用的框架具有共通性。因此，上述任一领域的进展均可促进其他领域的发展。本综述的最后一节还探讨了潜在应用与未来展望。