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==Identification of Causal Emergence==

==Identification of Causal Emergence==

Some works on quantifying emergence through causal measures and other information-theoretic indicators have been introduced previously. However, in practical applications, we can often only collect observational data and cannot obtain the true dynamics of the system. Therefore, identifying whether causal emergence has occurred in a system from observable data is a more important problem. The following introduces two identification methods of causal emergence. The first isg the approximate method based on [[Rosas causal emergence theory]] (the method based on mutual information approximation and the method based on [[machine learning]]). The second is the [[neural information compression]] (NIS, NIS+) method proposed by Chinese scholars.

Some works on quantifying emergence through measures of causal effects and other information-theoretic indicators have been introduced previously. However, in practical applications, we can often only collect observational data and cannot obtain the true dynamics of the system. Therefore, identifying whether causal emergence has occurred in a system from observable data is a more important problem. The following introduces two identification methods of causal emergence. The first isg the approximate method based on [[Rosas causal emergence theory]] (the method based on mutual information approximation and the method based on [[machine learning]]). The second is the [[neural information compression]] (NIS, NIS+) method proposed by Chinese scholars.

These experiments demonstrates that [[NIS+]] identifies causal emergence, discovers macroscopic dynamics, and develops coarse-graining strategies. Additionally, other experiments show that EI maximization enhances the model's e out-of-distribution generalization ability.

These experiments demonstrates that [[NIS+]] identifies causal emergence, discovers macroscopic dynamics, and develops coarse-graining strategies. Additionally, other experiments show that EI maximization enhances the model's e out-of-distribution generalization ability.

==Applications==

==Applications==