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====Rosas's Causal Emergence Theory====

====Rosas's Causal Emergence Theory====

Rosas et al. <ref name=":5" /> From the perspective of [[information decomposition]] theory, propose a method for defining causal emergence based on [[integrated information decomposition]], and further divide causal emergence into two parts: [[causal decoupling]] (Causal Decoupling) and [[downward causation]] (Downward Causation). Among them, causal decoupling represents the causal effect of the macroscopic state at the current moment on the macroscopic state at the next moment, and downward causation represents the causal effect of the macroscopic state at the previous moment on the microscopic state at the next moment. The schematic diagrams of causal decoupling and downward causation are shown in the following figure. The microscopic state input is <math>X_t\ (X_t^1,X_t^2,…,X_t^n ) </math>, and the macroscopic state is <math>V_t </math>, which is obtained by coarse-graining the microscopic state variable <math>X_t </math>, so it is a supervenient feature of <math>X_t </math>, <math>X_{t + 1} </math> and <math>V_{t + 1} </math> represent the microscopic and macroscopic states at the next moment respectively.

Rosas et al. <ref name=":5" /> From the perspective of [[information decomposition]] theory, propose a method for defining causal emergence based on [[integrated information decomposition]], and further divide causal emergence into two parts: [[causal decoupling]] (Causal Decoupling) and [[downward causation]] (Downward Causation). Among them, causal decoupling represents the causal effect of the macroscopic state at the current moment on the macroscopic state at the next moment, and downward causation represents the causal effect of the macroscopic state at the previous moment on the microscopic state at the next moment. The schematic diagrams of causal decoupling and downward causation are shown in the following figure. The microscopic state input is <math>X_t\ (X_t^1,X_t^2,…,X_t^n ) </math>, and the macroscopic state is <math>V_t </math>, which is obtained by coarse-graining the microscopic state variable <math>X_t </math>, so it is a supervenient feature of <math>X_t </math>, <math>X_{t + 1} </math> and <math>V_{t + 1} </math> represent the microscopic and macroscopic states at the next moment respectively.

 

[[文件:Causal Emergence Relationship Diagram.png|无|缩略图|300x300像素]]

 

[[文件:因果涌现关系图.png|无|缩略图]]

 

 

 

=====Partial Information Decomposition=====

=====Partial Information Decomposition=====

This method is based on the nonnegative decomposition of multivariate information theory proposed by Williams and Beer et al <ref name=":16" />. This paper uses [[partial information decomposition]] (PID) to decompose the [[mutual information]] between microstates and macrostates.

This method is based on the nonnegative decomposition of multivariate information theory proposed by Williams and Beer et al <ref name=":16" />. This paper uses [[partial information decomposition]] (PID) to decompose the [[mutual information]] between microstates and macrostates.

To identify causal emergence in the system, the author proposes a [[neural information squeezer]] (NIS) neural network architecture <ref name="NIS" />. This architecture is based on an encoder-dynamics learner-decoder framework, that is, the model consists of three parts, which are respectively used for coarse-graining the original data to obtain the macroscopic state, fitting the macroscopic dynamics and inverse coarse-graining operation (decoding the macroscopic state combined with random noise into the microscopic state). Among them, the authors use [[invertible neural network]] (INN) to construct the encoder (Encoder) and decoder (Decoder), which approximately correspond to the coarse-graining function [math]\phi[/math] and the inverse coarse-graining function [math]\phi^{\dagger}[/math] respectively. The reason for using [[invertible neural network]] is that we can simply invert this network to obtain the inverse coarse-graining function (i.e., [math]\phi^{\dagger}\approx \phi^{-1}[/math]). This model framework can be regarded as a neural information compressor. It puts the microscopic state data containing noise into a narrow information channel, compresses it into a macroscopic state, discards useless information, so that the causality of macroscopic dynamics is stronger, and then decodes it into a prediction of the microscopic state. The model framework of the NIS method is shown in the following figure:

To identify causal emergence in the system, the author proposes a [[neural information squeezer]] (NIS) neural network architecture <ref name="NIS" />. This architecture is based on an encoder-dynamics learner-decoder framework, that is, the model consists of three parts, which are respectively used for coarse-graining the original data to obtain the macroscopic state, fitting the macroscopic dynamics and inverse coarse-graining operation (decoding the macroscopic state combined with random noise into the microscopic state). Among them, the authors use [[invertible neural network]] (INN) to construct the encoder (Encoder) and decoder (Decoder), which approximately correspond to the coarse-graining function [math]\phi[/math] and the inverse coarse-graining function [math]\phi^{\dagger}[/math] respectively. The reason for using [[invertible neural network]] is that we can simply invert this network to obtain the inverse coarse-graining function (i.e., [math]\phi^{\dagger}\approx \phi^{-1}[/math]). This model framework can be regarded as a neural information compressor. It puts the microscopic state data containing noise into a narrow information channel, compresses it into a macroscopic state, discards useless information, so that the causality of macroscopic dynamics is stronger, and then decodes it into a prediction of the microscopic state. The model framework of the NIS method is shown in the following figure:

[[文件:The framework diagram of the NIS model.png|无|缩略图|替代=|800x800像素]]

[[文件:The framework diagram of the NIS model1.png|无|缩略图|600x600像素]]