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=====NIS=====

=====NIS=====

To identify causal emergence in the system, the author proposes a neural network architecture called [[neural information squeezer]] (NIS) <ref name="NIS" />. The architecture is based on an encoder-dynamics learner-decoder framework, consisting of three components: coarse-graining the raw data into macrostates, fitting the macrodynamics, and performing a reverse coarse-graining operation (decoding the macrostates, combined with random noise, back into microstates). Among them, the authors use [[invertible neural network]] (INN) to construct the encoder and decoder, which approximately correspond to the coarse-graining function ϕ and the inverse coarse-graining function ϕ† respectively. [[Invertible neural networks]] are used because they can be inverted to approximate theinverse coarse-graining function (i.e., [math]\phi^{\dagger}\approx \phi^{-1}[/math]). This model framework can be regarded as a neural information squeezer. The model compresses noisy microscopic state data into a macroscopic state through a narrow information channel,  discarding irrelevant information. This strengthens the causality of macroscopic dynamics and allows the model to get the predictions of the microscopic state via decoding. 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 network architecture called [[neural information squeezer]] (NIS) <ref name="NIS" />. The architecture is based on an encoder-dynamics learner-decoder framework, consisting of three components: coarse-graining the raw data into macrostates, fitting the macrodynamics, and performing a reverse coarse-graining operation (decoding the macrostates, combined with random noise, back into microstates). Among them, the authors use [[invertible neural network]] (INN) to construct the encoder and decoder, which approximately correspond to the coarse-graining function ϕ and the inverse coarse-graining function ϕ† respectively. [[Invertible neural networks]] are used because they can be inverted to approximate the inverse coarse-graining function (i.e., [math]\phi^{\dagger}\approx \phi^{-1}[/math]). This model framework can be regarded as a neural information squeezer. The model compresses noisy microscopic state data into a macroscopic state through a narrow information channel,  discarding irrelevant information. This strengthens the causality of macroscopic dynamics and allows the model to get the predictions of the microscopic state via decoding. The model framework of the NIS method is shown in the following figure:

[[文件:The_framework_diagram_of_the_NIS_model1.png|替代=|无框|600x600像素]]

[[文件:The_framework_diagram_of_the_NIS_model1.png|替代=|无框|600x600像素]]