更改

The results show that in the simple example shown in Figure (b), by maximizing <math>\mathrm{\Psi}</math> through the model constructed in Figure a, the experiment finds that the learned <math>\mathrm{\Psi}</math> is approximately equal to the true groundtruth <math>\mathrm{\Psi}</math>. This outcome verifies the effectiveness of model learning. This system is effective in identifying the occurrence of causal emergence. However, this method also has the problem of being difficult to deal with complex multivariate situations. This is because the number of neural networks on the right side of the figure is proportional to the number of macroscopic and microscopic variable pairs. Therefore, the more the number of microscopic variables (dimensions), the more the number of neural networks will increase proportionally, which will lead to an increase in computational complexity. In addition, this method is only tested on very few cases, so it cannot be scaled up yet. Moreover, since the network calculates an approximate index of causal emergence, it inherits the limitations of the earlier approximate algorithms.

The results show that in the simple example shown in Figure (b), by maximizing <math>\mathrm{\Psi}</math> through the model constructed in Figure a, the experiment finds that the learned <math>\mathrm{\Psi}</math> is approximately equal to the true groundtruth <math>\mathrm{\Psi}</math>. This outcome verifies the effectiveness of model learning. This system is effective in identifying the occurrence of causal emergence. However, this method also has the problem of being difficult to deal with complex multivariate situations. This is because the number of neural networks on the right side of the figure is proportional to the number of macroscopic and microscopic variable pairs. Therefore, the more the number of microscopic variables (dimensions), the more the number of neural networks will increase proportionally, which will lead to an increase in computational complexity. In addition, this method is only tested on very few cases, so it cannot be scaled up yet. Moreover, since the network calculates an approximate index of causal emergence, it inherits the limitations of the earlier approximate algorithms.

====Neural Information Compression Method====

====Neural Information Squeezer====

In recent years, emerging [[artificial intelligence]] technologies have overcome a series of major problems. Machine learning methods incorporate carefully designed [[neural network]] structures and [[automatic differentiation]] technologies. These technologies enable theapproximation of any function in a vast function space. Therefore, [[Zhang Jiang]] et al. proposed a data-driven method using neural networks to identify causal emergence from time series data <ref name="NIS">Zhang J, Liu K. Neural information squeezer for causal emergence[J]. Entropy, 2022, 25(1): 26.</ref><ref name=":6" />. This method can automatically extract effective coarse-graining strategies and macroscopic dynamics, overcoming various deficiencies of the Rosas method <ref name=":5" />.

In recent years, emerging [[artificial intelligence]] technologies have overcome a series of major problems. Machine learning methods incorporate carefully designed [[neural network]] structures and [[automatic differentiation]] technologies. These technologies enable theapproximation of any function in a vast function space. Therefore, [[Zhang Jiang]] et al. proposed a data-driven method using neural networks to identify causal emergence from time series data <ref name="NIS">Zhang J, Liu K. Neural information squeezer for causal emergence[J]. Entropy, 2022, 25(1): 26.</ref><ref name=":6" />. This method can automatically extract effective coarse-graining strategies and macroscopic dynamics, overcoming various deficiencies of the Rosas method <ref name=":5" />.

=====NIS=====

=====NIS=====

To identify causal emergence in the system, the author proposes a [[neural information squeezer]] (NIS) neural network architecture <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 network]] 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 compressor. 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 information squeezer]] (NIS) neural network architecture <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 network]] 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: