更改

=====Machine learning-based method=====

=====Machine learning-based method=====

Kaplanis et al. <ref name=":2" /> use a [[representation learning]] to learn the macroscopic state variable <math>V</math> by maximizing <math>\mathrm{\Psi}</math> (i.e., Equation {{EquationNote|1}}). Specifically, the authors use a neural network <math>f_{\theta}</math> to learn the representation function that coarsens the microscopic input <math>X_t</math> into the macroscopic output <math>V_t</math>. At the same time, they use neural networks <math>g_{\phi}</math> and <math>h_{\xi}</math> to learn the calculation of mutual information, such as <math>I(V_t;V_{t + 1})</math> and <math>\sum_i(I(V_{t + 1};X_{t}^i))</math>, respectively. Finally, this method optimizes the neural network by maximizing the difference between the two (i.e., <math>\mathrm{\Psi}</math>). The architecture diagram of this neural network system is shown in Figure a below.

Kaplanis et al. <ref name=":2" /> use a [[representation learning]] method to learn the macroscopic state variable <math>V</math> by maximizing <math>\mathrm{\Psi}</math> (i.e., Equation {{EquationNote|1}}). Specifically, the authors use a neural network <math>f_{\theta}</math> to learn the representation function that coarsens the microscopic input <math>X_t</math> into the macroscopic output <math>V_t</math>. At the same time, they use neural networks <math>g_{\phi}</math> and <math>h_{\xi}</math> to learn the calculation of mutual information, such as <math>I(V_t;V_{t + 1})</math> and <math>\sum_i(I(V_{t + 1};X_{t}^i))</math>, respectively. Finally, this method optimizes the neural network by maximizing the difference between the two terms (i.e., <math>\mathrm{\Psi}</math>). The architecture diagram of this neural network system is shown in Figure a below.

[[文件:Architectures for learning causal emergent representations1.png|居左|替代=|700x600像素]]

[[文件:Architectures for learning causal emergent representations1.png|居左|替代=|700x600像素]]