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======Comparison with classical theories======

======Comparison with classical theories======

The [[NIS]] framework has many similarities with the [[computational mechanics]] framework mentioned in the previous sections. NIS can be regarded as an <math>\epsilon</math>-machine. The set of all historical processes <math>\overleftarrow{S}</math> in [[computational mechanics]] can be regarded as a set of microscopic states. All <math>R \in \mathcal{R}</math> represent macroscopic states. The function <math>\eta</math> acts as a coarse-graining function, while <math>\epsilon</math> represents an effective coarse-graining strategy. <math>T</math> corresponds to a effective macroscopic dynamic. The characteristic of minimum randomness index characterizes the determinism of macroscopic dynamics and can be replaced by EI in causal emergence. At this point, the encoded macroscopic state converges to the effective state, which can be regarded as the [[causal state]] in computational mechanics.

The [[NIS]] framework has many similarities with the [[computational mechanics]] framework mentioned in the previous sections. NIS can be regarded as an <math>\epsilon</math>-machine. The set of all historical processes <math>\overleftarrow{S}</math> in [[computational mechanics]] can be regarded as a set of microscopic states. All <math>R \in \mathcal{R}</math> represent macroscopic states. The function <math>\eta</math> acts as a coarse-graining function, while <math>\epsilon</math> represents an effective coarse-graining strategy. <math>T</math> corresponds to an effective macroscopic dynamic. The characteristic of minimum randomness index characterizes the determinism of macroscopic dynamics and can be replaced by EI in causal emergence. At this point, the encoded macroscopic state converges to the effective state, which can be regarded as the [[causal state]] in computational mechanics.

At the same time, the [[NIS]] framework also has similarities with the G-emergence theory mentioned earlier. For example, [[NIS]] also adopts the idea of [[Granger causality]]: optimizing the effective macroscopic state by predicting the microscopic state at the next time step. However, there are several obvious differences between these two frameworks: a) In the G-emergence theory, the macroscopic state needs to be manually selected, while in [[NIS]], the macroscopic state is obtained by automatically optimizing the coarse-graining strategy; b) NIS uses neural networks to predict future states, whereas G-emergence relies on autoregressive techniques to fit the data.

At the same time, the [[NIS]] framework also has similarities with the G-emergence theory mentioned earlier. For example, [[NIS]] also adopts the idea of [[Granger causality]]: optimizing the effective macroscopic state by predicting the microscopic state at the next time step. However, there are several obvious differences between these two frameworks: a) In the G-emergence theory, the macroscopic state needs to be manually selected, while in [[NIS]], the macroscopic state is obtained by automatically optimizing the coarse-graining strategy; b) NIS uses neural networks to predict future states, whereas G-emergence relies on autoregressive techniques to fit the data.