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→Neural information squeezer
====Neural information squeezer====
====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 the approximation of any function in a vast function space. Therefore, Zhang 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 the approximation of any function in a vast function space. Therefore, Zhang 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's method <ref name=":5" />.
In this work, the input consists of time series data <math>(X_1,X_2,...,X_T )</math>, where <math>X_t\equiv (X_t^1,X_t^2,…,X_t^p )</math> and <math>p</math> denotes the dimensionality of the input data. The author assumes that this set of data is generated by a general [[stochastic dynamical system]]:
In this work, the input consists of time series data <math>(X_1,X_2,...,X_T )</math>, where <math>X_t\equiv (X_t^1,X_t^2,…,X_t^p )</math> and <math>p</math> denotes the dimensionality of the input data. The author assumes that this set of data is generated by a general [[stochastic dynamical system]]: