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====Causal emergence theory based on singular value decomposition====

====Causal emergence theory based on singular value decomposition====

[[Erik Hoel's causal emergence theory]] needs to specify a coarse-graining strategy in advance. Rosas' information decomposition theory does not completely solve this problem. Therefore, [[Zhang Jiang]] et al.<ref name=":2">Zhang J, Tao R, Yuan B. Dynamical Reversibility and A New Theory of Causal Emergence. arXiv preprint arXiv:2402.15054. 2024 Feb 23.</ref> further proposed the [[causal emergence theory based on singular value decomposition]].

[[Erik Hoel's causal emergence theory]] needs to specify a coarse-graining strategy in advance. Rosas' information decomposition theory does not completely solve this problem. Therefore, Zhang et al.<ref name=":2">Zhang J, Tao R, Yuan B. Dynamical Reversibility and A New Theory of Causal Emergence. arXiv preprint arXiv:2402.15054. 2024 Feb 23.</ref> further proposed the [[causal emergence theory based on singular value decomposition]].

=====Singular value decomposition of Markov chains=====

=====Singular value decomposition of Markov chains=====