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The effective information of a random iterative system can be decomposed into two terms:
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Determinism:
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'''Determinism''' describes the predictability of the system's future state based on the current state. The stronger the certainty, the smaller the randomness, and the easier it is to predict the future trend of the system.
Degeneracy:
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'''Degeneracy''' describes the ability to trace back the previous state from the current state. The weaker the degeneracy, the easier it is to infer the system's past evolutionary path. Among them, [math]\tilde{x}_{t+1}[/math] is a new [math]x_{t+1}[/math] variable obtained after intervention while keeping the causal mechanism unchanged.
The stronger the determinism and the weaker the degeneracy, the greater the effective information, leading to stronger causal effects.
After subtracting the macro effective information from the micro effective information, the causal emergence of the iterative system can be obtained as follows:
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其中，[math]W[/math]为粗粒化矩阵，它的阶数为n*m，m为宏观状态空间的维度，它的作用是把任意的微观态[math]x_t[/math]映射为宏观态[math]y_t[/math]。[math]W^{\dagger}[/math]为W的伪逆运算。式中第一项是由确定性引发的涌现，简称'''确定性涌现'''(Determinism Emergence)，第二项为简并性引发的涌现，简称'''简并性涌现'''。更详细的内容参看[[随机迭代系统的因果涌现]]。
其中，[math]W[/math]为粗粒化矩阵，它的阶数为n*m，m为宏观状态空间的维度，它的作用是把任意的微观态[math]x_t[/math]映射为宏观态[math]y_t[/math]。[math]W^{\dagger}[/math]为W的伪逆运算。式中第一项是由确定性引发的涌现，简称'''确定性涌现'''(Determinism Emergence)，第二项为简并性引发的涌现，简称'''简并性涌现'''。更详细的内容参看[[随机迭代系统的因果涌现]]。
==前馈神经网络==
==前馈神经网络==