预测、回溯和当前存储的信息量
Prediction, Retrodiction, and The Amount of Information Stored in the Present
摘要：
我们介绍了一个ambiguous随机动力系统的观点，比较他们的前向时间和反向时间表示，然后将它们整合到一个单一的时间对称表示。该观点在理论上、计算上和概念上都是有用的。在数学上，我们证明了过剩熵--复杂系统中一种常见的组织度量--不仅是过去和未来之间的互信息，而且是预测和追溯因果状态之间的互信息。实际上，我们利用预测和追溯之间的联系，直接计算过剩熵。从概念上讲，这些导致一个发现新的系统不变量的随机动力系统：神秘性（信息可访问性）和因果不可逆性。最后，我们引入一个时间对称表示，统一所有这些量，压缩成一个两个方向表示。由此产生的压缩提供了一个新的概念的信息量存储在现在。
英文摘要：
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically, computationally, and conceptually. Mathematically, we prove that the excess entropy--a familiar measure of organization in complex systems--is the mutual information not only between the past and future, but also between the predictive and retrodictive causal states. Practically, we exploit the connection between prediction and retrodiction to directly calculate the excess entropy. Conceptually, these lead one to discover new system invariants for stochastic dynamical systems: crypticity (information accessibility) and causal irreversibility. Ultimately, we introduce a time-symmetric representation that unifies all these quantities, compressing the two directional representations into one. The resulting compression offers a new conception of the amount of information stored in the present.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
