It is crucial to choose the appropriate scale in order to build an effective and informative representation of a complex system. Scientists carefully choose the scales for their experiments to extract the variables that describe the causalities in the system. They have found that the coarse scale(macro) is sometimes more causal and informative than the numerous-parameter observations(micro). The phenomenon that the causality emerges by coarse-graining is called Causal Emergence(CE). Based on information theory, a number of recent works have quantitatively shown that CE indeed occurs while coarse-graining a micro model to the macro. However, the existing works have not discussed the question of why and when the CE occurs. We quantitatively analyze the redistribution of uncertainties for coarse-graining and suggest that the redistribution of uncertainties is the cause of causal emergence. We further analyze the thresholds that determine if CE occurs or not. From the regularity of the transition probability matrix(TPM) of discrete systems, the mathematical expressions of the model properties are derived. The values of thresholds for different operations are computed. The results provide the critical and specific conditions of CE as helpful suggestions for choosing the proper coarse-graining operation. The results also provide a new way to better understand the nature of causality and causal emergence.

In this technical report, we introduce Effidit (Efficient and Intelligent Editing), a digital writing assistant that facilitates users to write higher-quality text more efficiently by using artificial intelligence (AI) technologies. Previous writing assistants typically provide the function of error checking (to detect and correct spelling and grammatical errors) and limited text-rewriting functionality. With the emergence of large-scale neural language models, some systems support automatically completing a sentence or a paragraph. In Effidit, we significantly expand the capacities of a writing assistant by providing functions in five categories: text completion, error checking, text polishing, keywords to sentences (K2S), and cloud input methods (cloud IME). In the text completion category, Effidit supports generation-based sentence completion, retrieval-based sentence completion, and phrase completion. In contrast, many other writing assistants so far only provide one or two of the three functions. For text polishing, we have three functions: (context-aware) phrase polishing, sentence paraphrasing, and sentence expansion, whereas many other writing assistants often support one or two functions in this category. The main contents of this report include major modules of Effidit, methods for implementing these modules, and evaluation results of some key methods.