Quantify the Causes of Causal Emergence: Critical Conditions of Uncertainty and Asymmetry in Causal Structure

TL;DR

This paper develops a quantitative framework to understand when and why causal emergence occurs, emphasizing the roles of uncertainty and asymmetry in causal structures, with implications for deep learning and complex systems.

Contribution

It introduces a novel quantification method based on Effective Information and Transition Probability Matrices to identify conditions leading to causal emergence.

Findings

Optimizing uncertainty and asymmetry enhances causal emergence.

Macroscopic models can outperform microscopic ones in representing systems.

The framework applies to deep learning and complex system analysis.

Abstract

Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is particularly pronounced in research domains associated with deep learning. However, investigations of causal relationships based on statistical and informational theories have posed an interesting and valuable challenge to large-scale models in the recent decade. Macroscopic models with fewer parameters can outperform their microscopic counterparts with more parameters in effectively representing the system. This valuable situation is called "Causal Emergence." This paper introduces a quantification framework, according to the Effective Information and Transition Probability Matrix, for assessing numerical conditions of Causal Emergence as theoretical constraints of its occurrence. Specifically, our results quantitatively prove the cause of Causal Emergence. By a particular coarse-graining strategy, optimizing uncertainty and asymmetry within the model's causal structure is significantly more influential than losing maximum information due to variations in model scales. Moreover, by delving into the potential exhibited by Partial Information Decomposition and Deep Learning networks in the study of Causal Emergence, we discuss potential application scenarios where our quantification framework could play a role in future investigations of Causal Emergence.