标题： 量化因果涌现的原因：因果结构中不确定性和不对称性的临界条件 显示英文标题

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

摘要： 对高级计算设备有益，具有大量参数的模型被越来越多地用于提取更多信息，以提高描述和预测客观系统模式的精度。 这一现象在与深度学习相关的研究领域尤为明显。 然而，在过去十年中，基于统计和信息理论的因果关系研究给大规模模型带来了有趣而有价值的挑战。 宏观模型在有效表示系统方面可以优于具有更多参数的微观模型。 这种有价值的情况被称为“因果涌现”。 本文根据有效信息和转移概率矩阵，引入了一个量化框架，用于评估因果涌现的数值条件，作为其发生的理论约束。 具体而言，我们的结果定量证明了因果涌现的原因。 通过一种特定的粗粒化策略，优化模型因果结构中的不确定性和不对称性，比由于模型规模变化而导致的最大信息丢失更具影响力。 此外，通过深入研究部分信息分解和深度学习网络在因果涌现研究中表现出的潜力，我们讨论了我们的量化框架在未来因果涌现研究中可能发挥作用的潜在应用场景。 显示英文摘要

摘要： 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.