We explore the relationship between causality, symmetry, and compression. We build on and generalize the known connection between learning and compression to a setting where causal models are not identifiable. We propose a framework where causality emerges as a consequence of compressing data across multiple environments. We define algorithmic causality as an alternative definition of causality when traditional assumptions for causal identifiability do not hold. We demonstrate how algorithmic causal and symmetric structures can emerge from minimizing upper bounds on Kolmogorov complexity, without knowledge of intervention targets. We hypothesize that these insights may also provide a novel perspective on the emergence of causality in machine learning models, such as large language models, where causal relationships may not be explicitly identifiable.

翻译：我们探讨了因果关系、对称性与压缩之间的内在联系。在因果模型不可辨识的情境下，我们基于并拓展了学习与压缩之间的已知关联。本文提出一个理论框架，其中因果关系作为跨多个环境压缩数据的自然结果而涌现。当传统因果可辨识性假设不成立时，我们定义了算法因果性作为因果关系的替代性定义。我们展示了如何通过最小化柯尔莫哥洛夫复杂度的上界，在无需干预目标先验知识的情况下，使算法因果结构与对称结构自然显现。我们推测这些发现或可为机器学习模型（如大语言模型）中因果关系的涌现提供新的视角，此类模型中的因果关系往往无法被显式辨识。