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关联。我们在学习与压缩的已知联系基础上进行扩展和泛化，将其应用于因果模型不可辨识的场景。我们提出了一个框架，其中因果关系作为跨多个环境压缩数据的结果而涌现。当传统因果可辨识性假设不成立时，我们将算法因果性定义为因果关系的替代性概念。我们展示了如何通过最小化柯尔莫哥洛夫复杂度的上界，在无需干预目标知识的情况下，使算法因果结构与对称结构自然涌现。我们推测这些见解也可能为机器学习模型（例如大型语言模型）中因果关系的涌现提供新的视角，在这些模型中因果关系可能无法被显式辨识。