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Symmetries and Causality: Causal Effect Identification Beyond IID Data

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

In the natural sciences, symmetries and cause-effect relationships are ubiquitous. Yet for complex machine-learning tasks, like world-modeling in reinforcement learning, they appear difficult to harness. We propose a formal description of statistical systems based on symmetries in data leaving causal mechanisms invariant. The result is an abstract, simple and general mathematical language for causal reasoning. This paper provides formal descriptions of models and queries, setting up this language, and the formal infrastructure and strategies for their mathematically rigorous identification fro

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