Binary acyclic SCMs can have observational distributions with constant description length while single-variable interventional oracles require Θ(n²) bits, with a further Θ(n) gap to counterfactuals.
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The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy
Binary acyclic SCMs can have observational distributions with constant description length while single-variable interventional oracles require Θ(n²) bits, with a further Θ(n) gap to counterfactuals.