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Learning to Fluctuate: Statistical Foundations for Causal Tabular Pretraining

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Causal tabular foundation models amortize effect estimation across synthetic mechanisms, but latent-effect supervision rewards posterior shrinkage instead of directly encoding the repeated-sample response needed in a fixed deployment population. We introduce fluctuation-supervised pretraining (FSP): each synthetic table is labeled by its average treatment effect plus its efficient influence-function fluctuation, while deployment remains a single frozen forward pass. Along the path $T_{λ,P}=θ(P)+λP_nψ_P$, we prove an endpoint transition: every fixed $λ<1$ retains label ambiguity of order $(1-λ)

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