Learning to Fluctuate: Statistical Foundations for Causal Tabular Pretraining

arXiv:2609.26290v1 Announce Type: cross Abstract: 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 $T_{\lambda,P}=\theta(P)+\lambda P_n\psi_P$, we prove an endpoint transition: every fixed $\lambda<1$ retains label ambiguity of order $(1-\lambda)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. One finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its resulting sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate the local $n^{-1}$ ATE risk that deployment observations cannot erase from the $\log N/M$ excess risk of a generic finite-dictionary episode-learning problem. Experiments trace the learned sampling response. With a raw-row/column backbone, FSP reduces large-effect-shift RMSE by 69.8% relative to latent supervision and by 39.5% relative to a released CausalPFN checkpoint on matched tables. Continuous-covariate experiments, known-effect semisynthesis and two randomized-study evaluations separate sampling-law fidelity from point-risk shrinkage and expose weak-overlap errors in both learned heads.

Abstract: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 $T_{\lambda,P}=\theta(P)+\lambda P_n\psi_P$, we prove an endpoint transition: every fixed $\lambda<1$ retains label ambiguity of order $(1-\lambda)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. One finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its resulting sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate the local $n^{-1}$ ATE risk that deployment observations cannot erase from the $\log N/M$ excess risk of a generic finite-dictionary episode-learning problem. Experiments trace the learned sampling response. With a raw-row/column backbone, FSP reduces large-effect-shift RMSE by 69.8% relative to latent supervision and by 39.5% relative to a released CausalPFN checkpoint on matched tables. Continuous-covariate experiments, known-effect semisynthesis and two randomized-study evaluations separate sampling-law fidelity from point-risk shrinkage and expose weak-overlap errors in both learned heads.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.26290 [stat.ML]

(or arXiv:2609.26290v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.26290 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Learning to Fluctuate: Statistical Foundations for Causal Tabular Pretraining

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