SC-PFN: A Causal Foundation Model with Amortized Statistical Correction

Prior-data fitted networks (PFNs) amortize causal effect estimation, but prediction loss averaged across tasks does not ensure unbiased estimation within each task. Neyman orthogonality motivates residual corrections that cancel first-order nuisance sensitivity in population estimating moments. We introduce SC-PFN (Statistical Correction PFN), a causal foundation model that jointly learns effect prediction and context-conditioned residual weighting. The model predicts observed variables to form residuals and assigns weights to context rows. Weighted residual averages give regularized coefficients, which query weights combine into an update of the base effect estimate. A single model is pretrained across back-door, front-door, and instrumental-variable settings under stated identifying assumptions and applied without dataset-specific parameter updates. We characterize the coefficients as constrained ridge solutions and bound the correction's response to residual perturbations with row and query weights held fixed. Experiments on synthetic and semi-synthetic causal benchmarks show lower mean effect-estimation error than evaluated baselines. Component comparisons and score-shuffling controls support the contribution of the correction and its observation-specific weights.