# Fluctuation-Supervised Pretraining

The work introduces fluctuation-supervised pretraining (FSP), labeling each synthetic table by its average treatment effect plus its efficient influence-function fluctuation while deployment remains a frozen forward pass; the author proves an endpoint transition along the path T_λ,P=θ(P)+λP_nψ_P, where every fixed λ<1 retains label ambiguity of order (1-λ)²/n whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order n^-2; experiments show that across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells, validation-selected Summary FSP deploys 11.

The work introduces fluctuation-supervised pretraining (FSP), labeling each synthetic table by its average treatment effect plus its efficient influence-function fluctuation while deployment remains a frozen forward pass; the author proves an endpoint transition along the path T_λ,P=θ(P)+λP_nψ_P, where every fixed λ<1 retains label ambiguity of order (1-λ)²/n whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order n^-2; experiments show that across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells, validation-selected Summary FSP deploys 11.