Tabular Foundation Models (TFMs) have demonstrated strong empirical performance as black-box inference engines through in-context learning. However, their use in transfer learning is limited by two obstacles: strict context-size constraints and sensitivity to distribution shifts between source and target tasks.
Directly pooling heterogeneous source data can therefore lead to negative transfer. To address these challenges, we propose Context-Constrained Transfer Learning via ANchoring and DIstillation (TL-ANDI), a posterior-aware distillation framework for TFMs.
TL-ANDI constructs a compact source context by solving a budget-constrained optimal transport problem whose cost jointly measures target covariate coverage and posterior compatibility. The selected anchor samples are then equipped with locally distilled labels and combined with a residual calibration step using target data.
