DrTab: Diagnose, Revise, and Re-read the Table

Tabular foundation models (TFMs) learn transferable prediction algorithms through large-scale pretraining and apply them to unseen tables through in-context learning (ICL). Recent studies further narrow the gap between pretrained models and specific downstream tasks through task-time fine-tuning. However, how much of this gap is correctable through adaptation, and how to diagnose this potential before parameter updates to guide adaptation effort, remain insufficiently characterized. To this end, under controlled gradient estimation error and local smoothness, we derive a lower bound on local improvement in the full-context objective from pre-update task signals, providing a theoretical basis for diagnosing adaptation potential. To put this theoretical insight into practice, we propose DrTab (Diagnose, Revise, and Re-read the Table). Grounded in our theoretical analysis, Diagnose uses information from the current training table to estimate the model's remaining potential for improvement on the task. Revise uses the diagnosis to determine whether to continue adaptation and to guide task-specific parameter updates, after which Re-read combines the revised model with the training table for in-context prediction. Experiments show that the pre-update gradient energy characterized by our theoretical analysis is strongly positively correlated with subsequent loss reduction, supporting its use as a diagnostic signal for adaptation potential. Furthermore, as an add-on adaptation framework for TFMs, DrTab demonstrates broader applicability across TFM backbones and achieves better tabular prediction performance than prior adaptation methods. Its performance gains on non-tabular out-of-distribution (OOD) tasks further demonstrate its effectiveness in enhancing TFM adaptation to new task types.