When Tabular Foundation Models Meet Strategic Tabular Data: A Prior Alignment Approach

Tabular foundation models via pretrained prior-data fitted networks (PFNs) achieve remarkable generalization performance on arbitrary testing tabular data, when sample distributions are independent of the deployed classifiers, i.e., a non-strategic regime. In a variety of real-world scenarios, however, once a classifier is deployed, individuals corresponding to tabular samples strategically manipulate their features to obtain favorable results, inducing feature distribution shifts at deployment, i.e., a strategic regime. As concurrent tabular foundation models exclusively overlook the strategic tabular data, we systematically explore the boundary of PFNs on strategic tabular data, characterizing their theoretical properties and empirical performance towards such a commonly encountered type of tabular data, offering a pioneer analysis on bridging PFNs and the society domain. To be first, we inform that such strategic manipulation creates a mismatch between the grounding, strategic prior and the pretrained prior. Subsequently, the prior mismatch leads to an inevitable posterior prediction bias of current tabular foundation models when applied to strategic environments. To address this challenge, we propose Strategic Prior-data Fitted Network (SPN), a strategy-aware framework that adapts tabular foundation models to strategic environments at inference time. SPN uses in-context learning to approximate post-manipulation inputs and then performs prediction for strategic tabular data. Experiments on real-world and synthetic tabular data show that SPN consistently improves performance and robustness under strategic manipulation compared to both tabular foundation models and classical tabular methods.