Towards Evaluating Data Priors for Tabular Foundation Models

Data-generating priors are a central component of tabular foundation models because they define the task distribution used during pretraining. However, priors are rarely evaluated as independent components, making it difficult to understand how much they affect downstream model behavior. This raises a methodological question: how can priors from different tabular foundation models be compared independently of the architectures and training protocols they were introduced with? To study this question, we implement a unified interface for publicly available priors from recent tabular foundation models and priors constructed from real datasets. We generate training tasks from each prior, train the same model architecture under a fixed training protocol, and evaluate the resulting models on shared downstream classification tasks. We compare priors through both generated-task statistics and downstream predictive performance. Our results show that different priors favor different downstream behaviors, with some achieving stronger absolute performance and others exhibiting more consistent relative rankings across datasets. We further find that data-level similarity only partially explains downstream behavior. We release our code and evaluation framework to support future reproducible studies of prior design.