Distributional Regression with Tabular Foundation Models: Evaluating Probabilistic Predictions via Proper Scoring Rules

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. Our code is available at https://github.com/automl/TFM-Playground/tree/prior-dev.

Tabular Foundation Models (TFMs) are currently the best approach to tabular prediction problems. They are constructed as transformers that approximate the Bayesian posterior predictive distribution based on a pre-training prior. These univariate predictors can be converted into multivariate ones autoregressively by sampling one target and adding it to the features. However, the faithfulness of the resulting joint has not been investigated. Furthermore, TFMs cannot be evaluated against the posterior itself, at least not on real-world datasets, because the ground-truth distribution is unknown. We therefore propose asking a different question: could a model's predictions result from any joint distribution? To answer this question, we pose two requirements that any such model must satisfy. The first is marginalization consistency, which demands that marginalized conditionals are equal to directly predicted marginals. The second is factorization consistency, which demands that different factorization orders result in equal joint distributions. Every TFM that we evaluate violates both of these requirements for both classification and regression across all datasets.

Foundation models for predictive machine learning on tabular data have recently gained significant traction in academia and industry. Research communities across disciplines are increasingly evaluating tabular foundation models on diverse datasets and tasks. However, these task- and discipline-specific evaluations remain largely inaccessible to model researchers because benchmark software and evaluation protocols are fragmented. As a result, model researchers rely on standard benchmarks, which are mostly defined for tasks where tabular foundation models already excel. The most challenging scenarios are excluded, limiting meaningful progress in the field by focusing on marginal improvements on IID data rather than on broader, more demanding challenges. To overcome this, we introduce BeyondArena, the first unified holistic benchmark for tabular data that supports diverse task types (IID, temporal, grouped), across sample size and feature dimensionality scales, with diverse feature types (with text, with high cardinality) from a broad range of disciplines. To enable unified benchmarking beyond standard benchmarks, we introduce Data Foundry, a Python framework and metadata schema for curating tabular datasets for predictive machine learning. Our results across 11 models and 142 curated datasets show that existing tabular foundation models excel on tiny- to medium-sized IID data, while traditional tree-based and deep learning models still dominate on non-IID, large, and high-dimensional datasets. BeyondArena guides model research for the most demanding challenges in tabular data, enabling progress towards truly foundational tabular models.