Reinforcement Learning Foundation Models Should Already Be A Thing

What determines the quality of a tabular foundation model? Unlike language or vision, tabular foundation models acquire their inductive biases almost entirely from synthetic pretraining distributions, yet the design of these distributions remains poorly understood. Standard synthetic priors are too well-behaved: they omit the irregularities and failure modes that determine deployment robustness. We introduce O'Prior, a compositional realism prior built around four coupled components: a hierarchical SCM meta-generator spanning diverse functional families; a modular realism engine covering heterogeneous marginals, missingness, and target transforms; an explicit stress module injecting confounding and support-query mismatch; and a curriculum-governed, leakage-safe generation protocol. To isolate prior design as the scientific variable, we hold architecture, optimizer, and compute budget fixed and vary only the synthetic task distribution. O'Prior yields consistent and substantial improvements in downstream accuracy and robustness across real tabular benchmarks, with gains concentrated in regimes characterized by distributional irregularities. Ablations confirm that mechanism diversity, realism composition, and shift-aware stress each contribute independently, their effects are not interchangeable. These results establish synthetic prior construction as a first-order and largely overlooked determinant of tabular foundation model quality

Tabular foundation models are pre-trained on one of three classes of corpus: curated datasets drawn from benchmark repositories, tables harvested at scale from the web, or synthetic tables sampled from a parametric generative prior. Despite the centrality of pre-training data to model performance, little is known about how these corpora relate to one another in distribution, and the impact this has on downstream performance. In this work we take three canonical, archetypal datasets used to train tabular foundation models; the T4 dataset represents web-scraped corpora, the TabFM dataset curated tables from Kaggle, and the TabICL dataset as the only well-used synthetic prior with publicly available parameters. We characterise each corpus using aggregate features over whole tables, columns and correlations, and compare them using discriminator AUCs and k-NN coverage metrics. We find that the TabICL synthetic prior occupies a narrow region of the space of real tables, that this mismatch cannot be closed by optimising prior hyper-parameters across more than 86 thousand configurations, and that curated and web-scraped corpora are broadly interchangeable on a distributional level in feature space. Surprisingly, the distributional gap between synthetic pre-training data and real tables has a clearly detectable effect on performance under neither feature-based proximity measures or TabICL's own internal representations, suggesting that coverage of the real-data distribution is not the primary driver of TabICL's generalisation.

Tabular Foundation Models (TFMs) achieve state-of-the-art zero-shot accuracy on small tabular datasets, but their in-context learning assumes approximately clean inputs: real- world missing values, outliers, and duplicates create a prior mismatch that degrades both accuracy and calibration. We study reinforcement learning for tabular data cleaning, a learned policy that sequences cleaning operators and introduce L2C-TFM with a model-aware reward (TFMAwareReward). We are explicit about what this reward optimizes: it regularizes the Wasserstein distance between the cleaned and the original (dirty) data, a distributional-stability term, which we measure as a diagnostic. Across six experiments on ten OpenML datasets: (i) three of seven reward designs collapse to degenerate strategies, so reward engineering is non-trivial; (ii) under an 8-seed repeated-holdout protocol the model-aware reward matches a random-forest-reward baseline on accuracy (p=0.38), with a benefit confined to minority-class macro-F1 under class imbalance that is partly a reward-agnostic calibrated-threshold effect; and (iii) a policy pre-trained on one dataset transfers to held-out datasets. A diagnostic analysis shows that the two distances are distinct objectives: cleaning tends to move data away from the prior, and prior-distance, not distance-to-dirty, is what tracks downstream quality. We therefore treat prior alignment as a motivating objective and a target for future work, not a property of the reward evaluated here. Code, datasets, and the nested evaluation harness are available at https://github.com/LaureBerti/Learn2Clean/tree/master/Learn2Clean_TFM.