From Behavior to Provenance: Attributing Tabular Foundation Models to Synthetic Pretraining Data

Tabular foundation models (TFMs) are commonly pretrained on large collections of procedurally generated synthetic tasks, yet it remains unclear how well these synthetic pretraining priors support the downstream tasks on which the models are evaluated. We study this question from a distribution-level attribution perspective. We recover or reconstruct the synthetic data generators of four TFMs and compare their generated tasks with datasets from two widely used tabular benchmarks. Each dataset is represented by a common set of structural descriptors capturing schema, feature distributions, dependence structure, response properties, and feature--response relationships. In this space, we measure how broadly and repeatedly each synthetic prior reaches benchmark tasks using structural coverage and normalized density, and examine whether stronger local support is associated with better predictive performance. We find substantial differences across synthetic pretraining priors: some generators provide consistently broader and denser support for benchmark tasks than others. Moreover, stronger synthetic-to-benchmark support is generally associated with better relative model performance. These results suggest that structural coverage provides a useful diagnostic for characterizing synthetic pretraining priors and relating their data-generating assumptions to downstream model behavior.

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.

Attributing model behavior to synthetic training data requires knowing what produced each training item before estimating what that item caused. A waveform-label pair does not preserve this knowledge. We propose a generation-provenance substrate in which a synthetic research object binds source specification, generated content, waveform, target, fact requirements, quality signals, review lineage, and immutable manifest identity. Producer and selection mechanism determine evidentiary meaning; storage location and variable name do not. We audit this substrate in a private Japanese care-handoff pipeline. A 113-asset review population contains 1.552 hours of synthetic speech across six scenario families; all items have linked audio, transcripts, candidate notes, and fact checklists, but human evidence is selective and source-specific. Two faithful-only manifests are scenario-seed-disjoint and immutably versioned, while exact upstream attribution remains blocked by floating generator aliases, missing per-clip TTS and code stamps, and an unversioned checking prompt. We argue that generation provenance is necessary but not sufficient for behavior attribution: it defines the candidate causal graph and audit units, whereas contributive attribution still requires frozen training runs and intervention or influence evidence. The paper contributes a compact provenance contract, an audit protocol, and a bounded case study for synthetic-data attribution; controlled research access may be offered, but we do not claim causal training-data attribution, clinical validity, or unrestricted public release.