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

arXiv: https://arxiv.org/abs/2610.02347 · HTML: https://mlsanity.com/paper/2610.02347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Model collapse from synthetic data, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 10 of its 13 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Model collapse from synthetic data](https://mlsanity.com/synth/model-collapse-from-synthetic-data/)

## Builds on (most cited first, 10 of 10)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [TabICLv2: A better, faster, scalable, and open tabular foundation model](https://mlsanity.com/paper/2602.11139/) (2026)
- [Orion-MSP: Multi-Scale Sparse Attention for Tabular In-Context Learning](https://mlsanity.com/paper/2511.02818/) (2025)
- [nanoTabPFN: A Lightweight and Educational Reimplementation of TabPFN](https://mlsanity.com/paper/2511.03634/) (2025)
- [Orion-Bix: Bi-Axial Attention for Tabular In-Context Learning](https://mlsanity.com/paper/2512.00181/) (2025)
- [LimiX-2: A Contextual Mechanism Network Towards General Structured-Data Intelligence](https://mlsanity.com/paper/2609.17488/) (2026)
- [Shaping the Prior: How Synthetic Task Distributions Determine Tabular Foundation Model Quality](https://mlsanity.com/paper/2605.18971/) (2026)

## Abstract (arXiv)

Training-data attribution aims to identify which training examples shape model behavior, yet validating such claims is difficult because causal training influence is rarely observable. We argue that controlled synthetic pretraining makes attribution experimentally testable. Using O'PRIOR, a provenance-rich synthetic task generator for tabular foundation models, we construct a testbed in which every pretraining task carries explicit lineage over structural mechanisms, missingness, confounding, shortcuts, and distribution shift. We combine behavior-conditioned attribution with counterfactual retraining and provenance-aware interventions to test both task-level faithfulness and mechanism-level consistency. On held-out real tasks, removing the top-attributed 5% of synthetic tasks decreases mean ROC-AUC by 0.013, compared with 0.002±0.004 under random removal, while removing bottom-attributed tasks improves performance by 0.003. Within shortcut-provenance tasks, targeted removal yields an effect of 0.043 versus 0.016 for matched random removal. Provenance discrimination is more modest by ranking AUROC (0.55-0.62), despite substantial top-k enrichment, revealing that provenance association and interventional faithfulness need not coincide. Our results establish synthetic provenance as a controlled setting for verifiable contributive attribution