# Do Tabular Foundation Models Know Physics? Contamination, Units, and the Deterministic Limit

arXiv: https://arxiv.org/abs/2609.02766 · HTML: https://mlsanity.com/paper/2609.02766/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [TabDPT: Scaling Tabular Foundation Models on Real Data](https://mlsanity.com/paper/2410.18164/) (2024)
- [TabM: Advancing Tabular Deep Learning with Parameter-Efficient Ensembling](https://mlsanity.com/paper/2410.24210/) (2024)
- [Better by Default: Strong Pre-Tuned MLPs and Boosted Trees on Tabular Data](https://mlsanity.com/paper/2407.04491/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Real-TabPFN: Improving Tabular Foundation Models via Continued Pre-training With Real-World Data](https://mlsanity.com/paper/2507.03971/) (2025)
- [Beyond IID: How General Are Tabular Foundation Models, Really?](https://mlsanity.com/paper/2606.30410/) (2026)
- [What exactly has TabPFN learned to do?](https://mlsanity.com/paper/2502.08978/) (2025)

## Abstract (arXiv)

Tabular foundation models (TFMs) learn to fill in tables the way language models fill in text, and tables are arguably the format in which most physical measurement arrives. Did they learn any physics in the process? They are Bayesian by construction, so the question is what their prior contains. We probe it directly, evaluating four of them (TabPFN-3, TabICLv2, TabDPT and Real-TabPFN-2.5) against six baselines on datasets sampled from 316 physical equations, in and out of domain. TFMs dominate, out of the box and after tuning. But we show that their prior can represent neither a noiseless mechanism nor physical units, which is why they interpolate physics without yet being able to act as physical models.