TFM for physics and physics for TFM: tabular foundation models, equation discovery and (astro)-physics

Do TFMs know physics? They learn to fill in tables the way language models fill in text, and tables are arguably the format in which most physical measurement arrives. So did they pick up any physics along the way? They are Bayesian by construction, so the real question is what their prior contains. I will present our recent study benchmarking TabPFN-3, TabICLv2, TabDPT, Real-TabPFN-2.5 and Seldon on physical phenomena. They dominate the baselines out of the box and after tuning — yet their prior cannot represent a noiseless mechanism, which is why they interpolate physics without (yet) acting as full-fledged physical models.

Symbolic regression is their forgotten cousin: same compression of tabular information, but into equations, buying extrapolation and interpretability. I will present our framework for reading tables through that lens, then make the case for the pretraining corpus that is missing: the Strasbourg astronomical Data Centre, decades of tabular data curated and cross-linked to the literature by expert documentalists — and where fine-tuning a TFM on it could lead: an agent that reads tables and writes equations.

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