Distance from galaxies: foundation models for paintings beat custom estimators with 40 times fewer examples

Without dedicated training, tabular foundation models estimate the shift to photometric red better than tools designed for, from only 1,000 reference galaxies.

Measuring the distance of a galaxy requires its redshift. Measuring it precisely requires a spectrum, which is expensive to obtain; large surveys of the sky are therefore often satisfied with images, from which a "photometric redshift" is deduced. Current methods are trained on rare spectral samples that are skewed towards bright galaxies that are easy to observe.

Biprateep Dey and Joshua Speagle show that tabular foundation models, pre-trained on synthetic regression problems, do better without specific training: they are simply provided with examples in context. On a reference dataset, they predict a complete probability distribution in a single pass and match or exceed trained estimators on more than 40,000 galaxies, with only 1,000 examples. The advantage is greatest when calibration data are missing, and persists even if conventional methods receive up to 10,000 additional spectra. For future image-only surveys, it would be sufficient to include a small representative sample to correct for selection bias.