Tabular foundation models for the estimation of probabilistic quasar photometric redshifts in S-PLUS

We assess whether tabular foundation models can be used as off-the-shelf probabilistic photometric-redshift estimators for quasars in the 12-band S-PLUS DR6 survey, where colour–redshift degeneracies produce multi-modal posteriors and spectroscopic training sets are shifted relative to the photometric population. TabPFN 2.5, RealTabPFN 2.5, and TabICL are benchmarked against eight task-specific baselines, including linear conditional Gaussians, FlexZBoost, mixture-density networks, normalising flows, random forests, and gradient-boosted trees. Models are evaluated with training sets from 500 to 121,626 quasars, using density metrics (CDE loss, log-likelihood, CRPS, PIT–KS, and 90% coverage), point metrics (RMSE, NMAD, bias, and catastrophic-outlier fractions), and importance-weighted scores that approximate deployment on the photometric target sample. Among all methods, TabPFN 2.5 is best or statistically tied for best on nearly all metrics, with the largest gains for small training sets and in difficult regimes — very bright sources, faint sources, high redshift — while retaining near-nominal calibration under covariate shift. Its main practical cost is shifted from training to inference: with frozen weights and no per-survey tuning, it remains tractable at the $\sim 10^5$-object scale studied here, but large support and target catalogues require substantial GPU/accelerator memory and can make full-catalogue inference computationally expensive. SHAP attributions identify WISE W1/W2 as the strongest individual predictors, with UV and optical bands providing refinements that are collectively non-negligible. We conclude that TabPFN 2.5 is a strong default for probabilistic quasar photo-$z$ estimation.