Valid for Free: Homophily-Gated Conformal Prediction for Training-Free Node Classification with Tabular Foundation Models

Tabular foundation models (TFMs) can classify the nodes of a graph without training on it, by reading node and neighborhood features as table rows next to labeled context rows. Work in this line reports predictive performance, not conformal coverage or prediction-set size. To our knowledge, we give the first reliability study of the setting, with TabICL as the TFM and half of each graph as labeled context. As for any predictor fixed before calibration, a frozen in-context predictor makes split conformal prediction exactly valid in finite samples, with no training, validation fold, or tuning on the target graph. An audit across ten graphs then shows that the training-free TabICL posterior has lower expected calibration error (ECE) than GCN with temperature scaling (GCN+TS) on nine of them. Its mean ECE over the ten graphs is 0.019, about 35 percent below the 0.029 of GCN+TS. We also introduce HG-DAPS, a training-free diffusion score whose homophily gate reads only the in-context labels, so the guarantee still holds. Relative to adaptive prediction sets (APS), it reduces mean set size by 5.8 to 17.1 percent on six homophilous graphs and changes it by under 1 percent on four heterophilous ones. On two binary, class-imbalanced graphs, a pre-registered trap case shows that gating on raw rather than adjusted homophily lowers coverage among low-homophily nodes by 0.27 and 0.12. Marginal coverage stays at the nominal 0.90 and masks this drop.