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

Nguyen Duy Long; Phung Minh Hien; Nguyen Trong Viet; Nguyen Thai Anh

cs.LGOct 6, 2026

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

Authors: Nguyen Duy Long, Phung Minh Hien, Nguyen Trong Viet, Nguyen Thai Anh

Organizations: Faculty of Information Technology, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam · Faculty of Engineering, School of Computer Science, The University of Sydney, Sydney, Australia · Faculty of Information Technology, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, Vietnam

Abstract

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.

Figures & tables

Fig. 1: Overview. (1) A featurizer

\phi

maps each node to a table row (reduced own features, one- and two-hop neighborhood means, one-hop extrema, log-degree), and a frozen TabICL reads the labeled context rows to return

\hat{p}(\cdot\mid v)

. (2) HG-DAPS mixes the score matrix

S^{\mathrm{full}}

(APS rows on

U

, one-hot LAC rows on

C

, written

S

in the panel) with its row-normalized neighbor average as in ( 4 ). The weight

\delta

comes from a homophily gate that reads context labels only. On CiteSeer,

\hat{h}_{\mathrm{adj}}=0.64

gives

\delta=0.29

, and the true-label score of the example node falls from

0.72

0.55

. (3) Only then is

U

split at random into

\mathcal{D}_{\mathrm{cal}}

and

\mathcal{D}_{\mathrm{test}}

, and

\hat{C}(v)=\{k:\tilde{S}_{v,k}\leq\hat{q}\}

keeps three labels where APS alone keeps four. Stages 1 and 2 do not depend on this split, so Lemma 1 gives

\Pr(y_{v^{\ast}}\in\hat{C}(v^{\ast}))\geq 1-\alpha

for a random test node

v^{\ast}

. Values are from one run (CiteSeer, context seed 0,

\alpha=0.10

, classes indexed from 0).

Dataset	$\hat{h}_{\mathrm{adj}}$	Acc	ECE (TabICL)	ECE (GCN+TS)	Cov (APS)	Size (APS)	Size (HG-DAPS)
Photo	0.79	0.960 $\pm$ 0.004	0.007 $\pm$ 0.001	0.017 $\pm$ 0.004	0.901 $\pm$ 0.002	1.047 $\pm$ 0.009	0.956 $\pm$ 0.004
Cora	0.79	0.868 $\pm$ 0.005	0.028 $\pm$ 0.004	0.034 $\pm$ 0.004	0.901 $\pm$ 0.004	1.362 $\pm$ 0.022	1.151 $\pm$ 0.018
Coauthor-CS	0.78	0.934 $\pm$ 0.001	0.008 $\pm$ 0.004	0.007 $\pm$ 0.002	0.900 $\pm$ 0.001	1.101 $\pm$ 0.014	0.988 $\pm$ 0.004
PubMed	0.68	0.877 $\pm$ 0.005	0.010 $\pm$ 0.002	0.014 $\pm$ 0.002	0.900 $\pm$ 0.001	1.198 $\pm$ 0.009	1.128 $\pm$ 0.017
CiteSeer	0.64	0.757 $\pm$ 0.011	0.041 $\pm$ 0.003	0.054 $\pm$ 0.014	0.902 $\pm$ 0.003	1.921 $\pm$ 0.060	1.719 $\pm$ 0.063
WikiCS	0.59	0.860 $\pm$ 0.003	0.015 $\pm$ 0.000	0.040 $\pm$ 0.004	0.900 $\pm$ 0.002	1.482 $\pm$ 0.022	1.229 $\pm$ 0.002

TABLE I: Training-free TabICL node classification at

\alpha=0.10

, mean

\pm

sd over 3 context seeds. Acc is TabICL accuracy. Coverage and set sizes are averaged over 20 calibration/test resplits per seed. ECE is compared with GCN+TS, the pre-registered comparator. Set sizes of APS and HG-DAPS share the same 0.90 coverage guarantee. Datasets are sorted by the context estimate

\hat{h}_{\mathrm{adj}}

Panel of Figure 3 — Fig. 2: Reliability audit at $\alpha=0.10$ . Datasets are ordered by the context estimate $\hat{h}_{\mathrm{adj}}$ (in parentheses), and the dashed rule separates homophilous ( $\hat{h}_{\mathrm{adj}}>0.5$ ) from heterophilous ( $\hat{h}_{\mathrm{adj}}<0.2$ ) graphs. (a) ECE with 15 equal-mass bins [ 21 ] for TabICL, GCN+TS, and MLP, with the TabICL and GCN+TS values in Table I . (b) Marginal coverage of LAC, APS, and RAPS on the TabICL posterior, averaged over 60 calibration/test resplits, as deviation from the nominal $0.90$ . Error bars are exact 95% Clopper-Pearson intervals [ 22 ] at each mean for $n_{\mathrm{test}}$ trials. They are sized for one test set, not for the 60-resplit mean, and every error bar covers the nominal level.

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Open paper AskPDF arXiv

Tabular foundation models (TFMs) provide predictive distributions for regression, but their prediction regions can exhibit undercoverage or overcoverage even when point predictions are accurate. We introduce C-USIM (Conditionally-Uniformized Score Integration Method), a lightweight application of highest predictive density split conformal prediction that accommodates multimodal predictions. Given calibration and test outputs, it requires no additional training or model inference. It provides finite-sample marginal validity under our assumptions. We bound conditional-marginal coverage gaps using distribution-estimation error and score discreteness, and examine coverage heterogeneity through percentile rank-score plots. Experiments with TabPFN and TabICL show improved marginal coverage accuracy and lower average conditional and group coverage errors. Under a fixed data budget, allocating more observations to calibration can reduce marginal coverage error despite less accurate point predictions.

Abstract

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