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

arXiv:2610.08564 · cs.LG · Submitted 2026-10-06 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Valid for Free".

Jane: The gist The training-free TabICL posterior has lower expected calibration error (ECE) than GCN with temperature scaling (GCN+TS) on nine of ten graphs,

Tom: First, who's behind it and why it matters.

Title and authors: Tom: So, we're looking at how they put all this together in "Valid for Free: Homophily-Gated Conformal Prediction for Training-Free Node Classification with Tabular Foundation Models".

Jane: The main thing here is that they show you can get a reliable set of predictions without ever having to train the model on your specific graph data itself.

Lu: It hinges on this idea of a frozen in-context predictor, which means you just read its features and labels as input rows into a tabular foundation model.

Meng: So, the core mechanism is that the Tabular Foundation Model reads those labeled context rows and predicts all the other nodes in the graph based on that knowledge.

Tom: And they prove this method is exactly valid for split conformal prediction using transductive exchangeability, which means no training protocol or validation fold to audit it.

Jane: That's a big deal because it removes one of the biggest hurdles in deploying these kinds of AI systems.

Lu: They also focused on using HG-DAPS, which is this training-free diffusion score.

Tom: This score uses a homophily gate that only looks at the in-context labels, and it shrinks the diffusion weight towards zero when the context has few intra-context edges.

Jane: So, if you have a graph where nodes are really similar, this score helps you select a smaller set size for your prediction without losing that validity guarantee.

Meng: Smaller set sizes mean less work when you're actually running this at scale.

Tom: They found that TabICL beats GCN+TS in terms of expected calibration error, or ECE, on nine out of ten datasets.

Jane: That mean ECE is zero point zero one nine across those ten graphs, which is about thirty-five percent lower than the GCN+TS value of zero point zero two nine.

Lu: They also addressed how this works on tricky graphs, showing that HG-DAPS avoids a specific loss between zero point one two and zero point two seven in low-homophily coverage that happens with raw homophily gating.

Tom: So, it's not just better accuracy; it's better calibration and a mechanism to control the prediction set size dynamically based on how similar the nodes are.

Jane: It means you can use these tabular foundation models for graph classification with a solid statistical guarantee, even if you don't have time or data to train anything new.

Lu: The implication is that we can start leveraging the structured knowledge in tabular data for complex graph problems without needing massive training sets for every single graph type.

Meng: If this works robustly on these benchmarks, it means the deployment pipeline could be much simpler because you skip that heavy initial training phase.

Tom: It's about using a fixed, pre-trained predictor and smart statistical splitting to get reliable results without needing a full training protocol.

Jane: What this does change for us is that we can move toward deploying more sophisticated AI on graphs much faster than before.

The paper's summary: Tom: So, we're looking at how they suggest improving this method for node classification in graphs, focusing on robustness in those tricky homophilous cases.

Jane: The main improvements are all about making it more robust, especially when dealing with those tricky homophilous graphs that we talked about earlier.

Lu: They focus on refining the adjusted homophily estimate they use for the gate, which is what makes HG-DAPS work better.

Tom: It's about using that adjusted estimate to select a diffusion weight delta that shrinks towards zero when the context has few intra-context edges.

Jane: So, if you have a graph where nodes are mostly similar, this adjustment helps control the prediction set size even more precisely than before.

Lu: They show that this refined gate also keeps the loss from low-homophily coverage down to less than zero point zero seven on those trap graphs.

Tom: That means we get better performance on those hard cases, not just better averages across ten datasets.

Jane: So the implication is that this isn't just one fixed method; it's a framework where you can tweak the gating mechanism to handle different graph structures better.

Lu: The authors are basically showing how to make the set size reduction more targeted, not just a blanket adjustment across all graphs.

Tom: And they confirm that this works because it still uses the adjusted homophily from Platonov et al., keeping the core validity intact.

Jane: It’s about taking a solid statistical foundation and adding this layer of adaptive control so it performs reliably across all scenarios.

Lu: The future direction seems to be applying this concept of context-aware gating to even more complex relational structures.

Tom: I'm just excited about the engineering side, because controlling that diffusion weight delta is a clean way to manage complexity in real systems.

Jane: It means we can expect these models to be more reliable when deployed on real-world data where homophily patterns change constantly.

The paper's improvements: Tom: So, we're wrapping up on "Valid for Free: Homophily-Gated Conformal Prediction for Training-Free Node Classification with Tabular Foundation Models".

Jane: Basically, this paper shows that you can use frozen tabular foundation models to classify nodes in a graph without ever training anything on that specific graph dataset.

Lu: It gives us a way to get reliable set sizes by using HG-DAPS, which adjusts the homophily gate based on context labels.

Meng: So, it means we can deploy these without needing a full training pipeline for every single new graph we see at scale.

Tom: And the results are pretty clean: TabICL beats GCN+TS in expected calibration error on nine out of ten benchmarks.

Jane: That means better calibration for the model's predictions, which is a huge confidence boost for any system using this approach.

Lu: The method proves that split conformal prediction works exactly with a frozen predictor, which is really important because it bypasses the need for a training protocol to audit it.

Tom: The main thing is that by using TabICL and HG-DAPS, we get better calibration and smaller set sizes than the baselines we were testing against.

Conclusion: Tom: So to wrap up on "Valid for Free: Homophily-Gated Conformal Prediction for Training-Free Node Classification with Tabular Foundation Models", this paper shows a way to classify graph nodes without any training protocol or validation fold.

Jane: Exactly, Tom. The main thing here is that they show you can get reliable set sizes by using HG-DAPS, which adjusts the homophily gate based on context labels.

Tom: It's about leveraging tabular knowledge and statistical guarantees without ever touching the training data of the specific graph.

Jane: The implication is that we can start building more sophisticated AI on graphs much faster because we skip that heavy initial training phase for every new graph we encounter.

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

Faculty of Information Technology, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam · Faculty of Engineering, School of Computer Science, The University of Sydney · Faculty of Information Technology, Van Lang School of Technology, Van Lang University

cs.LG

Submitted: 2026-10-06

Updated: 2026-10-06

Comments: 6 pages, 4 figures, 1 table

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 83/100

The gist: The gist The training-free TabICL posterior has lower expected calibration error (ECE) than GCN with temperature scaling (GCN+TS) on nine of ten graphs, and HG-DAPS reduces mean set size relative to

Key concepts

Tabular Foundation Models (TFMs): These models classify graph nodes by treating node and neighborhood features as rows in a table, similar to a spreadsheet. They predict missing nodes based on labeled context rows without needing prior training specifically on the target graph structure.
Split Conformal Prediction: This is a method used to make reliable predictions when you don't know the true distribution of your data. It involves splitting your data into calibration and test sets. The paper proves this works perfectly even with a fixed, frozen predictor without any training on the target graph.
HG-DAPS: This is a training-free diffusion score used to select how much influence context has on the prediction. It uses 'adjusted homophily' derived from in-context labels to shrink the diffusion weight, which helps reduce the required prediction set size while preserving reliability.

Terminology

Conformal Prediction — 1× in this paper · explained in 10 episodes
Foundation Model — 1× in this paper · explained in 3 episodes
Foundation Models — 1× in this paper · explained in 7 episodes

Summary

The gist The training-free TabICL posterior has lower expected calibration error (ECE) than GCN with temperature scaling (GCN+TS) on nine of ten graphs, and HG-DAPS reduces mean set size relative to APS on the six homophilous ones while avoiding the extra loss of 0.12 to 0.27 in lowhomophily coverage that raw-homophily gating causes on the two trap graphs;

How it works

Tabular foundation models (TFMs) can classify nodes of a graph without training on it, by reading node and neighborhood features as table rows next to labeled context rows. Each node becomes a row of its own and its neighborhood features, and a frozen TFM reads the labeled context rows and predicts the remaining nodes.

Valid for Free

The paper establishes that split conformal prediction is exactly valid for a frozen in-context predictor by the transductive exchangeability argument of [6], [7]. This validity holds with no training protocol to audit and no validation fold, though it does require a uniformly random calibration/test split of U. Lemma 1 proves that Pr yv∗ ∈ Cˆ(v∗) ≥ 1 − α for a random test node v∗.

Pre-registered Audit

An audit across ten graphs 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.

HG-DAPS

HG-DAPS is a training-free diffusion score whose homophily gate reads only the in-context labels, so the guarantee still holds. The adjusted homophily of Platonov et al. [8] is used to select the diffusion weight δ, which shrinks it toward 0 when the context has few intra-context edges. This leads to a score matrix update S˜ = (1 − δ) S full + δ D−1A Sfull, which preserves validity and allows for set size reduction on homophilous graphs.

Experimental Setup

The experimental setup uses ten standard node classification benchmarks, with context estimates hˆ adj from 0.00 to 0.79. The protocol involves drawing three 50% context splits C, and the remaining nodes form U. Models include TabICL on the feature table ϕ, and baselines such as a graph convolutional network (GCN) [28], a graph attention network (GAT) [29], and GCN with temperature scaling (GCN+TS), tuned on a validation fold carved from the context.

Results Summary

On nine of the ten datasets, TabICL has lower ECE than GCN+TS. HG-DAPS reduces mean set size relative to APS on the six homophilous ones by 5.8% (PubMed) to 17.1% (WikiCS). The adjusted gate avoids the extra loss of 0.12 to 0.27 in lowhomophily coverage that raw-homophily gating causes on the two trap graphs.

Conclusion

A frozen in-context predictor makes split conformal prediction exactly valid in finite samples with no training protocol to audit. HG-DAPS reduces mean set size relative to APS on the six homophilous ones. Its adjusted gate avoids the extra loss of 0.12 to 0.27 in lowhomophily coverage that raw-homophily gating causes on the two trap graphs. The guarantee averages over calibration draws, so one fixed calibration set can realize coverage below 1 − α. The set sizes are compared with APS only, not with LAC, RAPS, or DAPS with a context-tuned weight. The stratification of coverage is reported only on the trap graphs.

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Valid for Free: Homophily-Gated Conformal Prediction for Training-Free Node Classification with Tabular Foundation Models Nguyen Duy Long1, Phung Minh Hien1, Nguyen Trong Viet2, and Nguyen Thai Anh3, Email: longnd.b24cn364@stu.ptit.edu.vn, hienpm.b24cn199@stu.ptit.edu.vn, trng0882@uni.sydney.edu.au, anh.nt@vlu.edu

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2 2?? v 2 4 5 v

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A context row is the one-hot LAC score of its known label, S full c,k = 1[k!= yc], so known labels enter the diffusion as certain evidence, and evaluation rows keep their cached APS scores.

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TABLE I TRAINING-FREE TABICL NODE CLASSIFICATION AT α = 0.10 MEAN±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 hˆ adj.

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(a) Set size at the same 0.90 coverage guarantee APS HG-DAPS 0 0.25 0.5 0.75 1 raw edge homophily hedge of the context labels adjusted homophily hadj (b) Gate statistics, one marker per context split Photo Cora Coauthor-CS PubMed WikiCS CiteSeer Amazon-Ratings Actor Tolokers Minesweeper trap corner

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(a) TabICL GCN+TS MLP −2 −1 0 1 2 empirical coverage ¡ nominal level (percentage points)

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(b) LAC APS RAPS Fig. 2. Reliability audit at α = 0.10 Datasets are ordered by the context estimate hˆ adj (in parentheses) and the dashed rule separates homophilous (hˆ adj > 0.5) from heterophilous (hˆ adj < 0.2) graphs

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Fig. 3 HG-DAPS at α = 10, ordered as in Fig. 2 (a) Mean set size of APS and HG-DAPS at the same coverage guarantee with the relative change

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(b) Gate statistics per context split colored by set-size reduction By (2) the gap below the diagonal hˆ adj = hedge is P(1 − hedge)/(1 − P), which grows with class imbalance at fixed hedge. The shaded trap corner (hedge > 0.5, hˆ adj < 0.2) holds both trap datasets

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Trap case (H4) On Minesweeper and Tolokers the mean hedge is 0.69 and 0.59 (Fig. 3(b)), so the raw gate diffuses with δ = 0.34 and δ = 0.30, whereas the adjusted gate gives δ = 0.003 and δ = 0.05.

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Scope and limitations Lemma 1 and Corollary 1 hold for any frozen predictor, but the ECE and set-size results are specific to TabICL. We did not evaluate TabPFN v2, GraphPFN [9], or HeAD-CP [17] on the same posterior.

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REFERENCES [1] N. Hollmann, S. Müller, L. Purucker, A. Krishnakumar, M. Körfer, S. B. Hoo, R. T. Schirrmeister, and F. Hutter “Accurate predictions on small data with a tabular foundation model” Nature vol 637 pp 319–326 2025 [2] J. Qu D Holzmüller G Varoquaux M Le Morvan TabICL A tabular foundation model for in-context learning on large data in Proc Int Conf Machine Learning ICML vol 267 2025 pp 50 817–50 847 [3] A Hayler X Huang I. I. Ceylan M Bronstein B Finkelshtein Bringing graphs to the table Zero-shot node classification via tabular foundation models arXiv:2509.07143 [4] D Eremeev G Bazhenov O Platonov A Babenko L Prokhorenkova Turning tabular foundation models into graph foundation models NeurIPS 2025 Workshop on New Perspectives in Graph Machine Learning arXiv:2508.

Improvements for AI systems

Bold header: Valid for free split conformal prediction

This improvement enables deployment of node classification systems without any training protocol to audit, as split conformal prediction is exactly valid for a frozen in-context predictor by the transductive exchangeability argument of [6], [7], with no training protocol to audit and no validation fold.

Bold header: Reduced expected calibration error via TabICL

The system can achieve lower calibration error compared to established baselines, as training-free TabICL has lower expected calibration error (ECE) than GCN+TS on nine of them, with a mean ECE of 0.019, about 35 percent below the GCN+TS value of 0.029.

Bold header: Adaptive set size control via HG-DAPS

The system can dynamically adjust prediction set size based on homophily estimates, specifically by implementing HG-DAPS, a training-free diffusion score whose homophily gate reads only the in-context labels, which reduces mean set size by 5.8 to 17.1 percent on six homophilous graphs.

Bold header: Robustness against class imbalance

The system maintains reliable coverage even in challenging scenarios, as the adjusted gate gives δ ≤ 0.07 and mean set size changes by less than 1%, preventing the drop in low-homophily nodes that occurs when using raw edge homophily.