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REVIEW 4 major objections 5 minor 41 references

Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Rank-based conformal training enables GNN prediction sets to hit any predefined target coverage while reducing average set size by up to 11.28% on eight node-classification benchmarks.

desk verdict Rank-based conformal training for GNNs is a plausible empirical recipe, but the paper does not establish the advertised coverage guarantee and its evaluation may leak test labels. read the letter →

arxiv 2501.02767 v1 pith:2PQ3P2UJ submitted 2025-01-06 cs.LG cs.AI

Ting Wang , Zhixin Zhou , Rui Luo This is my paper · ORCID
classification cs.LGcs.AI
keywords graphneuralnetworksconformalpredictionnodeclassificationuncertaintyquantificationrank-basedconformityscoretrainingsetefficiencymarginalcoverage
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Graph neural networks used for node classification rarely come with guarantees that the set of plausible labels is right-sized. The paper proposes RCP-GNN, which folds conformal prediction into GNN training: a rank-based conformity score determines how many top classes to include, and a differentiable version of it is used as a training loss so the prediction sets themselves are optimized. The paper reports that on eight benchmark graphs the method reaches any pre-specified marginal coverage, usually closer to the target than competing calibration methods, while producing smaller average prediction sets, up to 11.28% smaller than the best baseline on Cora. If the guarantees hold, GNNs can be deployed in high-stakes settings with uncertainty sets that are both statistically valid and practically small.

What carries the argument

The load-bearing object is the rank-based conformity score of Eq. 13: $V(x_i,y_i) = [\text{rank of } \hat{\mu}_{y_i}(x_i) \text{ among class probabilities}] - 1 + \frac{1}{n}[\text{rank of } \hat{\mu}_{y_i}(x_i) \text{ among the calibration values for that class}]$. The first term decides how many top classes enter the prediction set; the second breaks ties and lets the calibration quantile set the threshold. For training, this hard ranking is replaced by a differentiable approximation $\tilde{V}(x_i,k) = \sum_j \operatorname{sigmoid}((\tilde{\mu}_j(x_i) - \tilde{\mu}_k(x_i))/\tau)$, and the quantile computation is smoothed using differentiable sorting; the resulting conformity loss $L_{\text{cp}}$ is minimized together with the cross-entropy loss on a topology-aware correction model. This mechanism is what lets prediction sets be adjusted during training rather than fixed after it.

What would settle it

Take one benchmark graph, train RCP-GNN using the paper's 50/50 test split for conformal training, then run the final rank-based conformal prediction on a completely separate calibration split that was never used in any training loss or threshold calculation, across many random splits at $\alpha = 0.1$; if average coverage falls below 0.9 by more than sampling error, the validity claim collapses.

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Extended reading notes

Core claim

The central discovery is that the rank of the true class's predicted probability, relative to all class probabilities at a node, can serve as a conformity score for GNNs and can be made differentiable so that conformal prediction is no longer a post-training afterthought. The paper defines $V(x_i,y_i)$ as the rank of the true class's probability among all classes plus a small tie-breaking term based on the rank of that probability within the calibration set; thresholds derived from these scores yield top-$k$ prediction sets with nominal $1-\alpha$ coverage. RCP-GNN then trains a correction GNN with a sigmoid-smoothed version of this ranking as a conformity loss, jointly with the prediction loss, so the learned probabilities are shaped to make prediction sets compact. On Cora, DBLP, CiteSeer, PubMed, Amazon-Computers, Amazon-Photo, Coauthor-CS, and Coauthor-Physics, the trained model reaches target coverage on all datasets and consistently reduces inefficiency, with up to 11.28% smaller prediction sets than the best baseline.

Load-bearing premise

The guarantee only holds if the calibration nodes used for the final threshold are interchangeable with the test nodes and were not touched while the correction model learned to shrink prediction sets; the paper does not prove this separation.

Editorial extensions

If this is right

  • Any predefined target marginal coverage, not just $\alpha = 0.05$ or $0.1$, should be reachable by the same training and calibration procedure, since the rank score and quantile adapt to $\alpha$.
  • Deploying the trained correction model with standard rank-based conformal prediction at test time gives prediction sets that are valid and smaller on average than post-hoc calibration baselines across eight graphs.
  • Topology-aware correction during conformal training is responsible for the efficiency gain: without the conformity loss, prediction sets are larger.
  • The rank-based score is performance-critical: replacing it with threshold or adaptive conformity scores within the same training scheme degrades efficiency or coverage.
  • Because the differentiable rank score is smooth in model parameters, conformal training scales to standard SGD mini-batching rather than requiring full retraining.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the rank score is as miscalibration-robust as claimed, a natural extension is to regression or link prediction, where the analogue of 'rank among class probabilities' would be rank of residuals; the paper lists link prediction as future work.
  • Editorial inference: the 50/50 split of test data into calibration and evaluation halves during conformal training suggests the final marginal coverage may depend on how the conformal-training calibration fold relates to the final conformal-prediction calibration set; an independent test would use a completely held-out calibration set untouched by training.
  • Editorial inference: because the method reduces prediction-set size most on Cora and least on DBLP, the gain likely depends on graph homophily or class balance; comparing datasets with controlled label noise could reveal where ranking helps.
  • Editorial inference: the smooth-sorting temperature and loss weight are dataset-tuned, so transferring to a new domain probably requires re-tuning; the reported insensitivity to temperature is only over the tested range.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes RCP-GNN, a conformal prediction method for GNN node classification built on a rank-based conformity score. It introduces a differentiable surrogate for rank-based scores, a conformal training loss L_cp that is optimized jointly with the prediction loss on a correction GNN, and an empirical evaluation on eight graph datasets. The central claim is that RCP-GNN achieves any predefined target marginal coverage while producing smaller prediction sets than existing baselines.

Significance. If the validity and efficiency claims are established, this would be a useful contribution: the code is released, the experiments cover eight datasets, ablation studies isolate the main components, and the differentiable rank score is a natural idea. The paper also reports coverage standard deviations over repeated calibration/test splits. However, the paper currently does not provide a validity proof for the rank-based score, and the experimental protocol for splitting the test data during conformal training is ambiguous; these issues bear directly on the central coverage and inefficiency claims.

major comments (4)
  1. [RANK, Eq. (13)] The rank-based conformity score in Eq. (13) is asserted, not proved. The second term, (1/n) times the rank of the predicted probability for the true class among the calibration nodes, makes the score a function of the entire calibration set, so the calibration scores are not values of a fixed score function evaluated at each node. The paper does not provide the exchangeability or quantile argument that would yield the claimed 1-alpha marginal coverage. In addition, the prediction set in Eq. (12) is defined by a top-r*_alpha rule and a threshold mu*, while the text says this is equivalent to thresholding the Eq. (13) score by Q; the equivalence is not demonstrated. A formal theorem is needed, including tie handling and the finite-sample quantile correction.
  2. [Conformal Training (test-data split)] The protocol for splitting the test data is ambiguous and potentially leaks labels into evaluation. The text says Dte is split 50/50 into Dhat_calib and Dhat_te and that 'a fraction' of test data is withheld before splitting, but the size of that fraction and the membership of the final evaluation set are not specified. If L_cp in Eq. (18) is computed on Dhat_te labels and GNN_cor is trained on them, and if the same nodes subsequently appear in Tables 3 and 4, the reported coverage is not a valid out-of-sample measurement. Please specify the exact split, which nodes are used for training GNN_cor, which are used for the final calibration, and which are used for evaluation, and ensure the final calibration set is exchangeable with and independent of the trained model.
  3. [Table 4 and Implementation] Table 4 reports inefficiency point estimates without standard deviations, although Table 3 reports standard deviations for coverage; without error bars, the claimed reductions (up to 11.28%) cannot be distinguished from sampling noise. The hyperparameters lambda, tau, and kappa are chosen by random search, but the paper does not state the selection criterion or whether selection is performed on the test set. If test-set coverage or inefficiency is used for selection, the empirical coverage is partly a product of model selection. Please state the selection protocol and add error bars to the inefficiency results.
  4. [Abstract and Experiments] The abstract claims 'any pre-defined target marginal coverage', but the experiments evaluate only alpha = 0.05 in Table 3 and alpha in {0.1, 0.2, 0.3} in Figure 2. Unless a general proof is supplied, the claim should be restricted to the tested values or accompanied by evidence for a wider range of alpha.
minor comments (5)
  1. [Throughout] There are repeated typos: 'Temperate scaling' should be 'Temperature scaling', 'withhold' should be 'withheld', and 'converge' should be 'coverage' in several places.
  2. [Eq. (20)] The cross-entropy loss in Eq. (20) is written in a binary form with log(1 - mu), which is not appropriate for multi-class node classification; a standard softmax cross-entropy loss should be used.
  3. [Eqs. (16)-(17)] Equation (17) uses Vtilde(x_i, k) for arbitrary class k, but Eq. (16) defines Vtilde only for the true label y_i; the score should be defined for all candidate labels.
  4. [Table 5] The annotation 'Marked: Best' is not supported by the Cora row, where RCP-GNN has size 1.92 versus RCP-THR's 1.65; the criterion for 'best' should be clarified.
  5. [Eq. (23)] The differentiable APS score in Eq. (23) mixes a sigmoid term and the original mu~_k(x_i), but the derivation from Eq. (9) is not explained; please provide the approximation used.

Circularity Check

2 steps flagged · score 6.0 of 10

Coverage results are not established: the rank score is inherited from the authors' own prior work, and the conformal-training loss is minimized on test data that is then used for evaluation.

  1. self citation load bearing [RANK: Rank-based Conformal Prediction, Eq. 13]
    "Following our previous work (Luo and Zhou 2024), we advancing CP to GNNs through rank-based conformity scores, named RANK, to directly reduce the inefficiency. ... V (xi, yi) = [rank of \hat\mu_{y_i}(x_i) in{\hat\mu_1(x_i), · · ·, \hat\mu_Y (x_i)}] − 1 + 1/n [rank of \hat\mu_{y_i}(x_i) in{\hat\mu_{y_i}(x_1), · · ·, \hat\mu_{y_i}(x_n)}] (13) and the quantile Q ... is employed to construct the prediction set with 1 − α coverage."

    The paper's central claim—achieving any predefined target marginal coverage—rests on Eq. 13 being a valid conformal score with an exchangeability-based coverage guarantee. The paper does not prove this property; it only states 'Following our previous work (Luo and Zhou 2024)' and then uses the score as the foundation for the method. The 'novel rank-based conformity score' is thus a load-bearing premise imported from the authors' own prior work rather than independently derived or verified in this manuscript. If the prior work's proof is assumed, the guarantee is imported by citation, not derived here.

  2. fitted input called prediction [Conformal Training, Eq. 18; Experiment/Metrics Eqs. 21–22]
    "Following the split CP approach (Lei, Rinaldo, and Wasserman 2013), we randomly split the test data set Dte into folds with 50%/50% as \hat{D}_calib/\hat{D}_te for calibration and constructing prediction sets. Before splitting the test data, a fraction of test data is withhold for further standard rank-based conformal prediction stage. ... Then the conformity loss function is defined by: Lcp = 1/|\hat{D}_te| 1/|Y| \sum_{i\in \hat{D}_te} c_i (18)"

    The correction model GNN_cor is trained by minimizing Lcp over \hat{D}_te (Eq. 18), which uses the true labels of half of the test set. The reported Coverage and Inefficiency metrics are defined on Dte (Eqs. 21–22), and the paper does not state that the 'withheld fraction' replaces Dte for the final evaluation. As written, the evaluation set overlaps with the data used to fit the model, so the reported 'pre-defined target marginal coverage' and inefficiency numbers are partly in-sample fits rather than out-of-sample predictions. The size of the withheld fraction and the calibration set used for the final standard rank-based CP are unspecified, so the exchangeable, model-independent calibration set required for a genuine conformal guarantee is not established.

full rationale

The paper presents two load-bearing circular/self-supporting steps. First, the rank-based conformity score (Eq. 13) and its coverage property are the foundation of the claimed marginal-coverage guarantee, but they are imported from the authors' own prior work (Luo and Zhou 2024) without proof or external verification; the paper's 'novel' score is therefore a self-citation used as the load-bearing premise. Second, and more concretely, conformal training minimizes Lcp on \hat{D}_te, a 50% fold of the test set, while coverage and inefficiency are reported on Dte; if the reported Dte includes \hat{D}_te, the empirical 'prediction' is a fitted in-sample quantity. The paper never specifies the size of the 'withheld fraction' or the calibration set used for the final standard rank-based CP, so the exchangeability and model-independence needed for a real conformal guarantee are not established. These issues are partial circularity (the headline numbers may reduce to a fit on test data) rather than a definitional identity: a properly executed rank-based split conformal method with a disjoint calibration set would be a legitimate construction. The score of 6 reflects the partial, load-bearing nature of the self-citation plus the test-set training loss; it is not 8–10 because the paper does attempt external benchmarks and does not merely rename a known result.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central method rests on an exchangeability assumption for graph data, a rank-based conformal score inherited from a self-cited prior work, and smooth approximations whose validity is only empirically checked. The three listed hyperparameters are tuned to make the method reach target coverage and reduce inefficiency.

free parameters (3)
  • Temperature tau = 0.01 to 10, median 1 selected
    Controls smooth approximation to hard ranks in Eq. 14 and directly affects the differentiable conformity scores and prediction set size.
  • Conformal loss weight lambda = 0.01 to 10
    Balances prediction loss and conformity loss in Eq. 19; the paper reports sensitivity to this choice.
  • Soft assignment margin kappa = 0 or 1
    Used in Eq. 17 to define the soft prediction-set assignment in the conformity loss.
assumptions (3)
  • domain assumption Calibration and test nodes are exchangeable in transductive node classification.
    Invoked in the Preliminaries after Eq. 3, following Huang et al. 2023; this is required for split conformal prediction to give marginal coverage.
  • domain assumption The rank-based conformity score of Eq. 13 is a valid conformal score.
    The paper states 'Following our previous work (Luo and Zhou 2024)' and does not provide a proof or independent validation of the score's coverage property.
  • domain assumption Smooth sorting and smooth quantile approximations preserve the conformal coverage guarantee.
    The differentiable versions in Eqs. 14-15 replace hard ranks and quantiles with sigmoid approximations; no analysis is given for how the approximation error affects coverage.

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Pith. "Pith review of Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training." pith.science (2026). https://pith.science/paper/2PQ3P2UJ

@misc{pith2026250102767,
  author       = {Pith},
  title        = {Pith review of: Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2PQ3P2UJ}},
  note         = {Machine review of arXiv:2501.02767}
}
read the original abstract

Graph Neural Networks (GNNs) has been widely used in a variety of fields because of their great potential in representing graph-structured data. However, lacking of rigorous uncertainty estimations limits their application in high-stakes. Conformal Prediction (CP) can produce statistically guaranteed uncertainty estimates by using the classifier's probability estimates to obtain prediction sets, which contains the true class with a user-specified probability. In this paper, we propose a Rank-based CP during training framework to GNNs (RCP-GNN) for reliable uncertainty estimates to enhance the trustworthiness of GNNs in the node classification scenario. By exploiting rank information of the classifier's outcome, prediction sets with desired coverage rate can be efficiently constructed. The strategy of CP during training with differentiable rank-based conformity loss function is further explored to adapt prediction sets according to network topology information. In this way, the composition of prediction sets can be guided by the goal of jointly reducing inefficiency and probability estimation errors. Extensive experiments on several real-world datasets show that our model achieves any pre-defined target marginal coverage while significantly reducing the inefficiency compared with state-of-the-art methods.

Figures

Figures reproduced from arXiv: 2501.02767 by the authors.

Figure 1
Figure 1. The framework of RCP-GNN. (a) Model training stage. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Results on different datasets. A lower curve means [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The coverage and inefficiency results with (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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