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REVIEW 3 major objections 5 minor 37 references

DeGLIF for Label Noise Robust Node Classification using GNNs

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read DeGLIF demonstrates that the leave-one-out influence function, which estimates how validation loss would change if a training node were removed, can identify and relabel noisy nodes in graphs, improving node classification without any…

desk verdict Practical denoising method with solid experiments; theory is looser than advertised—Theorem 1 is definitional and Theorem 2 doesn't match the algorithm. read the letter →

arxiv 2506.00244 v1 pith:RCD7ILPA submitted 2025-05-30 cs.LG stat.ML

Pintu Kumar , Nandyala Hemachandra This is my paper · ORCID
classification cs.LGstat.ML MSC 68T0762F35
keywords labelnoisegraphneuralnetworksinfluencefunctionnodeclassificationdenoisingrelabelingcleanvalidationsetleave-one-out
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

The paper proposes DeGLIF, a method that cleans noisy node labels in graphs using a small set of trusted clean labels and the leave-one-out influence function. The central claim is that estimating, for every training node, how much the clean set's loss would drop if that node were removed reliably flags mislabeled nodes, and that relabeling those nodes instead of deleting them yields the best retrained model. On Cora, Citeseer, and Amazon Photo with symmetric and pairwise label noise from 5% to 50%, DeGLIF's two variants beat the compared baselines in most settings, with larger gains at higher noise. The paper also proves that removing the flagged nodes does not increase clean-set risk (Theorem 1) and that relabeling them lowers risk further (Theorems 2 and 3). A reader should care because the method needs no information about the noise level or noise model, only a small clean sample, which is typically affordable when large-scale labeling is crowdsourced.

What carries the argument

The central object is the graph leave-one-out influence function, extended from earlier work to measure the effect of a removed node on clean validation loss. Its formula, $I(-z) = \frac{1}{n} H_\theta^{-1}\{ \nabla_\theta L((z_i,y_i),\hat{\theta}) - \sum_{k\in V_{\text{train}}} [\nabla_\theta L((M_k+\Delta_k,y_k),\hat{\theta}) - \nabla_\theta L((M_k,y_k),\hat{\theta})] \}$, combines the direct loss of dropping node $z$ with the ripple effect of deleting all edges incident to it, captured through $\Delta$, the change in the last-layer representation matrix $M$ of neighboring nodes. The paper multiplies this parameter change by the gradient of each clean point's loss to obtain $I_{\text{up}}(-z, v_i)$, the per-pair influence score of Eq. 5. Two detectors turn these scores into decisions, a modified majority vote over clean nodes (DeGLIF(mv)) and a thresholded sum (DeGLIF(sum)), and a relabeling rule picks the new class as the argmax of the predicted softmax excluding the current label, a choice Theorem 2 shows is at least as good as deletion.

What would settle it

Train the exact DeGLIF pipeline on Cora with 20% symmetric label noise, and for every flagged node compute the predicted clean-set loss change $I_{cv}(-z)$ alongside the realized change obtained by actually retraining from scratch with that node held out; if the two disagree in sign on a substantial fraction of flagged nodes, the first-order influence approximation that Theorem 1 relies on fails, and the method's gains would not transfer to new datasets or architectures.

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Extended reading notes

Core claim

The paper's discovery, stated on its own terms, is that the predicted change in validation loss caused by dropping one training node, computed cheaply with the first-order influence function rather than by retraining, is a sufficient signal for denoising graph data. Concretely, DeGLIF trains a GNN on the noisy set $\mathcal{D}$ and then computes $I_{\text{up}}(-z, v_i) = \nabla_\theta L(v_i, \hat{\theta})^\top I(-z)$ for every pair of a training node $z$ and a clean validation node $v_i$, where $I(-z)$ is the graph influence function that accounts for deleting $z$'s incident edges and the resulting representational shift. DeGLIF(mv) flags $z$ when this predicted loss change is negative for more than a $\lambda$ fraction of the clean nodes, while DeGLIF(sum) flags $z$ when $I_{cv}(-z) = \sum_{v_i \in \mathcal{D}_c} -I_{\text{up}}(-z, v_i)$ exceeds a threshold $\mu$. Both variants are provably safe: Theorem 1 gives $R(\hat{\theta}, \mathcal{D}_c) - R(\hat{\theta}_{-\mathcal{D}_n}, \mathcal{D}_c) \approx \frac{1}{n}\sum_{z\in\mathcal{D}_n} I_{cv}(-z) \geq 0$, meaning the flagged set can be removed without raising clean risk, and Theorems 2 and 3 show that relabeling those nodes, by flipping binary labels or assigning multiclass nodes the argmax of the predicted class distribution excluding the current label, reduces risk further than removal. Since neither the noise rate nor the noise model is needed or estimated, the method applies to any setting with a noisy graph plus a small clean sample.

Load-bearing premise

The method stands on the first-order influence estimate faithfully predicting how much the clean set's loss would drop when a training node is removed, with effects of many removals adding up; a secondary premise is that the noisy and clean sets differ only in their labels.

Editorial extensions

If this is right

  • Retraining a second GNN on the denoised set yields higher node-classification accuracy than GCN, Coteaching+, NRGNN, RTGNN, CP, CGNN, CRGNN, RNCGLN, PIGNN, and DGNN on Cora, Citeseer, and Amazon Photo under symmetric and pairwise label noise from 5% to 50%.
  • DeGLIF requires no information about the noise level or noise model and does not estimate them; its only extra resource is a small clean set of roughly 0.7–1.85% of the nodes.
  • Applying DeGLIF repeatedly reduces the fraction of noisy training labels and saturates within two to three rounds at most noise levels.
  • The relabeling rule alone puts 79% of identified noisy nodes back on their true class at 10% Cora noise, versus 14.3% for random reassignment, and stays above 58% at 50% noise.
  • Theorem 1 shows the flagged set can be removed without increasing clean-set risk, and Theorems 2 and 3 show relabeling the flagged nodes lowers risk further than removal, so denoising is safe whenever the influence approximation is accurate.

Reading between the lines

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

  • Combining DeGLIF's relabeling step with a noise-robust loss function is the obvious next test: the paper says the two are compatible but never measures whether their gains are additive.
  • Hessian inversion dominates DeGLIF's cost, so its practical ceiling on larger graphs depends on plugging in faster influence approximations from the i.i.d. literature, the paper's own suggested future work.
  • Because the method assumes the noisy set and the clean set differ only in labels, a clean set drawn from a different region of the graph, or any covariate shift, would be misread as label noise; a synthetic experiment varying the clean-set distribution would map that failure boundary.
  • The exact proof of relabeling safety is for binary labels, while the multiclass rule is justified by the analogous theorem plus an argmax choice; on heavily imbalanced graphs the rule could systematically favor majority classes, an effect the paper does not examine.
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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

3 major / 5 minor

Summary. The paper proposes DeGLIF, a denoising method for GNN node classification under label noise. DeGLIF trains a GNN on the noisy training set, uses a leave-one-out influence function adapted from prior graph influence work to estimate, for each training node z, the change in loss on a small clean validation set if z were removed, and then flags nodes whose estimated influence indicates a risk increase. Two detection rules are proposed: DeGLIF(mv), which flags nodes with negative influence on a majority of validation nodes, and DeGLIF(sum), which flags nodes whose summed negative influence exceeds a threshold. Flagged nodes are relabeled to the predicted class with highest probability other than the current label, and a second GNN is trained on the relabeled data. The paper claims Theorem 1 proves that nodes detected by DeGLIF(sum) can indeed increase risk, and Theorems 2 and 3 give theoretical support for relabeling. Experiments on Cora, Citeseer, and Amazon Photo under symmetric and pairwise label noise, with ten baselines, report consistent accuracy improvements, especially for DeGLIF(sum) at high noise levels.

Significance. If the theoretical claims were sound, this would be a useful contribution to noise-robust node classification: it is the first work to apply influence functions to label-noise denoising on graphs, it requires no noise-level or noise-model information, and the relabeling step is computationally cheap. The empirical study is broad and careful: multiple datasets, two noise models, ten baselines, five seeds, standard deviations, and ablations on the clean-set size, hyperparameters, and successive denoising. The code is provided. However, the paper's central theoretical support has serious gaps: Theorem 1 is largely definitional given the detection rule, Theorem 2 analyzes a soft-label scheme that the algorithm does not implement, and the proof of Theorem 2 appears to contain an algebraic error. The empirical results may still justify the method as a heuristic, but the claims as currently stated overstate the theoretical grounding.

major comments (3)
  1. [Section 3.1, Theorem 1, Appendix C.3] The guarantee in Theorem 1 is essentially enforced by the detection rule rather than established by the influence approximation. DeGLIF(sum) flags exactly the nodes with Icv(-z) > mu for mu >= 0, so the inequality (1/n) sum Icv(-z) >= 0 follows immediately from the threshold, independent of whether Eq. (5) accurately estimates the effect of removing z. The paper does not provide any direct comparison between the predicted Icv(-z) and the actual leave-one-out change in validation risk, nor does it test the additivity assumption for jointly removing the nodes in Dn. Since the abstract claims that the detected points 'can indeed increase risk,' the theorem as stated does not carry that weight: it needs either an empirical validation of Eq. (5) against true retraining or a reformulation as a conditional statement subject to the accuracy of the first-order influence approximation.
  2. [Section 3.2, Theorem 2, Appendix C.6] Theorem 2 analyzes a soft-label relabeling r(z_i) = [0, ..., phi_k(z), ..., 0] with a weight phi_k, but Algorithm 1 relabels noisy nodes to a hard one-hot label and trains with standard cross-entropy without any downweighting by phi_k. The 'least downweighting' argument in Section 3.2 does not bridge this gap, because the implemented relabeling never uses the weight phi_k. In addition, the stated bound 0 <= phi_k(z) <= 1 is inconsistent with the displayed formula: for f_k in (0,1), log f_k * (1 - f_m) is negative, and log(f_k(1-f_m)) is also negative. Finally, in the proof of Theorem 2, the step from sum_{z,v_i} (-Iup(-z,v_i)) * (f_m/(1-f_m) - 1) to sum_z (f_m/(1-f_m)) * sum_{v_i} (-Iup(-z,v_i)) drops the '-1' term, so the final lower bound R(theta_hat_{-Dn}, Dc) - R(theta_hat_r, Dc) >= 0 does not follow as written. The relabeling function therefore lacks the claimed theoretical support.
  3. [Section 4 and Section 5, Eq. (5)] The evaluation does not isolate the fidelity of the influence estimate, which is the load-bearing premise of the method. Table 4 reports how often flagged noisy nodes are relabeled to the correct class, and Figures 3 and 4 show hyperparameter sensitivity, but neither compares the predicted Icv(-z) with the true leave-one-out risk change nor measures the actual change in clean-set risk when the flagged set is removed. Since the entire detection argument rests on Icv(-z) tracking the true effect of node removal, the authors should add at least one direct diagnostic experiment, for example on Cora at several noise levels, correlating Icv(-z) with the actual R(theta_hat, Dc) - R(theta_hat_{-z}, Dc) and with the joint effect of removing the flagged set. Without such evidence, the empirical accuracy gains could arise from a forgiving relabeling step rather than from accurate influence estimates.
minor comments (5)
  1. [Section 1, contribution 4] The phrase 'Upto 8% higher interms of absolute value' should be corrected to 'up to 8% higher in terms of absolute value'.
  2. [Section 5.4] The word 'hpyerparameters' should be 'hyperparameters'.
  3. [Figure 6 caption] The caption says 'Green means goof accuracy'; this should be 'good accuracy'.
  4. [Algorithm 2 and Algorithm 3] Algorithm 2 line 7 reads 'if then Ci > lambda' with a dangling 'then', and Algorithm 3 sums over 'vj' while the surrounding text and Eq. (5) use 'vi'; these should be cleaned up.
  5. [Eq. (4)] The term '1 vi in Vtrain' is malformed; it should be written as an indicator function, e.g., 1_{v_i in V_train}.

Circularity Check

1 steps flagged · score 6.0 of 10

Theorem 1's guarantee that nodes flagged by DeGLIF(sum) increase clean-set risk is the detection threshold restated; the formal 'prediction' reduces by construction to the influence-based selection rule, although the empirical accuracy results are independent support.

  1. self definitional [Section 3.1, DeGLIF(sum) rule and Theorem 1; Appendix C.3 proof]
    "DeGLIF(sum): Define Icv(−z) := P vi∈Dc −Iup(−z, vi). Given µ, z is classified as noisy if Icv(−z) > µ. ... Theorem 1. Let ˆθ be an optimal parameter for GNN when the model is trained on noisy dataset (D), and ˆθ−Dn be the optimal parameter when the model is trained, removing training nodes in Dn. Then, R(ˆθ, Dc) − R(ˆθ−Dn , Dc) ≈ 1 n X z∈Dn Icv(−z) ≥ 0"

    The set Dn is defined, in the sentence just before Theorem 1, as the nodes satisfying Icv(−z) > μ with μ tuned over nonnegative values. The proof of Theorem 1 (Appendix C.3) expands the risk difference as (1/n) Σ_{z∈Dn} Σ_{vi∈Dc} (−Iup(−z,vi)) = (1/n) Σ_{z∈Dn} Icv(−z) and then lower-bounds this by (1/n) Σ_{z∈Dn} μ ≥ 0. The nonnegativity of the estimated risk decrease is therefore the detection rule itself, not a separate prediction from the influence approximation. The only substantive content left in the theorem is the unvalidated assumption that the first-order influence estimate in Eq. (5), plus additivity, equals the true leave-one-out risk change; absent a direct check of Eq. (5) against actual retraining, the formal guarantee is the flagging criterion restated.

full rationale

The formal claim for DeGLIF(sum) is partly circular: Theorem 1's conclusion is entailed by the threshold used to define the detected set, as shown in Appendix C.3. The relabelling theorems (Theorems 2 and 3) inherit the same threshold-based nonnegativity and additionally rely on the choice of φ_k = log f_k(1−f_m), so the 'theoretically motivated' relabeling is constructed to make the desired inequality hold rather than independently predicted. However, the paper's empirical accuracy comparisons, the relabeling-effectiveness table, and the successive-denosing experiments are external evidence that is not forced by the definition; the algorithm could have failed these tests. Citations to [1] for the GNN influence derivation are to external prior work, not self-citations, and the small number of author self-citations ([26], [27]) are not load-bearing. The main non-circular weakness is that the fidelity of Eq. (5) to true leave-one-out risk is assumed (additivity and first-order approximation) but never directly validated against retraining; that is a correctness risk rather than an additional circularity. Overall, one central formal prediction reduces by construction, so the score is 6 rather than 0.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced; the method uses existing model components. The soft-label reweighting φ_k appears only in the theoretical discussion and is not a new entity; the final algorithm discards it in favor of hard argmax labels.

free parameters (2)
  • λ (DeGLIF(mv) threshold) = tuned over {0.5,0.52,0.53,0.55,0.56,0.6} on the validation set
    Control parameter for the fraction of clean nodes that must see a loss decrease before a node is flagged as noisy. It determines how aggressively labels are relabeled.
  • μ (DeGLIF(sum) threshold) = tuned over {0,0.1,1,10,20} on the validation set
    Threshold on the cumulative influence Icv(-z). Higher μ flags fewer nodes and is tuned per dataset and noise level.
assumptions (6)
  • domain assumption The first-order Taylor expansion of the validation loss change (Eq. 5) is an accurate approximation of actual retraining.
    The entire noisy-node detection rests on this approximation; no experiment compares it against true leave-one-out retraining.
  • domain assumption Influence functions are additive when multiple training nodes are removed.
    Stated before Theorem 1: 'Similar to the approaches taken in [15], [1] and [30], we assume additivity of influence function when more than one node training node is removed.'
  • domain assumption The graph influence function formula of Chen et al. [1] applies to the GNN setup used here.
    Equations (3) and (4) are imported from [1] without re-derivation or empirical validation in this paper.
  • domain assumption The Hessian Hθ is invertible and its inverse is computable.
    Section 3: 'One can choose any model for Model-1 as far as the hessian obtained is invertible (matrix Hθ in Equation (4)).'
  • domain assumption The noisy training distribution and the clean set Dc differ only in label noise.
    Introduction: 'under the assumption that the only difference between the distribution of D and Dc is the noise in D.'
  • standard math Standard calculus and matrix algebra identities used in the Taylor expansion and influence derivations.
    Appendix C derivations rely on first-order optimality conditions, Taylor series, and inverse-matrix manipulations.

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Cite this review

Pith. "Pith review of DeGLIF for Label Noise Robust Node Classification using GNNs." pith.science (2026). https://pith.science/paper/RCD7ILPA

@misc{pith2026250600244,
  author       = {Pith},
  title        = {Pith review of: DeGLIF for Label Noise Robust Node Classification using GNNs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RCD7ILPA}},
  note         = {Machine review of arXiv:2506.00244}
}
read the original abstract

Noisy labelled datasets are generally inexpensive compared to clean labelled datasets, and the same is true for graph data. In this paper, we propose a denoising technique DeGLIF: Denoising Graph Data using Leave-One-Out Influence Function. DeGLIF uses a small set of clean data and the leave-one-out influence function to make label noise robust node-level prediction on graph data. Leave-one-out influence function approximates the change in the model parameters if a training point is removed from the training dataset. Recent advances propose a way to calculate the leave-one-out influence function for Graph Neural Networks (GNNs). We extend that recent work to estimate the change in validation loss, if a training node is removed from the training dataset. We use this estimate and a new theoretically motivated relabelling function to denoise the training dataset. We propose two DeGLIF variants to identify noisy nodes. Both these variants do not require any information about the noise model or the noise level in the dataset; DeGLIF also does not estimate these quantities. For one of these variants, we prove that the noisy points detected can indeed increase risk. We carry out detailed computational experiments on different datasets to show the effectiveness of DeGLIF. It achieves better accuracy than other baseline algorithms

Figures

Figures reproduced from arXiv: 2506.00244 by the authors.

Figure 1
Figure 1. Proposed DeGLIF architecture: We train Model-1 on noisy dataset [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Change in the fraction of noisy training nodes is plotted with the increase in count. The marker [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Relation between λ (Hyper parameter for DeGLIF(mv)) and noise level: X-axis denote the value of λ. The black line denotes accuracy, and the shaded region denotes 1-confidence interval when the model is trained on denoised data. 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Threshold 0.852 0.853 0.854 0.855 0.856 0.857 0.858 0.859 Accuracy 5% 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Threshold 0.75 0.76 0.77 0.78 0.79 Accu… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Relation between µ (Hyper parameter for DeGLIF(sum)) and noise level: X-axis denote the value of µ. The blue line denotes accuracy when the model is trained on denoised data, and the shaded region denotes 1-confidence interval. 6 Discussion In this paper, we address th…
Figure 5
Figure 5. Figure 5: Here experiment is performed on the binary cora-I with different choices for Model-1 and Model [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]
Figure 6
Figure 6. Figure 6: Comparision of DeGLIF with other baselines on binary datasets. For every row, the highest value [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]
Figure 7
Figure 7. Figure 7: Relation between λ (Hyper parameter for DeGLIF(mv)) and noise level: X-axis denote the value of λ. The black line denotes accuracy, and the shaded region denotes 1-confidence interval when the model is trained on denoised data. Page 24 [PITH_FULL_IMAGE:figures/full_fi…
Figure 8
Figure 8. Figure 8: Relation between µ (Hyper parameter for DeGLIF(sum)) and noise level: X-axis denote the value of µ. The blue line denotes accuracy when the model is trained on denoised data, and the shaded region denotes 1-confidence interval. Page 25 [PITH_FULL_IMAGE:figures/full_fi…

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    In a) Model-2 is a Graph sage with hidden dimension 16

    In both cases, Model-1 is GCN with hidden dimension 8. In a) Model-2 is a Graph sage with hidden dimension 16. b) Model-2 is Chebyshev Convolution with hidden dimension 16 and k=3 4,5,6,7 to form class 1. This results in 3673 nodes with label 0 and 3977 nodes with label 1. Res...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.