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This paper claims that label noise in graphs can be reliably detected by measuring influence contradiction—diffusion-weighted influence from other classes—and corrected with a soft neighbor-aware scheme, yielding top node-classification acc

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2026-08-03 08:16 UTC pith:BSPGHUIO

load-bearing objection ICGNN is a practical, well-tested noise-robust GNN pipeline with a genuinely new ICS detector; the 'consistent SOTA' claim is a bit ahead of its own significance tests, but the paper deserves serious review. the 4 major comments →

arxiv 2601.17469 v2 pith:BSPGHUIO submitted 2026-01-24 cs.LG

Identifying and Correcting Label Noise for Robust GNNs via Influence Contradiction

Wei Ju , Wei Zhang , Siyu Yi , Zhengyang Mao , Yifan Wang , Jingyang Yuan , Zhiping Xiao , Ziyue Qiao
show 1 more author
Ming Zhang
This is my paper
classification cs.LG
keywords label noisegraph neural networksinfluence contradiction scoregraph diffusionGaussian mixture modelpseudo-labelingsemi-supervised node classificationrobust learning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that label noise in graphs can be detected by measuring how much a labeled node is influenced by nodes of other classes—an 'influence contradiction'—computed through graph diffusion at both structure and attribute levels. It proposes ICGNN, which uses these scores with a two-component Gaussian mixture model to identify noisy labels, then softly corrects them by blending neighbor predictions and adds pseudo-labels for unlabeled nodes. If the homophily assumption holds, ICGNN should outperform existing robust GNN methods; the experiments claim it achieves the highest accuracy across six benchmark datasets, two noise types, and additional large-scale and heterophilous graphs. A sympathetic reader would care because label noise is common in real graph data, and the method offers a principled, structure-aware alternative to loss-based small-sample criteria.

Core claim

The central claim is that a graph-structure-aware noise indicator—the influence contradiction score (ICS)—can separate clean from noisy labeled nodes more reliably than loss-based criteria. ICS aggregates, for each labeled node, the diffusion-weighted influence arriving from nodes annotated with other classes, using a personalized PageRank diffusion matrix over the original graph and over a K-nearest-neighbor graph built from node representations. A Gaussian mixture model turns these scores into per-node confidence of being clean; noisy labels are then corrected by a convex combination of the original label and a soft neighbor-aggregated prediction, and pseudo-labels from unlabeled nodes add

What carries the argument

The influence contradiction score (ICS), Eqs. (3)–(5), is the central object: for each labeled node i it sums the normalized diffusion influence arriving from all nodes annotated with other classes, at both the structure level (graph diffusion matrix T) and attribute level (diffusion on a KNN affinity graph R). High ICS signals a label that conflicts with the node's neighborhood. A two-component Gaussian mixture model with expectation-maximization assigns a clean-label confidence β̂_i; the label update in Eq. (6) uses β̂_i to interpolate between the original label and h(z_i), a softmax over diffusion-weighted neighbor predictions (Eq. 7); Eq. (8) adds pseudo-label supervision from unlabeled

Load-bearing premise

The method assumes connected nodes tend to share the same class, so a labeled node that receives strong influence from other classes must have a wrong label; on heterophilic graphs or with class-correlated noise, that premise fails and high contradiction can simply reflect structural position.

What would settle it

Take a heterophilic two-class graph (e.g., an alternating ring or bipartite core) and inject 20% uniform label noise. Compute ICS for all labeled nodes and measure the clean/noisy separation (e.g., AUROC against ground-truth noise flags). If ICS's AUROC is statistically indistinguishable from chance while a feature-only classifier's is not, the central detection claim fails. Alternatively, on any of the paper's datasets, raise pair noise to 60%: the paper already reports accuracy falling to 20–47%; if a trivial baseline that ignores labels achieves comparable accuracy on the same noise, the la

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the homophily assumption holds, ICS separates clean from noisy labeled nodes more cleanly than the small-loss criterion, as supported by the paper's confidence-distribution plots.
  • Soft correction—mixing the original label with neighbor-averaged predictions—reduces confirmation bias compared with hard neighbor voting; the ablation study shows a clear drop in accuracy when noise cleaning is removed.
  • Fusing structure- and attribute-level ICS (α = 0.5) outperforms either alone, with the optimal blend depending on graph density; sparse graphs favor attribute information.
  • Pseudo-labeling unlabeled nodes via diffusion-weighted neighbor predictions helps at both low label rates and high noise rates; removing it degrades accuracy even at 60–80% noise.
  • The method is GNN-agnostic and scales to OGBN-arxiv, where some baselines run out of memory.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because ICS is a sum of diffusion influence, it conflates 'boundary position' with 'wrong label': on heterophilic graphs or when noise is class-correlated, clean boundary nodes may receive high contradiction. A testable extension is to calibrate ICS against a structural-role baseline before trusting it in such regimes.
  • The GMM's two-component assumption presumes a bimodal ICS distribution; under intermediate noise rates the modes may merge. A natural extension is to make the number of components adaptive or use a continuous confidence regression.
  • The correction in Eq. (6) trusts the classifier's own neighbor predictions, which can propagate early errors; an ensemble or a smaller held-out clean set for computing h(z_i) could harden the method when the classifier is weak or noise is high.
  • The paper tests a learnable α and finds it worse than the fixed 0.5, suggesting that an effective adaptive fusion of structure and attribute information remains an open problem worth exploring.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes ICGNN, a method for semi-supervised node classification on graphs with noisy labels. It introduces an Influence Contradiction Score (ICS) computed from graph diffusion (structure level) and from a KNN graph built on learned representations (attribute level), fuses the two scores, and fits a two-component Gaussian mixture model to assign each labeled node a clean-label confidence. Noisy labels are then corrected by a soft convex combination of the original label and neighbor predictions, and pseudo-labels for unlabeled nodes are generated in the same way. The method is evaluated on six benchmark datasets under 20% uniform and pair noise, with additional robustness sweeps, ablations, and large-scale/heterophilous tests (OGBN-arxiv, Cornell). The central claim is that ICGNN consistently achieves the highest accuracy across all datasets and noise types in Table 1.

Significance. If the empirical claim is sustained, ICGNN would be a practically attractive addition to the noisy-label GNN literature: it combines a graph-structure-aware detector with a soft correction scheme and pseudo-labeling, and the paper provides broad comparisons against strong baselines, ablations, robustness curves, a large-scale test, and a code link. The diagnostic evidence in Figure 5 (ICS/GMM confidence separation versus small-loss overlap) is a useful contribution if it holds across datasets. However, the paper's main claim is explicitly empirical, and the statistical support reported in Table 2 is not strong enough to support the 'consistently highest' wording. The significance of the work therefore depends on whether the authors can either provide stronger statistical evidence or appropriately hedge the claim.

major comments (4)
  1. [§4.2, Table 2, Observation (iii)] The central claim 'Across all datasets and noise types, our ICGNN consistently attains the highest performance' is stronger than the paper's own significance tests. For Pubmed, the margins over the runner-up are only 0.2–0.3 percentage points (80.3 vs 80.1 uniform; 80.6 vs 80.4 pair) and the reported Wilcoxon p-values are 0.1474 and 0.1050, which are not significant even at the 0.1 level used by the authors. With five runs per method, the rank-sum test cannot reliably resolve such small differences. Moreover, no multiple-comparison correction is applied across the 12 dataset/noise-type comparisons; at a Bonferroni-corrected threshold of about 0.0083, only the Amazon Photo uniform comparison would remain significant. Please report effect sizes/confidence intervals, use more seeds or a paired test, or restrict the claim to datasets where significance is established.
  2. [§3.1, Eqs. (3)–(5), (7); §4.8; Appendix D.4, Table 7] The detection and correction logic depends on the homophily premise that connected nodes tend to share the same class. On heterophilous graphs, a high ICS can indicate a node's genuine structural position rather than a wrong label. The Cornell experiment is only a single dataset with no significance test, and Appendix D.4 shows that at 60%/80% uniform noise, ICGNN accuracy drops to 47.0/26.0, while the text concedes that 'when the noise ratio becomes excessively high, utilizing these incorrect label information may do more harm than good.' This limitation should be stated in the main robustness discussion, and the claim of 'consistently greater resilience' should be qualified.
  3. [§3.3 and §4.7, Eq. (2)] The complexity analysis is not reconciled with Eq. (2), which defines T as the inverse of an N×N matrix. Computing T exactly would require O(N^3) time and O(N^2) memory, making the OGBN-arxiv result in Table 5 infeasible. The method must therefore be using an approximate diffusion (e.g., power iteration), but the approximation is not specified, and its computational cost and accuracy are not analyzed. Please state the algorithm used to compute T and R, and revise the complexity analysis accordingly.
  4. [Algorithm 1, step 6; §3.1; Appendix C.2] The attribute-level ICS is recomputed each epoch from the current encoder's representations, and those representations are trained with the GMM-corrected labels. Although Appendix C.2 correctly notes that no gradients flow through the ICS/GMM operations, the loop still feeds corrected labels back into the encoder, which in turn affects future attribute-level ICS values. The two-component GMM split is therefore not an independent assessment of clean versus noisy labels; it is an identifiability assumption that is not proven. Please validate the detector against the known noise mask on the benchmark datasets (e.g., precision and recall of detected noisy nodes), or discuss why this feedback cannot converge to a self-confirming but incorrect split.
minor comments (6)
  1. [Figure 1] The caption contains the placeholder text '在此处键入公式' ('insert formula here'), which should be removed.
  2. [Eqs. (3)–(4)] The index convention is unclear. The text says each row of T is an outward influence distribution, but Eq. (3) sums T_{ki} over k for a fixed i, which is a column operation. Also define whether the class-index sets C_j refer to labeled nodes only or to all nodes.
  3. [§4.4] The sentence 'CRGNN and ProCon is excluded from the comparison due to its relatively weak performance' contains a subject–verb agreement error and should specify which comparison and what threshold defines 'weak.'
  4. [§4.1 / §4.5] Sensitivity for the two other hyperparameters, the teleport probability ε and the number of nearest neighbors K, is not reported. Please either include a sensitivity table or state explicitly that Table 1 is conditional on these defaults.
  5. [Appendix D.4, Table 7] The observation that very high noise rates make the label information harmful is an important limitation. It should appear in the main text's robustness discussion rather than only in an appendix, since it bounds the meaning of 'robust.'
  6. [§3.1, GMM paragraph] The statement that the EM algorithm 'will converge eventually with theoretical guarantees' should cite the standard EM convergence theorem or be softened, since local convergence is what is guaranteed.

Circularity Check

0 steps flagged

No significant circularity; the load-bearing empirical claim is measured against clean test labels and external baselines, and no fitted quantity is renamed as a prediction.

full rationale

The paper's central claim is the test-set accuracy in Table 1, evaluated on clean test labels and compared with external baselines. None of the reported accuracies are defined by the method's own fitted values. ICS (Eq. 3) is a graph-diffusion statistic computed from the noisy labels and graph structure, used as a heuristic noise indicator under an explicit homophily assumption; it is not a derived prediction that reduces to its inputs. The GMM (Section 3.1) is fit to ICS values, and its posterior is used as a soft weight in label correction (Eq. 6), but the final classification accuracy is not the GMM's cluster assignment, so this is a clustering/self-training loop rather than a tautology. The pseudo-labeling loss (Eqs. 7-8) trains the model to match neighbor-aggregated predictions, a standard self-training technique; the paper does not claim a first-principles derivation whose conclusion is equivalent to its premise. Self-citations (Ju et al. 2024a/b, Yuan et al. 2023) appear only in related work and baseline comparisons and are not load-bearing. The statistical significance of the 'consistently highest' claim is weak in places (e.g., Pubmed p=0.1474/0.1050 in Table 2, with no multiple-comparison correction), and the homophily assumption and high-noise degradation (Table 7) are real limitations, but these are correctness/robustness concerns, not circularity under the definitions used here.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central contribution is algorithmic; it introduces no new physical entities. The main load-bearing premises are homophily, the validity of diffusion-based influence as a noise signal, and the reliability of neighbor predictions for correction. Hyperparameters α, ε, K are hand-set; GMM parameters are fit to the same labels being corrected.

free parameters (4)
  • α (ICS fusion weight) = 0.5
    Weight balancing structure-level and attribute-level ICS in Eq. (5); fixed after sensitivity experiments; a learnable version performed worse (Table 4).
  • ε (teleport probability) = 0.85
    PageRank diffusion parameter in Eq. (2); chosen by hand; controls global influence radius.
  • K (KNN neighbors for representation affinity graph) = 5
    Number of nearest neighbors used to build A_r before attribute-level diffusion; chosen by hand.
  • GMM component parameters (μ_q, σ_q, π_q) = estimated by EM on per-node ICS values
    Two-component Gaussian mixture fit to ICS; the component with smaller mean is declared clean. These are fitted to the same training labels that are later corrected.
axioms (5)
  • domain assumption Homophily: connected nodes tend to belong to the same class (Section 3.1).
    Used to justify ICS: a node that receives strong influence from other-class nodes is labeled noisy. This fails on heterophilic graphs; the paper tests Cornell, but both detection and correction rely on this assumption.
  • standard math Personalized PageRank diffusion matrix T is a valid global influence measure (Eq. (2)).
    Adopted from Klicpera et al. (2019) / Page et al. (1999); each row is treated as an influence distribution.
  • ad hoc to paper EM on a two-component GMM converges to a useful clean/noisy separation of ICS values (Section 3.1).
    EM convergence is local and the two-component split is chosen for the clean/noisy dichotomy; no guarantee that the fitted separation matches true noise labels.
  • domain assumption KNN graph in representation space approximates attribute-level influence (Eq. (4)).
    With very few labeled nodes (1-5%), the KNN graph over L nodes is noisy; its diffusion is assumed to capture class-conflicting influence.
  • domain assumption Soft labels from neighbor predictions are a reliable correction signal (Eqs. (6)-(7)).
    Assumes global neighbors' predictions are better than the noisy label; may break under high noise and heterophily.

pith-pipeline@v1.3.0-alltime-deepseek · 21999 in / 15936 out tokens · 168177 ms · 2026-08-03T08:16:21.457271+00:00 · methodology

0 comments
read the original abstract

Graph Neural Networks (GNNs) have shown remarkable capabilities in learning from graph-structured data with various applications such as social analysis and bioinformatics. However, the presence of label noise in real scenarios poses a significant challenge in learning robust GNNs, and their effectiveness can be severely impacted when dealing with noisy labels on graphs, often stemming from annotation errors or inconsistencies. To address this, in this paper we propose a novel approach called ICGNN that harnesses the structure information of the graph to effectively alleviate the challenges posed by noisy labels. Specifically, we first design a novel noise indicator that measures the influence contradiction score (ICS) based on the graph diffusion matrix to quantify the credibility of nodes with clean labels, such that nodes with higher ICS values are more likely to be detected as having noisy labels. Then we leverage the Gaussian mixture model to precisely detect whether the label of a node is noisy or not. Additionally, we develop a soft strategy to combine the predictions from neighboring nodes on the graph to correct the detected noisy labels. At last, pseudo-labeling for abundant unlabeled nodes is incorporated to provide auxiliary supervision signals and guide the model optimization. Experiments on benchmark datasets show the superiority of our approach over competitive baselines in noisy label scenarios.

Figures

Figures reproduced from arXiv: 2601.17469 by Jingyang Yuan, Ming Zhang, Siyu Yi, Wei Ju, Wei Zhang, Yifan Wang, Zhengyang Mao, Zhiping Xiao, Ziyue Qiao.

Figure 1
Figure 1. Figure 1: Illustration of the proposed framework ICGNN. Our model consists of two steps: (a) Noise detection by influence contradiction: the original graph and KNN-based representation affinity graph undergo graph diffusion from attribute and structure levels. From these two perspectives, the ICS values are calculated and fused, followed by a Gaussian mixture model for accurately identifying potential noisy labels; … view at source ↗
Figure 2
Figure 2. Figure 2: Robustness analysis against different levels of label noises on DBLP and Pubmed. 0.5 1 1.5 2 Label Rate (%) 72.0 74.0 76.0 78.0 80.0 82.0 Accuracy (%) NRGNN RTGNN CGNN DND-NET Ours (a) DBLP (Uniform) 0.5 1 1.5 2 Label Rate (%) 70.0 75.0 80.0 Accuracy (%) NRGNN RTGNN CGNN DND-NET Ours (b) DBLP (Pair) 0.5 1 1.5 2 Label Rate (%) 70.0 75.0 80.0 Accuracy (%) NRGNN RTGNN CGNN DND-NET Ours (c) Pubmed (Uniform) 0.… view at source ↗
Figure 3
Figure 3. Figure 3: The comparison w.r.t. different label rates on DBLP and Pubmed [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison w.r.t. different α on Coauthor CS, Amazon Photo, DBLP, Pubmed datasets. are shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Loss distribution (a and c) and confidence distribution (b and d) when training a GCN on Amazon Photo [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effectiveness of influence contradiction score as noise indicator (t-SNE visualization of the Amazon Photo dataset with 40% uniform noise ). the broad scalability and generalizability of our proposed ICGNN. The experimental results under uniform noise are shown in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Robustness analysis against different levels of label noises on four datasets. To illustrate the robustness of our proposed ICGNN under varying degrees of label noise, we systematically adjust the noise rate in increments of {10%, 20%, 30%, 40%}, while maintaining a fixed label rate of 1%. Our evaluation focuses on comparing the performance of our ICGNN against leading baselines (NRGNN, RTGNN, CGNN and DND… view at source ↗
Figure 9
Figure 9. Figure 9: Sensitivity analysis against different label rates on four datasets. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

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Reference graph

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