cs.LGAug 17, 2026

NICE: Scale-Stable Perturbations for Graph Neural Network Explanations via Noise Corruption

Authors: Ziluowen Luo, Jun Yin, Ruochen Liu, Ming Cheng, Shirui Pan, Chengqi Zhang, Senzhang Wang

Organizations: Central South University · Hong Kong Polytechnic University · Griffith University

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Post-hoc Graph Neural Network (GNN) explainers commonly follow a Perturb-Query paradigm, inferring the importance of graph elements based on queried predictions to perturbed inputs. However, such perturbations often introduce substantial distribution shift, undermining the reliability of the queried predictions used to derive explanations. While existing efforts mainly improve perturbed graphs or stabilize model predictions on them, we revisit the perturbation mechanism itself. We show that the widely used Element-wise Masking(EM) suppresses edge-induced messages toward zero, causing deterministic scale contraction that accumulates across message-passing layers, a phenomenon we term Scale Drift. Consequently, prediction changes under EM may conflate information corruption with deviations in propagation scale. As a scale-stable alternative to EM, we introduce Noise Corruption (NC), which perturbs each message through matched-norm random-direction corruption while preserving the expected squared message norm. Building on NC, we propose NICE, a Noise Corruption-based explanation framework, which learns a Stochastic Restoration Boundary (SRB) under NC-induced uncertainty, balancing target-prediction restoration against compactness. Furthermore, Boundary-Integrated Gradient (BIG) converts this boundary into edge attributions by accumulating each edge's contribution to reducing restoration risk along the restoration path. Experiments across multiple benchmarks demonstrate stronger explanation performance and model faithfulness while confirming that NC substantially reduces the Scale Drift induced by masking.

Figures & tables

Figure 1: Rethinking where the distribution shift enters the Perturb-Query pipeline. Existing efforts focus on ① or ③ (e.g. ProxyExplainer ( Chen et al. 2024 ) ), while this work focuses on ② the perturbation mechanism itself.
Figure 2: Comparison NC with EM in the message passing.
Figure 3: Preliminary experimental results. (a) t-SNE visualization of graph embeddings from the original graph and the same ground-truth explanation instantiated with EM and NC. (b)-(c) Message scale distribution shift across GCN and GIN. (d) Layer-wise mean scale under different perturbation mechanisms. (e) Cross-dataset summary of message-scale statistics.
MetricMethodMutagBenzeneAlkaneFluorideIndolePAINSR-CountR-MaxRank
F1Random20.06 ±\pm 0.5530.80 ±\pm 0.408.90 ±\pm 1.0924.52 ±\pm 0.4329.49 ±\pm 0.1029.00 ±\pm 0.2341.23 ±\pm 0.0834.95 ±\pm 0.4710
Saliency49.00 ±\pm 0.0747.29 ±\pm 0.010.00 ±\pm 0.0048.09 ±\pm 0.0050.03 ±\pm 0.0049.97 ±\pm 0.0137.97 ±\pm 0.0146.97 ±\pm 0.006
GuidedBP37.50 ±\pm 0.0045.31 ±\pm 0.0115.17 ±\pm 0.0041.68 ±\pm 0.0042.67 ±\pm 0.0051.66 ±\pm 0.0138.77 ±\pm 0.0147.03 ±\pm 0.005
GNNExplainer31.79 ±\pm 1.9025.88 ±\pm 1.0032.16 ±\pm 2.2130.95 ±\pm 0.4942.22 ±\pm 0.5038.97 ±\pm 0.0451.50 ±\pm 0.0945.80 ±\pm 1.018
PGExplainer51.67 ±\pm 0.2464.96 ±\pm 0.1826.39 ±\pm 0.0061.79 ±\pm 0.4046.65 ±\pm 0.0345.98 ±\pm 0.0052.65 ±\pm 0.0053.17 ±\pm 0.003
Refine43.60 ±\pm 0.8242.88 ±\pm 0.3111.48 ±\pm 0.0030.36 ±\pm 2.4237.39 ±\pm 0.0654.18 ±\pm 0.0753.73 ±\pm 0.0051.67 ±\pm 0.004
Table 1: Explanation performance of NICE. We retain the Top30% edges and compare them against ground-truth edges. Results are reported as Mean ±\pm Standard Deviation. The best is bold, and the second-best is underlined.
Figure 4: Fidelity under different sparsity budgets. We vary the explanation sparsity from Top10% to Top90% and measure the resulting Fidelity. Higher values indicate that the explanation better preserves the target model prediction.
Figure 5: Layer-wise message scale under the same GTExplainer configuration. EM causes persistent message-scale contraction, whereas NC remains closer to the clean computation across datasets and GNN backbones.
  Drepr↓D_{\mathrm{repr}}\downarrowDpred↓D_{\mathrm{pred}}\downarrow
DatasetMethodGTRandGTRand
R-CountEM0.31 ±\pm 0.090.63 ±\pm 0.220.57 ±\pm 0.150.59 ±\pm 0.12
NC0.07 ±\pm 0.020.08 ±\pm 0.020.02 ±\pm 0.010.04 ±\pm 0.04
Imp.77.42%87.30%96.49%93.22%
R-MaxEM0.45 ±\pm 0.100.61 ±\pm 0.110.36 ±\pm 0.160.48 ±\pm 0.18
NC0.16 ±\pm 0.030.16 ±\pm 0.040.14 ±\pm 0.050.13 ±\pm 0.06
Table 2: Controlled comparison of EM and NC under GTExplainer and Random. DreprD_{\mathrm{repr}} and DpredD_{\mathrm{pred}} measure representation distance and target-prediction normalized degradation. Imp. denotes the relative reduction ratio.
Figure 6: Hyperparameter sensitivity of SRB and BIG. We study the effects of the variation coefficient β\beta , compactness coefficient λrest\lambda_{\mathrm{rest}} , NC sample number NN , and BIG integration steps TT on performance, stability, compactness, and runtime.
Figure 7: Case study. Gate scores indicate restoration degrees, whereas BIG more clearly highlights edges.
MethodMean ↓\downarrowStd. ↓\downarrowRest. ↓\downarrowAUC ↑\uparrow
Full SRB0.23 ±\pm 0.060.06 ±\pm 0.020.27 ±\pm 0.110.87 ±\pm 0.00
w/o Var.0.37 ±\pm 0.080.19 ±\pm 0.070.41 ±\pm 0.130.83 ±\pm 0.06
w/o Comp.0.25 ±\pm 0.110.09 ±\pm 0.040.84 ±\pm 0.420.81 ±\pm 0.02
Table 3: Analysis of SRB. Results are averaged over Benzene.
Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

SymbolDescription
Graph and target GNN
G=(V,E)G=(\mathcal{V},\mathcal{E})Input graph with node set V\mathcal{V} and edge set E\mathcal{E} .
V={v1,…,vn}\mathcal{V}=\{v_{1},\ldots,v_{n}\}Set of nodes in graph GG .
E⊆V×V\mathcal{E}\subseteq\mathcal{V}\times\mathcal{V}Set of edges in graph GG .
viv_{i}The ii -th node in graph GG .
eij=(vi,vj)e_{ij}=(v_{i},v_{j})Edge between nodes viv_{i} and vjv_{j} .
Appendix
Table 4: Summary of notation (Part 1).
SymbolDescription
Noise Corruption
ϵe(l)\boldsymbol{\epsilon}_{e}^{(l)}Matched-norm random corruption of me(l)\mathbf{m}_{e}^{(l)} .
Pe(l)\mathcal{P}_{e}^{(l)}Distribution of the corrupted message ϵe(l)\boldsymbol{\epsilon}_{e}^{(l)} .
ϵ\boldsymbol{\epsilon}Collection of corruption variables sampled.
PNC\mathcal{P}_{\mathrm{NC}}Joint distribution of corruption variables.
f(G;ρ,ϵ)f(G;\boldsymbol{\rho},\boldsymbol{\epsilon})GNN prediction under restoration configuration ρ\boldsymbol{\rho} and NC realization ϵ\boldsymbol{\epsilon} .
Appendix
Table 5: Summary of notation (Part 2).
StatisticGraphsAverage NodesAverage EdgesNode FeaturesClassesTrain/Test
Mutag1,768~29.15~60.831421597/177
Benzene12,000~20.58~43.6414210800/1200
Alkane1,125~21.39~45.381421012/113
Fluoride8,671~21.36~45.371427803/868
B-XAIC5,000~34.60~75.1911245000/5000
Appendix
Table 6: The statistics of the evaluated datasets and the split.
DatasetTarget Acc. (%)Positive Ratio (%)Ground-Truth ExplanationGT Edge Ratio (%) Mean ±\pm Std.
Mutagencity100.0036.20NOX2{}\mathrm{NO}{\vphantom{\mathrm{X}}}_{\smash[t]{\mathrm{2}}} and NHX2{}\mathrm{NH}{\vphantom{\mathrm{X}}}_{\smash[t]{\mathrm{2}}} groups3.78±6.853.78\pm 6.85
Benzene93.1750.00Benzene ring13.17±13.6013.17\pm 13.60
Alkane100.0033.33Alkane chain and {}{}\mathrm{C}\hbox to0.0pt{\raisebox{0.86108pt}{{-}}\hss}\raisebox{-0.86108pt}{{-}}\mathrm{O} group1.46±2.101.46\pm 2.10
Fluoride96.3117.61Fluorine atom and {}{}\mathrm{C}\hbox to0.0pt{\raisebox{0.86108pt}{{-}}\hss}\raisebox{-0.86108pt}{{-}}\mathrm{O} group2.69±6.042.69\pm 6.04
Indole98.6836.70Fused benzene–pyrrole structure11.54±16.8511.54\pm 16.85
PAINS91.8432.94Detected PAINS alert substructure10.34±17.0110.34\pm 17.01
Appendix
Table 7: Predictive performance of the target GINs and statistics of the ground-truth explanations. The GT edge ratio is the proportion of ground-truth explanatory edges among all edges, averaged over the graphs included in explanation evaluation.
 sBIG=−ρ⋆⊙1T∑k=1T∇ρR^y∗(ρ(k))\mathbf{s}^{\mathrm{BIG}}=-\boldsymbol{\rho}^{\star}\odot\frac{1}{T}\sum_{k=1}^{T}\nabla_{\boldsymbol{\rho}}\widehat{\mathcal{R}}_{y^{*}}(\boldsymbol{\rho}^{(k)}) 
Appendix
Algorithm 1 BIG-Based Explanation Generation
MetricMethodMutagBenzeneAlkaneFluorideIndolePAINSR-CountR-Max
PrecRandom15.58 ±\pm 0.6829.90 ±\pm 0.575.17 ±\pm 0.6319.23 ±\pm 0.3431.46 ±\pm 0.0831.74 ±\pm 0.1968.52 ±\pm 0.1530.96 ±\pm 1.03
Saliency38.70 ±\pm 0.2444.98 ±\pm 0.020.00 ±\pm 0.0037.79 ±\pm 0.0051.52 ±\pm 0.0052.39 ±\pm 0.0263.18 ±\pm 0.0141.14 ±\pm 0.00
GuidedBP30.74 ±\pm 0.0043.35 ±\pm 0.028.86 ±\pm 0.0033.73 ±\pm 0.0044.85 ±\pm 0.0054.74 ±\pm 0.0164.43 ±\pm 0.0141.67 ±\pm 0.00
GNNExplainer24.47 ±\pm 1.5119.68 ±\pm 0.4424.84 ±\pm 1.8723.20 ±\pm 0.6843.41 ±\pm 0.5542.31 ±\pm 0.1085.03 ±\pm 1.0842.59 ±\pm 1.33
PGExplainer39.74 ±\pm 0.2266.20 ±\pm 0.1315.53 ±\pm 0.0049.96 ±\pm 0.3348.76 ±\pm 0.0349.00 ±\pm 0.0088.02 ±\pm 0.0051.15 ±\pm 0.00
Refine34.43 ±\pm 0.7542.77 ±\pm 0.476.17 ±\pm 0.0019.84 ±\pm 2.1140.89 ±\pm 0.0858.01 ±\pm 0.0586.40 ±\pm 0.0848.65 ±\pm 0.00
Appendix
Table 8: Precision of NICE and the compared baselines. The best result is highlighted in bold, and the second-best result is underlined.
Figure 8: Fidelity under varying edge-retention ratios on Alkane-Carbonyl and Fluoride-Carbonyl. NICE preserves the target prediction particularly well under compact explanation budgets, while the performance gap gradually narrows as more edges are retained. Higher values indicate better model faithfulness.
Figure 9: Distribution of target-class prediction confidence under the original graph, Element-wise Mask (EM), and Noise Corruption (NC) on four representative datasets. For each graph, we instantiate the same ground-truth explanation with EM and NC and record the resulting target-class confidence. Compared with EM, NC generally preserves a confidence distribution that remains closer to the clean computation, while EM more often shifts samples toward low-confidence predictions.
  Drepr↓D_{\mathrm{repr}}\downarrowDpred↓D_{\mathrm{pred}}\downarrow
DatasetMethodGTRandGTRand
MutagEM0.77 ±\pm 0.120.46 ±\pm 0.190.53 ±\pm 0.170.29 ±\pm 0.02
NC0.45 ±\pm 0.140.38 ±\pm 0.120.52 ±\pm 0.110.44 ±\pm 0.11
Imp.41.56%17.39%1.89%-51.72%
BenzeneEM0.03 ±\pm 0.070.11 ±\pm 0.090.77 ±\pm 0.260.38 ±\pm 0.18
NC0.03 ±\pm 0.030.06 ±\pm 0.040.74 ±\pm 0.150.43 ±\pm 0.26
Appendix
Table 9: Controlled comparison of EM and NC under GTExplainer and Random. DreprD_{\mathrm{repr}} and DpredD_{\mathrm{pred}} measure representation distance and target-prediction normalized degradation. Imp. denotes the relative reduction ratio.
More in this topic

GNN Explainability

Graph neural network explainability studies how to identify and communicate the features, nodes, edges, and subgraphs behind graph-model predictions.

See all 82 papers

Explore similar work

CardsList
Jul 23, 2026

Towards Faithful Graph Explanations with Synergistic Edge Effects via Granular Balls

Instance-level explanations aim to reveal the rationale behind a model's decisions for a specific graph. Previous methods explain graph neural networks (GNNs) by selecting important edges to induce subgraphs, where edge importance is assessed by perturbing each edge and observing changes in the model predictions. However, they often neglect the synergistic effects among edges, which are crucial for accurately characterizing edge importance. To address this issue, we propose SeeExplainer, a parameter-free explainer to interpret GNNs. Specifically, we first introduce a granular-ball graph refinement mechanism that decomposes a graph into several disjoint granular-balls with no fixed size, and utilize them as nodes to construct a structural graph. This process can better capture the synergistic effects among edges. Then, we perturb nodes and edges in the structural graph to generate explanatory subgraphs based on their respective contributions. Experiments on several graph classification datasets of different networks show that SeeExplainer outperforms state-of-the-art baselines.

Jiancu Chen, Shuyin Xia, Guan Wang +2

Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Big Data Intelligent Computing, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, School of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China · School of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing, China

Graph Neural NetworksGNN Explainability
AskPDF
May 8, 2026

Why Self-Inconsistency Arises in GNN Explanations and How to Exploit It

Recent work has observed that explanations produced by Self-Interpretable Graph Neural Networks (SI-GNNs) can be self-inconsistent: when the model is reapplied to its own explanatory graph subset, it may produce a different explanation. However, why self-inconsistency arises remains poorly understood. In this work, we first identify re-explanation-induced context perturbation as the direct cause of score variation. We then introduce a latent signal assignment hypothesis to explain why only some edges are sensitive to this perturbation, and analyze how conciseness regularization affects latent signal assignment. Given that self-inconsistent edges do not provide stable evidence for the model's prediction, we propose Self-Denoising (SD), a model-agnostic and training-free post-processing strategy that calibrates explanations with only one additional forward pass. Experiments across representative SI-GNN frameworks, backbone architectures, and benchmark datasets support our hypothesis and show that SD consistently improves explanation quality while adding only about 4--6% computational overhead in practice.

Wenxin Tai, Yaqian Liu, Ting Zhong +1

University of Electronic Science and Technology of China

Explanation StabilityGNN Explainability
AskPDF
Jun 4, 2026

Beyond Soft Masks: Hard-Perturbation Mixup Explainer for Robust GNN Explainability

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a range of applications involving graph-structured data, particularly in high-stakes domains. However, the opaque nature of their decision-making processes limits their trustworthiness and broader adoption. Existing post-hoc explanation methods aim to improve explainability by identifying subgraphs that influence GNN predictions and adopt mixup strategies to alleviate the out-of-distribution (OOD) issue caused by using subgraphs for prediction. Yet, these approaches typically rely on soft masks, which are inherently unable to fully eliminate label-irrelevant information, allowing redundant structures to leak into the mixup process and hindering the resolution of the OOD problem, thereby degrading explanation fidelity. In this work, we propose HPME, a Hard-Perturbation Mixup Explanation framework grounded in a generalized Graph Information Bottleneck, which leverages graph pooling to extract discrete explanatory subgraphs and to yield an information-capacity bound to thoroughly compress label-irrelevant components. Furthermore, we introduce a novel mixup strategy built upon structure-level replacement, generating in-distribution explanations to effectively mitigate the distribution shift. Extensive experiments on diverse tasks demonstrate that HPME achieves state-of-the-art performance in generating robust and interpretable explanations across both synthetic and real-world datasets.

Jialiang Yin, Zheng Zhao, Linsey Pang +3

Xi’an Jiaotong University · Xi’an, China · PayPal +2

OOD GeneralizationGNN Explainability
AskPDF