AdvSynGNN: Structure-Adaptive Graph Neural Nets via Adversarial Synthesis and Self-Corrective Propagation

Rong Fu; Chunlei Meng; Shuo Yin; Kun Liu; Simon Fong

cs.LGFeb 19, 2026

AdvSynGNN: Structure-Adaptive Graph Neural Nets via Adversarial Synthesis and Self-Corrective Propagation

Authors: Rong Fu, Chunlei Meng, Shuo Yin, Kun Liu, Simon Fong

Organizations: Independent Researcher

Abstract

Graph neural networks frequently encounter significant performance degradation when confronted with structural noise or non-homophilous topologies. To address these systemic vulnerabilities, we present AdvSynGNN, a comprehensive architecture designed for resilient node-level representation learning. The proposed framework orchestrates multi-resolution structural synthesis alongside contrastive objectives to establish geometry-sensitive initializations. We develop a transformer backbone that adaptively accommodates heterophily by modulating attention mechanisms through learned topological signals. Central to our contribution is an integrated adversarial propagation engine, where a generative component identifies potential connectivity alterations while a discriminator enforces global coherence. Furthermore, label refinement is achieved through a residual correction scheme guided by per-node confidence metrics, which facilitates precise control over iterative stability. Empirical evaluations demonstrate that this synergistic approach effectively optimizes predictive accuracy across diverse graph distributions while maintaining computational efficiency. The study concludes with practical implementation protocols to ensure the robust deployment of the AdvSynGNN system in large-scale environments.

Figures & tables

Figure 1: Overview of the AdvSynGNN framework for structure-adaptive graph learning. The pipeline begins with Multi-scale Feature Synthesis , which generates node embeddings $X_{\text{MS}}$ by aggregating local and multi-hop contextual signals. In the core processing stage, we employ Contrastive Representation Alignment to stabilize embeddings via a self-supervised loss $\mathcal{L}_{\text{ssl}}$ . Simultaneously, an Adversarial Synthesis module, consisting of a GAN-based Generative Adversary and a Structural Discriminator , proposes heterophily-oriented edge flips to produce a perturbed adjacency $\widetilde{A}^{\prime}$ . These signals feed into the Adaptive Residual Correction engine, where label estimates are refined through confidence-weighted propagation using per-node calibration $c_{i}$ (or $\alpha_{i}$ ) to mitigate structural noise. The refined representations are then processed by a Heterophily-Adaptive Graph Transformer that incorporates a learned structural attention bias $\phi_{ij}$ to differentiate between compatible and noisy neighbors. Finally, the Robust Diffusion module computes a steady-state prediction $Z^{(\infty)}$ , which is integrated via Prediction Fusion and a lightweight Ensemble to produce the final resilient node labels $Y_{\text{final}}$ . Shaded blocks indicate modules that are jointly optimized during the end-to-end training phase.

Dataset	Length	TimeGAN	SigCWGAN	GMMN	RCGAN	GAT-GAN	AdvSynGNN
ECG	16	0.061	0.053	0.058	0.058	0.060	0.055
	64	0.121	0.148	0.149	0.151	0.049	0.044
	128	0.152	0.147	0.148	0.154	0.048	0.042
	256	0.154	0.167	0.156	0.168	0.047	0.040
Traffic	16	0.027	0.034	0.020	0.027	0.030	0.025
	64	0.141	0.107	0.130	0.136	0.017	0.014

Table 1: Benchmark evaluation of forecasting performance (Mean Absolute Error). Datasets are described in the text (ECG: physiological time series; Traffic: traffic flow; Motor: industrial sensor series).

Method	ArXiv	Products	Proteins	DBLP	PCQM4Mv2 (MAE $\downarrow$ )
GCN [ 11 ]	$71.74\pm 0.21$	$83.90\pm 0.18$	$72.51\pm 0.31$	$86.01\pm 0.22$	$0.148\pm 0.003$
GraphGAN [ 59 ]	$68.50\pm 0.28$	$80.25\pm 0.24$	$70.12\pm 0.35$	$82.30\pm 0.19$	$0.144\pm 0.004$
DnnGAN [ 70 ]	$70.85\pm 0.19$	$82.67\pm 0.20$	$71.25\pm 0.27$	$87.45\pm 0.23$	$0.139\pm 0.003$
GMP-GL [ 71 ]	$71.20\pm 0.22$	$83.10\pm 0.17$	$71.80\pm 0.29$	$87.90\pm 0.21$	$0.137\pm 0.005$
Att-GAN [ 72 ]	$71.55\pm 0.25$	$83.45\pm 0.19$	$72.05\pm 0.26$	$88.25\pm 0.20$	$0.135\pm 0.004$
TenGAN [ 73 ]	$71.90\pm 0.23$	$83.80\pm 0.18$	$72.30\pm 0.28$	$89.50\pm 0.22$	$0.133\pm 0.003$

Table 2: Performance summary across five random seeds (mean

\pm

std). Node classification accuracy (%, higher is better) and PCQM4Mv2 MAE (lower is better). Bold indicates the best result.

Method	arXiv-AstroPh	arXiv-GrQc	Wikipedia	Amazon2M
GraphGAN [ 59 ]	$85.5\pm 0.31$	$84.9\pm 0.29$	$81.3\pm 0.33$	$78.50\pm 0.42$
DnnGAN [ 70 ]	$96.0\pm 0.18$	$95.0\pm 0.20$	$99.0\pm 0.09$	$80.25\pm 0.38$
GFformer [ 79 ]	$94.2\pm 0.22$	$93.5\pm 0.24$	$98.1\pm 0.15$	$85.12\pm 0.35$
VCR-GRAPHORMER [ 80 ]	$94.8\pm 0.19$	$94.0\pm 0.21$	$98.5\pm 0.12$	$76.09\pm 0.45$
SGFormer [ 76 ]	$95.0\pm 0.17$	$94.5\pm 0.19$	$98.7\pm 0.11$	$89.09\pm 0.28$
Proformer [ 81 ]	$95.1\pm 0.16$	$94.6\pm 0.18$	$98.8\pm 0.10$	$89.48\pm 0.30$

Table 3: Link prediction AUC (%, higher is better). Bold indicates the best result. All results are averaged over five independent runs with different random seeds.

Configuration	Node Accuracy (%) $\pm$ std			$\Delta\mathrm{AUC}$ (pp)	Shapley $\phi$ (%)
Configuration	ArXiv	Proteins	WikiCS	$\Delta\mathrm{AUC}$ (pp)	Shapley $\phi$ (%)
Full AdvSynGNN	75.48 $\pm$ 0.15	86.40 $\pm$ 0.18	81.22 $\pm$ 0.21	0	–
w/o GAN-only	73.65 $\pm$ 0.20	84.25 $\pm$ 0.22	78.30 $\pm$ 0.25	-2.07	24.7
w/o confidence-only	74.20 $\pm$ 0.19	84.91 $\pm$ 0.20	78.95 $\pm$ 0.23	-1.26	15.1
w/o multi-scale + bias	73.65 $\pm$ 0.20	84.12 $\pm$ 0.22	78.40 $\pm$ 0.24	-1.83	22.0
w/o GAN + w/o confidence	72.11 $\pm$ 0.23	82.93 $\pm$ 0.26	76.95 $\pm$ 0.28	-5.90	57.8

Table 4: Ablation study on node classification accuracy (%, mean

\pm

std) and robustness (ROC-AUC drop) under 5% hybrid perturbation on OGBN-Proteins. “w/o A+B” denotes simultaneous removal of modules A and B; Shapley values approximate marginal contribution on Proteins.

Method	5% Del	10% Del	5% Add	Hybrid
GCN [ 11 ]	-3.21	-6.74	-4.83	-7.95
GraphGAN [ 59 ]	-5.47	-9.82	-7.16	-11.03
Graphormer [ 61 ]	-2.78	-5.63	-3.95	-6.41
SGFormer [ 76 ]	-1.95	-4.27	-2.86	-5.12
AdvSynGNN	-0.82	-1.93	-1.14	-2.05

Table 5: Relative ROC–AUC degradation under structural perturbations on OGBN-Proteins

Method	Final Accuracy (%)	$\boldsymbol{\mathcal{K}}$ (%)	Parameter Stability
TGAT [ 86 ]	88.14	-12.67	0.318
TGN [ 87 ]	89.51	-9.24	0.285
APAN [ 88 ]	90.74	-7.85	0.241
AdvSynGNN	95.42	-2.31	0.127

Table 6: Incremental learning performance on TGB–Wikipedia

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	$\lVert\widetilde{A}\rVert_{2}$	Acc (%)	$\lVert\widetilde{A}^{\prime}\rVert_{2}$	Acc after clip (%)	$T_{\mathrm{conv}}$
wikiCS [ 77 ]	1.27	81.22	0.980	80.19	18
Chameleon [ 89 ]	1.43	76.73	0.980	76.70	22
Squirrel [ 89 ]	1.51	41.05	0.980	41.02	25

Appendix

Table 7: Impact of spectral clipping on heterophilous graphs. The column

\lVert\widetilde{A}\rVert_{2}

reports the estimated spectral norm prior to clipping. The column

\lVert\widetilde{A}^{\prime}\rVert_{2}

reports the spectral norm after clipping. The quantity

T_{\mathrm{conv}}

denotes the number of residual steps required to reach the convergence tolerance.

Dataset	$\lVert\widetilde{A}\rVert_{2}$	$\max_{i}c_{i}$	$\kappa$	Clip	Steps to conv.	Acc. (%)
wikiCS	1.27	0.95	1.21	No	—	81.22
wikiCS	0.98	0.95	0.93	Yes	18	80.19
Chameleon	1.43	0.92	1.32	No	—	76.73
Chameleon	0.98	0.92	0.90	Yes	22	76.70
Squirrel	1.51	0.94	1.42	No	—	41.05
Squirrel	0.98	0.94	0.92	Yes	25	41.02

Appendix

Table 8: Convergence behaviour versus spectral contraction factor

\kappa

on heterophilous benchmarks. “Clip” denotes whether spectral clipping was applied. The quantity

\kappa

is estimated as

\lVert\widetilde{A}\rVert_{2}\cdot\max_{i}c_{i}

. Divergence is declared when

\lVert R^{(t+1)}-R^{(t)}\rVert_{2}>1

for

t\geq 50

Figure 2: Comparative embedding shifts under hybrid perturbations: (a) Original graph (b) GCN embeddings (c) Graphormer embeddings (d) AdvSynGNN embeddings. Color intensity indicates $\|h_{i}-h_{\text{pert},i}\|_{2}$ magnitude.

Dataset	$\xi_{d}$	$\xi_{f}$	$\xi_{h}$
OGB-Proteins	0.73	1.82 $\pm$ 0.31	0.86
DBLP	0.68	1.45 $\pm$ 0.28	0.79

Appendix

Table 9: Edge modification characteristics (

\delta=10\%

)

Figure 3: t-SNE visualization of GAN-enhanced embeddings

Figure 4: Attention patterns on heterophilous subgraph

Figure 5: Visualization of GAN-induced structural perturbations: original structure and embedding, three perturbation levels and corresponding perturbed embeddings

Dataset	AdvSynGNN			Ablation (w/o GAN)
	PN	PS	$\Delta\mathrm{AUC}\downarrow$	PN	PS	$\Delta\mathrm{AUC}\downarrow$
OGBN-ArXiv	$\mathbf{0.91}$	$\mathbf{0.88}$	$\mathbf{-3.7\%}$	0.52	0.49	$-1.2\%$
OGBN-Products	$\mathbf{0.93}$	$\mathbf{0.90}$	$\mathbf{-4.1\%}$	0.50	0.48	$-1.0\%$
GOOD-Motif [ 28 ]	$\mathbf{0.95}$	$\mathbf{0.92}$	$\mathbf{-5.9\%}$	0.55	0.53	$-1.8\%$

Appendix

Table 10: Causal effect of GAN perturbations. Probability of necessity (PN) and sufficiency (PS) are computed for retaining

\mathcal{E}_{\mathrm{GAN}}

with respect to achieving test AUC within

1\%

of the full model. Counterfactual

\Delta\mathrm{AUC}

is obtained by removing

\mathcal{E}_{\mathrm{GAN}}

via an explicit do intervention. Higher PN/PS and more negative

\Delta\mathrm{AUC}

indicate stronger causal benefit. Bold marks the strongest effect per column.

Figure 6: Wasserstein adversarial losses (smoothed with a 5-epoch moving average) for discriminator and generator during training on OGBN-Proteins.

Figure 7: Per-epoch $\ell_{2}$ gradient norms of the final convolutional block for discriminator and generator. The dashed horizontal line indicates a conservative clipping threshold of $1.0$ .

Figure 8: Edge-flip entropy $\mathcal{H}$ (Eq. 64 ) computed over the candidate edge set across training epochs. Higher values indicate richer perturbation diversity.

Method	$\mathcal{R}_{\text{abs}}$	$\mathcal{R}_{\text{rel}}$
GCN [ 11 ]	27.34	0.38 $\pm$ 0.12
Graphormer [ 61 ]	19.67	0.27 $\pm$ 0.09
AdvSynGNN (w/o GAN)	15.02	0.21 $\pm$ 0.07
AdvSynGNN	8.91	0.13 $\pm$ 0.04

Appendix

Table 11: Embedding consistency metrics

Negative Sampling Strategy	Node Acc (%)	$\Delta$ AUC (pp)
Random negatives only	$85.12\pm 0.23$	$-1.88$
Structure-aware negatives only	$85.90\pm 0.21$	$-1.21$
Mixed (proposed)	$\mathbf{86.40\pm 0.18}$	$\mathbf{0}$

Appendix

Table 12: Comparison of negative sampling strategies on OGBN-Proteins under a 5% hybrid perturbation budget. Reported are node accuracy (%) and changes in AUC (in percentage points) relative to the mixed strategy.

Configuration	Node Acc (%)	$\Delta\mathrm{AUC}$ (pp)	Notes
$\delta=0.05$ (perturbation strength)	$85.92\pm 0.20$	$-1.42$	Weaker perturbation; small drop in robustness.
$\delta=0.10$ (default)	$86.40\pm 0.18$	$0$	Default setting; balances accuracy and robustness.
$\delta=0.20$	$85.71\pm 0.22$	$-1.03$	Stronger perturbation; modest accuracy decrease.
$T=10$ (residual steps)	$85.63\pm 0.24$	$-1.55$	Under-propagation; residuals not fully propagated.
$T=20$ (default)	$86.40\pm 0.18$	$0$	Default setting; sufficient convergence.
$T=50$	$86.38\pm 0.19$	$-0.08$	Marginal improvement; larger compute cost.

Appendix

Table 13: Sensitivity analysis on key hyper-parameters (OGBN-Proteins, 5% hybrid perturbation). Results report mean

\pm

standard deviation over five random seeds.

\Delta\mathrm{AUC}

is reported in percentage points relative to the default configuration

\{\delta=0.10,T=20,\gamma=0.5\}

Module	Time Complexity	Dominant Operation
Multi-scale feature synthesis	$\mathcal{O}\!\bigl(T(N+E)d\bigr)$	sparse propagation with $d$ -dim vectors
Contrastive pretraining	$\mathcal{O}\!\bigl(Nkd\bigr)$	negative sampling and similarity computation
GAN generator	$\mathcal{O}\!\bigl(K(N+E)d_{g}\bigr)$	small edge-MLP and sampling (generator dim $d_{g}$ )
GAN discriminator	$\mathcal{O}\!\bigl(K(N+E)d\bigr)$	message passing on perturbed graphs
Confidence estimator	$\mathcal{O}\!\bigl(Nd\bigr)$	per-node MLP projections
Residual propagation	$\mathcal{O}\!\bigl(T(N+E)d\bigr)$	sparse mat-vec per iteration

Appendix

Table 14: Per-module time complexity in the sparse-graph regime.

Method	Parameters	Time/Epoch (s)	Dataset
Graphormer [ 61 ]	119.5M	563	OGB-Proteins
GraphGPS [ 60 ]	138.1M	480	OGB-Proteins
NodeFormer [ 82 ]	86.0M	5.37	ogbn-papers100M
GraphGPS++ [ 90 ]	138.5M	465	PCQM4Mv2
SGFormer [ 76 ]	113.6M	2.48	ogbn-papers100M
RoofGAN [ 74 ]	127.3M	318	RoofNet

Appendix

Table 15: Resource efficiency comparison on large-scale graph benchmarks

Component	Parameter	Value
GAN Training	Generator learning rate	1e-4
	Discriminator learning rate	1e-4
	Critic steps per generator step ( $n_{c}$ )	5
	Gradient penalty coefficient	10.0
Residual Propagation	Max residual iteration steps ( $T$ )	20
	Confidence ceiling ( $\bar{c}$ )	0.98

Appendix

Table 16: Key hyperparameters for AdvSynGNN. All values apply to both node-level and graph-level tasks unless noted.

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Structure-Feature Aligned Graph Learning via Alternating Constrained Optimization

Chengcheng Yan, Qingsong Wang

College of Artificial Intelligence, Shaoxing Institute of Technology, Shaoxing, 312000, China. · School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China.

Graph Neural Networks Graph Representation Learning Node Classification

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We introduce a constrained two-view framework for node prediction that aligns structure-conditioned GNN embeddings with a structure-free feature prior learned by an anchor model. Conventional Graph Neural Networks (GNNs) couple feature transformation and neighborhood aggregation, which renders them vulnerable to topology noise and heterophilous connections. To decouple this dependency, our framework utilizes an independent anchor network to capture intrinsic attribute features via a self-supervised reconstruction objective. Furthermore, we propose a Channel-Split Adaptive Gated GNN (CSAG-GNN) that dynamically routes representations between global spectral smoothing and local spatial discrimination through a node-wise gating mechanism. We propose a stable cyclic alternating optimization strategy to solve the resulting coupled bi-level objective, preventing mutual representation drift during training. Empirical results on both homophilous and heterophilous benchmarks show balanced performance gains and structural robustness over competitive baselines.

Abstract

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