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

TL;DR

This work presents AdvSynGNN, a comprehensive architecture designed for resilient node-level representation learning that orchestrates multi-resolution structural synthesis alongside contrastive objectives to establish geometry-sensitive initializations and develops a transformer backbone that adaptively accommodates heterophily through learned topological signals.

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 (8)

• 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 $\widetilde{A}'$. 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.
• 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.
• 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

Theorems & Definitions (8)

• Theorem B.1: Residual convergence
• proof
• Lemma B.2: Spectral clipping with confidence ceiling
• proof
• Theorem C.1: Convergence under Spectral Clipping
• proof
• Proposition E.1: Adversarial perturbations induce sensitivity control and uniformity regularization
• proof