Title: Enhancing Graph Neural Network Resilience via Topology-Aware Gaussian Graph Repair

Graph neural networks (GNNs) have demonstrated significant efficacy in processing graph-structured data; however, their performance is intrinsically tied to the integrity of the underlying graph topology. In practical scenarios, observed graphs are frequently flawed, characterized by noisy edges linking unrelated nodes or the absence of critical edges that hinders effective information propagation. While current robust graph learning approaches typically tackle these issues by either discarding questionable edges or deriving new graph structures during the training phase, these methods have notable limitations. Specifically, simply removing edges fails to restore lost connections, and learning a new graph structure can impose substantial optimization burdens.

To address these challenges, this study introduces Topology-Aware Gaussian Repair (TAGR), a streamlined framework designed to facilitate robust message passing within GNNs. Unlike methods that rely on learning dense adjacency matrices, TAGR generates a sparse feature-neighborhood graph through an adaptive Gaussian kernel. This component is integrated with a topology-aware residual correction mechanism that adjusts the original observed graph based on local structural and feature consistency. The Gaussian repair aspect adds auxiliary links between nodes with similar features, whereas the residual correction ensures the preservation and appropriate reweighting of the initial topology. Importantly, the resulting repaired graph is compatible with standard GNN architectures, requiring no modifications to the models themselves.

Comprehensive evaluations on benchmark citation networks indicate that TAGR significantly boosts GNN robustness in environments with both noisy and missing edges. Further analysis reveals that the primary improvement in robustness stems from the Gaussian feature-neighborhood repair, while the topology-aware residual correction enhances stability particularly when the observed graph suffers from incompleteness. These findings imply that lightweight sparse graph repair offers a more effective path to robustness compared to the complexity of dense graph structure learning.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC