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TAGR offers a lightweight solution for enhancing Graph Neural Network robustness by repairing imperfect graph topologies without requiring architectural changes. The method combines sparse feature-based edge generation with residual correction to handle both noisy and missing connections effectively. This approach prioritizes computational efficiency and stability over complex dense structure learning, making it practical for real-world applications with imperfect data.
Topology-Aware Gaussian Graph Repair for Robust Graph Neural Networks
arXiv:2606.03462v1 Announce Type: new Abstract: Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.
Abstract:Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.
Machine Learning (cs.LG); Social and Information Networks (cs.SI)
arXiv:2606.03462 [cs.LG]
(or arXiv:2606.03462v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.03462 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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