# Topology-Aware Gaussian Graph Repair for Robust Graph Neural Networks

arXiv: https://arxiv.org/abs/2606.03462 · HTML: https://mlsanity.com/paper/2606.03462/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 13 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Towards Robust Graph Neural Networks for Noisy Graphs with Sparse Labels](https://mlsanity.com/paper/2201.00232/) (2022)
- [Graph-Revised Convolutional Network](https://mlsanity.com/paper/1911.07123/) (2019)

## Abstract (arXiv)

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.