# Efficient Low-Rank GNN Defense Against Structural Attacks

arXiv: https://arxiv.org/abs/2309.10136 · HTML: https://mlsanity.com/paper/2309.10136/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Predicting multicellular function through multi-layer tissue networks](https://mlsanity.com/paper/1707.04638/) (2017)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)

## Built on by (most cited first, 2 of 2)

- [Diffusion on Graph: Augmentation of Graph Structure for Node Classification](https://mlsanity.com/paper/2503.12563/) (2025)
- [Fixed-point graph convolutional networks against adversarial attacks](https://mlsanity.com/paper/2511.00083/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have been shown to possess strong representation abilities over graph data. However, GNNs are vulnerable to adversarial attacks, and even minor perturbations to the graph structure can significantly degrade their performance. Existing methods either are ineffective against sophisticated attacks or require the optimization of dense adjacency matrices, which is time-consuming and prone to local minima. To remedy this problem, we propose an Efficient Low-Rank Graph Neural Network (ELR-GNN) defense method, which aims to learn low-rank and sparse graph structures for defending against adversarial attacks, ensuring effective defense with greater efficiency. Specifically, ELR-GNN consists of two modules: a Coarse Low-Rank Estimation Module and a Fine-Grained Estimation Module. The first module adopts the truncated Singular Value Decomposition (SVD) to initialize the low-rank adjacency matrix estimation, which serves as a starting point for optimizing the low-rank matrix. In the second module, the initial estimate is refined by jointly learning a low-rank sparse graph structure with the GNN model. Sparsity is incorporated into the learned low-rank adjacency matrix by pruning weak connections, which can reduce redundant data while maintaining valuable information. As a result, instead of using the dense adjacency matrix directly, ELR-GNN can learn a low-rank and sparse estimate of it in a simple, efficient and easy to optimize manner. The experimental results demonstrate that ELR-GNN outperforms the state-of-the-art GNN defense methods in the literature, in addition to being very efficient and easy to train.