# Exploring High-Order Structure for Robust Graph Structure Learning

arXiv: https://arxiv.org/abs/2203.11492 · HTML: https://mlsanity.com/paper/2203.11492/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [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)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)
- [A Restricted Black-box Adversarial Framework Towards Attacking Graph Embedding Models](https://mlsanity.com/paper/1908.01297/) (2019)
- [Certifiable Robustness to Graph Perturbations](https://mlsanity.com/paper/1910.14356/) (2019)
- [Certifiable Robustness and Robust Training for Graph Convolutional Networks](https://mlsanity.com/paper/1906.12269/) (2019)
- [Efficient Robustness Certificates for Discrete Data: Sparsity-Aware Randomized Smoothing for Graphs, Images and More](https://mlsanity.com/paper/2008.12952/) (2020)
- [Adversarial Training Methods for Network Embedding](https://mlsanity.com/paper/1908.11514/) (2019)
- [Robustness, Privacy, and Generalization of Adversarial Training](https://mlsanity.com/paper/2012.13573/) (2020)

## Abstract (arXiv)

Recent studies show that Graph Neural Networks (GNNs) are vulnerable to adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs to make wrong predictions. Some researches explore specific properties of clean graphs such as the feature smoothness to defense the attack, but the analysis of it has not been well-studied. In this paper, we analyze the adversarial attack on graphs from the perspective of feature smoothness which further contributes to an efficient new adversarial defensive algorithm for GNNs. We discover that the effect of the high-order graph structure is a smoother filter for processing graph structures. Intuitively, the high-order graph structure denotes the path number between nodes, where larger number indicates closer connection, so it naturally contributes to defense the adversarial perturbation. Further, we propose a novel algorithm that incorporates the high-order structural information into the graph structure learning. We perform experiments on three popular benchmark datasets, Cora, Citeseer and Polblogs. Extensive experiments demonstrate the effectiveness of our method for defending against graph adversarial attacks.