# Power up! Robust Graph Convolutional Network via Graph Powering

arXiv: https://arxiv.org/abs/1905.10029 · HTML: https://mlsanity.com/paper/1905.10029/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 15 of 15)

- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [threaTrace: Detecting and Tracing Host-based Threats in Node Level Through Provenance Graph Learning](https://mlsanity.com/paper/2111.04333/) (2021)
- [AutoGL: A Library for Automated Graph Learning](https://mlsanity.com/paper/2104.04987/) (2021)
- [Knowledge Graph Completion with Counterfactual Augmentation](https://mlsanity.com/paper/2302.13083/) (2023)
- [Graph Convolutional Networks with Dual Message Passing for Subgraph Isomorphism Counting and Matching](https://mlsanity.com/paper/2112.08764/) (2021)
- [Adversarial Attack Framework on Graph Embedding Models with Limited Knowledge](https://mlsanity.com/paper/2105.12419/) (2021)
- [Graph Augmentation Learning](https://mlsanity.com/paper/2203.09020/) (2022)
- [Adversarially Robust Neural Architecture Search for Graph Neural Networks](https://mlsanity.com/paper/2304.04168/) (2023)
- [AGNN: Alternating Graph-Regularized Neural Networks to Alleviate Over-Smoothing](https://mlsanity.com/paper/2304.07014/) (2023)
- [Node Feature Kernels Increase Graph Convolutional Network Robustness](https://mlsanity.com/paper/2109.01785/) (2021)
- [Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification](https://mlsanity.com/paper/2101.09306/) (2021)
- [Towards Lightweight Graph Neural Network Search with Curriculum Graph Sparsification](https://mlsanity.com/paper/2406.16357/) (2024)
- [Resisting Graph Adversarial Attack via Cooperative Homophilous Augmentation](https://mlsanity.com/paper/2211.08068/) (2022)
- [T- Hop: Tensor representation of paths in graph convolutional networks](https://mlsanity.com/paper/2204.04983/) (2022)
- [T- Hop: A framework for studying the importance path information in molecular graphs for chemical property prediction](https://mlsanity.com/paper/2407.14270/) (2024)

## Abstract (arXiv)

Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. By challenging the classical graph Laplacian, we propose a new convolution operator that is provably robust in the spectral domain and is incorporated in the GCN architecture to improve expressivity and interpretability. By extending the original graph to a sequence of graphs, we also propose a robust training paradigm that encourages transferability across graphs that span a range of spatial and spectral characteristics. The proposed approaches are demonstrated in extensive experiments to simultaneously improve performance in both benign and adversarial situations.