# Node Feature Kernels Increase Graph Convolutional Network Robustness

arXiv: https://arxiv.org/abs/2109.01785 · HTML: https://mlsanity.com/paper/2109.01785/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 4 Sep 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [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)
- [A Random Matrix Approach to Neural Networks](https://mlsanity.com/paper/1702.05419/) (2017)
- [Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks](https://mlsanity.com/paper/2005.11879/) (2020)
- [Coloring graph neural networks for node disambiguation](https://mlsanity.com/paper/1912.06058/) (2019)
- [Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures](https://mlsanity.com/paper/2001.08370/) (2020)
- [Graph Neural Networks: Taxonomy, Advances and Trends](https://mlsanity.com/paper/2012.08752/) (2020)
- [Reliable Graph Neural Networks via Robust Aggregation](https://mlsanity.com/paper/2010.15651/) (2020)
- [Power up! Robust Graph Convolutional Network via Graph Powering](https://mlsanity.com/paper/1905.10029/) (2019)

## Built on by (most cited first, 5 of 5)

- [Graph Neural Networks Use Graphs When They Shouldn't](https://mlsanity.com/paper/2309.04332/) (2023)
- [RDGSL: Dynamic Graph Representation Learning with Structure Learning](https://mlsanity.com/paper/2309.02025/) (2023)
- [Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagation](https://mlsanity.com/paper/2208.09779/) (2022)
- [A Simple and Yet Fairly Effective Defense for Graph Neural Networks](https://mlsanity.com/paper/2402.13987/) (2024)
- [Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks](https://mlsanity.com/paper/2404.17947/) (2024)

## Abstract (arXiv)

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.