# Batch Virtual Adversarial Training for Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1902.09192 · HTML: https://mlsanity.com/paper/1902.09192/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

## Built on by (most cited first, 30 of 33)

- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Local Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2109.03856/) (2021)
- [Model Stealing Attacks Against Inductive Graph Neural Networks](https://mlsanity.com/paper/2112.08331/) (2021)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Are Defenses for Graph Neural Networks Robust?](https://mlsanity.com/paper/2301.13694/) (2023)
- [Tree Decomposed Graph Neural Network](https://mlsanity.com/paper/2108.11022/) (2021)
- [Metropolis-Hastings Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2203.14082/) (2022)
- [Adversarial Training for Graph Neural Networks: Pitfalls, Solutions, and New Directions](https://mlsanity.com/paper/2306.15427/) (2023)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Defending Graph Convolutional Networks against Dynamic Graph Perturbations via Bayesian Self-supervision](https://mlsanity.com/paper/2203.03762/) (2022)
- [CAP: Co-Adversarial Perturbation on Weights and Features for Improving Generalization of Graph Neural Networks](https://mlsanity.com/paper/2110.14855/) (2021)
- [Adaptive Kernel Graph Neural Network](https://mlsanity.com/paper/2112.04575/) (2021)
- [NOSMOG: Learning Noise-robust and Structure-aware MLPs on Graphs](https://mlsanity.com/paper/2208.10010/) (2022)
- [Spectral Adversarial Training for Robust Graph Neural Network](https://mlsanity.com/paper/2211.10896/) (2022)
- [SCR: Training Graph Neural Networks with Consistency Regularization](https://mlsanity.com/paper/2112.04319/) (2021)
- [Understanding and Improvement of Adversarial Training for Network Embedding from an Optimization Perspective](https://mlsanity.com/paper/2105.08007/) (2021)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)
- [Calibrating and Improving Graph Contrastive Learning](https://mlsanity.com/paper/2101.11525/) (2021)
- [EDoG: Adversarial Edge Detection For Graph Neural Networks](https://mlsanity.com/paper/2212.13607/) (2022)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [On Generalization of Graph Autoencoders with Adversarial Training](https://mlsanity.com/paper/2107.02658/) (2021)
- [Network representation learning: A macro and micro view](https://mlsanity.com/paper/2111.10772/) (2021)
- [LEReg: Empower Graph Neural Networks with Local Energy Regularization](https://mlsanity.com/paper/2203.10565/) (2022)
- [Context-based Virtual Adversarial Training for Text Classification with Noisy Labels](https://mlsanity.com/paper/2206.11851/) (2022)
- [Distributional Signals for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2304.03507/) (2023)
- [Understanding the Robustness of Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2406.13920/) (2024)
- [Adversarial Training for Graph Neural Networks via Graph Subspace Energy Optimization](https://mlsanity.com/paper/2412.18886/) (2024)

## Abstract (arXiv)

We present batch virtual adversarial training (BVAT), a novel regularization method for graph convolutional networks (GCNs). BVAT addresses the shortcoming of GCNs that do not consider the smoothness of the model's output distribution against local perturbations around the input. We propose two algorithms, sample-based BVAT and optimization-based BVAT, which are suitable to promote the smoothness of the model for graph-structured data by either finding virtual adversarial perturbations for a subset of nodes far from each other or generating virtual adversarial perturbations for all nodes with an optimization process. Extensive experiments on three citation network datasets Cora, Citeseer and Pubmed and a knowledge graph dataset Nell validate the effectiveness of the proposed method, which establishes state-of-the-art results in the semi-supervised node classification tasks.