# Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attacks

arXiv: https://arxiv.org/abs/2407.10867 · HTML: https://mlsanity.com/paper/2407.10867/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 99 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 30 of 73)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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 Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Certified Defenses for Data Poisoning Attacks](https://mlsanity.com/paper/1706.03691/) (2017)
- [Poisoning Web-Scale Training Datasets is Practical](https://mlsanity.com/paper/2302.10149/) (2023)
- [Poisoning Language Models During Instruction Tuning](https://mlsanity.com/paper/2305.00944/) (2023)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning](https://mlsanity.com/paper/1804.00308/) (2018)
- [Towards Poisoning of Deep Learning Algorithms with Back-gradient Optimization](https://mlsanity.com/paper/1708.08689/) (2017)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses](https://mlsanity.com/paper/2012.10544/) (2020)
- [Witches' Brew: Industrial Scale Data Poisoning via Gradient Matching](https://mlsanity.com/paper/2009.02276/) (2020)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [On the linearity of large non-linear models: when and why the tangent kernel is constant](https://mlsanity.com/paper/2010.01092/) (2020)
- [Adversarial Machine Learning -- Industry Perspectives](https://mlsanity.com/paper/2002.05646/) (2020)
- [MetaPoison: Practical General-purpose Clean-label Data Poisoning](https://mlsanity.com/paper/2004.00225/) (2020)
- [RAB: Provable Robustness Against Backdoor Attacks](https://mlsanity.com/paper/2003.08904/) (2020)

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

- [Exact Certification of (Graph) Neural Networks Against Label Poisoning](https://mlsanity.com/paper/2412.00537/) (2024)
- [UTrace: Poisoning Forensics for Private Collaborative Learning](https://mlsanity.com/paper/2409.15126/) (2024)
- [Robustness Certificates for Neural Networks Against Data Poisoning and Evasion Attacks](https://mlsanity.com/paper/2512.20865/) (2025)
- [Exact Certification of Neural Networks and Partition Aggregation Ensembles against Label Poisoning](https://mlsanity.com/paper/2604.11416/) (2026)
- [Large Language Models in Misinformation Ecosystems: Misuse, Defense, and Vulnerability](https://mlsanity.com/paper/2607.10402/) (2026)

## Abstract (arXiv)

Generalization of machine learning models can be severely compromised by data poisoning, where adversarial changes are applied to the training data. This vulnerability has led to interest in certifying (i.e., proving) that such changes up to a certain magnitude do not affect test predictions. We, for the first time, certify Graph Neural Networks (GNNs) against poisoning attacks, including backdoors, targeting the node features of a given graph. Our certificates are white-box and based upon (i) the neural tangent kernel, which characterizes the training dynamics of sufficiently wide networks; and (ii) a novel reformulation of the bilevel optimization problem describing poisoning as a mixed-integer linear program. Consequently, we leverage our framework to provide fundamental insights into the role of graph structure and its connectivity on the worst-case robustness behavior of convolution-based and PageRank-based GNNs. We note that our framework is more general and constitutes the first approach to derive white-box poisoning certificates for NNs, which can be of independent interest beyond graph-related tasks.