# Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach

arXiv: https://arxiv.org/abs/2310.06396 · HTML: https://mlsanity.com/paper/2310.06396/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 93 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [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)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)

## Built on by (most cited first, 24 of 24)

- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Can Large Language Models Improve the Adversarial Robustness of Graph Neural Networks?](https://mlsanity.com/paper/2408.08685/) (2024)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)
- [Distributed-Order Fractional Graph Operating Network](https://mlsanity.com/paper/2411.05274/) (2024)
- [PointDifformer: Robust Point Cloud Registration With Neural Diffusion and Transformer](https://mlsanity.com/paper/2404.14034/) (2024)
- [SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds](https://mlsanity.com/paper/2402.08653/) (2024)
- [Symplectic Neural Flows for Modeling and Discovery](https://mlsanity.com/paper/2412.16787/) (2024)
- [PosDiffNet: Positional Neural Diffusion for Point Cloud Registration in a Large Field of View with Perturbations](https://mlsanity.com/paper/2401.03167/) (2024)
- [Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphs](https://mlsanity.com/paper/2406.03097/) (2024)
- [Bridging Large Language Models and Graph Structure Learning Models for Robust Representation Learning](https://mlsanity.com/paper/2410.12096/) (2024)
- [PRFusion: Toward Effective and Robust Multi-Modal Place Recognition with Image and Point Cloud Fusion](https://mlsanity.com/paper/2410.04939/) (2024)
- [Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach](https://mlsanity.com/paper/2311.06942/) (2023)
- [Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium](https://mlsanity.com/paper/2505.14463/) (2025)
- [A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data](https://mlsanity.com/paper/2511.13514/) (2025)
- [Adversarial Robustness of Link Sign Prediction in Signed Graphs](https://mlsanity.com/paper/2401.10590/) (2024)
- [Graph Adversarial Diffusion Convolution](https://mlsanity.com/paper/2406.02059/) (2024)
- [Information propagation dynamics in Deep Graph Networks](https://mlsanity.com/paper/2410.10464/) (2024)
- [Improving Adversarial Robustness via Phase and Amplitude-aware Prompting](https://mlsanity.com/paper/2502.03758/) (2025)
- [JANUS: A Dual-Constraint Generative Framework for Stealthy Node Injection Attacks](https://mlsanity.com/paper/2509.13266/) (2025)
- [Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustness](https://mlsanity.com/paper/2509.21879/) (2025)
- [Lyapunov Stable Graph Neural Flow](https://mlsanity.com/paper/2603.12557/) (2026)
- [TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglement](https://mlsanity.com/paper/2604.15370/) (2026)
- [Let Prompts Bridge Defense Knowledge: Transferable Graph Purification via Vulnerability-Aware GPL](https://mlsanity.com/paper/2608.29054/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at https://github.com/zknus/NeurIPS-2023-HANG-Robustness.