# Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium

arXiv: https://arxiv.org/abs/2505.14463 · HTML: https://mlsanity.com/paper/2505.14463/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Stealing Links from Graph Neural Networks](https://mlsanity.com/paper/2005.02131/) (2020)
- [Adversarial Attacks on Node Embeddings via Graph Poisoning](https://mlsanity.com/paper/1809.01093/) (2018)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Hiding Individuals and Communities in a Social Network](https://mlsanity.com/paper/1608.00375/) (2016)
- [TDGIA:Effective Injection Attacks on Graph Neural Networks](https://mlsanity.com/paper/2106.06663/) (2021)
- [Attacking Graph-based Classification via Manipulating the Graph Structure](https://mlsanity.com/paper/1903.00553/) (2019)
- [Scalable Attack on Graph Data by Injecting Vicious Nodes](https://mlsanity.com/paper/2004.13825/) (2020)
- [A Unified Framework for Data Poisoning Attack to Graph-based Semi-supervised Learning](https://mlsanity.com/paper/1910.14147/) (2019)
- [Inductive Graph Unlearning](https://mlsanity.com/paper/2304.03093/) (2023)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [A Hard Label Black-box Adversarial Attack Against Graph Neural Networks](https://mlsanity.com/paper/2108.09513/) (2021)
- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
- [Group Property Inference Attacks Against Graph Neural Networks](https://mlsanity.com/paper/2209.01100/) (2022)
- [Robust Mid-Pass Filtering Graph Convolutional Networks](https://mlsanity.com/paper/2302.08048/) (2023)

## Built on by (most cited first, 1 of 1)

- [TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglement](https://mlsanity.com/paper/2604.15370/) (2026)

## Abstract (arXiv)

Adversarial attacks to graph analytics are gaining increased attention. To date, two lines of countermeasures have been proposed to resist various graph adversarial attacks from the perspectives of either graph per se or graph neural networks. Nevertheless, a fundamental question lies in whether there exists an intrinsic adversarial resilience state within a graph regime and how to find out such a critical state if exists. This paper contributes to tackle the above research questions from three unique perspectives: i) we regard the process of adversarial learning on graph as a complex multi-object dynamic system, and model the behavior of adversarial attack; ii) we propose a generalized theoretical framework to show the existence of critical adversarial resilience state; and iii) we develop a condensed one-dimensional function to capture the dynamic variation of graph regime under perturbations, and pinpoint the critical state through solving the equilibrium point of dynamic system. Multi-facet experiments are conducted to show our proposed approach can significantly outperform the state-of-the-art defense methods under five commonly-used real-world datasets and three representative attacks.