# TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglement

arXiv: https://arxiv.org/abs/2604.15370 · HTML: https://mlsanity.com/paper/2604.15370/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## 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)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (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)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Stealing Links from Graph Neural Networks](https://mlsanity.com/paper/2005.02131/) (2020)
- [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)
- [Epidemic processes in complex networks](https://mlsanity.com/paper/1408.2701/) (2014)
- [Attacking Graph-based Classification via Manipulating the Graph Structure](https://mlsanity.com/paper/1903.00553/) (2019)
- [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)
- [MDGNN: Multi-Relational Dynamic Graph Neural Network for Comprehensive and Dynamic Stock Investment Prediction](https://mlsanity.com/paper/2402.06633/) (2024)
- [Robust Mid-Pass Filtering Graph Convolutional Networks](https://mlsanity.com/paper/2302.08048/) (2023)
- [Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium](https://mlsanity.com/paper/2505.14463/) (2025)

## Abstract (arXiv)

Graph adversarial attacks are usually produced from the two perspectives of topology/structure and node feature, both of them represent the paramount characteristics learned by today's deep learning models. Although some defense countermeasures are proposed at present, they fails to disclose the intrinsic reasons why these two aspects necessitate and how they are adequately fused to co-learn the graph representation. Towards this question, we in this paper propose an adversarial defense approach through locating the graph's critical state of adversarial resilience, resorting to the equilibrium-point theory in the discipline of complex dynamic system (CDS). In brief, our work has three novelties: i) Adversarial-Attack Modeling, i.e. map a graph regime into CDS, and use the oscillation of dynamic system to model the behavior of adversarial perturbation; ii) 2D Topology-Feature-Entangled Function Design for Perturbed Graph, i.e. project graph topology and node feature as two characteristic spaces, and define two-dimensional entangled perturbation functions to represent the dynamic variance under adversarial attacks; and iii) Location of Critical State of Adversarial Resilience, i.e. utilize the equilibrium-point theory to locate the graph's critical state of attack resilience resorting to the perturbation-reflected 2D function. Finally, multi-facet experiments on five commonly-used realistic datasets validate the effectiveness of our proposed approach, and the results show our approach can significantly outperform the state-of-the-art baselines under four representative graph adversarial attacks.