# Fixed-point graph convolutional networks against adversarial attacks

arXiv: https://arxiv.org/abs/2511.00083 · HTML: https://mlsanity.com/paper/2511.00083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Hiding Individuals and Communities in a Social Network](https://mlsanity.com/paper/1608.00375/) (2016)
- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)
- [Reliable Graph Neural Networks via Robust Aggregation](https://mlsanity.com/paper/2010.15651/) (2020)
- [EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks](https://mlsanity.com/paper/2205.13892/) (2022)
- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [Robust Mid-Pass Filtering Graph Convolutional Networks](https://mlsanity.com/paper/2302.08048/) (2023)
- [Illuminati: Towards Explaining Graph Neural Networks for Cybersecurity Analysis](https://mlsanity.com/paper/2303.14836/) (2023)
- [Efficient Low-Rank GNN Defense Against Structural Attacks](https://mlsanity.com/paper/2309.10136/) (2023)

## Abstract (arXiv)

Adversarial attacks present a significant risk to the integrity and performance of graph neural networks, particularly in tasks where graph structure and node features are vulnerable to manipulation. In this paper, we present a novel model, called fixed-point iterative graph convolutional network (Fix-GCN), which achieves robustness against adversarial perturbations by effectively capturing higher-order node neighborhood information in the graph without additional memory or computational complexity. Specifically, we introduce a versatile spectral modulation filter and derive the feature propagation rule of our model using fixed-point iteration. Unlike traditional defense mechanisms that rely on additional design elements to counteract attacks, the proposed graph filter provides a flexible-pass filtering approach, allowing it to selectively attenuate high-frequency components while preserving low-frequency structural information in the graph signal. By iteratively updating node representations, our model offers a flexible and efficient framework for preserving essential graph information while mitigating the impact of adversarial manipulation. We demonstrate the effectiveness of the proposed model through extensive experiments on various benchmark graph datasets, showcasing its resilience against adversarial attacks.