# Robust Mid-Pass Filtering Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2302.08048 · HTML: https://mlsanity.com/paper/2302.08048/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (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)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)
- [Certifiable Robustness and Robust Training for Graph Convolutional Networks](https://mlsanity.com/paper/1906.12269/) (2019)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learning](https://mlsanity.com/paper/2111.04314/) (2021)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [Attacking Graph Convolutional Networks via Rewiring](https://mlsanity.com/paper/1906.03750/) (2019)
- [A Unified Framework for Data Poisoning Attack to Graph-based Semi-supervised Learning](https://mlsanity.com/paper/1910.14147/) (2019)

## Built on by (most cited first, 17 of 17)

- [Can Large Language Models Improve the Adversarial Robustness of Graph Neural Networks?](https://mlsanity.com/paper/2408.08685/) (2024)
- [ConeSep: Cone-based Robust Noise-Unlearning Compositional Network for Composed Image Retrieval](https://mlsanity.com/paper/2604.20358/) (2026)
- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [Homophily Enhanced Graph Domain Adaptation](https://mlsanity.com/paper/2505.20089/) (2025)
- [Understanding and Mitigating Under-Confidence in GNNs from the Final Layer](https://mlsanity.com/paper/2505.11335/) (2025)
- [Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attention](https://mlsanity.com/paper/2305.13115/) (2023)
- [Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks](https://mlsanity.com/paper/2411.02279/) (2024)
- [Talos: A More Effective and Efficient Adversarial Defense for GNN Models Based on the Global Homophily of Graphs](https://mlsanity.com/paper/2406.03833/) (2024)
- [Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks](https://mlsanity.com/paper/2302.08727/) (2023)
- [Unsupervised Episode Generation for Graph Meta-learning](https://mlsanity.com/paper/2306.15217/) (2023)
- [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)
- [Fixed-point graph convolutional networks against adversarial attacks](https://mlsanity.com/paper/2511.00083/) (2025)
- [TopFeaRe: Locating Critical State of Adversarial Resilience for Graphs Regarding Topology-Feature Entanglement](https://mlsanity.com/paper/2604.15370/) (2026)
- [NK-GAD: Neighbor Knowledge-Enhanced Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2604.15668/) (2026)
- [Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2606.24956/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.