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Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…

Discrete Mathematics · Computer Science 2024-03-26 Lucia Testa , Stefania Sardellitti , Sergio Barbarossa

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…

Machine Learning · Computer Science 2022-05-20 Max Wasserman , Saurabh Sihag , Gonzalo Mateos , Alejandro Ribeiro

Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian…

Machine Learning · Computer Science 2018-02-07 Federico Monti , Karl Otness , Michael M. Bronstein

While the advent of Graph Neural Networks (GNNs) has greatly improved node and graph representation learning in many applications, the neighborhood aggregation scheme exposes additional vulnerabilities to adversaries seeking to extract…

Machine Learning · Computer Science 2021-06-15 Peiyuan Liao , Han Zhao , Keyulu Xu , Tommi Jaakkola , Geoffrey Gordon , Stefanie Jegelka , Ruslan Salakhutdinov

Despite its success in the image domain, adversarial training did not (yet) stand out as an effective defense for Graph Neural Networks (GNNs) against graph structure perturbations. In the pursuit of fixing adversarial training (1) we show…

Machine Learning · Computer Science 2023-12-05 Lukas Gosch , Simon Geisler , Daniel Sturm , Bertrand Charpentier , Daniel Zügner , Stephan Günnemann

Graph convolutional networks are becoming indispensable for deep learning from graph-structured data. Most of the existing graph convolutional networks share two big shortcomings. First, they are essentially low-pass filters, thus the…

Machine Learning · Computer Science 2022-06-23 Zonghan Wu , Shirui Pan , Guodong Long , Jing Jiang , Chengqi Zhang

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…

Machine Learning · Statistics 2020-05-14 Abram Magner , Mayank Baranwal , Alfred O. Hero

Spectral Graph Neural Networks (GNNs) with various graph filters have received extensive affirmation due to their promising performance in graph learning problems. However, it is known that GNNs do not always perform well. Although graph…

Machine Learning · Computer Science 2022-02-18 Zhixian Chen , Tengfei Ma , Yang Wang

Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include…

Machine Learning · Computer Science 2021-01-29 Dominik Alfke , Martin Stoll

Deep neural networks (DNNs) are becoming commonplace in critical applications, making their susceptibility to backdoor (trojan) attacks a significant problem. In this paper, we introduce a novel backdoor attack detection pipeline, detecting…

Computer Vision and Pattern Recognition · Computer Science 2025-02-27 Akash Vartak , Khondoker Murad Hossain , Tim Oates

Graph convolution networks (GCNs) are extensively utilized in various graph tasks to mine knowledge from spatial data. Our study marks the pioneering attempt to quantitatively investigate the GCN robustness over omnipresent heterophilic…

Machine Learning · Computer Science 2023-12-29 Chenyang Qiu , Guoshun Nan , Tianyu Xiong , Wendi Deng , Di Wang , Zhiyang Teng , Lijuan Sun , Qimei Cui , Xiaofeng Tao

Graph condensation has recently emerged as a prevalent technique to improve the training efficiency for graph neural networks (GNNs). It condenses a large graph into a small one such that a GNN trained on this small synthetic graph can…

Machine Learning · Computer Science 2025-04-01 Jiahao Wu , Ning Lu , Zeiyu Dai , Kun Wang , Wenqi Fan , Shengcai Liu , Qing Li , Ke Tang

Graph neural networks (GNNs) have achieved remarkable success in various domains, yet they often struggle with domain adaptation due to significant structural distribution shifts and insufficient exploration of transferable patterns. One of…

Machine Learning · Computer Science 2025-10-16 Haoyu Zhang , Yuxuan Cheng , Wenqi Fan , Yulong Chen , Yifan Zhang

Graph neural networks (GNNs) have recently been shown to be vulnerable to adversarial attacks, where slight perturbations in the graph structure can lead to erroneous predictions. However, current robust models for defending against such…

Machine Learning · Computer Science 2023-12-15 Ao Liu , Wenshan Li , Tao Li , Beibei Li , Hanyuan Huang , Pan Zhou

Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…

Machine Learning · Computer Science 2020-12-23 Jia Li , Tomas Yu , Da-Cheng Juan , Arjun Gopalan , Hong Cheng , Andrew Tomkins

Deep learning on graph structures has shown exciting results in various applications. However, few attentions have been paid to the robustness of such models, in contrast to numerous research work for image or text adversarial attack and…

Machine Learning · Computer Science 2018-06-08 Hanjun Dai , Hui Li , Tian Tian , Xin Huang , Lin Wang , Jun Zhu , Le Song

Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph…

Machine Learning · Computer Science 2020-04-30 Zekun Tong , Yuxuan Liang , Changsheng Sun , David S. Rosenblum , Andrew Lim

Graph Neural Networks (GNNs) have demonstrated commendable performance for graph-structured data. Yet, GNNs are often vulnerable to adversarial structural attacks as embedding generation relies on graph topology. Existing efforts are…

Machine Learning · Computer Science 2024-09-04 Xing Ai , Guanyu Zhu , Yulin Zhu , Yu Zheng , Gaolei Li , Jianhua Li , Kai Zhou

This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…

Signal Processing · Electrical Eng. & Systems 2025-03-18 Kaito Nitani , Seisuke Kyochi

Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to…

Computer Vision and Pattern Recognition · Computer Science 2021-12-08 Hichem Sahbi