Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to transfer spectral filters between graphs of variable size and topology. This misbelief has limited the development of spectral networks for multi-graph tasks in favor of spatial graph networks. However, recent works have proved the stability of spectral filters under graph perturbation. Our work complements and emphasizes further the high quality of spectral transferability by benchmarking spectral graph networks on tasks involving graphs of different size and connectivity. Numerical experiments exhibit favorable performance on graph regression, graph classification, and node classification problems on two graph benchmarks. The implementation of our experiments is available on GitHub for reproducibility.
University of Pennsylvania（宾夕法尼亚大学）；Dept. of Electrical and Systems Eng.（电气与系统工程系）；Philadelphia, PA 19143（费城，PA 19143）
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound v…
LMU Munich（慕尼黑大学）；Technion - Israel Institute of Technology（以色列理工学院）；University of Tromsø（特罗姆瑟大学）
We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be transferred between different graphs. It is hence important to study the GCNN transferability: the capacity of the network to have approximately the same repercussion on different graphs that represent the same phenomenon. Transferability ensures that GCNNs trained on certain graphs generalize if the graphs in the test set represent the same phenomena as th…
University of Pennsylvania（宾夕法尼亚大学）；Duke University（杜克大学）
We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs), which we call a Hyper-graph Expansion Neural Network (HENN), and provide the first bounds on the stability and transferability error of a hypergraph signal processing model. To do so, we provide a framework for bounding the stability and transferability error of GNNs across arbitrary graphs via spectral similarity. By bounding the difference between two graph shift operators (GSOs) in the positive semi-definite sense via their eigenvalue spectrum, we show that this error depends only …
Ludwig Maximilian University of Munich（慕尼黑路德维希-马克西米利安大学）；Università della Svizzera italiana（瑞士意大利语区大学）；University of Tromsø（特罗姆瑟大学）；Imperial College London（伦敦帝国理工学院）；Twitter（推特）
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signals on graphs unseen in the training set. It is thus important to transfer ConvNets between graphs. Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter or ConvNet s…
Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed with pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and stability to graph deformations. These properties help explain the good performance of GNNs that can be obs…
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the dataset consists of signals defined on many different graphs, and the learned filters should generalize to signals on new graphs, not present in the training set. A necessary condition for transferability (the ability to transfer filters) is stability. Namely, given a graph filt…
The Transferability of Downsamped Sparse Graph Convolutional Networks
School of Information Science and Technology, Fudan University（复旦大学信息科学与技术学院）；State Key Laboratory of Integrated Chips and Systems, Fudan University（复旦大学集成芯片与系统国家重点实验室）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）
University of Bonn（波恩大学）；Fraunhofer Institute for Intelligent Analysis and Information Systems (IAIS)（弗劳恩霍夫智能分析与信息系统研究所（IAIS））；Fraunhofer Institute for Algorithms and Scientific Computing (SCAI)（弗劳恩霍夫算法与科学计算研究所（SCAI））
There is an emerging trend of embedding knowledge graphs (KGs) in continuous vector spaces in order to use those for machine learning tasks. Recently, many knowledge graph embedding (KGE) models have been proposed that learn low dimensional representations while trying to maintain the structural properties of the KGs such as the similarity of nodes depending on their edges to other nodes. KGEs can be used to address tasks within KGs such as the prediction of novel links and the disambiguation of entities. They can also be used for downstream tasks like question answering and fact-checking. Ove…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；USDA ARS Global Change and Photosynthesis Research Unit（美国农业部农业研究局全球变化与光合作用研究单位）
Transfer learning refers to the transfer of knowledge or information from a relevant source domain to a target domain. However, most existing transfer learning theories and algorithms focus on IID tasks, where the source/target samples are assumed to be independent and identically distributed. Very little effort is devoted to theoretically studying the knowledge transferability on non-IID tasks, e.g., cross-network mining. To bridge the gap, in this paper, we propose rigorous generalization bounds and algorithms for cross-network transfer learning from a source graph to a target graph. The cru…
On Transferring Transferability: Towards a Theory for Size Generalization
Department of Computing and Mathematical Sciences, Caltech（加州理工学院计算与数学科学系）；Department of Applied Mathematics and Statistics and the Mathematical Institute for Data Science, Johns Hopkins University（约翰霍普金斯大学应用数学与统计学系及数据科学数学研究所）
LLM as GNN: Graph Vocabulary Learning for Text-Attributed Graph Foundation Models
Rutgers University（罗格斯大学）；Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（穆罕默德·本·扎耶德人工智能大学）；University of Science and Technology of China（中国科学技术大学）；Meta AI；North Carolina State University（北卡罗来纳州立大学）
Limit Analysis of Graph Neural Networks with Wireless Conflict Graphs
Department of Electrical and Systems Engineering, University of Pennsylvania（宾夕法尼亚大学电气与系统工程系）；Halıcıoğlu Data Science Institute, UCSD（加州大学圣地亚哥分校Halıcıoğlu数据科学研究所）
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Emory University（埃默里大学）；University of Washington（华盛顿大学）；Georgia Institute of Technology（佐治亚理工学院）
Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as …
University of the Witwatersrand（金山大学）；University of Johannesburg（约翰内斯堡大学）
Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and sy…
Understanding the Robustness of Graph Neural Networks against Adversarial Attacks
School of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院）；School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications（重庆邮电大学网络安全与信息法学院）；School of Software Engineering, Chengdu University of Information Technology（成都信息科技学院软件工程学院）；School of Computer and Information Science, Chongqing Normal University（重庆师范大学计算机与信息科学学院）；School of Computer Science, University of Technology Sydney（悉尼大学计算机科学学院）
Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, the present work introduces a new framework, hydrodynamic interaction graph neural network (HIGNN), for inferring and predicting the particles' dynamics in Stokes suspensions. It overcomes the limitations of traditional approaches in computational efficiency, accuracy, and/or transferability. In particular, by uniting the data structure represented by a graph and the neural networks with l…
Sampling Transferable Graph Neural Networks with Limited Graph Information
Department of Applied Mathematics and Statistics, Johns Hopkins University（应用数学与统计学系，约翰霍普金斯大学）；Department of Statistics and Data Science, Yale University（统计与数据科学系，耶鲁大学）；Department of Electrical and Computer Engineering, University of Rochester（电气与计算机工程系，罗切斯特大学）
We apply a temporal edge prediction model for weighted dynamic graphs to predict time-dependent changes in molecular structure. Each molecule is represented as a complete graph in which each atom is a vertex and all vertex pairs are connected by an edge weighted by the Euclidean distance between atom pairs. We ingest a sequence of complete molecular graphs into a dynamic graph neural network (GNN) to predict the graph at the next time step. Our dynamic GNN predicts atom-to-atom distances with a mean absolute error of 0.017 Å, which is considered ``chemically accurate'' for molecular simulation…
LITIS Lab（LITIS实验室）；University of Rouen Normandy（鲁昂诺曼底大学）
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain…
Zhejiang University of Technology（浙江工业大学）；Hangzhou Dianzi University（杭州电子科技大学）
Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas others may trade off clean example performance, such as smoothingbased defense. Most suffer from high complexity or low transferability. To address this problem, we proposed EGC2, an enhanced graph classification model with easy graph compression. EGC2 captures the relationship between the features of different nodes by constructing feature graphs and improvin…
Virginia Tech（弗吉尼亚理工大学）；Tsinghua University（清华大学）；University of California at Berkeley（加州大学伯克利分校）
Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. By challenging the classical graph Laplacian, we propose a new convolution operator that is provably robust in the spectral domain and is incorporated in the GCN architecture to improve expressivity and interpretability. By extending the original graph to a sequence of graphs, we also propose a robust training paradigm that encourages transfe…
Graph neural networks emerge as a promising modeling method for applications dealing with datasets that are best represented in the graph domain. In specific, developing recommendation systems often require addressing sparse structured data which often lacks the feature richness in either the user and/or item side and requires processing within the correct context for optimal performance. These datasets intuitively can be mapped to and represented as networks or graphs. In this paper, we propose the Hierarchical BiGraph Neural Network (HBGNN), a hierarchical approach of using GNNs as recommend…
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. Graph conductance is sensitive to these noisy `dangling sets'. Spectral clustering inherits this sensitivity. The second part of the paper starts from a previously proposed form of regularized spectral clustering and shows that it is related to the graph conductance on a `regulari…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we leverage graph signal processing to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topol…
University of Alcalá（阿尔卡拉大学）；European Commission, Joint Research Center（欧盟委员会联合研究中心）
Autonomous vehicles navigate in dynamically changing environments under a wide variety of conditions, being continuously influenced by surrounding objects. Modelling interactions among agents is essential for accurately forecasting other agents' behaviour and achieving safe and comfortable motion planning. In this work, we propose SCOUT, a novel Attention-based Graph Neural Network that uses a flexible and generic representation of the scene as a graph for modelling interactions, and predicts socially-consistent trajectories of vehicles and Vulnerable Road Users (VRUs) under mixed traffic cond…
This paper presents an audio-visual approach for voice separation which produces state-of-the-art results at a low latency in two scenarios: speech and singing voice. The model is based on a two-stage network. Motion cues are obtained with a lightweight graph convolutional network that processes face landmarks. Then, both audio and motion features are fed to an audio-visual transformer which produces a fairly good estimation of the isolated target source. In a second stage, the predominant voice is enhanced with an audio-only network. We present different ablation studies and comparison to sta…
University of California, Berkeley（加州大学伯克利分校）；University of Pennsylvania（宾夕法尼亚大学）
Dynamical systems comprised of autonomous agents arise in many relevant problems such as multi-agent robotics, smart grids, or smart cities. Controlling these systems is of paramount importance to guarantee a successful deployment. Optimal centralized controllers are readily available but face limitations in terms of scalability and practical implementation. Optimal decentralized controllers, on the other hand, are difficult to find. In this paper, we propose a framework using graph neural networks (GNNs) to learn decentralized controllers from data. While GNNs are naturally distributed archit…
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-based GCNs have achieved impressive results in many graph related analytics tasks. However, spectral-based models cannot directly work on directed graphs. In this paper, we propose an improved spectral-based GCN for the directed graph by leveraging redefined Laplacians to improve it…
Rice Univ.（莱斯大学）；Univ. of Pennsylvania（宾夕法尼亚大学）；Cambridge University（剑桥大学）
Dynamical systems consisting of a set of autonomous agents face the challenge of having to accomplish a global task, relying only on local information. While centralized controllers are readily available, they face limitations in terms of scalability and implementation, as they do not respect the distributed information structure imposed by the network system of agents. Given the difficulties in finding optimal decentralized controllers, we propose a novel framework using graph neural networks (GNNs) to \emph{learn} these controllers. GNNs are well-suited for the task since they are naturally …
Stevens Institute of Technology（史蒂文斯理工学院）；Michigan Technological University（密歇根理工大学）
Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs, vectorless verification of power/thermal grids, representation learning of large graphs, etc. However, prior spectral graph sparsification methods rely on fast Laplacian matrix solvers that are usually challenging to implement in practice. This work, for the first time, introduces a solver-free approach (SF-GRASS) for spectral graph sparsification by leveragi…
