Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the homophily assumption and have shown limited performance on the heterophilous graphs. While several methods have been developed with new architectures to address heterophily, we argue that by learning graph representations across two spaces i.e., topology and feature space GCNs can address heterophily. In this work, we experimentally demonstrate the performance of the proposed GCN framework over semi-supervised node classification task on both homophilous and heterophilous graph benchmarks by learning and combining representations across the topological and the feature spaces.
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph…
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；Google Research（谷歌研究院）；University of California, Berkeley（加州大学伯克利分校）
In node classification tasks, graph convolutional neural networks (GCNs) have demonstrated competitive performance over traditional methods on diverse graph data. However, it is known that the performance of GCNs degrades with increasing number of layers (oversmoothing problem) and recent studies have also shown that GCNs may perform worse in heterophilous graphs, where neighboring nodes tend to belong to different classes (heterophily problem). These two problems are usually viewed as unrelated, and thus are studied independently, often at the graph filter level from a spectral perspective. W…
Xi'an Jiaotong University（西安交通大学）；Xi'an University of Science and Technology（西安科技大学）
In representation learning on the graph-structured data, under heterophily (or low homophily), many popular GNNs may fail to capture long-range dependencies, which leads to their performance degradation. To solve the above-mentioned issue, we propose a graph convolutional networks with structure learning (GCN-SL), and furthermore, the proposed approach can be applied to node classification. The proposed GCN-SL contains two improvements: corresponding to node features and edges, respectively. In the aspect of node features, we propose an efficient-spectral-clustering (ESC) and an ESC with ancho…
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. Bu…
Tianjin University（天津大学）；Meituan（美团）；The Hong Kong Polytechnic University（香港理工大学）
Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to a…
Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Ada…
Graph Neural Networks (GNNs) have achieved remarkable performance in modeling graphs for various applications. However, most existing GNNs assume the graphs exhibit strong homophily in node labels, i.e., nodes with similar labels are connected in the graphs. They fail to generalize to heterophilic graphs where linked nodes may have dissimilar labels and attributes. Therefore, in this paper, we investigate a novel framework that performs well on graphs with either homophily or heterophily. More specifically, we propose a label-wise message passing mechanism to avoid the negative effects caused …
Graph neural networks (GNNs) have significantly improved the representation power for graph-structured data. Despite of the recent success of GNNs, the graph convolution in most GNNs have two limitations. Since the graph convolution is performed in a small local neighborhood on the input graph, it is inherently incapable to capture long-range dependencies between distance nodes. In addition, when a node has neighbors that belong to different classes, i.e., heterophily, the aggregated messages from them often negatively affect representation learning. To address the two common problems of graph…
Adaptive Heterogeneous Graph Neural Networks: Bridging Heterophily and Heterogeneity
State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（通用人工智能国家重点实验室，智能科学与技术学院，北京大学）
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）；School of Cyberspace, Hangzhou Dianzi University（杭州电子科技大学网络空间安全学院）
Graph Convolutional Network (GCN) has shown remarkable potential of exploring graph representation. However, the GCN aggregating mechanism fails to generalize to networks with heterophily where most nodes have neighbors from different classes, which commonly exists in real-world networks. In order to make the propagation and aggregation mechanism of GCN suitable for both homophily and heterophily (or even their mixture), we introduce block modeling into the framework of GCN so that it can realize "block-guided classified aggregation", and automatically learn the corresponding aggregation rules…
How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学张江高等研究院）；Shanghai AI Laboratory（上海人工智能实验室）；School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）；Zhejiang Institute of Optoelectronics（浙江光电研究院）；Zhejiang Normal University（浙江师范大学）；Department of Computer Science and Technology, Cambridge University（剑桥大学计算机科学与技术系）
Understanding Heterophily for Graph Neural Networks
Beihang University（北京航空航天大学）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；Shen Yuan Honors College, Beihang University（北京航空航天大学沈元荣誉学院）；School of Artificial Intelligence, Hebei University of Technology（河北工业大学人工智能学院）
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the effect of graph topology and node features on performance, and are even surpassed by some models that do not consider graph structure or node properties. We quantify the information overlap between graph topology, node features, and labels in order to determine graph convolution's representation power in the node classification task. In this work, we first deter…
University of Cambridge（剑桥大学）；Twitter（推特）；University of Oxford（牛津大学）
Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their ov…
Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks
School of New Media and Communication, Tianjin University（天津大学新媒体与传播学院）；College of Intelligence and Computing, Tianjin University（天津大学智能与计算学院）；Yazhou Bay Innovation Institute, Hainan Tropical Ocean University（海南热带海洋大学亚龙湾创新研究院）；Key Lab of Education Blockchain and Intelligent Technology, Guangxi Normal University（广西师范大学教育区块链与智能技术重点实验室）
Beijing Institute of Technology（北京理工大学）；Renmin University of China（中国人民大学）
Graph convolutional networks (GCNs) have achieved promising performance on various graph-based tasks. However they suffer from over-smoothing when stacking more layers. In this paper, we present a quantitative study on this observation and develop novel insights towards the deeper GCN. First, we interpret the current graph convolutional operations from an optimization perspective and argue that over-smoothing is mainly caused by the naive first-order approximation of the solution to the optimization problem. Subsequently, we introduce two metrics to measure the over-smoothing on node-level tas…
National University of Singapore（新加坡国立大学）；University of Wisconsin（威斯康星大学）；N.1 Institute for Health（N.1健康研究所）
This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace-Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We then define spectral filters via the LB operator on a graph. We explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters and define an update of the LB operator for pooling in the LBCNN. We employ the brain image data from Alzheimer's Disease Neuroimaging Initiative (ADNI) and demonstrate the use of the proposed LB-CNN. Based on the…
Hefei University of Technology（合肥工业大学）；University of Science and Technology of China（中国科学技术大学）
Graph Convolutional Networks (GCNs) are state-of-the-art graph based representation learning models by iteratively stacking multiple layers of convolution aggregation operations and non-linear activation operations. Recently, in Collaborative Filtering (CF) based Recommender Systems (RS), by treating the user-item interaction behavior as a bipartite graph, some researchers model higher-layer collaborative signals with GCNs. These GCN based recommender models show superior performance compared to traditional works. However, these models suffer from training difficulty with non-linear activation…
The conventional sliced Wasserstein is defined between two probability measures that have realizations as vectors. When comparing two probability measures over images, practitioners first need to vectorize images and then project them to one-dimensional space by using matrix multiplication between the sample matrix and the projection matrix. After that, the sliced Wasserstein is evaluated by averaging the two corresponding one-dimensional projected probability measures. However, this approach has two limitations. The first limitation is that the spatial structure of images is not captured effi…
Convolutional neural networks are among the most successful architectures in deep learning with this success at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers only in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spat…
Graph clustering discovers groups or communities within networks. Deep learning methods such as autoencoders (AE) extract effective clustering and downstream representations but cannot incorporate rich structural information. While Graph Neural Networks (GNN) have shown great success in encoding graph structure, typical GNNs based on convolution or attention variants suffer from over-smoothing, noise, heterophily, are computationally expensive and typically require the complete graph being present. Instead, we propose Self-Supervised Contrastive Graph Clustering (SCGC), which imposes graph-str…
Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects
MathLab, International School for Advanced Studies (SISSA)（数学实验室，国际先进研究学院（SISSA））；Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne（生物医学成像组，瑞士联邦理工学院）；Laboratoire de Physique de l’ENS Lyon, CNRS UMR 5672（Lyon 大学物理实验室，CNRS UMR 5672）
Research Center for Information Technology Innovation, Academia Sinica（中央研究院资讯科技创新研究中心）；KKBOX Inc.（KKBOX公司）
Being able to predict whether a song can be a hit has impor- tant applications in the music industry. Although it is true that the popularity of a song can be greatly affected by exter- nal factors such as social and commercial influences, to which degree audio features computed from musical signals (whom we regard as internal factors) can predict song popularity is an interesting research question on its own. Motivated by the recent success of deep learning techniques, we attempt to ex- tend previous work on hit song prediction by jointly learning the audio features and prediction models usin…
We present a method to learn a diverse group of object categories from an unordered point set. We propose our Pyramid Point network, which uses a dense pyramid structure instead of the traditional 'U' shape, typically seen in semantic segmentation networks. This pyramid structure gives a second look, allowing the network to revisit different layers simultaneously, increasing the contextual information by creating additional layers with less noise. We introduce a Focused Kernel Point convolution (FKP Conv), which expands on the traditional point convolutions by adding an attention mechanism to …
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Oversmoothing has been assumed to be the major cause of performance drop in deep graph convolutional networks (GCNs). In this paper, we propose a new view that deep GCNs can actually learn to anti-oversmooth during training. This work interprets a standard GCN architecture as layerwise integration of a Multi-layer Perceptron (MLP) and graph regularization. We analyze and conclude that before training, the final representation of a deep GCN does over-smooth, however, it learns anti-oversmoothing during training. Based on the conclusion, the paper further designs a cheap but effective trick to i…
Hainan University（海南大学）；Yangtze Normal University（长江师范学院）
Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they have high computational complexity and too many preconditions. In this paper, to overcome these drawbacks, we propose three novel RLS optimization algorithms for training feedforward neural networks, convolutional neural networks and recurrent neural networks (including long short-term memory networks), by using the error backpropagation and our average-approxi…
Accurate estimation of predictive uncertainty (model calibration) is essential for the safe application of neural networks. Many instances of miscalibration in modern neural networks have been reported, suggesting a trend that newer, more accurate models produce poorly calibrated predictions. Here, we revisit this question for recent state-of-the-art image classification models. We systematically relate model calibration and accuracy, and find that the most recent models, notably those not using convolutions, are among the best calibrated. Trends observed in prior model generations, such as de…
Self-Attention Empowered Graph Convolutional Network for Structure Learning and Node Embedding
School of Electronic and Information Engineering, Xi’an Jiaotong University（西安交通大学电子与信息工程学院）；College of Geomatics, Xi’an University of Science and Technology（西安科技大学测绘学院）
Software Engineering Institute of Guangzhou（广州软件学院）；Guangdong University of Technology（广东工业大学）；Guangdong Polytechnic Normal University（广东技术师范大学）
Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing, over-fitting, difficult to train, and strong homophily assumption. For example, Simple Graph Convolution (SGC) is known to suffer from the first and fourth limitations. To tackle these limitations, we identify a set of key designs including (D1) dilated convolution, (D2) multi-channel learning, (D3) self-attention score, and (D4) sign factor to boost learning from…
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…
Beyond Graph Convolutional Network: An Interpretable Regularizer-centered Optimization Framework
College of Computer and Data Science, Fuzhou University（福州大学计算机与数据科学学院）；School of Computer Science, Beijing University of Posts and Telecommunications（北京邮电大学计算机学院）
Michigan State University（密歇根州立大学）；Sun Yat-sen University（中山大学）
Efforts to improve the adversarial robustness of convolutional neural networks have primarily focused on developing more effective adversarial training methods. In contrast, little attention was devoted to analyzing the role of architectural elements (such as topology, depth, and width) on adversarial robustness. This paper seeks to bridge this gap and present a holistic study on the impact of architectural design on adversarial robustness. We focus on residual networks and consider architecture design at the block level, i.e., topology, kernel size, activation, and normalization, as well as a…
Rethinking Structure Learning For Graph Neural Networks
Nanyang Technological University（南洋理工大学）；School of Software Technology（软件技术学院）；Mila - Quebec Artificial Intelligence Institute（米拉-魁北克人工智能研究所）；Zhejiang University（浙江大学）；College of Big Data Internet（大数据互联网学院）；Shenzhen University（深圳大学）
University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究院）；Canadian Institute for Advanced Research（加拿大高等研究院）；SRI International（SRI国际研究院）
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address this limitation by revisiting a particular family of spectral graph networks, Chebyshev GCNs, showing its efficacy in solving graph classification tasks with a variable graph structure and size. Chebyshev GCNs restrict graphs to have at most one edge between any pair of nodes. To th…
Toward a Robust R2D2 Paradigm for Radio-interferometric Imaging: Revisiting Deep Neural Network Training and Architecture
Institute of Sensors, Signals and Systems, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom（传感器、信号与系统研究所，赫里奥特-瓦特大学）；EPCC, University of Edinburgh, Potterrow, Edinburgh EH8 9BT, United Kingdom（爱丁堡大学埃平中心）
The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional synthesis representations. In this paper, we start by addressing a more general model, revealing interesting ties to fully connected networks. We then show that this multi-layer construction admits a brand new interpretation in a unique symbiosis between synthesis and analysis models: while the deepest layer indeed provides a synthesis representation, the mid-l…
