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 improve GCN training. We verify our conclusions and evaluate the trick on three citation networks and further provide insights on neighborhood aggregation in GCNs.
Rutgers University - New Brunswick（罗格斯大学-新不伦瑞克分校）；Department of Computer Science（计算机科学系）
Applying Global Self-attention (GSA) mechanism over features has achieved remarkable success on Convolutional Neural Networks (CNNs). However, it is not clear if Graph Convolutional Networks (GCNs) can similarly benefit from such a technique. In this paper, inspired by the similarity between CNNs and GCNs, we study the impact of the Global Self-attention mechanism on GCNs. We find that consistent with the intuition, the GSA mechanism allows GCNs to capture feature-based vertex relations regardless of edge connections; As a result, the GSA mechanism can introduce extra expressive power to the G…
Guangdong University of Finance & Economics（广东财经大学）
Graph convolutional networks (GCNs) have achieved remarkable learning ability for dealing with various graph structural data recently. In general, deep GCNs do not work well since graph convolution in conventional GCNs is a special form of Laplacian smoothing, which makes the representation of different nodes indistinguishable. In the literature, multi-scale information was employed in GCNs to enhance the expressive power of GCNs. However, over-smoothing phenomenon as a crucial issue of GCNs remains to be solved and investigated. In this paper, we propose two novel multi-scale GCN frameworks b…
Graph Convolutional Networks (GCNs) have been drawing significant attention with the power of representation learning on graphs. Unlike Convolutional Neural Networks (CNNs), which are able to take advantage of stacking very deep layers, GCNs suffer from vanishing gradient, over-smoothing and over-fitting issues when going deeper. These challenges limit the representation power of GCNs on large-scale graphs. This paper proposes DeeperGCN that is capable of successfully and reliably training very deep GCNs. We define differentiable generalized aggregation functions to unify different message agg…
Harbin Institute of Technology（哈尔滨工业大学）；NetEase（网易）
Graph Convolutional Networks (GCNs) are powerful for processing graph-structured data and have achieved state-of-the-art performance in several tasks such as node classification, link prediction, and graph classification. However, it is inevitable for deep GCNs to suffer from an over-smoothing issue that the representations of nodes will tend to be indistinguishable after repeated graph convolution operations. To address this problem, we propose the Graph Partner Neural Network (GPNN) which incorporates a de-parameterized GCN and a parameter-sharing MLP. We provide empirical and theoretical ev…
Aspect-level sentiment classification aims to identify the sentiment polarity towards a specific aspect term in a sentence. Most current approaches mainly consider the semantic information by utilizing attention mechanisms to capture the interactions between the context and the aspect term. In this paper, we propose to employ graph convolutional networks (GCNs) on the dependency tree to learn syntax-aware representations of aspect terms. GCNs often show the best performance with two layers, and deeper GCNs do not bring additional gain due to over-smoothing problem. However, in some cases, impo…
Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心）；Tsinghua University（清华大学）；Tencent AI Lab（腾讯人工智能实验室）
Increasing the depth of GCN, which is expected to permit more expressivity, is shown to incur performance detriment especially on node classification. The main cause of this lies in over-smoothing. The over-smoothing issue drives the output of GCN towards a space that contains limited distinguished information among nodes, leading to poor expressivity. Several works on refining the architecture of deep GCN have been proposed, but it is still unknown in theory whether or not these refinements are able to relieve over-smoothing. In this paper, we first theoretically analyze how general GCNs act …
Beijing University of Posts and Telecommunications（北京邮电大学）
Traffic prediction has gradually attracted the attention of researchers because of the increase in traffic big data. Therefore, how to mine the complex spatio-temporal correlations in traffic data to predict traffic conditions more accurately become a difficult problem. Previous works combined graph convolution networks (GCNs) and self-attention mechanism with deep time series models (e.g. recurrent neural networks) to capture the spatio-temporal correlations separately, ignoring the relationships across time and space. Besides, GCNs are limited by over-smoothing issue and self-attention is li…
Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to over-smoothing. Despite the apparent consensus, we observe that there exists a discrepancy between the theoretical understanding of over-smoothing and the practical capabilities of GCNs. Specifically, we argue that over-smoothing does not necessarily happen in practice, a deeper model is provably expressive, can converge to global optimum with linear convergence rate, and achieve very high training accuracy as long as properly trained. Despite b…
Bridging Smoothness and Approximation: Theoretical Insights into Over-Smoothing in Graph Neural Networks
South China Agricultural University（华南农业大学）；City University of Hong Kong（香港城市大学）；Zhejiang Normal University（浙江师范大学）；Zhejiang Institute of Optoelectronics（浙江光电研究所）；The University of Sydney（悉尼大学）
The Hong Kong Polytechnic University（香港理工大学）；ETH Zurich（苏黎世联邦理工学院）
Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits…
Indian Institute of Technology Gandhinagar（印度理工学院甘地讷格尔分校）
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 …
Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature
FPT Software AI Center（FPT软件人工智能中心）；University of Science, Vietnam National University Ho Chi Minh City（越南国家大学胡志明市分校科学大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of California, Los Angeles（加州大学洛杉矶分校）；National University of Singapore（新加坡国立大学）
Graph Convolutional Networks (GCNs) have gained significant developments in representation learning on graphs. However, current GCNs suffer from two common challenges: 1) GCNs are only effective with shallow structures; stacking multiple GCN layers will lead to over-smoothing. 2) GCNs do not scale well with large, dense graphs due to the recursive neighborhood expansion. We generalize the propagation strategies of current GCNs as a \emph{"Sink$\to$Source"} mode, which seems to be an underlying cause of the two challenges. To address these issues intrinsically, in this paper, we study the infor…
Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning
Institute of Big Data Science and Industry（大数据科学与产业研究院）；Shanxi University（山西大学）；Key Laboratory of Evolutionary Science Intelligence of Shanxi Province（山西省进化科学智能重点实验室）；Zhengzhou University of Aeronautics（郑州航空工业大学）
Renmin University of China（中国人民大学）；Fudan University（复旦大学）；Alibaba Group（阿里巴巴集团）
Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theor…
Graph convolutional networks (GCNs) have been proved to be very practical to handle various graph-related tasks. It has attracted considerable research interest to study deep GCNs, due to their potential superior performance compared with shallow ones. However, simply increasing network depth will, on the contrary, hurt the performance due to the over-smoothing problem. Adding residual connection is proved to be effective for learning deep convolutional neural networks (deep CNNs), it is not trivial when applied to deep GCNs. Recent works proposed an initial residual mechanism that did allevia…
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…
Hong Kong University of Science and Technology（香港科技大学）；The University of Hong Kong（香港大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Sun Yat-sen University（中山大学）
Recently over-smoothing phenomenon of Transformer-based models is observed in both vision and language fields. However, no existing work has delved deeper to further investigate the main cause of this phenomenon. In this work, we make the attempt to analyze the over-smoothing problem from the perspective of graph, where such problem was first discovered and explored. Intuitively, the self-attention matrix can be seen as a normalized adjacent matrix of a corresponding graph. Based on the above connection, we provide some theoretical analysis and find that layer normalization plays a key role in…
\emph{Over-fitting} and \emph{over-smoothing} are two main obstacles of developing deep Graph Convolutional Networks (GCNs) for node classification. In particular, over-fitting weakens the generalization ability on small dataset, while over-smoothing impedes model training by isolating output representations from the input features with the increase in network depth. This paper proposes DropEdge, a novel and flexible technique to alleviate both issues. At its core, DropEdge randomly removes a certain number of edges from the input graph at each training epoch, acting like a data augmenter and …
Singapore University of Technology and Design (SUTD)（新加坡科技设计大学）
This work investigates the compatibility between label smoothing (LS) and knowledge distillation (KD). Contemporary findings addressing this thesis statement take dichotomous standpoints: Muller et al. (2019) and Shen et al. (2021b). Critically, there is no effort to understand and resolve these contradictory findings, leaving the primal question -- to smooth or not to smooth a teacher network? -- unanswered. The main contributions of our work are the discovery, analysis and validation of systematic diffusion as the missing concept which is instrumental in understanding and resolving these con…
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…
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…
Ben-Gurion University（本-古里安大学）；University of British Columbia（不列颠哥伦比亚大学）
Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the…
Zhejiang Normal University（浙江师范大学）；School of AI, Bangalore（班加罗尔人工智能学院）；Guizhou University（贵州大学）；Western University（西安大略大学）
Graph Convolutional Networks (GCNs) are widely used in many applications yet still need large amounts of labelled data for training. Besides, the adjacency matrix of GCNs is stable, which makes the data processing strategy cannot efficiently adjust the quantity of training data from the built graph structures.To further improve the performance and the self-learning ability of GCNs,in this paper, we propose an efficient self-supervised learning strategy of GCNs,named randomly removed links with a fixed step at one region (RRLFSOR).RRLFSOR can be regarded as a new data augmenter to improve over-…
National University of Singapore（新加坡国立大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Knowledge Distillation (KD) aims to distill the knowledge of a cumbersome teacher model into a lightweight student model. Its success is generally attributed to the privileged information on similarities among categories provided by the teacher model, and in this sense, only strong teacher models are deployed to teach weaker students in practice. In this work, we challenge this common belief by following experimental observations: 1) beyond the acknowledgment that the teacher can improve the student, the student can also enhance the teacher significantly by reversing the KD procedure; 2) a poo…
Quantifying the Optimization and Generalization Advantages of Graph Neural Networks Over Multilayer Perceptrons
RIKEN AIP（日本学术振兴会先进研究所）；The University of Hong Kong（香港大学）；National University of Singapore（新加坡国立大学）；The University of New South Wales（新南威尔士大学）；University of Tokyo（东京大学）
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）
University of Technology Sydney（悉尼科技大学）；The University of Sydney（悉尼大学）；Northeastern University（东北大学）；Aalborg University（奥尔堡大学）
Graph convolutional networks (GCNs) and their variants have achieved great success in dealing with graph-structured data. Nevertheless, it is well known that deep GCNs suffer from the over-smoothing problem, where node representations tend to be indistinguishable as more layers are stacked up. The theoretical research to date on deep GCNs has focused primarily on expressive power rather than trainability, an optimization perspective. Compared to expressivity, trainability attempts to address a more fundamental question: Given a sufficiently expressive space of models, can we successfully find …
Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification
Department of Electrical, Computer, and Systems Engineering（电气、计算机与系统工程系）；Rensselaer Polytechnic Institute（伦塞拉尔理工大学）；Department of Electrical and Systems Engineering（电气与系统工程系）；University of Pennsylvania（宾夕法尼亚大学）
Chongqing University（重庆大学）；The University of Queensland（昆士兰大学）
Graph Convolutional Networks (GCNs) achieve great success in non-Euclidean structure data processing recently. In existing studies, deeper layers are used in CCNs to extract deeper features of Euclidean structure data. However, for non-Euclidean structure data, too deep GCNs will confront with problems like "neighbor explosion" and "over-smoothing", it also cannot be applied to large datasets. To address these problems, we propose a model called PathSAGE, which can learn high-order topological information and improve the model's performance by expanding the receptive field. The model randomly …
TSC: A Simple Two-Sided Constraint against Over-Smoothing
School of Computer and Information Technology, Shanxi University（山西大学计算机与信息技术学院）；College of Physics and Electronic Engineering, Shanxi University（山西大学物理与电子工程学院）
Southwest Petroleum University（西南石油大学）；East China Normal University（华东师范大学）
Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which…
A graph convolutional network (GCN) employs a graph filtering kernel tailored for data with irregular structures. However, simply stacking more GCN layers does not improve performance; instead, the output converges to an uninformative low-dimensional subspace, where the convergence rate is characterized by the graph spectrum -- this is the known over-smoothing problem in GCN. In this paper, we propose a sparse graph learning algorithm incorporating a new spectrum prior to compute a graph topology that circumvents over-smoothing while preserving pairwise correlations inherent in data. Specifica…
The Australian Artificial Intelligence Institute (AAII), University of Technology Sydney（悉尼科技大学澳大利亚人工智能研究所（AAII））；Australian Catholic University（澳大利亚天主教大学）
Graph Convolutional Neural Networks (GCNs) has been generally accepted to be an effective tool for node representations learning. An interesting way to understand GCNs is to think of them as a message passing mechanism where each node updates its representation by accepting information from its neighbours (also known as positive samples). However, beyond these neighbouring nodes, graphs have a large, dark, all-but forgotten world in which we find the non-neighbouring nodes (negative samples). In this paper, we show that this great dark world holds a substantial amount of information that might…
Graph convolutional network (GCN) based approaches have achieved significant progress for solving complex, graph-structured problems. GCNs incorporate the graph structure information and the node (or edge) features through message passing and computes 'deep' node representations. Despite significant progress in the field, designing GCN architectures for heterogeneous graphs still remains an open challenge. Due to the schema of a heterogeneous graph, useful information may reside multiple hops away. A key question is how to perform message passing to incorporate information of neighbors multipl…
National Engineering School of Sousse, University of Sousse, LATIS – Laboratory of Advanced Technology and Intelligent Systems（苏塞国家工程学校，苏塞大学，先进技术和智能系统实验室）；BASIRA Lab, Imperial-X and Department of Computing, Imperial College London（BASIRA实验室，Imperial-X和伦敦帝国理工学院计算系）
Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions arise: (i) how to design a differentiable exchange protocol (e.g., a 1-hop Laplacian smoothing in the original GCN), and (ii) how to characterize the trade-off in complexity with respect to the local updates. In this paper, we show that state-of-the-art results can be achieved by adapting the number of communication steps independently at every node. In particula…
Graph Convolutional Networks (GCNs) is the state-of-the-art method for learning graph-structured data, and training large-scale GCNs requires distributed training across multiple accelerators such that each accelerator is able to hold a partitioned subgraph. However, distributed GCN training incurs prohibitive overhead of communicating node features and feature gradients among partitions for every GCN layer during each training iteration, limiting the achievable training efficiency and model scalability. To this end, we propose PipeGCN, a simple yet effective scheme that hides the communicatio…
Beijing Institute of Technology（北京理工大学）；Guangdong Laboratory of Machine Perception and Intelligent Computing（广东省机器感知与智能计算实验室）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）
Stability and Generalization of lp-Regularized Stochastic Learning for GCN
University of Electronic Science and Technology of China（电子科技大学）；Northwestern Polytechnical University（西北工业大学）；Nanjing Audit University（南京审计大学）；Zhejiang Normal University（浙江师范大学）
Graph Convolutional Networks (GCNs), which use a message-passing paradigm with stacked convolution layers, are foundational methods for learning graph representations. Recent GCN models use various residual connection techniques to alleviate the model degradation problem such as over-smoothing and gradient vanishing. Existing residual connection techniques, however, fail to make extensive use of underlying graph structure as in the graph spectral domain, which is critical for obtaining satisfactory results on heterophilic graphs. In this paper, we introduce ClenshawGCN, a GNN model that employ…
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Graph convolutional networks (GCNs), aiming to integrate high-order neighborhood information through stacked graph convolution layers, have demonstrated remarkable power in many network analysis tasks. However, topological limitations, including over-smoothing and local topology homophily, limit its capability to represent networks. Existing studies only perform feature convolution on network topology, which inevitably introduces unbalance between topology and features. Considering that in real world, the information network consists of not only the node-level citation information but also the…
Boston University（波士顿大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；The University of Hong Kong（香港大学）；Zhejiang University（浙江大学）；Microsoft（微软）
Deep learning systems have been successfully applied to Euclidean data such as images, video, and audio. In many applications, however, information and their relationships are better expressed with graphs. Graph Convolutional Networks (GCNs) appear to be a promising approach to efficiently learn from graph data structures, having shown advantages in many critical applications. As with other deep learning modalities, hardware acceleration is critical. The challenge is that real-world graphs are often extremely large and unbalanced; this poses significant performance demands and design challenge…
Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different clusters without human annotations, is a fundamental yet challenging task. However, we observed that the existing methods suffer from the representation collapse problem and easily tend to encode samples with different classes into the same latent embedding. Consequently, the discriminative capability of nodes is limited, resulting in sub-optimal clustering performance. To address this problem, we propose a novel deep graph clustering algorithm termed Improved Dual Correlation Reducti…
