Graph Neural Networks (GNNs) have recently been used for node and graph classification tasks with great success, but GNNs model dependencies among the attributes of nearby neighboring nodes rather than dependencies among observed node labels. In this work, we consider the task of inductive node classification using GNNs in supervised and semi-supervised settings, with the goal of incorporating label dependencies. Because current GNNs are not universal (i.e., most-expressive) graph representations, we propose a general collective learning approach to increase the representation power of any existing GNN. Our framework combines ideas from collective classification with self-supervised learning, and uses a Monte Carlo approach to sampling embeddings for inductive learning across graphs. We evaluate performance on five real-world network datasets and demonstrate consistent, significant improvement in node classification accuracy, for a variety of state-of-the-art GNNs.
This paper studies Dropout Graph Neural Networks (DropGNNs), a new approach that aims to overcome the limitations of standard GNN frameworks. In DropGNNs, we execute multiple runs of a GNN on the input graph, with some of the nodes randomly and independently dropped in each of these runs. Then, we combine the results of these runs to obtain the final result. We prove that DropGNNs can distinguish various graph neighborhoods that cannot be separated by message passing GNNs. We derive theoretical bounds for the number of runs required to ensure a reliable distribution of dropouts, and we prove s…
Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a …
University of Antwerp（安特卫普大学）；Pontificia Universidad Católica de Chile（智利天主教大学）；IMFD（智利数学与计算机科学研究所）
Characterizing the separation power of graph neural networks (GNNs) provides an understanding of their limitations for graph learning tasks. Results regarding separation power are, however, usually geared at specific GNN architectures, and tools for understanding arbitrary GNN architectures are generally lacking. We provide an elegant way to easily obtain bounds on the separation power of GNNs in terms of the Weisfeiler-Leman (WL) tests, which have become the yardstick to measure the separation power of GNNs. The crux is to view GNNs as expressions in a procedural tensor language describing th…
The Logical Expressiveness of Temporal GNNs via Two-Dimensional Product Logics
RPTU Kaiserslautern-Landau（亚琛工业大学凯撒斯劳滕-兰道分校）；Queen Mary University of London（伦敦女王大学）；University of Łódź（卢宾大学）；Theoretical Computer Science / Formal Methods（理论计算机科学/形式方法）；University of Kassel（卡塞尔大学）
Graph Neural Network (GNN) is a popular architecture for the analysis of chemical molecules, and it has numerous applications in material and medicinal science. Current lines of GNNs developed for molecular analysis, however, do not fit well on the training set, and their performance does not scale well with the complexity of the network. In this paper, we propose an auxiliary module to be attached to a GNN that can boost the representation power of the model without hindering with the original GNN architecture. Our auxiliary module can be attached to a wide variety of GNNs, including those th…
PLA Strategy Support Force Information Engineering University（中国人民解放军战略支援部队信息工程大学）
The Graph Neural Network (GNN) has been widely used for graph data representation. However, the existing researches only consider the ideal balanced dataset, and the imbalanced dataset is rarely considered. Traditional methods such as resampling, reweighting, and synthetic samples that deal with imbalanced datasets are no longer applicable in GNN. This paper proposes an ensemble model called Boosting-GNN, which uses GNNs as the base classifiers during boosting. In Boosting-GNN, higher weights are set for the training samples that are not correctly classified by the previous classifier, thus ac…
Message passing neural networks (MPNNs) have become a dominant flavor of graph neural networks (GNNs) in recent years. Yet, MPNNs come with notable limitations; namely, they are at most as powerful as the 1-dimensional Weisfeiler-Leman (1-WL) test in distinguishing graphs in a graph isomorphism testing frame-work. To this end, researchers have drawn inspiration from the k-WL hierarchy to develop more expressive GNNs. However, current k-WL-equivalent GNNs are not practical for even small values of k, as k-WL becomes combinatorially more complex as k grows. At the same time, several works have f…
Expressivity and Generalization: Fragment-Biases for Molecular GNNs
School of Computation, Information & Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院）；Munich Data Science Institute（慕尼黑数据科学研究所）；Helmholtz Center for Computational Health（亥姆霍兹计算健康中心）
This paper studies the expressive power of graph neural networks falling within the message-passing framework (GNNmp). Two results are presented. First, GNNmp are shown to be Turing universal under sufficient conditions on their depth, width, node attributes, and layer expressiveness. Second, it is discovered that GNNmp can lose a significant portion of their power when their depth and width is restricted. The proposed impossibility statements stem from a new technique that enables the repurposing of seminal results from distributed computing and leads to lower bounds for an array of decision,…
Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics. The correspondence has even led to new, higher-order GNNs corresponding to the WL algorithm in higher dimensions. The purpose of this paper is to explain these descriptive characterisations of GNNs.
Criteo AI Lab（Criteo AI实验室）；Yandex；HSE University（高等经济大学）；MIPT（莫斯科物理技术学院）
Graph neural networks (GNNs) are powerful models that have been successful in various graph representation learning tasks. Whereas gradient boosted decision trees (GBDT) often outperform other machine learning methods when faced with heterogeneous tabular data. But what approach should be used for graphs with tabular node features? Previous GNN models have mostly focused on networks with homogeneous sparse features and, as we show, are suboptimal in the heterogeneous setting. In this work, we propose a novel architecture that trains GBDT and GNN jointly to get the best of both worlds: the GBDT…
The University of Tokyo（东京大学）；Preferred Networks, Inc.（Preferred Networks公司）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there is little explanation of why it works empirically from the viewpoint of learning theory. In this study, we derive the optimization and generalization guarantees of transductive learning algorithms that include multi-scale GNNs. Using the boosting theory, we prove the convergence of the training error under weak learning-type conditions. By combining it with …
Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusion
IST Austria（IST奥地利研究院）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences（多学科科学研究所数学生物物理组）；Max Planck Institute of Molecular Cell Biology and Genetics（分子细胞生物学和遗传学马克斯·普朗克研究所）；Max Planck Institute for the Physics of Complex Systems（复杂系统物理马克斯·普朗克研究所）；Dresden University of Technology（德累斯顿技术大学）
Graph data are pervasive in many real-world applications. Recently, increasing attention has been paid on graph neural networks (GNNs), which aim to model the local graph structures and capture the hierarchical patterns by aggregating the information from neighbors with stackable network modules. Motivated by the observation that different nodes often require different iterations of aggregation to fully capture the structural information, in this paper, we propose to explicitly sample diverse iterations of aggregation for different nodes to boost the performance of GNNs. It is a challenging ta…
On the Computational Capability of Graph Neural Networks: A Circuit Complexity Bound Perspective
The University of Hong Kong（香港大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Simons Institute for the Theory of Computing at UC Berkeley（加州大学伯克利分校西蒙斯理论计算研究所）；UC Berkeley（加州大学伯克利分校）
The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model $f(X)$. However, with the recent popularity of graph neural networks (GNNs), directly encoding graph structure $A$ into a model, i.e., $f(A, X)$, has become the more common approach. While we show that graph Laplacian regularization brings little-to-no benefit to existing GNNs, and propose a simple but non-trivial variant of graph Laplacian regularization, called Propagation-regularization (P-reg), to boost the performance of existing GNN models.…
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressiveness of graph neural networks (GNNs), showing that the neighborhood aggregation GNNs were at most as powerful as 1-WL test in distinguishing graph structures. There were also improvements proposed in analogy to $k$-WL test ($k>1$). However, the aggregators in these GNNs are far from injective as required by the WL test, and suffer from weak distinguishing strength, making it become expressive bottlenecks. In this paper, we improve the expressiveness by exploring powerful aggregators. We reformulate ag…
University of Oxford（牛津大学）；RWTH Aachen University（亚琛工业大学）
Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic. In order to break this expressiveness barrier, GNNs have been enhanced with random node initialization (RNI), where the idea is to train and run the models with randomized initial node features. In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs …
Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Although sufficiently deep GNNs are shown theoretically capable of fully preserving graph structures, most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. To overcome this fundamental challenge, we propose Eigen-GNN, a simple yet effective and general plug-in module to boost GNNs ability in preserving graph structures. Specifically, we integrate the eigenspace of graph structures with…
Nanyang Technological University（南洋理工大学）；Shanghai AI Laboratory（上海人工智能实验室）；SenseTime Research（商汤科技研究院）
Training Graph Neural Networks (GNNs) on large graphs is challenging due to the conflict between the high memory demand and limited GPU memory. Recently, distributed full-graph GNN training has been widely adopted to tackle this problem. However, the substantial inter-GPU communication overhead can cause severe throughput degradation. Existing communication compression techniques mainly focus on traditional DNN training, whose bottleneck lies in synchronizing gradients and parameters. We find they do not work well in distributed GNN training as the barrier is the layer-wise communication of fe…
Princeton University（普林斯顿大学）；Zhongguancun Haihua Institute for Frontier Information Technology（中关村海华前沿信息技术研究院）；Peking University（北京大学）；Pazhou Lab（琶洲实验室）；Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets…
We study and compare different Graph Neural Network extensions that increase the expressive power of GNNs beyond the Weisfeiler-Leman test. We focus on (i) GNNs based on higher order WL methods, (ii) GNNs that preprocess small substructures in the graph, (iii) GNNs that preprocess the graph up to a small radius, and (iv) GNNs that slightly perturb the graph to compute an embedding. We begin by presenting a simple improvement for this last extension that strictly increases the expressive power of this GNN variant. Then, as our main result, we compare the expressiveness of these extensions to ea…
Carnegie Mellon Uni.（卡内基梅隆大学）；Michigan State Uni.（密歇根州立大学）；Snap Inc.（Snap公司）
Message Passing Neural Networks (MPNNs) are a common type of Graph Neural Network (GNN), in which each node's representation is computed recursively by aggregating representations (messages) from its immediate neighbors akin to a star-shaped pattern. MPNNs are appealing for being efficient and scalable, how-ever their expressiveness is upper-bounded by the 1st-order Weisfeiler-Lehman isomorphism test (1-WL). In response, prior works propose highly expressive models at the cost of scalability and sometimes generalization performance. Our work stands between these two regimes: we introduce a gen…
University of Cambridge（剑桥大学）；Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）
Knowledge distillation is a learning paradigm for boosting resource-efficient graph neural networks (GNNs) using more expressive yet cumbersome teacher models. Past work on distillation for GNNs proposed the Local Structure Preserving loss (LSP), which matches local structural relationships defined over edges across the student and teacher's node embeddings. This paper studies whether preserving the global topology of how the teacher embeds graph data can be a more effective distillation objective for GNNs, as real-world graphs often contain latent interactions and noisy edges. We propose Grap…
Carnegie Mellon University（卡内基梅隆大学）；Pittsburgh, PA 15213, USA（美国宾夕法尼亚州匹兹堡市（15213））
The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings indistinguishable. We take a closer look at two different interpretations, aiming to quantify oversmoothing. Our main contribution is PairNorm, a novel normalization layer that is based on a careful analysis of the graph convolution operator, which prevents all node embeddings from becoming too similar. What is more, PairNorm is fast, easy to implement without any change t…
MuGSI: Distilling GNNs with Multi-Granularity Structural Information for Graph Classification
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Carnegie Mellon University（卡内基梅隆大学）；University of Southern California（南加利福尼亚大学）
Beijing University of Posts and Telecommunications（北京邮电大学）；Singapore Management University（新加坡管理大学）
Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important role in both graph signal processing and graph representation learning, existing studies are biased toward spatial approaches, and there is no comprehensive review on spectral GNNs so far. In this paper, we summarize the recent development of spectral GNNs, including model, theory, and application. Specifically, we first discuss the connection between spatial G…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Criteo AI（科韬人工智能）
Prediction of protein-ligand (PL) binding affinity remains the key to drug discovery. Popular approaches in recent years involve graph neural networks (GNNs), which are used to learn the topology and geometry of PL complexes. However, GNNs are computationally heavy and have poor scalability to graph sizes. On the other hand, traditional machine learning (ML) approaches, such as gradient-boosted decision trees (GBDTs), are lightweight yet extremely efficient for tabular data. We propose to use PL interaction features along with PL graph-level features in GBDT. We show that this combination outp…
Texas A&M University（德克萨斯A&M大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning them as model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. …
Operational Research Center（运筹学研究中心）；Massachusetts Institute of Technology（麻省理工学院）；Institute for Applied Computational Science（应用计算科学研究所）；Harvard University（哈佛大学）；Harvard School of Engineering and Applied Sciences（哈佛工程与应用科学学院）
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to compare different architectures and how to construct GNNs systematically. Here, we propose a hierarchy of GNNs based on their aggregation regions. We derive theoretical results about the discriminative power and feature representation capabilities of each class. Then, we show how this framework can be utilized to systematically construct arbitrarily powerful GNN…
