图形神经网络（GNN）已成功用于许多涉及图形结构数据的问题，从而实现了最新的性能。 GNN通常采用消息通话方案，其中每个节点都使用置换不变的聚合函数从其邻居中汇总信息。标准良好的选择（例如平均值或总和函数）具有有限的功能，因为它们无法捕获邻居之间的相互作用。在这项工作中，我们使用信息理论框架正式化了这些交互，该框架特别包括协同信息。在此定义的驱动下，我们介绍了图排序注意（山羊）层，这是一种新型的GNN组件，可捕获邻域中的节点之间的相互作用。这是通过通过注意机制学习局部节点顺序并使用复发性神经网络聚合器来处理订购表示的来实现的。这种设计使我们能够利用置换敏感的聚合器，同时维持所提出的山羊层的排列量表。山羊模型展示了其在捕获复杂信息（例如中心中心性和节点的有效大小）中的建模图指标中提高的性能。在实用用例中，通过在几个现实世界节点分类基准中成功证实了其出色的建模能力。

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with the pace of new research, proper experimental design, fair evaluation, and independent benchmarks are essential. Design of strong baselines is an indispensable element of such works. In this thesis, we explore multiple approaches to graph classification. We focus on Graph Neural Networks (GNNs), which emerged as a de facto standard deep learning technique for graph representation learning. Classical approaches, such as graph descriptors and molecular fingerprints, are also addressed. We design fair evaluation experimental protocol and choose proper datasets collection. This allows us to perform numerous experiments and rigorously analyze modern approaches. We arrive to many conclusions, which shed new light on performance and quality of novel algorithms. We investigate application of Jumping Knowledge GNN architecture to graph classification, which proves to be an efficient tool for improving base graph neural network architectures. Multiple improvements to baseline models are also proposed and experimentally verified, which constitutes an important contribution to the field of fair model comparison.

Pre-publication draft of a book to be published byMorgan & Claypool publishers. Unedited version released with permission. All relevant copyrights held by the author and publisher extend to this pre-publication draft.

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance. * Equal contribution. † Work partially performed while in Tokyo, visiting Prof. Ken-ichi Kawarabayashi.

图形神经网络（GNNS）在各种基于图形的应用中显示了优势。大多数现有的GNNS假设图形结构的强大奇妙并应用邻居的置换不变本地聚合以学习每个节点的表示。然而，它们未能概括到异质图，其中大多数相邻节点具有不同的标签或特征，并且相关节点远处。最近的几项研究通过组合中央节点的隐藏表示（即，基于多跳的方法）的多个跳数来解决这个问题，或者基于注意力分数对相邻节点进行排序（即，基于排名的方法）来解决这个问题。结果，这些方法具有一些明显的限制。一方面，基于多跳的方法没有明确区分相关节点的大量多跳社区，导致严重的过平滑问题。另一方面，基于排名的模型不与结束任务进行联合优化节点排名，并导致次优溶液。在这项工作中，我们呈现图表指针神经网络（GPNN）来解决上述挑战。我们利用指针网络从大量的多跳邻域选择最相关的节点，这根据与中央节点的关系来构造有序序列。然后应用1D卷积以从节点序列中提取高级功能。 GPNN中的基于指针网络的Ranker是以端到端的方式与其他部件进行联合优化的。在具有异质图的六个公共节点分类数据集上进行了广泛的实验。结果表明，GPNN显着提高了最先进方法的分类性能。此外，分析还揭示了拟议的GPNN在过滤出无关邻居并减少过平滑的特权。

We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-theart results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a proteinprotein interaction dataset (wherein test graphs remain unseen during training).

图形神经网络（GNNS）依赖于图形结构来定义聚合策略，其中每个节点通过与邻居的信息组合来更新其表示。已知GNN的限制是，随着层数的增加，信息被平滑，压扁并且节点嵌入式变得无法区分，对性能产生负面影响。因此，实用的GNN模型雇用了几层，只能在每个节点周围的有限邻域利用图形结构。不可避免地，实际的GNN不会根据图的全局结构捕获信息。虽然有几种研究GNNS的局限性和表达性，但是关于图形结构数据的实际应用的问题需要全局结构知识，仍然没有答案。在这项工作中，我们通过向几个GNN模型提供全球信息并观察其对下游性能的影响来认证解决这个问题。我们的研究结果表明，全球信息实际上可以为共同的图形相关任务提供显着的好处。我们进一步确定了一项新的正规化策略，导致所有考虑的任务的平均准确性提高超过5％。

图表可以模拟实体之间的复杂交互，它在许多重要的应用程序中自然出现。这些应用程序通常可以投入到标准图形学习任务中，其中关键步骤是学习低维图表示。图形神经网络（GNN）目前是嵌入方法中最受欢迎的模型。然而，邻域聚合范例中的标准GNN患有区分\ EMPH {高阶}图形结构的有限辨别力，而不是\ EMPH {低位}结构。为了捕获高阶结构，研究人员求助于主题和开发的基于主题的GNN。然而，现有的基于主基的GNN仍然仍然遭受较少的辨别力的高阶结构。为了克服上述局限性，我们提出了一个新颖的框架，以更好地捕获高阶结构的新框架，铰接于我们所提出的主题冗余最小化操作员和注射主题组合的新颖框架。首先，MGNN生成一组节点表示W.R.T.每个主题。下一阶段是我们在图案中提出的冗余最小化，该主题在彼此相互比较并蒸馏出每个主题的特征。最后，MGNN通过组合来自不同图案的多个表示来执行节点表示的更新。特别地，为了增强鉴别的功率，MGNN利用重新注射功能来组合表示的函数w.r.t.不同的主题。我们进一步表明，我们的拟议体系结构增加了GNN的表现力，具有理论分析。我们展示了MGNN在节点分类和图形分类任务上的七个公共基准上表现出最先进的方法。

Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the position/location of a given node with respect to all other nodes of the graph. Here we propose Position-aware Graph Neural Networks (P-GNNs), a new class of GNNs for computing position-aware node embeddings. P-GNN first samples sets of anchor nodes, computes the distance of a given target node to each anchor-set, and then learns a non-linear distance-weighted aggregation scheme over the anchor-sets. This way P-GNNs can capture positions/locations of nodes with respect to the anchor nodes. P-GNNs have several advantages: they are inductive, scalable, and can incorporate node feature information. We apply P-GNNs to multiple prediction tasks including link prediction and community detection. We show that P-GNNs consistently outperform state of the art GNNs, with up to 66% improvement in terms of the ROC AUC score.Node embedding methods can be categorized into Graph Neural Networks (GNNs) approaches (Scarselli et al., 2009),

在过去几年中，人们对代表性学习的图形神经网络（GNN）的兴趣不大。GNN提供了一个一般有效的框架，可以从图形结构化数据中学习。但是，GNN通常仅使用一个非常有限的邻域的信息来避免过度光滑。希望为模型提供更多信息。在这项工作中，我们将个性化Pagerank（PPR）的极限分布纳入图形注意力网络（GATS）中，以反映较大的邻居信息，而无需引入过度光滑。从直觉上讲，基于个性化Pagerank的消息聚合对应于无限的许多邻里聚合层。我们表明，对于四个广泛使用的基准数据集，我们的模型优于各种基线模型。我们的实施已在线公开。

消息传递已作为设计图形神经网络（GNN）的有效工具的发展。但是，消息传递的大多数现有方法简单地简单或平均所有相邻的功能更新节点表示。它们受到两个问题的限制，即（i）缺乏可解释性来识别对GNN的预测重要的节点特征，以及（ii）特征过度混合，导致捕获长期依赖和无能为力的过度平滑问题在异质或低同质的下方处理图。在本文中，我们提出了一个节点级胶囊图神经网络（NCGNN），以通过改进的消息传递方案来解决这些问题。具体而言，NCGNN表示节点为节点级胶囊组，其中每个胶囊都提取其相应节点的独特特征。对于每个节点级胶囊，开发了一个新颖的动态路由过程，以适应适当的胶囊，以从设计的图形滤波器确定的子图中聚集。 NCGNN聚集仅有利的胶囊并限制无关的消息，以避免交互节点的过度混合特征。因此，它可以缓解过度平滑的问题，并通过同粒或异质的图表学习有效的节点表示。此外，我们提出的消息传递方案本质上是可解释的，并免于复杂的事后解释，因为图形过滤器和动态路由过程确定了节点特征的子集，这对于从提取的子分类中的模型预测最为重要。关于合成和现实图形的广泛实验表明，NCGNN可以很好地解决过度光滑的问题，并为半监视的节点分类产生更好的节点表示。它的表现优于同质和异质的艺术状态。

节点分类是关系学习中的一个核心任务，在两个密钥原理上具有当前最先进的静脉：（i）预测是节点邻居的排序的禁用 - 不变，并且（ii）预测是函数节点的$ r $ -hop邻域拓扑和属性，$ r \ geq 2 $。图形神经网络和集体推理方法（例如，信仰传播）依赖于最多$ r $-hops的信息。在这项工作中，我们研究了使用更强大的置换不变功能，有时可以避免对分类器的需求收集超过$ 1 $ -hop的信息。为此，我们介绍了一个新的架构，集旋转，概括了德·德斯集（Zaheer等，2017），一种简单而广泛使用的置换不变表示。设置捻线仪理论上提高了DeadSets的表现力，使其捕获更高阶依赖性，同时保持其简单性和低计算成本。经验上，我们看到了在若干任务中的Deplsets套装以及各种图形神经网络和集体推理方案的准确性改进，同时展示了其实现简单和计算效率。

Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to information propagation bottlenecks, as information is repeatedly compressed at intermediary node representations, which causes loss of information, making it practically impossible to gather meaningful signals from distant nodes. To address this issue, we propose shortest path message passing neural networks, where the node representations of a graph are propagated to each node in the shortest path neighborhoods. In this setting, nodes can directly communicate between each other even if they are not neighbors, breaking the information bottleneck and hence leading to more adequately learned representations. Theoretically, our framework generalizes message passing neural networks, resulting in provably more expressive models, and we show that some recent state-of-the-art models are special instances of this framework. Empirically, we verify the capacity of a basic model of this framework on dedicated synthetic experiments, and on real-world graph classification and regression benchmarks, and obtain state-of-the-art results.

在本文中，我们提供了一种使用图形神经网络（GNNS）的理论，用于多节点表示学习（我们有兴趣学习一组多个节点的表示）。我们知道GNN旨在学习单节点表示。当我们想学习涉及多个节点的节点集表示时，先前作品中的常见做法是直接将GNN学习的多节点表示与节点集的关节表示。在本文中，我们显示了这种方法的基本限制，即无法捕获节点集中节点之间的依赖性，并且认为直接聚合各个节点表示不会导致多个节点的有效关节表示。然后，我们注意到，以前的一些成功的工作作品用于多节点表示学习，包括密封，距离编码和ID-GNN，所有使用的节点标记。这些方法根据应用GNN之前的与目标节点集的关系，首先标记图中的节点。然后，在标记的图表中获得的节点表示被聚合到节点集表示中。通过调查其内部机制，我们将这些节点标记技术统一到单个和最基本的形式，即标记技巧。我们证明，通过标记技巧，可以获得足够富有表现力的GNN学习最具表现力的节点集表示，因此原则上可以解决节点集的任何联合学习任务。关于一个重要的双节点表示学习任务，链接预测，验证了我们理论的实验。我们的工作建立了使用GNN在节点集上使用GNN进行联合预测任务的理论基础。

计算机视觉和机器学习中的许多问题都可以作为代表高阶关系的超图的学习。 HyperGraph Learning的最新方法基于消息传递扩展了图形神经网络，这在建模远程依赖性和表达能力方面很简单但根本上有限。另一方面，基于张量的模棱两可的神经网络具有最大的表现力，但是由于沉重的计算和对固定顺序超中件的严格假设，它们的应用受到了超图的限制。我们解决了这些问题，并目前呈现了模棱两可的HyperGraph神经网络（EHNN），这是实现一般超图学习最大表达性的层的首次尝试。我们还提出了基于超网（EHNN-MLP）和自我注意力（EHNN-TransFormer）的两个实用实现，这些实现易于实施，理论上比大多数消息传递方法更具表现力。我们证明了它们在一系列超图学习问题中的能力，包括合成K边缘识别，半监督分类和视觉关键点匹配，并报告对强烈消息传递基线的改进性能。我们的实施可从https://github.com/jw9730/ehnn获得。

Graph神经网络（GNN）最近已成为使用图的机器学习的主要范式。对GNNS的研究主要集中于消息传递神经网络（MPNNS）的家族。与同构的Weisfeiler-Leman（WL）测试类似，这些模型遵循迭代的邻域聚合过程以更新顶点表示，并通过汇总顶点表示来更新顶点图表。尽管非常成功，但在过去的几年中，对MPNN进行了深入的研究。因此，需要新颖的体系结构，这将使该领域的研究能够脱离MPNN。在本文中，我们提出了一个新的图形神经网络模型，即所谓的$ \ pi $ -gnn，该模型学习了每个图的“软”排列（即双随机）矩阵，从而将所有图形投影到一个共同的矢量空间中。学到的矩阵在输入图的顶点上强加了“软”顺序，并基于此顺序，将邻接矩阵映射到向量中。这些向量可以被送入完全连接或卷积的层，以应对监督的学习任务。在大图的情况下，为了使模型在运行时间和记忆方面更有效，我们进一步放松了双随机矩阵，以使其排列随机矩阵。我们从经验上评估了图形分类和图形回归数据集的模型，并表明它与最新模型达到了性能竞争。

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key architectures, iii) has an open-source, easy-to-use and reproducible code infrastructure, and iv) is flexible for researchers to experiment with new theoretical ideas. As of December 2022, the GitHub repository has reached 2,000 stars and 380 forks, which demonstrates the utility of the proposed open-source framework through the wide usage by the GNN community. In this paper, we present an updated version of our benchmark with a concise presentation of the aforementioned framework characteristics, an additional medium-sized molecular dataset AQSOL, similar to the popular ZINC, but with a real-world measured chemical target, and discuss how this framework can be leveraged to explore new GNN designs and insights. As a proof of value of our benchmark, we study the case of graph positional encoding (PE) in GNNs, which was introduced with this benchmark and has since spurred interest of exploring more powerful PE for Transformers and GNNs in a robust experimental setting.

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection between these models and the Weisfeiler-Leman (WL) test of isomorphism, an algorithm that can successfully test isomorphism for a broad class of graphs. Recently, much research has focused on measuring the expressive power of GNNs. For instance, it has been shown that standard MPNNs are at most as powerful as WL in terms of distinguishing non-isomorphic graphs. However, these studies have largely ignored the distances between the representations of nodes/graphs which are of paramount importance for learning tasks. In this paper, we define a distance function between nodes which is based on the hierarchy produced by the WL algorithm, and propose a model that learns representations which preserve those distances between nodes. Since the emerging hierarchy corresponds to a tree, to learn these representations, we capitalize on recent advances in the field of hyperbolic neural networks. We empirically evaluate the proposed model on standard node and graph classification datasets where it achieves competitive performance with state-of-the-art models.

图形神经网络（GNNS）最流行的设计范例是1跳消息传递 - 反复反复从1跳邻居聚集特征。但是，1-HOP消息传递的表达能力受Weisfeiler-Lehman（1-WL）测试的界定。最近，研究人员通过同时从节点的K-Hop邻居汇总信息传递到K-HOP消息。但是，尚无分析K-Hop消息传递的表达能力的工作。在这项工作中，我们从理论上表征了K-Hop消息传递的表达力。具体而言，我们首先正式区分了两种k-hop消息传递的内核，它们在以前的作品中经常被滥用。然后，我们通过表明它比1-Hop消息传递更强大，从而表征了K-Hop消息传递的表现力。尽管具有较高的表达能力，但我们表明K-Hop消息传递仍然无法区分一些简单的常规图。为了进一步增强其表现力，我们引入了KP-GNN框架，该框架通过利用每个跳跃中的外围子图信息来改善K-HOP消息。我们证明，KP-GNN可以区分几乎所有常规图，包括一些距离常规图，这些图无法通过以前的距离编码方法来区分。实验结果验证了KP-GNN的表达能力和有效性。 KP-GNN在所有基准数据集中都取得了竞争成果。