我们研究了深GCN模型中的自适应层图形卷积。我们建议ADAGPR在GCNII网络的每一层中学习通用的Pageranks，以诱导适应性卷积。我们表明，ADAGPR结合的概括是由归一化邻接矩阵的特征值谱的多项式按概括性Pagerank系数数量的顺序界定的。通过分析概括范围，我们表明过度厚度取决于汇总的较高阶段矩阵矩阵和模型深度。我们使用基准真实数据对节点分类进行了评估，并表明ADAGPR与现有的图形卷积网络相比提供了改进的精确度，同时证明了针对超平面的稳健性。此外，我们证明了对层概括的PageRanks系数的分析使我们能够在每个层上定性地了解模型解释的卷积。

我们研究了从高阶图卷积中的有效学习，并直接从邻接矩阵进行节点分类学习。我们重新访问缩放的图形残留网络，并从残留层中删除Relu激活，并在每个残留层上应用一个重量矩阵。我们表明，所得模型导致新的图卷积模型作为归一化邻接矩阵，残留权重矩阵和残差缩放参数的多项式。此外，我们提出了直接绘制多项式卷积模型和直接从邻接矩阵学习的自适应学习。此外，我们提出了完全自适应模型，以学习每个残留层的缩放参数。我们表明，所提出的方法的概括界限是特征值谱，缩放参数和残留权重的上限的多项式。通过理论分析，我们认为所提出的模型可以通过限制卷积的更高端口和直接从邻接矩阵学习来获得改进的概括界限。我们使用一套真实数据，我们证明所提出的方法获得了提高的非全粒图淋巴结分类的精度。

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 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: Initial residual and Identity mapping. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi-and fullsupervised tasks. Code is available at https: //github.com/chennnM/GCNII.

Over-fitting and 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 also a message passing reducer. Furthermore, we theoretically demonstrate that DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by it. More importantly, our DropEdge is a general skill that can be equipped with many other backbone models (e.g. GCN, ResGCN, GraphSAGE, and JKNet) for enhanced performance. Extensive experiments on several benchmarks verify that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs. The effect of DropEdge on preventing over-smoothing is empirically visualized and validated as well. Codes are released on https://github.com/DropEdge/DropEdge.

Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. MixHop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets. 1 We use "like", as graph edges are not axis-aligned.

Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of graph NNs via their asymptotic behaviors as the layer size tends to infinity. Our strategy is to generalize the forward propagation of a Graph Convolutional Network (GCN), which is a popular graph NN variant, as a specific dynamical system. In the case of a GCN, we show that when its weights satisfy the conditions determined by the spectra of the (augmented) normalized Laplacian, its output exponentially approaches the set of signals that carry information of the connected components and node degrees only for distinguishing nodes. Our theory enables us to relate the expressive power of GCNs with the topological information of the underlying graphs inherent in the graph spectra. To demonstrate this, we characterize the asymptotic behavior of GCNs on the Erdős -Rényi graph. We show that when the Erdős -Rényi graph is sufficiently dense and large, a broad range of GCNs on it suffers from the "information loss" in the limit of infinite layers with high probability. Based on the theory, we provide a principled guideline for weight normalization of graph NNs. We experimentally confirm that the proposed weight scaling enhances the predictive performance of GCNs in real data 1 .

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.

提高GCN的深度（预计将允许更多表达性）显示出损害性能，尤其是在节点分类上。原因的主要原因在于过度平滑。过度平滑的问题将GCN的输出驱动到一个在节点之间包含有限的区别信息的空间，从而导致表现不佳。已经提出了一些有关完善GCN架构的作品，但理论上仍然未知这些改进是否能够缓解过度平衡。在本文中，我们首先从理论上分析了通用GCN如何与深度增加的作用，包括通用GCN，GCN，具有偏见，RESGCN和APPNP。我们发现所有这些模型都以通用过程为特征：所有节点融合到Cuboid。在该定理下，我们建议通过在每个训练时期随机去除一定数量的边缘来减轻过度光滑的状态。从理论上讲，Dropedge可以降低过度平滑的收敛速度，或者可以减轻尺寸崩溃引起的信息损失。对模拟数据集的实验评估已可视化不同GCN之间过度平滑的差异。此外，对几个真正的基准支持的广泛实验，这些实验始终如一地改善各种浅GCN和深度GCN的性能。

图形神经网络已成为从图形结构数据学习的不可缺少的工具之一，并且它们的实用性已在各种各样的任务中显示。近年来，建筑设计的巨大改进，导致各种预测任务的性能更好。通常，这些神经架构在同一层中使用可知的权重矩阵组合节点特征聚合和特征转换。这使得分析从各种跳过的节点特征和神经网络层的富有效力来挑战。由于不同的图形数据集显示在特征和类标签分布中的不同级别和异常级别，因此必须了解哪些特征对于没有任何先前信息的预测任务是重要的。在这项工作中，我们将节点特征聚合步骤和深度与图形神经网络分离，并经验分析了不同的聚合特征在预测性能中发挥作用。我们表明，并非通过聚合步骤生成的所有功能都很有用，并且通常使用这些较少的信息特征可能对GNN模型的性能有害。通过我们的实验，我们表明学习这些功能的某些子集可能会导致各种数据集的性能更好。我们建议使用Softmax作为常规器，并从不同跳距的邻居聚合的功能的“软选择器”;和L2 - GNN层的标准化。结合这些技术，我们呈现了一个简单浅的模型，特征选择图神经网络（FSGNN），并经验展示所提出的模型比九个基准数据集中的最先进的GNN模型实现了可比或甚至更高的准确性节点分类任务，具有显着的改进，可达51.1％。

图形神经网络（GNNS）对图表上的半监督节点分类展示了卓越的性能，结果是它们能够同时利用节点特征和拓扑信息的能力。然而，大多数GNN隐含地假设曲线图中的节点和其邻居的标签是相同或一致的，其不包含在异质图中，其中链接节点的标签可能不同。因此，当拓扑是非信息性的标签预测时，普通的GNN可以显着更差，而不是在每个节点上施加多层Perceptrons（MLPS）。为了解决上述问题，我们提出了一种新的$ -laplacian基于GNN模型，称为$ ^ P $ GNN，其消息传递机制来自离散正则化框架，并且可以理论上解释为多项式图的近似值在$ p $ -laplacians的频谱域上定义过滤器。光谱分析表明，新的消息传递机制同时用作低通和高通滤波器，从而使$ ^ P $ GNNS对同性恋和异化图有效。关于现实世界和合成数据集的实证研究验证了我们的调查结果，并证明了$ ^ P $ GNN明显优于异交基准的几个最先进的GNN架构，同时在同性恋基准上实现竞争性能。此外，$ ^ p $ gnns可以自适应地学习聚合权重，并且对嘈杂的边缘具有强大。

图形神经网络（GNNS）由于其强大的表示能力而广泛用于图形结构化数据处理。通常认为，GNNS可以隐式消除非预测性的噪音。但是，对图神经网络中隐式降解作用的分析仍然开放。在这项工作中，我们进行了一项全面的理论研究，并分析了隐式denoising在GNN中发生的何时以及为什么发生。具体而言，我们研究噪声矩阵的收敛性。我们的理论分析表明，隐式转化很大程度上取决于连接性，图形大小和GNN体系结构。此外，我们通过扩展图形信号降解问题来正式定义并提出对抗图信号denoising（AGSD）问题。通过解决这样的问题，我们得出了一个可靠的图形卷积，可以增强节点表示的平滑度和隐式转化效果。广泛的经验评估验证了我们的理论分析和我们提出的模型的有效性。

A central challenge of building more powerful Graph Neural Networks (GNNs) is the oversmoothing phenomenon, where increasing the network depth leads to homogeneous node representations and thus worse classification performance. While previous works have only demonstrated that oversmoothing is inevitable when the number of graph convolutions tends to infinity, in this paper, we precisely characterize the mechanism behind the phenomenon via a non-asymptotic analysis. Specifically, we distinguish between two different effects when applying graph convolutions -- an undesirable mixing effect that homogenizes node representations in different classes, and a desirable denoising effect that homogenizes node representations in the same class. By quantifying these two effects on random graphs sampled from the Contextual Stochastic Block Model (CSBM), we show that oversmoothing happens once the mixing effect starts to dominate the denoising effect, and the number of layers required for this transition is $O(\log N/\log (\log N))$ for sufficiently dense graphs with $N$ nodes. We also extend our analysis to study the effects of Personalized PageRank (PPR) on oversmoothing. Our results suggest that while PPR mitigates oversmoothing at deeper layers, PPR-based architectures still achieve their best performance at a shallow depth and are outperformed by the graph convolution approach on certain graphs. Finally, we support our theoretical results with numerical experiments, which further suggest that the oversmoothing phenomenon observed in practice may be exacerbated by the difficulty of optimizing deep GNN models.

Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials. GCN simplifies ChebNet by utilizing only the first two Chebyshev polynomials while still outperforming it on real-world datasets. GPR-GNN and BernNet demonstrate that the Monomial and Bernstein bases also outperform the Chebyshev basis in terms of learning the spectral graph convolutions. Such conclusions are counter-intuitive in the field of approximation theory, where it is established that the Chebyshev polynomial achieves the optimum convergent rate for approximating a function. In this paper, we revisit the problem of approximating the spectral graph convolutions with Chebyshev polynomials. We show that ChebNet's inferior performance is primarily due to illegal coefficients learnt by ChebNet approximating analytic filter functions, which leads to over-fitting. We then propose ChebNetII, a new GNN model based on Chebyshev interpolation, which enhances the original Chebyshev polynomial approximation while reducing the Runge phenomenon. We conducted an extensive experimental study to demonstrate that ChebNetII can learn arbitrary graph convolutions and achieve superior performance in both full- and semi-supervised node classification tasks. Most notably, we scale ChebNetII to a billion graph ogbn-papers100M, showing that spectral-based GNNs have superior performance. Our code is available at https://github.com/ivam-he/ChebNetII.

近年来，监督学习环境的几个结果表明，古典统计学习 - 理论措施，如VC维度，不充分解释深度学习模型的性能，促使在无限宽度和迭代制度中的工作摆动。但是，对于超出监督环境之外的神经网络成功几乎没有理论解释。在本文中，我们认为，在一些分布假设下，经典学习 - 理论措施可以充分解释转导造型中的图形神经网络的概括。特别是，我们通过分析节点分类问题图卷积网络的概括性特性，对神经网络的性能进行严格分析神经网络。虽然VC维度确实导致该设置中的琐碎泛化误差界限，但我们表明转导变速器复杂性可以解释用于随机块模型的图形卷积网络的泛化特性。我们进一步使用基于转换的Rademacher复杂性的泛化误差界限来展示图形卷积和网络架构在实现较小的泛化误差方面的作用，并在图形结构可以帮助学习时提供洞察。本文的调查结果可以重新新的兴趣在学习理论措施方面对神经网络的概括，尽管在特定问题中。

Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the features of neighboring nodes. However, they fail to directly characterize and leverage the structural information. In this paper, we propose multi-duplicated characterization of graph structures using information gain ratio (IGR) for GNNs (MSI-GNN), which enhances the performance of node classification by using an i-hop adjacency matrix as the structural information of the graph data. In MSI-GNN, the i-hop adjacency matrix is adaptively adjusted by two methods: (i) structural features in the matrix are selected based on the IGR, and (ii) the selected features in (i) for each node are duplicated and combined flexibly. In an experiment, we show that our MSI-GNN outperforms GCN, H2GCN, and GCNII in terms of average accuracies in benchmark graph datasets.

我们提出了图形耦合振荡器网络（GraphCon），这是一个新颖的图形学习框架。它基于普通微分方程（ODE）的二阶系统的离散化，该系统建模了非线性控制和阻尼振荡器网络，并通过基础图的邻接结构结合。我们的框架的灵活性允许作为耦合函数任何基本的GNN层（例如卷积或注意力），通过该函数，通过该函数通过该函数通过该函数通过该函数通过所提出的ODES的动力学来构建多层深神经网络。我们将GNN中通常遇到的过度厚度问题与基础ode的稳态稳定性联系起来，并表明零二核能能量稳态对于我们提出的ODE不稳定。这表明所提出的框架减轻了过度厚度的问题。此外，我们证明GraphCon减轻了爆炸和消失的梯度问题，以促进对多层GNN的训练。最后，我们证明我们的方法在各种基于图形的学习任务方面就最先进的方法提供了竞争性能。

图形卷积网络（GCN）类似于卷积神经网络（CNN），通常基于两个主要操作 - 空间和点的卷积。在GCN的背景下，与CNN不同，通常选择基于图形laplacian的预定的​​空间操作员，通常只允许学习点的操作。但是，学习有意义的空间操作员对于开发更具表现力的GCN以提高性能至关重要。在本文中，我们提出了PathGCN，这是一种从图上的随机路径学习空间操作员的新方法。我们分析方法的收敛及其与现有GCN的差异。此外，我们讨论了将我们所学的空间操作员与点卷积相结合的几种选择。我们在众多数据集上进行的广泛实验表明，通过适当地学习空间和角度的卷积，可以固有地避免诸如过度光滑的现象，并实现新的最先进的性能。

图表神经网络（GNNS）在图形结构数据的表现中表现出巨大的成功。在捕获图形拓扑中，GNN中的层展图表卷积显示为强大。在此过程中，GNN通常由预定义的内核引导，例如拉普拉斯矩阵，邻接矩阵或其变体。但是，预定义的内核的采用可能会限制不同图形的必要性：图形和内核之间的不匹配将导致次优性能。例如，当高频信息对于图表具有重要意义时，聚焦在低频信息上的GNN可能无法实现令人满意的性能，反之亦然。为了解决这个问题，在本文中，我们提出了一种新颖的框架 - 即，即Adaptive Kernel图神经网络（AKGNN） - 这将在第一次尝试时以统一的方式适应最佳图形内核。在所提出的AKGNN中，我们首先设计一种数据驱动的图形内核学习机制，它通过修改图拉普拉斯的最大特征值来自适应地调制全通过和低通滤波器之间的平衡。通过此过程，AKGNN了解高频信号之间的最佳阈值以减轻通用问题。稍后，我们通过参数化技巧进一步减少参数的数量，并通过全局读出功能增强富有表现力。在确认的基准数据集中进行了广泛的实验，并且有希望的结果通过与最先进的GNNS比较，展示了我们所提出的Akgnn的出色表现。源代码在公开上可用：https://github.com/jumxglhf/akgnn。

尽管在深度学习的其他应用领域中取得了非常深的架构，但流行的图神经网络是浅层模型。这降低了建模能力，并使模型无法捕获远程关系。浅设计的主要原因是过度平滑的，这导致节点状态随着深度的增加而变得更加相似。我们建立在GNNS和Pagerank之间的紧密联系的基础上，为此，个性化的Pagerank介绍了对个性化向量的考虑。通过这个想法，我们提出了个性化的Pagerank图神经网络（PPRGNN），该神经网络将图形卷积网络扩展到无限深度模型，该模型有机会将邻居聚集重置回每个迭代中的初始状态。我们引入了一个很好的解释调整，以重置重置并证明我们的方法与独特解决方案的收敛性，而无需放置任何限制，即使无限地进行了许多邻居聚集。与个性化的Pagerank一样，我们的结果不会过度光滑。在这样做的同时，在我们保持内存复杂性恒定的同时，时间复杂性保持线性，而与网络的深度无关，使其比较大图。我们从经验上展示了方法对各种节点和图形分类任务的有效性。在几乎所有情况下，PPRGNN优于可比较的方法。

由于学习节点表示的优越性，图形神经网络（GNNS）受到了巨大的关注。这些模型依赖于消息传递和特征转换功能来从邻居编码结构和功能信息。然而，堆叠更多的卷积层显着降低了GNN的性能。大多数最近的研究将此限制属于过平滑问题，其中节点嵌入式会聚到无法区分的向量。通过许多实验观察，我们认为，主要因素降低性能是不稳定的正向标准化和后向梯度因特征变换的不当设计而导致的，尤其是对于未发生过平滑的浅GNN。因此，我们提出了一个名为Ortho-GConv的新型正交特征转换，这通常可以增加现有的GNN骨干，以稳定模型训练并改善模型的泛化性能。具体地，我们从三个视角综合地维持特征变换的正交性，即混合权重初始化，正交变换和正交正规。通过用ortho-gconv配备现有的GNN（例如GCN，JKNET，GCNII），我们展示了正交特征变换的一般性以实现稳定训练，并显示其对节点和图形分类任务的有效性。