我们从光谱的角度解决图形生成问题，首先生成图形laplacian光谱的主要部分，然后构建与这些特征值和特征向量相匹配的图。光谱调节允许直接建模全局和局部图结构，并有助于克服单发图生成器的表达性和模式崩溃问题。我们的新颖的甘（Spectre）称为Spectre，可以使用一声模型来产生比以前可能更大的图。Spectre的表现优于最先进的深度自动回归发电机在建模忠诚方面，同时还避免了昂贵的顺序产生和对节点排序的依赖。一个很好的例子，在相当大的合成和现实图形中，Specter的幽灵比最佳竞争对手的最佳竞争对手的改进是4到170倍，该竞争对手不合适，比自回旋发电机快23至30倍。

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.

这项工作引入了离题，这是一种用于生成具有分类节点和边缘属性图的图形的离散denoising扩散模型。我们的模型定义了一个扩散过程，该过程逐步编辑了具有噪声（添加或删除边缘，更改类别）的图形以及学会恢复此过程的图形变压器网络。有了这两种成分，我们将分布学习将上的分布学习减少到一个简单的分类任务序列。我们通过提出一个新的马尔可夫噪声模型来进一步提高样品质量，该模型在扩散过程中保留节点和边缘类型的边际分布，并通过在每个扩散步骤中添加从嘈杂图中得出的辅助图理论特征。最后，我们提出了一个指导程序，以根据图形级特征调理生成。总体而言，离题可以在分子和非分子数据集上达到最新性能，在平面图数据集上，有效性提高了3倍。特别是，这是第一个模型，将鳞片缩放到包含130万个药物样分子的大型鳄梨调子数据集，而无需使用分子特异性表示，例如微笑或片段。

Denoising diffusion probabilistic models and score matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on continuous Gaussian perturbations. Instead, in this work, we suggest using discrete noise for the forward Markov process. This ensures that in every intermediate step the graph remains discrete. Compared to the previous approach, our experimental results on four datasets and multiple architectures show that using a discrete noising process results in higher quality generated samples indicated with an average MMDs reduced by a factor of 1.5. Furthermore, the number of denoising steps is reduced from 1000 to 32 steps leading to a 30 times faster sampling procedure.

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.

在本文中，我们提出了多分辨率的等级图变分性Autiachoders（MGVAE），第一层级生成模型以多分辨率和等分的方式学习和生成图。在每个分辨率级别，MGVAE采用更高的顺序消息，以便在学习中对图进行编码，同时学习将其分配到互斥的集群中并赋予最终产生潜在分布的层次结构的较低分辨率。然后，MGVAE构造分层生成模型以改变地解码成粗糙的图形的层次。重要的是，我们提出的框架是关于节点排序的端到端排列等级。MGVAE通过多种生成任务实现竞争结果，包括一般图生成，分子产生，无监督的分子表示学习，以预测分子特性，引用图的链路预测，以及基于图的图像生成。

我们考虑一拍概率解码器，该解码器在分布上映射到集合或图形之前的矢量形状。这些功能可以集成到变分性自动化器（VAE），生成的对抗网络（GAN）或标准化流动中，并在药物发现中具有重要应用。设置和图形生成最常通过生成点（有时是边缘权重）i.i.d.从正态分布，使用变压器层或图形神经网络处理它们以及先前的向量。该架构旨在产生可交换的分布（集合的所有排列同样可能），但由于I.I.D的随机性，难以训练。一代。我们提出了一种新的对抗性定义，并表明，VAES和GAN中的交换性实际上是不必要的。然后，我们引入TOP-N，一个确定性，不可交换的集合创建机制，该创建机制学会从培训参考集中选择最相关的点。 Top-n可以替换i.i.d.在任何VAE或GaN中生成 - 它更容易训练，更好地捕获数据中的复杂依赖关系。 Top-n优于I.I.D在SetMnist重建时生成15％，生成较近合成分子数据集的真正分布的34％的集合，并且能够在经典QM9数据集上培训时产生更多样化的分子。随着一次性生成的改进基础，我们的算法有助于设计更有效的分子生成方法。

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.

图形结构数据的深层生成模型为化学合成问题提供了一个新的角度：通过优化直接生成分子图的可区分模型，可以在化学结构的离散和广阔空间中侧键入昂贵的搜索程序。我们介绍了Molgan，这是一种用于小分子图的隐式，无似然生成模型，它规避了对以前基于可能性的方法的昂贵图形匹配程序或节点订购启发式方法的需求。我们的方法适应生成对抗网络（GAN）直接在图形结构数据上操作。我们将方法与增强学习目标结合起来，以鼓励具有特定所需化学特性的分子产生。在QM9化学数据库的实验中，我们证明了我们的模型能够生成接近100％有效化合物。莫尔根（Molgan）与最近使用基于字符串的分子表示（微笑）表示的提案和基于似然的方法直接生成图的方法进行了比较。 https://github.com/nicola-decao/molgan上的代码

Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as well as permutation invariance to node orderings in underlying graph distributions. Current leading autoregressive models fail to capture the permutation invariance nature of graphs for the reliance on generation ordering and have high time complexity. Here, we propose a continuous-time generative diffusion process for permutation invariant graph generation to mitigate these issues. Specifically, we first construct a forward diffusion process defined by a stochastic differential equation (SDE), which smoothly converts graphs within the complex distribution to random graphs that follow a known edge probability. Solving the corresponding reverse-time SDE, graphs can be generated from newly sampled random graphs. To facilitate the reverse-time SDE, we newly design a position-enhanced graph score network, capturing the evolving structure and position information from perturbed graphs for permutation equivariant score estimation. Under the evaluation of comprehensive metrics, our proposed generative diffusion process achieves competitive performance in graph distribution learning. Experimental results also show that GraphGDP can generate high-quality graphs in only 24 function evaluations, much faster than previous autoregressive models.

近年来，基于Weisfeiler-Leman算法的算法和神经架构，是一个众所周知的Graph同构问题的启发式问题，它成为具有图形和关系数据的机器学习的强大工具。在这里，我们全面概述了机器学习设置中的算法的使用，专注于监督的制度。我们讨论了理论背景，展示了如何将其用于监督的图形和节点表示学习，讨论最近的扩展，并概述算法的连接（置换 - ）方面的神经结构。此外，我们概述了当前的应用和未来方向，以刺激进一步的研究。

We consider the problem of modelling high-dimensional distributions and generating new examples of data with complex relational feature structure coherent with a graph skeleton. The model we propose tackles the problem of generating the data features constrained by the specific graph structure of each data point by splitting the task into two phases. In the first it models the distribution of features associated with the nodes of the given graph, in the second it complements the edge features conditionally on the node features. We follow the strategy of implicit distribution modelling via generative adversarial network (GAN) combined with permutation equivariant message passing architecture operating over the sets of nodes and edges. This enables generating the feature vectors of all the graph objects in one go (in 2 phases) as opposed to a much slower one-by-one generations of sequential models, prevents the need for expensive graph matching procedures usually needed for likelihood-based generative models, and uses efficiently the network capacity by being insensitive to the particular node ordering in the graph representation. To the best of our knowledge, this is the first method that models the feature distribution along the graph skeleton allowing for generations of annotated graphs with user specified structures. Our experiments demonstrate the ability of our model to learn complex structured distributions through quantitative evaluation over three annotated graph datasets.

图表无处不在地编码许多域中现实世界对象的关系信息。图形生成的目的是从类似于观察到的图形的分布中生成新图形，由于深度学习模型的最新进展，人们的关注越来越大。在本文中，我们对现有的图形生成文献进行了全面综述，从各种新兴方法到其广泛的应用领域。具体来说，我们首先提出了深图生成的问题，并与几个相关的图形学习任务讨论了它的差异。其次，我们根据模型架构将最新方法分为三类，并总结其生成策略。第三，我们介绍了深图生成的三个关键应用领域。最后，我们重点介绍了深图生成的未来研究中的挑战和机遇。

在过去十年中，图形内核引起了很多关注，并在结构化数据上发展成为一种快速发展的学习分支。在过去的20年中，该领域发生的相当大的研究活动导致开发数十个图形内核，每个图形内核都对焦于图形的特定结构性质。图形内核已成功地成功地在广泛的域中，从社交网络到生物信息学。本调查的目标是提供图形内核的文献的统一视图。特别是，我们概述了各种图形内核。此外，我们对公共数据集的几个内核进行了实验评估，并提供了比较研究。最后，我们讨论图形内核的关键应用，并概述了一些仍有待解决的挑战。

Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, substantial research efforts have been devoted to applying deep learning methods to graphs, resulting in beneficial advances in graph analysis techniques. In this survey, we comprehensively review the different types of deep learning methods on graphs. We divide the existing methods into five categories based on their model architectures and training strategies: graph recurrent neural networks, graph convolutional networks, graph autoencoders, graph reinforcement learning, and graph adversarial methods. We then provide a comprehensive overview of these methods in a systematic manner mainly by following their development history. We also analyze the differences and compositions of different methods. Finally, we briefly outline the applications in which they have been used and discuss potential future research directions.

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.

已经为图形生成模型提出了广泛的模型，需要采用有效的方法来评估其质量。到目前为止，大多数技术都使用基于子图计数的传统指标或随机初始化的图形神经网络（GNN）的表示。我们建议使用对比训练的GNN而不是随机GNN的表示形式，并表明这给出了更可靠的评估指标。但是，传统方法和基于GNN的方法都没有主导另一方：我们举例说明每种方法无法区分的示例。我们证明了图形子结构网络（GSN），以一种结合两种方法的方式，可以更好地区分图形数据集之间的距离。

图形神经网络（GNN）已被证明可以实现竞争结果，以解决与图形相关的任务，例如节点和图形分类，链接预测和节点以及各种域中的图形群集。大多数GNN使用消息传递框架，因此称为MPNN。尽管有很有希望的结果，但据报道，MPNN会遭受过度平滑，过度阵型和不足的影响。文献中已经提出了图形重新布线和图形池作为解决这些局限性的解决方案。但是，大多数最先进的图形重新布线方法无法保留该图的全局拓扑，因此没有可区分（电感），并且需要调整超参数。在本文中，我们提出了Diffwire，这是一个在MPNN中进行图形重新布线的新型框架，它通过利用LOV \'ASZ绑定来原理，完全可区分且无参数。我们的方法通过提出两个新的，mpnns中的新的互补层来提供统一的图形重新布线：首先，ctlayer，一个学习通勤时间并将其用作边缘重新加权的相关函数；其次，Gaplayer是优化光谱差距的图层，具体取决于网络的性质和手头的任务。我们从经验上验证了我们提出的方法的价值，并使用基准数据集分别验证了这些层的每个层以进行图形分类。 Diffwire将通勤时间的可学习性汇集到相关的曲率定义，为发展更具表现力的MPNN的发展打开了大门。

图神经网络（GNN）是非欧盟数据的强大深度学习方法。流行的GNN是通信算法（MPNNS），它们在本地图中汇总并结合了信号。但是，浅的mpnns倾向于错过远程信号，并且在某些异质图上表现不佳，而深度mpnns可能会遇到过度平滑或过度阵型等问题。为了减轻此类问题，现有的工作通常会从欧几里得数据上训练神经网络或修改图形结构中借用归一化技术。然而，这些方法在理论上并不是很好地理解，并且可能会提高整体计算复杂性。在这项工作中，我们从光谱图嵌入中汲取灵感，并提出$ \ texttt {powerembed} $ - 一种简单的层归一化技术来增强mpnns。我们显示$ \ texttt {powerembed} $可以证明图形运算符的顶部 - $ k $引导特征向量，该算子可以防止过度光滑，并且对图形拓扑是不可知的；同时，它产生了从本地功能到全球信号的表示列表，避免了过度阵列。我们将$ \ texttt {powerembed} $应用于广泛的模拟和真实图表，并展示其竞争性能，尤其是对于异性图。

图形神经网络（GNN）已在许多图分析任务（例如节点分类和链接预测）上实现了最新结果。然而，事实证明，图形群集等图形上的重要无监督问题对GNN的进步具有更大的抵抗力。图群集的总体目标与GNN中的节点合并相同 - 这是否意味着GNN池方法在聚类图上做得很好？令人惊讶的是，答案是没有的 - 当前的GNN合并方法通常无法恢复群集结构，而在简单的基线（例如应用于学习的表示形式上的K-均值）良好工作的情况下。我们通过仔细设计一组实验来进一步研究，以研究图形结构和属性数据中的不同信噪比情景。为了解决这些方法在聚类中的性能不佳，我们引入了深层模块化网络（DMON），这是一种受群集质量模块化量度启发的无监督池方法，并显示了它如何解决现实世界图的挑战性聚类结构的恢复。同样，在现实世界中，我们表明DMON产生的高质量簇与地面真相标签密切相关，从而实现了最先进的结果，比不同指标的其他合并方法提高了40％以上。