In this paper, we investigate the degree of explainability of graph neural networks (GNNs). Existing explainers work by finding global/local subgraphs to explain a prediction, but they are applied after a GNN has already been trained. Here, we propose a meta-learning framework for improving the level of explainability of a GNN directly at training time, by steering the optimization procedure towards what we call `interpretable minima'. Our framework (called MATE, MetA-Train to Explain) jointly trains a model to solve the original task, e.g., node classification, and to provide easily processable outputs for downstream algorithms that explain the model's decisions in a human-friendly way. In particular, we meta-train the model's parameters to quickly minimize the error of an instance-level GNNExplainer trained on-the-fly on randomly sampled nodes. The final internal representation relies upon a set of features that can be `better' understood by an explanation algorithm, e.g., another instance of GNNExplainer. Our model-agnostic approach can improve the explanations produced for different GNN architectures and use any instance-based explainer to drive this process. Experiments on synthetic and real-world datasets for node and graph classification show that we can produce models that are consistently easier to explain by different algorithms. Furthermore, this increase in explainability comes at no cost for the accuracy of the model.
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models. Here, based on an optimization method, we investigate the feasibility of improving graph classification performance while simplifying the model learning process. Inspired by progress in structural information assessment, we optimize the given data sample from graphs to encoding trees. In particular, we minimize the structural entropy of the transformed encoding tree to decode the key structure underlying a graph. This transformation is denoted as structural optimization. Furthermore, we propose a novel feature combination scheme, termed hierarchical reporting, for encoding trees. In this scheme, features are transferred from leaf nodes to root nodes by following the hierarchical structures of encoding trees. We then present an implementation of the scheme in a tree kernel and a convolutional network to perform graph classification. The tree kernel follows label propagation in the Weisfeiler-Lehman (WL) subtree kernel, but it has a lower runtime complexity $O(n)$. The convolutional network is a special implementation of our tree kernel in the deep learning field and is called Encoding Tree Learning (ETL). We empirically validate our tree kernel and convolutional network with several graph classification benchmarks and demonstrate that our methods achieve better performance and lower computational consumption than competing approaches.
Graph Contrastive Learning (GCL) establishes a new paradigm for learning graph representations without human annotations. Although remarkable progress has been witnessed recently, the success behind GCL is still left somewhat mysterious. In this work, we first identify several critical design considerations within a general GCL paradigm, including augmentation functions, contrasting modes, contrastive objectives, and negative mining techniques. Then, to understand the interplay of different GCL components, we conduct extensive, controlled experiments over a set of benchmark tasks on datasets across various domains. Our empirical studies suggest a set of general receipts for effective GCL, e.g., simple topology augmentations that produce sparse graph views bring promising performance improvements; contrasting modes should be aligned with the granularities of end tasks. In addition, to foster future research and ease the implementation of GCL algorithms, we develop an easy-to-use library PyGCL, featuring modularized CL components, standardized evaluation, and experiment management. We envision this work to provide useful empirical evidence of effective GCL algorithms and offer several insights for future research.
Graph classification is an important problem with applications across many domains, like chemistry and bioinformatics, for which graph neural networks (GNNs) have been state-of-the-art (SOTA) methods. GNNs are designed to learn node-level representation based on neighborhood aggregation schemes, and to obtain graph-level representation, pooling methods are applied after the aggregation operation in existing GNN models to generate coarse-grained graphs. However,due to highly diverse applications of graph classification, and the performance of existing pooling methods vary on different graphs. In other words, it is a challenging problem to design a universal pooling architecture to perform well in most cases, leading to a demand for data-specific pooling methods in real-world applications. To address this problem, we propose to use neural architecture search (NAS) to search for adaptive pooling architectures for graph classification. Firstly we designed a unified framework consisting of four modules: Aggregation, Pooling, Readout, and Merge, which can cover existing human-designed pooling methods for graph classification. Based on this framework, a novel search space is designed by incorporating popular operations in human-designed architectures. Then to enable efficient search, a coarsening strategy is proposed to continuously relax the search space, thus a differentiable search method can be adopted. Extensive experiments on six real-world datasets from three domains are conducted, and the results demonstrate the effectiveness and efficiency of the proposed framework.
We propose an extension to the transformer neural network architecture for general-purpose graph learning by adding a dedicated pathway for pairwise structural information, called edge channels. The resultant framework - which we call Edge-augmented Graph Transformer (EGT) - can directly accept, process and output structural information of arbitrary form, which is important for effective learning on graph-structured data. Our model exclusively uses global self-attention as an aggregation mechanism rather than static localized convolutional aggregation. This allows for unconstrained long-range dynamic interactions between nodes. Moreover, the edge channels allow the structural information to evolve from layer to layer, and prediction tasks on edges/links can be performed directly from the output embeddings of these channels. We verify the performance of EGT in a wide range of graph-learning experiments on benchmark datasets, in which it outperforms Convolutional/Message-Passing Graph Neural Networks. EGT sets a new state-of-the-art for the quantum-chemical regression task on the OGB-LSC PCQM4Mv2 dataset containing 3.8 million molecular graphs. Our findings indicate that global self-attention based aggregation can serve as a flexible, adaptive and effective replacement of graph convolution for general-purpose graph learning. Therefore, convolutional local neighborhood aggregation is not an essential inductive bias.
Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention. However, most graph embedding methods have problems such as tedious parameter tuning or poor explanation. This paper presents a simple and hyperparameter-free whole graph embedding method based on the DHC (Degree, H-index, and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The DHC-E can provide a trade-off between simplicity and quality for supervised classification learning tasks involving molecular, social, and brain networks. Moreover, it performs well in lower-dimensional graph visualization. Overall, the DHC-E is simple, hyperparameter-free, and explainable for whole graph embedding with promising potential for exploring graph classification and lower-dimensional graph visualization.
Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas others may trade off clean example performance, such as smoothingbased defense. Most suffer from high complexity or low transferability. To address this problem, we proposed EGC2, an enhanced graph classification model with easy graph compression. EGC2 captures the relationship between the features of different nodes by constructing feature graphs and improving the aggregation of the node-level representations. To achieve lower-complexity defense applied to graph classification models, EGC2 utilizes a centrality-based edge-importance index to compress the graphs, filtering out trivial structures and adversarial perturbations in the input graphs, thus improving the model's robustness. Experiments on ten benchmark datasets demonstrate that the proposed feature read-out and graph compression mechanisms enhance the robustness of multiple basic models, resulting in a state-of-the-art performance in terms of accuracy and robustness against various adversarial attacks.
In the big data era, the relationship between entries becomes more and more complex. Many graph (or network) algorithms have already paid attention to dynamic networks, which are more suitable than static ones for fitting the complex real-world scenarios with evolving structures and features. To contribute to the dynamic network representation learning and mining research, we provide a new bunch of label-adequate, dynamics-meaningful, and attribute-sufficient dynamic networks from the health domain. To be specific, in our proposed repository DPPIN, we totally have 12 individual dynamic network datasets at different scales, and each dataset is a dynamic protein-protein interaction network describing protein-level interactions of yeast cells. We hope these domain-specific node features, structure evolution patterns, and node and graph labels could inspire the regularization techniques to increase the performance of graph machine learning algorithms in a more complex setting. Also, we link potential applications with our DPPIN by designing various dynamic graph experiments, where DPPIN could indicate future research opportunities for some tasks by presenting challenges on state-of-the-art baseline algorithms. Finally, we identify future directions to improve the utility of this repository and welcome constructive inputs from the community. All resources (e.g., data and code) of this work are deployed and publicly available at https://github.com/DongqiFu/DPPIN.
Graph neural networks (GNNs) have been widely used in various graph-related problems such as node classification and graph classification, where superior performance is mainly established when natural node features are available. However, it is not well understood how GNNs work without natural node features, especially regarding the various ways to construct artificial ones. In this paper, we point out the two types of artificial node features, i.e., positional and structural node features, and provide insights on why each of them is more appropriate for certain tasks, i.e., positional node classification, structural node classification, and graph classification. Extensive experimental results on 10 benchmark datasets validate our insights, thus leading to a practical guideline on the choices between different artificial node features for GNNs on non-attributed graphs. The code is available at https://github.com/zjzijielu/gnn-positional-structural-node-features.
In this paper, we propose a novel pooling layer for graph neural networks based on maximizing the mutual information between the pooled graph and the input graph. Since the maximum mutual information is difficult to compute, we employ the Shannon capacity of a graph as an inductive bias to our pooling method. More precisely, we show that the input graph to the pooling layer can be viewed as a representation of a noisy communication channel. For such a channel, sending the symbols belonging to an independent set of the graph yields a reliable and error-free transmission of information. We show that reaching the maximum mutual information is equivalent to finding a maximum weight independent set of the graph where the weights convey entropy contents. Through this communication theoretic standpoint, we provide a distinct perspective for posing the problem of graph pooling as maximizing the information transmission rate across a noisy communication channel, implemented by a graph neural network. We evaluate our method, referred to as Maximum Entropy Weighted Independent Set Pooling (MEWISPool), on graph classification tasks and the combinatorial optimization problem of the maximum independent set. Empirical results demonstrate that our method achieves the state-of-the-art and competitive results on graph classification tasks and the maximum independent set problem in several benchmark datasets.
Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.
Federated learning has emerged as an important paradigm for training machine learning models in different domains. For graph-level tasks such as graph classification, graphs can also be regarded as a special type of data samples, which can be collected and stored in separate local systems. Similar to other domains, multiple local systems, each holding a small set of graphs, may benefit from collaboratively training a powerful graph mining model, such as the popular graph neural networks (GNNs). To provide more motivation towards such endeavors, we analyze real-world graphs from different domains to confirm that they indeed share certain graph properties that are statistically significant compared with random graphs. However, we also find that different sets of graphs, even from the same domain or same dataset, are non-IID regarding both graph structures and node features. To handle this, we propose a graph clustered federated learning (GCFL) framework that dynamically finds clusters of local systems based on the gradients of GNNs, and theoretically justify that such clusters can reduce the structure and feature heterogeneity among graphs owned by the local systems. Moreover, we observe the gradients of GNNs to be rather fluctuating in GCFL which impedes high-quality clustering, and design a gradient sequence-based clustering mechanism based on dynamic time warping (GCFL+). Extensive experimental results and in-depth analysis demonstrate the effectiveness of our proposed frameworks.
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models can be severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higher-order signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.
Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the Weisfeiler--Lehman (WL) test. However, these results suffer from some limitations, both because they were derived using the Stone--Weierstrass theorem -- which is existential in nature, -- and because they assume that the target function to be approximated must be continuous. Furthermore, all current results are dedicated to graph classification/regression tasks, where the GNN must produce a single output for the whole graph, while also node classification/regression problems, in which an output is returned for each node, are very common. In this paper, we propose an alternative way to demonstrate the approximation capability of GNNs that overcomes these limitations. Indeed, we show that GNNs are universal approximators in probability for node classification/regression tasks, as they can approximate any measurable function that satisfies the 1--WL equivalence on nodes. The proposed theoretical framework allows the approximation of generic discontinuous target functions and also suggests the GNN architecture that can reach a desired approximation. In addition, we provide a bound on the number of the GNN layers required to achieve the desired degree of approximation, namely $2r-1$, where $r$ is the maximum number of nodes for the graphs in the domain.
The recent emergence of contrastive learning approaches facilitates the application on graph representation learning (GRL), introducing graph contrastive learning (GCL) into the literature. These methods contrast semantically similar and dissimilar sample pairs to encode the semantics into node or graph embeddings. However, most existing works only performed \textbf{model-level} evaluation, and did not explore the combination space of modules for more comprehensive and systematic studies. For effective \textbf{module-level} evaluation, we propose a framework that decomposes GCL models into four modules: (1) a \textbf{sampler} to generate anchor, positive and negative data samples (nodes or graphs); (2) an \textbf{encoder} and a \textbf{readout} function to get sample embeddings; (3) a \textbf{discriminator} to score each sample pair (anchor-positive and anchor-negative); and (4) an \textbf{estimator} to define the loss function. Based on this framework, we conduct controlled experiments over a wide range of architectural designs and hyperparameter settings on node and graph classification tasks. Specifically, we manage to quantify the impact of a single module, investigate the interaction between modules, and compare the overall performance with current model architectures. Our key findings include a set of module-level guidelines for GCL, e.g., simple samplers from LINE and DeepWalk are strong and robust; an MLP encoder associated with Sum readout could achieve competitive performance on graph classification. Finally, we release our implementations and results as OpenGCL, a modularized toolkit that allows convenient reproduction, standard model and module evaluation, and easy extension. OpenGCL is available at \url{https://github.com/thunlp/OpenGCL}.
HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-ange relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-in-play module for improving the representational power of HGCNNs. Specifically, HERALD adaptively optimizes the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned. Furthermore, HERALD employs the self-attention mechanism to capture the non-local paired-nodes relation. Extensive experiments on various popular hypergraph datasets for node classification and graph classification tasks demonstrate that our approach obtains consistent and considerable performance enhancement, proving its effectiveness and generalization ability.
Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.
The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer.
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes the fixed points of a target graph system and decodes them to estimate the stationary properties of the system without the prior knowledge of existing solvers or intermediate solutions. The forward propagation of CGS proceeds in three steps: (1) constructing the input dependent linear contracting iterative maps, (2) computing the fixed-points of the linear maps, and (3) decoding the fixed-points to estimate the properties. The contractivity of the constructed linear maps guarantees the existence and uniqueness of the fixed points following the Banach fixed point theorem. To train CGS efficiently, we also derive a tractable analytical expression for its gradient by leveraging the implicit function theorem. We evaluate the performance of CGS by applying it to various network-analytic and graph benchmark problems. The results indicate that CGS has competitive capabilities for predicting the stationary properties of graph systems, irrespective of whether the target systems are linear or non-linear. CGS also shows high performance for graph classification problems where the existence or the meaning of a fixed point is hard to be clearly defined, which highlights the potential of CGS as a general graph neural network architecture.
Graph Attention Networks (GATs) are one of the most popular GNN architectures and are considered as the state-of-the-art architecture for representation learning with graphs. In GAT, every node attends to its neighbors given its own representation as the query. However, in this paper we show that GAT computes a very limited kind of attention: the ranking of the attention scores is unconditioned on the query node. We formally define this restricted kind of attention as static attention and distinguish it from a strictly more expressive dynamic attention. Because GATs use a static attention mechanism, there are simple graph problems that GAT cannot express: in a controlled problem, we show that static attention hinders GAT from even fitting the training data. To remove this limitation, we introduce a simple fix by modifying the order of operations and propose GATv2: a dynamic graph attention variant that is strictly more expressive than GAT. We perform an extensive evaluation and show that GATv2 outperforms GAT across 11 OGB and other benchmarks while we match their parametric costs. Our code is available at https://github.com/tech-srl/how_attentive_are_gats . GATv2 is available as part of the PyTorch Geometric library, the Deep Graph Library, and the TensorFlow GNN library.