The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood node information. Though effective for various tasks, in this paper, we show that they are potentially a problematic factor underlying all GNN methods for learning on certain datasets, as they force the node representations similar, making the nodes gradually lose their identity and become indistinguishable. Hence, we augment the aggregation operations with their dual, i.e. diversification operators that make the node more distinct and preserve the identity. Such augmentation replaces the aggregation with a two-channel filtering process that, in theory, is beneficial for enriching the node representations. In practice, the proposed two-channel filters can be easily patched on existing GNN methods with diverse training strategies, including spectral and spatial (message passing) methods. In the experiments, we observe desired characteristics of the models and significant performance boost upon the baselines on 9 node classification tasks.
Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.
Graph neural networks (GNNs) have demonstrated strong performance on a wide variety of tasks due to their ability to model non-uniform structured data. Despite their promise, there exists little research exploring methods to make them more efficient at inference time. In this work, we explore the viability of training quantized GNNs, enabling the usage of low precision integer arithmetic during inference. We identify the sources of error that uniquely arise when attempting to quantize GNNs, and propose an architecturally-agnostic method, Degree-Quant, to improve performance over existing quantization-aware training baselines commonly used on other architectures, such as CNNs. We validate our method on six datasets and show, unlike previous attempts, that models generalize to unseen graphs. Models trained with Degree-Quant for INT8 quantization perform as well as FP32 models in most cases; for INT4 models, we obtain up to 26% gains over the baselines. Our work enables up to 4.7x speedups on CPU when using INT8 arithmetic.
We propose PiNet, a generalised differentiable attention-based pooling mechanism for utilising graph convolution operations for graph level classification. We demonstrate high sample efficiency and superior performance over other graph neural networks in distinguishing isomorphic graph classes, as well as competitive results with state of the art methods on standard chemo-informatics datasets.
We present an end-to-end, interpretable, deep-learning architecture to learn a graph kernel that predicts the outcome of chronic disease drug prescription. This is achieved through a deep metric learning collaborative with a Support Vector Machine objective using a graphical representation of Electronic Health Records. We formulate the predictive model as a binary graph classification problem with an adaptive learned graph kernel through novel cross-global attention node matching between patient graphs, simultaneously computing on multiple graphs without training pair or triplet generation. Results using the Taiwanese National Health Insurance Research Database demonstrate that our approach outperforms current start-of-the-art models both in terms of accuracy and interpretability.
Feature interactions are essential for achieving high accuracy in recommender systems. Many studies take into account the interaction between every pair of features. However, this is suboptimal because some feature interactions may not be that relevant to the recommendation result, and taking them into account may introduce noise and decrease recommendation accuracy. To make the best out of feature interactions, we propose a graph neural network approach to effectively model them, together with a novel technique to automatically detect those feature interactions that are beneficial in terms of recommendation accuracy. The automatic feature interaction detection is achieved via edge prediction with an L0 activation regularization. Our proposed model is proved to be effective through the information bottleneck principle and statistical interaction theory. Experimental results show that our model (i) outperforms existing baselines in terms of accuracy, and (ii) automatically identifies beneficial feature interactions.
In this paper, a novel multi-view methodology for graph-based neural networks is proposed. A systematic and methodological adaptation of the key concepts of classical deep learning methods such as convolution, pooling and multi-view architectures is developed for the context of non-Euclidean manifolds. The aim of the proposed work is to present a novel multi-view graph convolution layer, as well as a new view pooling layer making use of: a) a new hybrid Laplacian that is adjusted based on feature distance metric learning, b) multiple trainable representations of a feature matrix of a graph, using trainable distance matrices, adapting the notion of views to graphs and c) a multi-view graph aggregation scheme called graph view pooling, in order to synthesise information from the multiple generated views. The aforementioned layers are used in an end-to-end graph neural network architecture for graph classification and show competitive results to other state-of-the-art methods.
Graph Neural Networks (GNNs) have recently caught great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or MathNet, with interrelated convolution and pooling strategies. The underlying method takes graphs in different structures as input and assembles consistent graph representations for readout layers, which then accomplishes label prediction. To achieve this, the multiresolution graph representations are first constructed and fed into graph convolutional layers for processing. The hierarchical graph pooling layers are then involved to downsample graph resolution while simultaneously remove redundancy within graph signals. The whole workflow could be formed with a multi-level graph analysis, which not only helps embed the intrinsic topological information of each graph into the GNN, but also supports fast computation of forward and adjoint graph transforms. We show by extensive experiments that the proposed framework obtains notable accuracy gains on graph classification and regression tasks with performance stability. The proposed MathNet outperforms various existing GNN models, especially on big data sets.
Graph neural networks get significant attention for graph representation and classification in machine learning community. Attention mechanism applied on the neighborhood of a node improves the performance of graph neural networks. Typically, it helps to identify a neighbor node which plays more important role to determine the label of the node under consideration. But in real world scenarios, a particular subset of nodes together, but not the individual pairs in the subset, may be important to determine the label of the graph. To address this problem, we introduce the concept of subgraph attention for graphs. On the other hand, hierarchical graph pooling has been shown to be promising in recent literature. But due to noisy hierarchical structure of real world graphs, not all the hierarchies of a graph play equal role for graph classification. Towards this end, we propose a graph classification algorithm called SubGattPool which jointly learns the subgraph attention and employs two different types of hierarchical attention mechanisms to find the important nodes in a hierarchy and the importance of individual hierarchies in a graph. Experimental evaluation with different types of graph classification algorithms shows that SubGattPool is able to improve the state-of-the-art or remains competitive on multiple publicly available graph classification datasets. We conduct further experiments on both synthetic and real world graph datasets to justify the usefulness of different components of SubGattPool and to show its consistent performance on other downstream tasks.
Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.
Recently, there has been an increasing interest in (supervised) learning with graph data, especially using graph neural networks. However, the development of meaningful benchmark datasets and standardized evaluation procedures is lagging, consequently hindering advancements in this area. To address this, we introduce the TUDataset for graph classification and regression. The collection consists of over 120 datasets of varying sizes from a wide range of applications. We provide Python-based data loaders, kernel and graph neural network baseline implementations, and evaluation tools. Here, we give an overview of the datasets, standardized evaluation procedures, and provide baseline experiments. All datasets are available at www.graphlearning.io. The experiments are fully reproducible from the code available at www.github.com/chrsmrrs/tudataset.
Graph classification, which aims to identify the category labels of graphs, plays a significant role in drug classification, toxicity detection, protein analysis etc. However, the limitation of scale in the benchmark datasets makes it easy for graph classification models to fall into over-fitting and undergeneralization. To improve this, we introduce data augmentation on graphs (i.e. graph augmentation) and present four methods:random mapping, vertex-similarity mapping, motif-random mapping and motif-similarity mapping, to generate more weakly labeled data for small-scale benchmark datasets via heuristic transformation of graph structures. Furthermore, we propose a generic model evolution framework, named M-Evolve, which combines graph augmentation, data filtration and model retraining to optimize pre-trained graph classifiers. Experiments on six benchmark datasets demonstrate that the proposed framework helps existing graph classification models alleviate over-fitting and undergeneralization in the training on small-scale benchmark datasets, which successfully yields an average improvement of 3 - 13% accuracy on graph classification tasks.
While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this paper, we propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese graph neural network to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, MGMN also exhibits stronger robustness as the sizes of the two input graphs increase.
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 {\em 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: {\em Initial residual} and {\em 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 full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .
Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.
Graph neural networks are promising architecture for learning and inference with graph-structured data. Yet difficulties in modelling the ``parts'' and their ``interactions'' still persist in terms of graph classification, where graph-level representations are usually obtained by squeezing the whole graph into a single vector through graph pooling. From complex systems point of view, mixing all the parts of a system together can affect both model interpretability and predictive performance, because properties of a complex system arise largely from the interaction among its components. We analyze the intrinsic difficulty in graph classification under the unified concept of ``resolution dilemmas'' with learning theoretic recovery guarantees, and propose ``SLIM'', an inductive neural network model for Structural Landmarking and Interaction Modelling. It turns out, that by solving the resolution dilemmas, and leveraging explicit interacting relation between component parts of a graph to explain its complexity, SLIM is more interpretable, accurate, and offers new insight in graph representation learning.
One intriguing property of deep neural networks (DNNs) is their inherent vulnerability to backdoor attacks -- a trojan model responds to trigger-embedded inputs in a highly predictable manner while functioning normally otherwise. Despite the plethora of prior work on DNNs for continuous data (e.g., images), the vulnerability of graph neural networks (GNNs) for discrete-structured data (e.g., graphs) is largely unexplored, which is highly concerning given their increasing use in security-sensitive domains. To bridge this gap, we present GTA, the first backdoor attack on GNNs. Compared with prior work, GTA departs in significant ways: graph-oriented -- it defines triggers as specific subgraphs, including both topological structures and descriptive features, entailing a large design spectrum for the adversary; input-tailored -- it dynamically adapts triggers to individual graphs, thereby optimizing both attack effectiveness and evasiveness; downstream model-agnostic -- it can be readily launched without knowledge regarding downstream models or fine-tuning strategies; and attack-extensible -- it can be instantiated for both transductive (e.g., node classification) and inductive (e.g., graph classification) tasks, constituting severe threats for a range of security-critical applications. Through extensive evaluation using benchmark datasets and state-of-the-art models, we demonstrate the effectiveness of GTA. We further provide analytical justification for its effectiveness and discuss potential countermeasures, pointing to several promising research directions.
General graphs are difficult for learning due to their irregular structures. Existing works employ message passing along graph edges to extract local patterns using customized graph kernels, but few of them are effective for the integration of such local patterns into global features. In contrast, in this paper we study the methods to transfer the graphs into trees so that explicit orders are learned to direct the feature integration from local to global. To this end, we apply the breadth first search (BFS) to construct trees from the graphs, which adds direction to the graph edges from the center node to the peripheral nodes. In addition, we proposed a novel projection scheme that transfer the trees to image representations, which is suitable for conventional convolution neural networks (CNNs) and recurrent neural networks (RNNs). To best learn the patterns from the graph-tree-images, we propose TreeRNN, a 2D RNN architecture that recurrently integrates the image pixels by rows and columns to help classify the graph categories. We evaluate the proposed method on several graph classification datasets, and manage to demonstrate comparable accuracy with the state-of-the-art on MUTAG, PTC-MR and NCI1 datasets.
In this paper we present Spektral, an open-source Python library for building graph neural networks with TensorFlow and the Keras application programming interface. Spektral implements a large set of methods for deep learning on graphs, including message-passing and pooling operators, as well as utilities for processing graphs and loading popular benchmark datasets. The purpose of this library is to provide the essential building blocks for creating graph neural networks, focusing on the guiding principles of user-friendliness and quick prototyping on which Keras is based. Spektral is, therefore, suitable for absolute beginners and expert deep learning practitioners alike. In this work, we present an overview of Spektral's features and report the performance of the methods implemented by the library in scenarios of node classification, graph classification, and graph regression.