Graph Neural Networks (GNNs) are a class of neural networks designed to extract information from the graphical structure of data. Graph Convolutional Networks (GCNs) are a widely used type of GNN for transductive graph learning problems which apply convolution to learn information from graphs. GCN is a challenging algorithm from an architecture perspective due to inherent sparsity, low data reuse, and massive memory capacity requirements. Traditional neural algorithms exploit the high compute capacity of GPUs to achieve high performance for both inference and training. The architectural decision to use a GPU for GCN inference is a question explored in this work. GCN on both CPU and GPU was characterized in order to better understand the implications of graph size, embedding dimension, and sampling on performance.
The opaqueness of the multi-hop fact verification model imposes imperative requirements for explainability. One feasible way is to extract rationales, a subset of inputs, where the performance of prediction drops dramatically when being removed. Though being explainable, most rationale extraction methods for multi-hop fact verification explore the semantic information within each piece of evidence individually, while ignoring the topological information interaction among different pieces of evidence. Intuitively, a faithful rationale bears complementary information being able to extract other rationales through the multi-hop reasoning process. To tackle such disadvantages, we cast explainable multi-hop fact verification as subgraph extraction, which can be solved based on graph convolutional network (GCN) with salience-aware graph learning. In specific, GCN is utilized to incorporate the topological interaction information among multiple pieces of evidence for learning evidence representation. Meanwhile, to alleviate the influence of noisy evidence, the salience-aware graph perturbation is induced into the message passing of GCN. Moreover, the multi-task model with three diagnostic properties of rationale is elaborately designed to improve the quality of an explanation without any explicit annotations. Experimental results on the FEVEROUS benchmark show significant gains over previous state-of-the-art methods for both rationale extraction and fact verification.
In recent years, semi-supervised graph learning with data augmentation (DA) is currently the most commonly used and best-performing method to enhance model robustness in sparse scenarios with few labeled samples. Differing from homogeneous graph, DA in heterogeneous graph has greater challenges: heterogeneity of information requires DA strategies to effectively handle heterogeneous relations, which considers the information contribution of different types of neighbors and edges to the target nodes. Furthermore, over-squashing of information is caused by the negative curvature that formed by the non-uniformity distribution and strong clustering in complex graph. To address these challenges, this paper presents a novel method named Semi-Supervised Heterogeneous Graph Learning with Multi-level Data Augmentation (HG-MDA). For the problem of heterogeneity of information in DA, node and topology augmentation strategies are proposed for the characteristics of heterogeneous graph. And meta-relation-based attention is applied as one of the indexes for selecting augmented nodes and edges. For the problem of over-squashing of information, triangle based edge adding and removing are designed to alleviate the negative curvature and bring the gain of topology. Finally, the loss function consists of the cross-entropy loss for labeled data and the consistency regularization for unlabeled data. In order to effectively fuse the prediction results of various DA strategies, the sharpening is used. Existing experiments on public datasets, i.e., ACM, DBLP, OGB, and industry dataset MB show that HG-MDA outperforms current SOTA models. Additionly, HG-MDA is applied to user identification in internet finance scenarios, helping the business to add 30% key users, and increase loans and balances by 3.6%, 11.1%, and 9.8%.
Continual graph learning routinely finds its role in a variety of real-world applications where the graph data with different tasks come sequentially. Despite the success of prior works, it still faces great challenges. On the one hand, existing methods work with the zero-curvature Euclidean space, and largely ignore the fact that curvature varies over the coming graph sequence. On the other hand, continual learners in the literature rely on abundant labels, but labeling graph in practice is particularly hard especially for the continuously emerging graphs on-the-fly. To address the aforementioned challenges, we propose to explore a challenging yet practical problem, the self-supervised continual graph learning in adaptive Riemannian spaces. In this paper, we propose a novel self-supervised Riemannian Graph Continual Learner (RieGrace). In RieGrace, we first design an Adaptive Riemannian GCN (AdaRGCN), a unified GCN coupled with a neural curvature adapter, so that Riemannian space is shaped by the learnt curvature adaptive to each graph. Then, we present a Label-free Lorentz Distillation approach, in which we create teacher-student AdaRGCN for the graph sequence. The student successively performs intra-distillation from itself and inter-distillation from the teacher so as to consolidate knowledge without catastrophic forgetting. In particular, we propose a theoretically grounded Generalized Lorentz Projection for the contrastive distillation in Riemannian space. Extensive experiments on the benchmark datasets show the superiority of RieGrace, and additionally, we investigate on how curvature changes over the graph sequence.
Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of problems where the connectivity patterns of data may not be directly accessible. In this work, we generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. The original dDGM architecture used the Euclidean plane to encode latent features based on which the latent graphs were generated. By incorporating Riemannian geometry into the model and generating more complex embedding spaces, we can improve the performance of the latent graph inference system. In particular, we propose a computationally tractable approach to produce product manifolds of constant curvature model spaces that can encode latent features of varying structure. The latent representations mapped onto the inferred product manifold are used to compute richer similarity measures that are leveraged by the latent graph learning model to obtain optimized latent graphs. Moreover, the curvature of the product manifold is learned during training alongside the rest of the network parameters and based on the downstream task, rather than it being a static embedding space. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.
Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision transformer, which applies to image patches, we propose a new Transformer-based graph neural network: Patch Graph Transformer (PatchGT). Unlike previous transformer-based models for learning graph representations, PatchGT learns from non-trainable graph patches, not from nodes directly. It can help save computation and improve the model performance. The key idea is to segment a graph into patches based on spectral clustering without any trainable parameters, with which the model can first use GNN layers to learn patch-level representations and then use Transformer to obtain graph-level representations. The architecture leverages the spectral information of graphs and combines the strengths of GNNs and Transformers. Further, we show the limitations of previous hierarchical trainable clusters theoretically and empirically. We also prove the proposed non-trainable spectral clustering method is permutation invariant and can help address the information bottlenecks in the graph. PatchGT achieves higher expressiveness than 1-WL-type GNNs, and the empirical study shows that PatchGT achieves competitive performances on benchmark datasets and provides interpretability to its predictions. The implementation of our algorithm is released at our Github repo: https://github.com/tufts-ml/PatchGT.
Routine clinical visits of a patient produce not only image data, but also non-image data containing clinical information regarding the patient, i.e., medical data is multi-modal in nature. Such heterogeneous modalities offer different and complementary perspectives on the same patient, resulting in more accurate clinical decisions when they are properly combined. However, despite its significance, how to effectively fuse the multi-modal medical data into a unified framework has received relatively little attention. In this paper, we propose an effective graph-based framework called HetMed (Heterogeneous Graph Learning for Multi-modal Medical Data Analysis) for fusing the multi-modal medical data. Specifically, we construct a multiplex network that incorporates multiple types of non-image features of patients to capture the complex relationship between patients in a systematic way, which leads to more accurate clinical decisions. Extensive experiments on various real-world datasets demonstrate the superiority and practicality of HetMed. The source code for HetMed is available at https://github.com/Sein-Kim/Multimodal-Medical.
Traffic forecasting as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the spatio-temporal heterogeneity and non-stationarity implied in the traffic stream, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (i.e., METR-LA and PEMS-BAY) and a new large-scale traffic speed dataset called EXPY-TKY that covers 1843 expressway road links in Tokyo. Our model outperformed the state-of-the-arts on all three datasets. Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle the road links and time slots with different patterns and be robustly adaptive to any anomalous traffic situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.
Graph neural networks (GNNs) have shown their superiority in modeling graph data. Owing to the advantages of federated learning, federated graph learning (FGL) enables clients to train strong GNN models in a distributed manner without sharing their private data. A core challenge in federated systems is the non-IID problem, which also widely exists in real-world graph data. For example, local data of clients may come from diverse datasets or even domains, e.g., social networks and molecules, increasing the difficulty for FGL methods to capture commonly shared knowledge and learn a generalized encoder. From real-world graph datasets, we observe that some structural properties are shared by various domains, presenting great potential for sharing structural knowledge in FGL. Inspired by this, we propose FedStar, an FGL framework that extracts and shares the common underlying structure information for inter-graph federated learning tasks. To explicitly extract the structure information rather than encoding them along with the node features, we define structure embeddings and encode them with an independent structure encoder. Then, the structure encoder is shared across clients while the feature-based knowledge is learned in a personalized way, making FedStar capable of capturing more structure-based domain-invariant information and avoiding feature misalignment issues. We perform extensive experiments over both cross-dataset and cross-domain non-IID FGL settings, demonstrating the superiority of FedStar.
Existing Graph Neural Networks (GNNs) follow the message-passing mechanism that conducts information interaction among nodes iteratively. While considerable progress has been made, such node interaction paradigms still have the following limitation. First, the scalability limitation precludes the broad application of GNNs in large-scale industrial settings since the node interaction among rapidly expanding neighbors incurs high computation and memory costs. Second, the over-smoothing problem restricts the discrimination ability of nodes, i.e., node representations of different classes will converge to indistinguishable after repeated node interactions. In this work, we propose a novel hop interaction paradigm to address these limitations simultaneously. The core idea is to convert the interaction target among nodes to pre-processed multi-hop features inside each node. We design a simple yet effective HopGNN framework that can easily utilize existing GNNs to achieve hop interaction. Furthermore, we propose a multi-task learning strategy with a self-supervised learning objective to enhance HopGNN. We conduct extensive experiments on 12 benchmark datasets in a wide range of domains, scales, and smoothness of graphs. Experimental results show that our methods achieve superior performance while maintaining high scalability and efficiency. The code is at https://github.com/JC-202/HopGNN.
Analogical reasoning is the process of discovering and mapping correspondences from a target subject to a base subject. As the most well-known computational method of analogical reasoning, Structure-Mapping Theory (SMT) abstracts both target and base subjects into relational graphs and forms the cognitive process of analogical reasoning by finding a corresponding subgraph (i.e., correspondence) in the target graph that is aligned with the base graph. However, incorporating deep learning for SMT is still under-explored due to several obstacles: 1) the combinatorial complexity of searching for the correspondence in the target graph; 2) the correspondence mining is restricted by various cognitive theory-driven constraints. To address both challenges, we propose a novel framework for Analogical Reasoning (DeepGAR) that identifies the correspondence between source and target domains by assuring cognitive theory-driven constraints. Specifically, we design a geometric constraint embedding space to induce subgraph relation from node embeddings for efficient subgraph search. Furthermore, we develop novel learning and optimization strategies that could end-to-end identify correspondences that are strictly consistent with constraints driven by the cognitive theory. Extensive experiments are conducted on synthetic and real-world datasets to demonstrate the effectiveness of the proposed DeepGAR over existing methods.
Knowledge graph embedding (KGE) aims at learning powerful representations to benefit various artificial intelligence applications. Meanwhile, contrastive learning has been widely leveraged in graph learning as an effective mechanism to enhance the discriminative capacity of the learned representations. However, the complex structures of KG make it hard to construct appropriate contrastive pairs. Only a few attempts have integrated contrastive learning strategies with KGE. But, most of them rely on language models ( e.g., Bert) for contrastive pair construction instead of fully mining information underlying the graph structure, hindering expressive ability. Surprisingly, we find that the entities within a relational symmetrical structure are usually similar and correlated. To this end, we propose a knowledge graph contrastive learning framework based on relation-symmetrical structure, KGE-SymCL, which mines symmetrical structure information in KGs to enhance the discriminative ability of KGE models. Concretely, a plug-and-play approach is proposed by taking entities in the relation-symmetrical positions as positive pairs. Besides, a self-supervised alignment loss is designed to pull together positive pairs. Experimental results on link prediction and entity classification datasets demonstrate that our KGE-SymCL can be easily adopted to various KGE models for performance improvements. Moreover, extensive experiments show that our model could outperform other state-of-the-art baselines.
One of the challenges in studying the interactions in large graphs is to learn their diverse pattern and various interaction types. Hence, considering only one distribution and model to study all nodes and ignoring their diversity and local features in their neighborhoods, might severely affect the overall performance. Based on the structural information of the nodes in the graph and the interactions between them, the main graph can be divided into multiple sub-graphs. This graph partitioning can tremendously affect the learning process, however the overall performance is highly dependent on the clustering method to avoid misleading the model. In this work, we present a new framework called KD-SGL to effectively learn the sub-graphs, where we define one global model to learn the overall structure of the graph and multiple local models for each sub-graph. We assess the performance of the proposed framework and evaluate it on public datasets. Based on the achieved results, it can improve the performance of the state-of-the-arts spatiotemporal models with comparable results compared to ensemble of models with less complexity.
The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way to relate structural and functional networks quantified by diffusion tensor imaging and resting-state functional MRI. As one of the state-of-the-art approaches for network analysis, graph convolutional networks (GCN) have been separately used to analyze functional and structural networks, but have not been applied to explore inter-network relationships. In this work, we propose to couple the two networks of an individual by adding inter-network edges between corresponding brain regions, so that the joint structure-function graph can be directly analyzed by a single GCN. The weights of inter-network edges are learnable, reflecting non-uniform structure-function coupling strength across the brain. We apply our Joint-GCN to predict age and sex of 662 participants from the public dataset of the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA) based on their functional and micro-structural white-matter networks. Our results support that the proposed Joint-GCN outperforms existing multi-modal graph learning approaches for analyzing structural and functional networks.
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically exploited to improve efficiency of learning tasks. In this work, we initiate the study on heterogeneous graph sparsification and develop sampling-based algorithms for constructing sparsifiers that are provably sparse and preserve important information in the original graphs. We have performed extensive experiments to confirm that the proposed method can improve time and space complexities of representation learning while achieving comparable, or even better performance in subsequent graph learning tasks based on the learned embedding.
We introduce a new benchmark dataset, Placenta, for node classification in an underexplored domain: predicting microanatomical tissue structures from cell graphs in placenta histology whole slide images. This problem is uniquely challenging for graph learning for a few reasons. Cell graphs are large (>1 million nodes per image), node features are varied (64-dimensions of 11 types of cells), class labels are imbalanced (9 classes ranging from 0.21% of the data to 40.0%), and cellular communities cluster into heterogeneously distributed tissues of widely varying sizes (from 11 nodes to 44,671 nodes for a single structure). Here, we release a dataset consisting of two cell graphs from two placenta histology images totalling 2,395,747 nodes, 799,745 of which have ground truth labels. We present inductive benchmark results for 7 scalable models and show how the unique qualities of cell graphs can help drive the development of novel graph neural network architectures.
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to model complex patterns is essentially constrained by its polynomially growing capacity. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution, owing to the exponential growth property. Different from Euclidean space, which expands polynomially, the hyperbolic space grows exponentially which makes it gains natural advantages in abstracting tree-like or scale-free graphs with hierarchical organizations. In this tutorial, we aim to give an introduction to this emerging field of graph representation learning with the express purpose of being accessible to all audiences. We first give a brief introduction to graph representation learning as well as some preliminary Riemannian and hyperbolic geometry. We then comprehensively revisit the hyperbolic embedding techniques, including hyperbolic shallow models and hyperbolic neural networks. In addition, we introduce the technical details of the current hyperbolic graph neural networks by unifying them into a general framework and summarizing the variants of each component. Moreover, we further introduce a series of related applications in a variety of fields. In the last part, we discuss several advanced topics about hyperbolic geometry for graph representation learning, which potentially serve as guidelines for further flourishing the non-Euclidean graph learning community.
We introduce pyGSL, a Python library that provides efficient implementations of state-of-the-art graph structure learning models along with diverse datasets to evaluate them on. The implementations are written in GPU-friendly ways, allowing one to scale to much larger network tasks. A common interface is introduced for algorithm unrolling methods, unifying implementations of recent state-of-the-art techniques and allowing new methods to be quickly developed by avoiding the need to rebuild the underlying unrolling infrastructure. Implementations of differentiable graph structure learning models are written in PyTorch, allowing us to leverage the rich software ecosystem that exists e.g., around logging, hyperparameter search, and GPU-communication. This also makes it easy to incorporate these models as components in larger gradient based learning systems where differentiable estimates of graph structure may be useful, e.g. in latent graph learning. Diverse datasets and performance metrics allow consistent comparisons across models in this fast growing field. The full code repository can be found on https://github.com/maxwass/pyGSL.
Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can provide practical constraints in the GL approach. One applicable constraint can infer a graph with desired frequency signatures, i.e., spectral templates. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional graph signals. To address this issue and in the case of the underlying graph having graph product structure, we propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity rather than learning them directly from high-dimensional graph signals, which, to the best of our knowledge, has not been addressed in the related areas. In contrast to the rare current approaches, our approach can learn all types of product graphs (with more than two graphs) without knowing the type of graph products and has fewer parameters. Experimental results on both the synthetic and real-world data, i.e., brain signal analysis and multi-view object images, illustrate explainable and meaningful factor graphs supported by expert-related research, as well as outperforming the rare current restricted approaches.
This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph setting with homogeneous layers, we propose a bivariate polynomial graph filter model. We then consider the topology inference problems thru adapting existing spectral methods. We propose two solutions for the required spectral estimation step: a simplified solution via unfolding the multi-attribute data into matrices, and an exact solution via nearest Kronecker product decomposition (NKD). Interestingly, we show that strong inter-layer coupling can degrade the performance of the unfolding solution while the NKD solution is robust to inter-layer coupling effects. Numerical experiments show efficacy of our methods.