Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods.
Graph-level contrastive learning, aiming to learn the representations for each graph by contrasting two augmented graphs, has attracted considerable attention. Previous studies usually simply assume that a graph and its augmented graph as a positive pair, otherwise as a negative pair. However, it is well known that graph structure is always complex and multi-scale, which gives rise to a fundamental question: after graph augmentation, will the previous assumption still hold in reality? By an experimental analysis, we discover the semantic information of an augmented graph structure may be not consistent as original graph structure, and whether two augmented graphs are positive or negative pairs is highly related with the multi-scale structures. Based on this finding, we propose a multi-scale subgraph contrastive learning architecture which is able to characterize the fine-grained semantic information. Specifically, we generate global and local views at different scales based on subgraph sampling, and construct multiple contrastive relationships according to their semantic associations to provide richer self-supervised signals. Extensive experiments and parametric analyzes on eight graph classification real-world datasets well demonstrate the effectiveness of the proposed method.
Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.
The "Graph pre-training and fine-tuning" paradigm has significantly improved Graph Neural Networks(GNNs) by capturing general knowledge without manual annotations for downstream tasks. However, due to the immense gap of data and tasks between the pre-training and fine-tuning stages, the model performance is still limited. Inspired by prompt fine-tuning in Natural Language Processing(NLP), many endeavors have been made to bridge the gap in graph domain. But existing methods simply reformulate the form of fine-tuning tasks to the pre-training ones. With the premise that the pre-training graphs are compatible with the fine-tuning ones, these methods typically operate in transductive setting. In order to generalize graph pre-training to inductive scenario where the fine-tuning graphs might significantly differ from pre-training ones, we propose a novel graph prompt based method called Inductive Graph Alignment Prompt(IGAP). Firstly, we unify the mainstream graph pre-training frameworks and analyze the essence of graph pre-training from graph spectral theory. Then we identify the two sources of the data gap in inductive setting: (i) graph signal gap and (ii) graph structure gap. Based on the insight of graph pre-training, we propose to bridge the graph signal gap and the graph structure gap with learnable prompts in the spectral space. A theoretical analysis ensures the effectiveness of our method. At last, we conduct extensive experiments among nodes classification and graph classification tasks under the transductive, semi-inductive and inductive settings. The results demonstrate that our proposed method can successfully bridge the data gap under different settings.
Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.
There has been a recent surge in transformer-based architectures for learning on graphs, mainly motivated by attention as an effective learning mechanism and the desire to supersede handcrafted operators characteristic of message passing schemes. However, concerns over their empirical effectiveness, scalability, and complexity of the pre-processing steps have been raised, especially in relation to much simpler graph neural networks that typically perform on par with them across a wide range of benchmarks. To tackle these shortcomings, we consider graphs as sets of edges and propose a purely attention-based approach consisting of an encoder and an attention pooling mechanism. The encoder vertically interleaves masked and vanilla self-attention modules to learn an effective representations of edges, while allowing for tackling possible misspecifications in input graphs. Despite its simplicity, the approach outperforms fine-tuned message passing baselines and recently proposed transformer-based methods on more than 70 node and graph-level tasks, including challenging long-range benchmarks. Moreover, we demonstrate state-of-the-art performance across different tasks, ranging from molecular to vision graphs, and heterophilous node classification. The approach also outperforms graph neural networks and transformers in transfer learning settings, and scales much better than alternatives with a similar performance level or expressive power.
Graph neural networks (GNNs) have demonstrated significant success in various applications, such as node classification, link prediction, and graph classification. Active learning for GNNs aims to query the valuable samples from the unlabeled data for annotation to maximize the GNNs' performance at a lower cost. However, most existing algorithms for reinforced active learning in GNNs may lead to a highly imbalanced class distribution, especially in highly skewed class scenarios. GNNs trained with class-imbalanced labeled data are susceptible to bias toward majority classes, and the lower performance of minority classes may lead to a decline in overall performance. To tackle this issue, we propose a novel class-balanced and reinforced active learning framework for GNNs, namely, GCBR. It learns an optimal policy to acquire class-balanced and informative nodes for annotation, maximizing the performance of GNNs trained with selected labeled nodes. GCBR designs class-balance-aware states, as well as a reward function that achieves trade-off between model performance and class balance. The reinforcement learning algorithm Advantage Actor-Critic (A2C) is employed to learn an optimal policy stably and efficiently. We further upgrade GCBR to GCBR++ by introducing a punishment mechanism to obtain a more class-balanced labeled set. Extensive experiments on multiple datasets demonstrate the effectiveness of the proposed approaches, achieving superior performance over state-of-the-art baselines.
Reducing a graph while preserving its overall structure is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no specific downstream task in mind. In this paper, we present an approach for subsampling graph structures using an Ising model defined on either the nodes or edges and learning the external magnetic field of the Ising model using a graph neural network. Our approach is task-specific as it can learn how to reduce a graph for a specific downstream task in an end-to-end fashion. For this, the task's loss function does not have to be differentiable. We showcase the versatility of our approach on four distinct applications: image segmentation, explainability for graph classification, 3D shape sparsification, and sparse approximate matrix inverse determination.
Graph Neural Networks (GNNs) have demonstrated their effectiveness in various graph learning tasks, yet their reliance on neighborhood aggregation during inference poses challenges for deployment in latency-sensitive applications, such as real-time financial fraud detection. To address this limitation, recent studies have proposed distilling knowledge from teacher GNNs into student Multi-Layer Perceptrons (MLPs) trained on node content, aiming to accelerate inference. However, these approaches often inadequately explore structural information when inferring unseen nodes. To this end, we introduce SimMLP, a Self-supervised framework for learning MLPs on graphs, designed to fully integrate rich structural information into MLPs. Notably, SimMLP is the first MLP-learning method that can achieve equivalence to GNNs in the optimal case. The key idea is to employ self-supervised learning to align the representations encoded by graph context-aware GNNs and neighborhood dependency-free MLPs, thereby fully integrating the structural information into MLPs. We provide a comprehensive theoretical analysis, demonstrating the equivalence between SimMLP and GNNs based on mutual information and inductive bias, highlighting SimMLP's advanced structural learning capabilities. Additionally, we conduct extensive experiments on 20 benchmark datasets, covering node classification, link prediction, and graph classification, to showcase SimMLP's superiority over state-of-the-art baselines, particularly in scenarios involving unseen nodes (e.g., inductive and cold-start node classification) where structural insights are crucial. Our codes are available at: https://github.com/Zehong-Wang/SimMLP.
Graph learning is crucial in the fields of bioinformatics, social networks, and chemicals. Although high-order graphlets, such as cycles, are critical to achieving an informative graph representation for node classification, edge prediction, and graph recognition, modeling high-order topological characteristics poses significant computational challenges, restricting its widespread applications in machine learning. To address this limitation, we introduce the concept of \textit{message detouring} to hierarchically characterize cycle representation throughout the entire graph, which capitalizes on the contrast between the shortest and longest pathways within a range of local topologies associated with each graph node. The topological feature representations derived from our message detouring landscape demonstrate comparable expressive power to high-order \textit{Weisfeiler-Lehman} (WL) tests but much less computational demands. In addition to the integration with graph kernel and message passing neural networks, we present a novel message detouring neural network, which uses Transformer backbone to integrate cycle representations across nodes and edges. Aside from theoretical results, experimental results on expressiveness, graph classification, and node classification show message detouring can significantly outperform current counterpart approaches on various benchmark datasets.
This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks' performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.
The graph classification problem has been widely studied; however, achieving an interpretable model with high predictive performance remains a challenging issue. This paper proposes an interpretable classification algorithm for attributed graph data, called LAGRA (Learning Attributed GRAphlets). LAGRA learns importance weights for small attributed subgraphs, called attributed graphlets (AGs), while simultaneously optimizing their attribute vectors. This enables us to obtain a combination of subgraph structures and their attribute vectors that strongly contribute to discriminating different classes. A significant characteristics of LAGRA is that all the subgraph structures in the training dataset can be considered as a candidate structures of AGs. This approach can explore all the potentially important subgraphs exhaustively, but obviously, a naive implementation can require a large amount of computations. To mitigate this issue, we propose an efficient pruning strategy by combining the proximal gradient descent and a graph mining tree search. Our pruning strategy can ensure that the quality of the solution is maintained compared to the result without pruning. We empirically demonstrate that LAGRA has superior or comparable prediction performance to the standard existing algorithms including graph neural networks, while using only a small number of AGs in an interpretable manner.
Given a graph with textual attributes, we enable users to `chat with their graph': that is, to ask questions about the graph using a conversational interface. In response to a user's questions, our method provides textual replies and highlights the relevant parts of the graph. While existing works integrate large language models (LLMs) and graph neural networks (GNNs) in various ways, they mostly focus on either conventional graph tasks (such as node, edge, and graph classification), or on answering simple graph queries on small or synthetic graphs. In contrast, we develop a flexible question-answering framework targeting real-world textual graphs, applicable to multiple applications including scene graph understanding, common sense reasoning, and knowledge graph reasoning. Toward this goal, we first develop a Graph Question Answering (GraphQA) benchmark with data collected from different tasks. Then, we propose our G-Retriever method, introducing the first retrieval-augmented generation (RAG) approach for general textual graphs, which can be fine-tuned to enhance graph understanding via soft prompting. To resist hallucination and to allow for textual graphs that greatly exceed the LLM's context window size, G-Retriever performs RAG over a graph by formulating this task as a Prize-Collecting Steiner Tree optimization problem. Empirical evaluations show that our method outperforms baselines on textual graph tasks from multiple domains, scales well with larger graph sizes, and mitigates hallucination.~\footnote{Our codes and datasets are available at: \url{https://github.com/XiaoxinHe/G-Retriever}}
A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the NNGP kernel is fixed, and tunable only through a small number of hyperparameters, eliminating any possibility of representation learning. This contrasts with finite-width NNs, which are often believed to perform well precisely because they are able to learn representations. Thus in simplifying NNs to make them theoretically tractable, NNGPs may eliminate precisely what makes them work well (representation learning). This motivated us to understand whether representation learning is necessary in a range of graph classification tasks. We develop a precise tool for this task, the graph convolutional deep kernel machine. This is very similar to an NNGP, in that it is an infinite width limit and uses kernels, but comes with a `knob' to control the amount of representation learning. We found that representation learning is necessary (in the sense that it gives dramatic performance improvements) in graph classification tasks and heterophilous node classification tasks, but not in homophilous node classification tasks.
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material properties. Traditionally, such datasets consist of inputs given as meshes with a large number of nodes representing the problem geometry (seen as graphs), and corresponding outputs obtained with a numerical solver. This means the supervised learning model must be able to handle large and sparse graphs with continuous node attributes. In this work, we focus on Gaussian process regression, for which we introduce the Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel. In contrast to existing graph kernels, the proposed SWWL kernel enjoys positive definiteness and a drastic complexity reduction, which makes it possible to process datasets that were previously impossible to handle. The new kernel is first validated on graph classification for molecular datasets, where the input graphs have a few tens of nodes. The efficiency of the SWWL kernel is then illustrated on graph regression in computational fluid dynamics and solid mechanics, where the input graphs are made up of tens of thousands of nodes.
Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.
Can we model Non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The Non-Euclidean property have posed a long term challenge in graph modeling. Despite recent graph neural networks and graph transformers efforts encoding graphs as Euclidean vectors, recovering the original graph from vectors remains a challenge. In this paper, we introduce GraphsGPT, featuring an Graph2Seq encoder that transforms Non-Euclidean graphs into learnable Graph Words in the Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from Graph Words to ensure information equivalence. We pretrain GraphsGPT on $100$M molecules and yield some interesting findings: (1) The pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on $8/9$ graph classification and regression tasks. (2) The pretrained GraphGPT serves as a strong graph generator, demonstrated by its strong ability to perform both few-shot and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known Non-Euclidean challenges. (4) The edge-centric pretraining framework GraphsGPT demonstrates its efficacy in graph domain tasks, excelling in both representation and generation. Code is available at \href{https://github.com/A4Bio/GraphsGPT}{GitHub}.
Deep graph models (e.g., graph neural networks and graph transformers) have become important techniques for leveraging knowledge across various types of graphs. Yet, the neural scaling laws on graphs, i.e., how the performance of deep graph models changes with model and dataset sizes, have not been systematically investigated, casting doubts on the feasibility of achieving large graph models. To fill this gap, we benchmark many graph datasets from different tasks and make an attempt to establish the neural scaling laws on graphs from both model and data perspectives. The model size we investigated is up to 100 million parameters, and the dataset size investigated is up to 50 million samples. We first verify the validity of such laws on graphs, establishing proper formulations to describe the scaling behaviors. For model scaling, we identify that despite the parameter numbers, the model depth also plays an important role in affecting the model scaling behaviors, which differs from observations in other domains such as CV and NLP. For data scaling, we suggest that the number of graphs can not effectively measure the graph data volume in scaling law since the sizes of different graphs are highly irregular. Instead, we reform the data scaling law with the number of nodes or edges as the metric to address the irregular graph sizes. We further demonstrate that the reformed law offers a unified view of the data scaling behaviors for various fundamental graph tasks including node classification, link prediction, and graph classification. This work provides valuable insights into neural scaling laws on graphs, which can serve as an important tool for collecting new graph data and developing large graph models.
Graph contrastive learning (GCL) has emerged as a state-of-the-art strategy for learning representations of diverse graphs including social and biomedical networks. GCL widely uses stochastic graph topology augmentation, such as uniform node dropping, to generate augmented graphs. However, such stochastic augmentations may severely damage the intrinsic properties of a graph and deteriorate the following representation learning process. We argue that incorporating an awareness of cohesive subgraphs during the graph augmentation and learning processes has the potential to enhance GCL performance. To this end, we propose a novel unified framework called CTAug, to seamlessly integrate cohesion awareness into various existing GCL mechanisms. In particular, CTAug comprises two specialized modules: topology augmentation enhancement and graph learning enhancement. The former module generates augmented graphs that carefully preserve cohesion properties, while the latter module bolsters the graph encoder's ability to discern subgraph patterns. Theoretical analysis shows that CTAug can strictly improve existing GCL mechanisms. Empirical experiments verify that CTAug can achieve state-of-the-art performance for graph representation learning, especially for graphs with high degrees. The code is available at https://doi.org/10.5281/zenodo.10594093, or https://github.com/wuyucheng2002/CTAug.
Recently, Transformers for graph representation learning have become increasingly popular, achieving state-of-the-art performance on a wide-variety of graph datasets, either alone or in combination with message-passing graph neural networks (MP-GNNs). Infusing graph inductive-biases in the innately structure-agnostic transformer architecture in the form of structural or positional encodings (PEs) is key to achieving these impressive results. However, designing such encodings is tricky and disparate attempts have been made to engineer such encodings including Laplacian eigenvectors, relative random-walk probabilities (RRWP), spatial encodings, centrality encodings, edge encodings etc. In this work, we argue that such encodings may not be required at all, provided the attention mechanism itself incorporates information about the graph structure. We introduce Eigenformer, a Graph Transformer employing a novel spectrum-aware attention mechanism cognizant of the Laplacian spectrum of the graph, and empirically show that it achieves performance competetive with SOTA Graph Transformers on a number of standard GNN benchmarks. Additionally, we theoretically prove that Eigenformer can express various graph structural connectivity matrices, which is particularly essential when learning over smaller graphs.