Daily Papers

Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges for human experts when designing versatile graph learning approaches. Facing these challenges, large language models (LLMs) offer a potential solution due to the extensive knowledge and the human-like intelligence. This paper proposes a novel conceptual prototype for designing versatile graph learning methods with LLMs, with a particular focus on the "where" and "how" perspectives. From the "where" perspective, we summarize four key graph learning procedures, including task definition, graph data feature engineering, model selection and optimization, deployment and serving. We then explore the application scenarios of LLMs in these procedures across a wider spectrum. In the "how" perspective, we align the abilities of LLMs with the requirements of each procedure. Finally, we point out the promising directions that could better leverage the strength of LLMs towards versatile graph learning methods.

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB.

Conversational recommender systems (CRS) enable the traditional recommender systems to explicitly acquire user preferences towards items and attributes through interactive conversations. Reinforcement learning (RL) is widely adopted to learn conversational recommendation policies to decide what attributes to ask, which items to recommend, and when to ask or recommend, at each conversation turn. However, existing methods mainly target at solving one or two of these three decision-making problems in CRS with separated conversation and recommendation components, which restrict the scalability and generality of CRS and fall short of preserving a stable training procedure. In the light of these challenges, we propose to formulate these three decision-making problems in CRS as a unified policy learning task. In order to systematically integrate conversation and recommendation components, we develop a dynamic weighted graph based RL method to learn a policy to select the action at each conversation turn, either asking an attribute or recommending items. Further, to deal with the sample efficiency issue, we propose two action selection strategies for reducing the candidate action space according to the preference and entropy information. Experimental results on two benchmark CRS datasets and a real-world E-Commerce application show that the proposed method not only significantly outperforms state-of-the-art methods but also enhances the scalability and stability of CRS.

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.

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.

Graph Structure Learning (GSL) focuses on capturing intrinsic dependencies and interactions among nodes in graph-structured data by generating novel graph structures. Graph Neural Networks (GNNs) have emerged as promising GSL solutions, utilizing recursive message passing to encode node-wise inter-dependencies. However, many existing GSL methods heavily depend on explicit graph structural information as supervision signals, leaving them susceptible to challenges such as data noise and sparsity. In this work, we propose GraphEdit, an approach that leverages large language models (LLMs) to learn complex node relationships in graph-structured data. By enhancing the reasoning capabilities of LLMs through instruction-tuning over graph structures, we aim to overcome the limitations associated with explicit graph structural information and enhance the reliability of graph structure learning. Our approach not only effectively denoises noisy connections but also identifies node-wise dependencies from a global perspective, providing a comprehensive understanding of the graph structure. We conduct extensive experiments on multiple benchmark datasets to demonstrate the effectiveness and robustness of GraphEdit across various settings. We have made our model implementation available at: https://github.com/HKUDS/GraphEdit.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

This paper introduces GET-Zero, a model architecture and training procedure for learning an embodiment-aware control policy that can immediately adapt to new hardware changes without retraining. To do so, we present Graph Embodiment Transformer (GET), a transformer model that leverages the embodiment graph connectivity as a learned structural bias in the attention mechanism. We use behavior cloning to distill demonstration data from embodiment-specific expert policies into an embodiment-aware GET model that conditions on the hardware configuration of the robot to make control decisions. We conduct a case study on a dexterous in-hand object rotation task using different configurations of a four-fingered robot hand with joints removed and with link length extensions. Using the GET model along with a self-modeling loss enables GET-Zero to zero-shot generalize to unseen variation in graph structure and link length, yielding a 20% improvement over baseline methods. All code and qualitative video results are on https://get-zero-paper.github.io

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

Graph generation with Machine Learning is an open problem with applications in various research fields. In this work, we propose to cast the generative process of a graph into a sequential one, relying on a node ordering procedure. We use this sequential process to design a novel generative model composed of two recurrent neural networks that learn to predict the edges of graphs: the first network generates one endpoint of each edge, while the second network generates the other endpoint conditioned on the state of the first. We test our approach extensively on five different datasets, comparing with two well-known baselines coming from graph literature, and two recurrent approaches, one of which holds state of the art performances. Evaluation is conducted considering quantitative and qualitative characteristics of the generated samples. Results show that our approach is able to yield novel, and unique graphs originating from very different distributions, while retaining structural properties very similar to those in the training sample. Under the proposed evaluation framework, our approach is able to reach performances comparable to the current state of the art on the graph generation task.

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) with one model. We first propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder which can also be decoded, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Then we formulate prediction tasks including regression and classification as (conditional) generation, which enables our LGD to solve tasks of all levels and all types with provable guarantees. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across generation and regression tasks.

Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to construct a graph among images is to treat each image as a node and assign pairwise image similarities as weights to corresponding edges. It is well known that pairwise similarities between images are sensitive to the noise in feature representations, leading to unreliable graph structures. We address this problem from the viewpoint of statistical tests. By viewing the feature vector of each node as an independent sample, the decision of whether creating an edge between two nodes based on their similarity in feature representation can be thought as a {it single} statistical test. To improve the robustness in the decision of creating an edge, multiple samples are drawn and integrated by {it multiple} statistical tests to generate a more reliable similarity measure, consequentially more reliable graph structure. The corresponding elegant matrix form named B-Attention is designed for efficiency. The effectiveness of multiple tests for graph structure learning is verified both theoretically and empirically on multiple clustering and ReID benchmark datasets. Source codes are available at https://github.com/Thomas-wyh/B-Attention.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees (AST). A group of works add additional edges to ASTs to convert source code into graphs and use graph neural networks to learn representations for program graphs. Although these works provide additional control or data flow information to ASTs for downstream tasks, they neglect an important aspect of structure information in AST itself: the different types of nodes and edges. In ASTs, different nodes contain different kinds of information like variables or control flow, and the relation between a node and all its children can also be different. To address the information of node and edge types, we bring the idea of heterogeneous graphs to learning on source code and present a new formula of building heterogeneous program graphs from ASTs with additional type information for nodes and edges. We use the ASDL grammar of programming language to define the node and edge types of program graphs. Then we use heterogeneous graph neural networks to learn on these graphs. We evaluate our approach on two tasks: code comment generation and method naming. Both tasks require reasoning on the semantics of complete code snippets. Experiment results show that our approach outperforms baseline models, including homogeneous graph-based models, showing that leveraging the type information of nodes and edges in program graphs can help in learning program semantics.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Graph representation learning has emerged as a powerful technique for addressing real-world problems. Various downstream graph learning tasks have benefited from its recent developments, such as node classification, similarity search, and graph classification. However, prior arts on graph representation learning focus on domain specific problems and train a dedicated model for each graph dataset, which is usually non-transferable to out-of-domain data. Inspired by the recent advances in pre-training from natural language processing and computer vision, we design Graph Contrastive Coding (GCC) -- a self-supervised graph neural network pre-training framework -- to capture the universal network topological properties across multiple networks. We design GCC's pre-training task as subgraph instance discrimination in and across networks and leverage contrastive learning to empower graph neural networks to learn the intrinsic and transferable structural representations. We conduct extensive experiments on three graph learning tasks and ten graph datasets. The results show that GCC pre-trained on a collection of diverse datasets can achieve competitive or better performance to its task-specific and trained-from-scratch counterparts. This suggests that the pre-training and fine-tuning paradigm presents great potential for graph representation learning.

Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly aims at accelerating and improving higher-order graph learning results. We apply the acceleration procedure from the dimensional of network motifs. Specifically, the refined degree for nodes and edges are conducted in two stages: (1) employ motif degree of nodes to refine the adjacency matrix of the network; and (2) employ motif degree of edges to refine the transition probability matrix in the learning process. In order to assess the efficiency of the proposed framework, four popular network representation algorithms are modified and examined. By evaluating the performance of OFFER, both link prediction results and clustering results demonstrate that the graph representation learning algorithms enhanced with OFFER consistently outperform the original algorithms with higher efficiency.

Posterior sampling allows the exploitation of prior knowledge of the environment's transition dynamics to improve the sample efficiency of reinforcement learning. The prior is typically specified as a class of parametric distributions, a task that can be cumbersome in practice, often resulting in the choice of uninformative priors. In this work, we propose a novel posterior sampling approach in which the prior is given as a (partial) causal graph over the environment's variables. The latter is often more natural to design, such as listing known causal dependencies between biometric features in a medical treatment study. Specifically, we propose a hierarchical Bayesian procedure, called C-PSRL, simultaneously learning the full causal graph at the higher level and the parameters of the resulting factored dynamics at the lower level. For this procedure, we provide an analysis of its Bayesian regret, which explicitly connects the regret rate with the degree of prior knowledge. Our numerical evaluation conducted in illustrative domains confirms that C-PSRL strongly improves the efficiency of posterior sampling with an uninformative prior while performing close to posterior sampling with the full causal graph.

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more. While LLMs have advanced the state-of-the-art on these tasks with structure implications, whether LLMs could explicitly process textual descriptions of graphs and structures, map them to grounded conceptual spaces, and perform structured operations remains underexplored. To this end, we propose NLGraph (Natural Language Graph), a comprehensive benchmark of graph-based problem solving designed in natural language. NLGraph contains 29,370 problems, covering eight graph reasoning tasks with varying complexity from simple tasks such as connectivity and shortest path up to complex problems such as maximum flow and simulating graph neural networks. We evaluate LLMs (GPT-3/4) with various prompting approaches on the NLGraph benchmark and find that 1) language models do demonstrate preliminary graph reasoning abilities, 2) the benefit of advanced prompting and in-context learning diminishes on more complex graph problems, while 3) LLMs are also (un)surprisingly brittle in the face of spurious correlations in graph and problem settings. We then propose Build-a-Graph Prompting and Algorithmic Prompting, two instruction-based approaches to enhance LLMs in solving natural language graph problems. Build-a-Graph and Algorithmic prompting improve the performance of LLMs on NLGraph by 3.07% to 16.85% across multiple tasks and settings, while how to solve the most complicated graph reasoning tasks in our setup with language models remains an open research question. The NLGraph benchmark and evaluation code are available at https://github.com/Arthur-Heng/NLGraph.

Learning to represent free text is a core task in many clinical machine learning (ML) applications, as clinical text contains observations and plans not otherwise available for inference. State-of-the-art methods use large language models developed with immense computational resources and training data; however, applying these models is challenging because of the highly varying syntax and vocabulary in clinical free text. Structured information such as International Classification of Disease (ICD) codes often succinctly abstracts the most important facts of a clinical encounter and yields good performance, but is often not as available as clinical text in real-world scenarios. We propose a multi-view learning framework that jointly learns from codes and text to combine the availability and forward-looking nature of text and better performance of ICD codes. The learned text embeddings can be used as inputs to predictive algorithms independent of the ICD codes during inference. Our approach uses a Graph Neural Network (GNN) to process ICD codes, and Bi-LSTM to process text. We apply Deep Canonical Correlation Analysis (DCCA) to enforce the two views to learn a similar representation of each patient. In experiments using planned surgical procedure text, our model outperforms BERT models fine-tuned to clinical data, and in experiments using diverse text in MIMIC-III, our model is competitive to a fine-tuned BERT at a tiny fraction of its computational effort.

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: We formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.

Graph Neural Networks (GNNs) have advanced graph structure understanding via recursive information exchange and aggregation among graph nodes. To improve model robustness, self-supervised learning (SSL) has emerged as a promising approach for data augmentation. However, existing methods for generating pre-trained graph embeddings often rely on fine-tuning with specific downstream task labels, which limits their usability in scenarios where labeled data is scarce or unavailable. To address this, our research focuses on advancing the generalization capabilities of graph models in challenging zero-shot learning scenarios. Inspired by the success of large language models (LLMs), we aim to develop a graph-oriented LLM that can achieve high generalization across diverse downstream datasets and tasks, even without any information available from the downstream graph data. In this work, we present the GraphGPT framework that aligns LLMs with graph structural knowledge with a graph instruction tuning paradigm. Our framework incorporates a text-graph grounding component to establish a connection between textual information and graph structures. Additionally, we propose a dual-stage instruction tuning paradigm, accompanied by a lightweight graph-text alignment projector. This paradigm explores self-supervised graph structural signals and task-specific graph instructions, to guide LLMs in understanding complex graph structures and improving their adaptability across different downstream tasks. Our framework is evaluated on supervised and zero-shot graph learning tasks, demonstrating superior generalization and outperforming state-of-the-art baselines.

Graph representation learning nowadays becomes fundamental in analyzing graph-structured data. Inspired by recent success of contrastive methods, in this paper, we propose a novel framework for unsupervised graph representation learning by leveraging a contrastive objective at the node level. Specifically, we generate two graph views by corruption and learn node representations by maximizing the agreement of node representations in these two views. To provide diverse node contexts for the contrastive objective, we propose a hybrid scheme for generating graph views on both structure and attribute levels. Besides, we provide theoretical justification behind our motivation from two perspectives, mutual information and the classical triplet loss. We perform empirical experiments on both transductive and inductive learning tasks using a variety of real-world datasets. Experimental experiments demonstrate that despite its simplicity, our proposed method consistently outperforms existing state-of-the-art methods by large margins. Moreover, our unsupervised method even surpasses its supervised counterparts on transductive tasks, demonstrating its great potential in real-world applications.

Graphs can model complex relationships between objects, enabling a myriad of Web applications such as online page/article classification and social recommendation. While graph neural networks(GNNs) have emerged as a powerful tool for graph representation learning, in an end-to-end supervised setting, their performance heavily rely on a large amount of task-specific supervision. To reduce labeling requirement, the "pre-train, fine-tune" and "pre-train, prompt" paradigms have become increasingly common. In particular, prompting is a popular alternative to fine-tuning in natural language processing, which is designed to narrow the gap between pre-training and downstream objectives in a task-specific manner. However, existing study of prompting on graphs is still limited, lacking a universal treatment to appeal to different downstream tasks. In this paper, we propose GraphPrompt, a novel pre-training and prompting framework on graphs. GraphPrompt not only unifies pre-training and downstream tasks into a common task template, but also employs a learnable prompt to assist a downstream task in locating the most relevant knowledge from the pre-train model in a task-specific manner. Finally, we conduct extensive experiments on five public datasets to evaluate and analyze GraphPrompt.

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.

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

Graph learning has become indispensable for interpreting and harnessing relational data in diverse fields, ranging from recommendation systems to social network analysis. In this context, a variety of GNNs have emerged as promising methodologies for encoding the structural information of graphs. By effectively capturing the graph's underlying structure, these GNNs have shown great potential in enhancing performance in graph learning tasks, such as link prediction and node classification. However, despite their successes, a significant challenge persists: these advanced methods often face difficulties in generalizing to unseen graph data that significantly differs from the training instances. In this work, our aim is to advance the graph learning paradigm by developing a general graph foundation model. This model is designed to understand the complex topological patterns present in diverse graph data, enabling it to excel in zero-shot graph learning tasks across different downstream datasets. To achieve this goal, we address several key technical challenges in our OpenGraph model. Firstly, we propose a unified graph tokenizer to adapt our graph model to generalize well on unseen graph data, even when the underlying graph properties differ significantly from those encountered during training. Secondly, we develop a scalable graph transformer as the foundational encoder, which effectively captures node-wise dependencies within the global topological context. Thirdly, we introduce a data augmentation mechanism enhanced by a LLM to alleviate the limitations of data scarcity in real-world scenarios. Extensive experiments validate the effectiveness of our framework. By adapting our OpenGraph to new graph characteristics and comprehending the nuances of diverse graphs, our approach achieves remarkable zero-shot graph learning performance across various settings and domains.

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

Recent prevailing works on graph machine learning typically follow a similar methodology that involves designing advanced variants of graph neural networks (GNNs) to maintain the superior performance of GNNs on different graphs. In this paper, we aim to streamline the GNN design process and leverage the advantages of Large Language Models (LLMs) to improve the performance of GNNs on downstream tasks. We formulate a new paradigm, coined "LLMs-as-Consultants," which integrates LLMs with GNNs in an interactive manner. A framework named LOGIN (LLM Consulted GNN training) is instantiated, empowering the interactive utilization of LLMs within the GNN training process. First, we attentively craft concise prompts for spotted nodes, carrying comprehensive semantic and topological information, and serving as input to LLMs. Second, we refine GNNs by devising a complementary coping mechanism that utilizes the responses from LLMs, depending on their correctness. We empirically evaluate the effectiveness of LOGIN on node classification tasks across both homophilic and heterophilic graphs. The results illustrate that even basic GNN architectures, when employed within the proposed LLMs-as-Consultants paradigm, can achieve comparable performance to advanced GNNs with intricate designs. Our codes are available at https://github.com/QiaoYRan/LOGIN.

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.

Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

Large language models (LLMs) such as GPT-4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications, including answering queries, code generation, and more. Parallelly, graph-structured data, an intrinsic data type, is pervasive in real-world scenarios. Merging the capabilities of LLMs with graph-structured data has been a topic of keen interest. This paper bifurcates such integrations into two predominant categories. The first leverages LLMs for graph learning, where LLMs can not only augment existing graph algorithms but also stand as prediction models for various graph tasks. Conversely, the second category underscores the pivotal role of graphs in advancing LLMs. Mirroring human cognition, we solve complex tasks by adopting graphs in either reasoning or collaboration. Integrating with such structures can significantly boost the performance of LLMs in various complicated tasks. We also discuss and propose open questions for integrating LLMs with graph-structured data for the future direction of the field.

For supervised learning with tabular data, decision tree ensembles produced via boosting techniques generally dominate real-world applications involving iid training/test sets. However for graph data where the iid assumption is violated due to structured relations between samples, it remains unclear how to best incorporate this structure within existing boosting pipelines. To this end, we propose a generalized framework for iterating boosting with graph propagation steps that share node/sample information across edges connecting related samples. Unlike previous efforts to integrate graph-based models with boosting, our approach is anchored in a principled meta loss function such that provable convergence can be guaranteed under relatively mild assumptions. Across a variety of non-iid graph datasets with tabular node features, our method achieves comparable or superior performance than both tabular and graph neural network models, as well as existing hybrid strategies that combine the two. Beyond producing better predictive performance than recently proposed graph models, our proposed techniques are easy to implement, computationally more efficient, and enjoy stronger theoretical guarantees (which make our results more reproducible).

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks. In this paper, we develop Peregrine, a pattern-aware graph mining system that directly explores the subgraphs of interest while avoiding exploration of unnecessary subgraphs, and simultaneously bypassing expensive computations throughout the mining process. We design a pattern-based programming model that treats "graph patterns" as first class constructs and enables Peregrine to extract the semantics of patterns, which it uses to guide its exploration. Our evaluation shows that Peregrine outperforms state-of-the-art distributed and single machine graph mining systems, and scales to complex mining tasks on larger graphs, while retaining simplicity and expressivity with its "pattern-first" programming approach.

In recent years, graph pre-training has gained significant attention, focusing on acquiring transferable knowledge from unlabeled graph data to improve downstream performance. Despite these recent endeavors, the problem of negative transfer remains a major concern when utilizing graph pre-trained models to downstream tasks. Previous studies made great efforts on the issue of what to pre-train and how to pre-train by designing a variety of graph pre-training and fine-tuning strategies. However, there are cases where even the most advanced "pre-train and fine-tune" paradigms fail to yield distinct benefits. This paper introduces a generic framework W2PGNN to answer the crucial question of when to pre-train (i.e., in what situations could we take advantage of graph pre-training) before performing effortful pre-training or fine-tuning. We start from a new perspective to explore the complex generative mechanisms from the pre-training data to downstream data. In particular, W2PGNN first fits the pre-training data into graphon bases, each element of graphon basis (i.e., a graphon) identifies a fundamental transferable pattern shared by a collection of pre-training graphs. All convex combinations of graphon bases give rise to a generator space, from which graphs generated form the solution space for those downstream data that can benefit from pre-training. In this manner, the feasibility of pre-training can be quantified as the generation probability of the downstream data from any generator in the generator space. W2PGNN offers three broad applications: providing the application scope of graph pre-trained models, quantifying the feasibility of pre-training, and assistance in selecting pre-training data to enhance downstream performance. We provide a theoretically sound solution for the first application and extensive empirical justifications for the latter two applications.

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.

Following the success of Word2Vec embeddings, graph embeddings (GEs) have gained substantial traction. GEs are commonly generated and evaluated extrinsically on downstream applications, but intrinsic evaluations of the original graph properties in terms of topological structure and semantic information have been lacking. Understanding these will help identify the deficiency of the various families of GE methods when vectorizing graphs in terms of preserving the relevant knowledge or learning incorrect knowledge. To address this, we propose RESTORE, a framework for intrinsic GEs assessment through graph reconstruction. We show that reconstructing the original graph from the underlying GEs yields insights into the relative amount of information preserved in a given vector form. We first introduce the graph reconstruction task. We generate GEs from three GE families based on factorization methods, random walks, and deep learning (with representative algorithms from each family) on the CommonSense Knowledge Graph (CSKG). We analyze their effectiveness in preserving the (a) topological structure of node-level graph reconstruction with an increasing number of hops and (b) semantic information on various word semantic and analogy tests. Our evaluations show deep learning-based GE algorithm (SDNE) is overall better at preserving (a) with a mean average precision (mAP) of 0.54 and 0.35 for 2 and 3-hop reconstruction respectively, while the factorization-based algorithm (HOPE) is better at encapsulating (b) with an average Euclidean distance of 0.14, 0.17, and 0.11 for 1, 2, and 3-hop reconstruction respectively. The modest performance of these GEs leaves room for further research avenues on better graph representation learning.

Evaluating and enhancing the general capabilities of large language models (LLMs) has been an important research topic. Graph is a common data structure in the real world, and understanding graph data is a crucial part for advancing general intelligence. To evaluate and enhance the graph understanding abilities of LLMs, in this paper, we propose a benchmark named GraphInstruct, which comprehensively includes 21 classical graph reasoning tasks, providing diverse graph generation pipelines and detailed reasoning steps. Based on GraphInstruct, we further construct GraphLM through efficient instruction-tuning, which shows prominent graph understanding capability. In order to enhance the LLM with graph reasoning capability as well, we propose a step mask training strategy, and construct a model named GraphLM+. As one of the pioneering efforts to enhance the graph understanding and reasoning abilities of LLMs, extensive experiments have demonstrated the superiority of GraphLM and GraphLM+ over other LLMs. We look forward to more researchers exploring the potential of LLMs in the graph data mining domain through GraphInstruct. Our code for generating GraphInstruct is released publicly at: https://github.com/CGCL-codes/GraphInstruct.

GraphRAG addresses significant challenges in Retrieval-Augmented Generation (RAG) by leveraging graphs with embedded knowledge to enhance the reasoning capabilities of Large Language Models (LLMs). Despite its promising potential, the GraphRAG community currently lacks a unified framework for fine-grained decomposition of the graph-based knowledge retrieval process. Furthermore, there is no systematic categorization or evaluation of existing solutions within the retrieval process. In this paper, we present LEGO-GraphRAG, a modular framework that decomposes the retrieval process of GraphRAG into three interconnected modules: subgraph-extraction, path-filtering, and path-refinement. We systematically summarize and classify the algorithms and neural network (NN) models relevant to each module, providing a clearer understanding of the design space for GraphRAG instances. Additionally, we identify key design factors, such as Graph Coupling and Computational Cost, that influence the effectiveness of GraphRAG implementations. Through extensive empirical studies, we construct high-quality GraphRAG instances using a representative selection of solutions and analyze their impact on retrieval and reasoning performance. Our findings offer critical insights into optimizing GraphRAG instance design, ultimately contributing to the advancement of more accurate and contextually relevant LLM applications.

Recent years have witnessed the great success of graph pre-training for graph representation learning. With hundreds of graph pre-training tasks proposed, integrating knowledge acquired from multiple pre-training tasks has become a popular research topic. In this paper, we identify two important collaborative processes for this topic: (1) select: how to select an optimal task combination from a given task pool based on their compatibility, and (2) weigh: how to weigh the selected tasks based on their importance. While there currently has been a lot of work focused on weighing, comparatively little effort has been devoted to selecting. This paper proposes a novel instance-level framework for integrating multiple graph pre-training tasks, Weigh And Select (WAS), where the two collaborative processes, weighing and selecting, are combined by decoupled siamese networks. Specifically, it first adaptively learns an optimal combination of tasks for each instance from a given task pool, based on which a customized instance-level task weighing strategy is learned. Extensive experiments on 16 graph datasets across node-level and graph-level downstream tasks have demonstrated that by combining a few simple but classical tasks, WAS can achieve comparable performance to other leading counterparts. The code is available at https://github.com/TianyuFan0504/WAS.

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine learning is witnessing a paradigm transition from shallow methods to more sophisticated deep learning approaches. The capabilities of foundation models to generalize and adapt motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm. This paradigm envisions models that are pre-trained on extensive graph data and can be adapted for various graph tasks. Despite this burgeoning interest, there is a noticeable lack of clear definitions and systematic analyses pertaining to this new domain. To this end, this article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies. We proceed to classify the existing work related to GFMs into three distinct categories, based on their dependence on graph neural networks and large language models. In addition to providing a thorough review of the current state of GFMs, this article also outlooks potential avenues for future research in this rapidly evolving domain.

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Graph neural networks (GNNs) have been successfully applied to learning representation on graphs in many relational tasks. Recently, researchers study neural architecture search (NAS) to reduce the dependence of human expertise and explore better GNN architectures, but they over-emphasize entity features and ignore latent relation information concealed in the edges. To solve this problem, we incorporate edge features into graph search space and propose Edge-featured Graph Neural Architecture Search to find the optimal GNN architecture. Specifically, we design rich entity and edge updating operations to learn high-order representations, which convey more generic message passing mechanisms. Moreover, the architecture topology in our search space allows to explore complex feature dependence of both entities and edges, which can be efficiently optimized by differentiable search strategy. Experiments at three graph tasks on six datasets show EGNAS can search better GNNs with higher performance than current state-of-the-art human-designed and searched-based GNNs.

Information extraction (IE) is an important task in Natural Language Processing (NLP), involving the extraction of named entities and their relationships from unstructured text. In this paper, we propose a novel approach to this task by formulating it as graph structure learning (GSL). By formulating IE as GSL, we enhance the model's ability to dynamically refine and optimize the graph structure during the extraction process. This formulation allows for better interaction and structure-informed decisions for entity and relation prediction, in contrast to previous models that have separate or untied predictions for these tasks. When compared against state-of-the-art baselines on joint entity and relation extraction benchmarks, our model, GraphER, achieves competitive results.

Accurately predicting road networks from satellite images requires a global understanding of the network topology. We propose to capture such high-level information by introducing a graph-based framework that simulates the addition of sequences of graph edges using a reinforcement learning (RL) approach. In particular, given a partially generated graph associated with a satellite image, an RL agent nominates modifications that maximize a cumulative reward. As opposed to standard supervised techniques that tend to be more restricted to commonly used surrogate losses, these rewards can be based on various complex, potentially non-continuous, metrics of interest. This yields more power and flexibility to encode problem-dependent knowledge. Empirical results on several benchmark datasets demonstrate enhanced performance and increased high-level reasoning about the graph topology when using a tree-based search. We further highlight the superiority of our approach under substantial occlusions by introducing a new synthetic benchmark dataset for this task.

With the increasing number of new neural architecture designs and substantial existing neural architectures, it becomes difficult for the researchers to situate their contributions compared with existing neural architectures or establish the connections between their designs and other relevant ones. To discover similar neural architectures in an efficient and automatic manner, we define a new problem Neural Architecture Retrieval which retrieves a set of existing neural architectures which have similar designs to the query neural architecture. Existing graph pre-training strategies cannot address the computational graph in neural architectures due to the graph size and motifs. To fulfill this potential, we propose to divide the graph into motifs which are used to rebuild the macro graph to tackle these issues, and introduce multi-level contrastive learning to achieve accurate graph representation learning. Extensive evaluations on both human-designed and synthesized neural architectures demonstrate the superiority of our algorithm. Such a dataset which contains 12k real-world network architectures, as well as their embedding, is built for neural architecture retrieval.

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is still on primary stage. In this paper, we move towards this goal from the perspective of generalization. To be specific, we first establish high probability bounds of generalization gap and gradients in transductive learning with consideration of stochastic optimization. After that, we provide high probability bounds of generalization gap for popular GNNs. The theoretical results reveal the architecture specific factors affecting the generalization gap. Experimental results on benchmark datasets show the consistency between theoretical results and empirical evidence. Our results provide new insights in understanding the generalization of GNNs.

Graph Neural Networks (GNNs) have been popularly used for analyzing non-Euclidean data such as social network data and biological data. Despite their success, the design of graph neural networks requires a lot of manual work and domain knowledge. In this paper, we propose a Graph Neural Architecture Search method (GraphNAS for short) that enables automatic search of the best graph neural architecture based on reinforcement learning. Specifically, GraphNAS first uses a recurrent network to generate variable-length strings that describe the architectures of graph neural networks, and then trains the recurrent network with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation data set. Extensive experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that GraphNAS can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network. On node classification tasks, GraphNAS can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

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.

The need to analyze graphs is ubiquitous across various fields, from social networks to biological research and recommendation systems. Therefore, enabling the ability of large language models (LLMs) to process graphs is an important step toward more advanced general intelligence. However, current LLM benchmarks on graph analysis require models to directly reason over the prompts describing graph topology, and are thus limited to small graphs with only a few dozens of nodes. In contrast, human experts typically write programs based on popular libraries for task solving, and can thus handle graphs with different scales. To this end, a question naturally arises: can LLMs analyze graphs like professionals? In this paper, we introduce ProGraph, a manually crafted benchmark containing 3 categories of graph tasks. The benchmark expects solutions based on programming instead of directly reasoning over raw inputs. Our findings reveal that the performance of current LLMs is unsatisfactory, with the best model achieving only 36% accuracy. To bridge this gap, we propose LLM4Graph datasets, which include crawled documents and auto-generated codes based on 6 widely used graph libraries. By augmenting closed-source LLMs with document retrieval and fine-tuning open-source ones on the codes, we show 11-32% absolute improvements in their accuracies. Our results underscore that the capabilities of LLMs in handling structured data are still under-explored, and show the effectiveness of LLM4Graph in enhancing LLMs' proficiency of graph analysis. The benchmark, datasets and enhanced open-source models are available at https://github.com/BUPT-GAMMA/ProGraph.

Task planning in language agents is emerging as an important research topic alongside the development of large language models (LLMs). It aims to break down complex user requests in natural language into solvable sub-tasks, thereby fulfilling the original requests. In this context, the sub-tasks can be naturally viewed as a graph, where the nodes represent the sub-tasks, and the edges denote the dependencies among them. Consequently, task planning is a decision-making problem that involves selecting a connected path or subgraph within the corresponding graph and invoking it. In this paper, we explore graph learning-based methods for task planning, a direction that is orthogonal to the prevalent focus on prompt design. Our interest in graph learning stems from a theoretical discovery: the biases of attention and auto-regressive loss impede LLMs' ability to effectively navigate decision-making on graphs, which is adeptly addressed by graph neural networks (GNNs). This theoretical insight led us to integrate GNNs with LLMs to enhance overall performance. Extensive experiments demonstrate that GNN-based methods surpass existing solutions even without training, and minimal training can further enhance their performance. The performance gain increases with a larger task graph size.

Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones.

Many graph representation learning (GRL) problems are dynamic, with millions of edges added or removed per second. A fundamental workload in this setting is dynamic link prediction: using a history of graph updates to predict whether a given pair of vertices will become connected. Recent schemes for link prediction in such dynamic settings employ Transformers, modeling individual graph updates as single tokens. In this work, we propose HOT: a model that enhances this line of works by harnessing higher-order (HO) graph structures; specifically, k-hop neighbors and more general subgraphs containing a given pair of vertices. Harnessing such HO structures by encoding them into the attention matrix of the underlying Transformer results in higher accuracy of link prediction outcomes, but at the expense of increased memory pressure. To alleviate this, we resort to a recent class of schemes that impose hierarchy on the attention matrix, significantly reducing memory footprint. The final design offers a sweetspot between high accuracy and low memory utilization. HOT outperforms other dynamic GRL schemes, for example achieving 9%, 7%, and 15% higher accuracy than - respectively - DyGFormer, TGN, and GraphMixer, for the MOOC dataset. Our design can be seamlessly extended towards other dynamic GRL workloads.

We introduce a self-supervised approach for learning node and graph level representations by contrasting structural views of graphs. We show that unlike visual representation learning, increasing the number of views to more than two or contrasting multi-scale encodings do not improve performance, and the best performance is achieved by contrasting encodings from first-order neighbors and a graph diffusion. We achieve new state-of-the-art results in self-supervised learning on 8 out of 8 node and graph classification benchmarks under the linear evaluation protocol. For example, on Cora (node) and Reddit-Binary (graph) classification benchmarks, we achieve 86.8% and 84.5% accuracy, which are 5.5% and 2.4% relative improvements over previous state-of-the-art. When compared to supervised baselines, our approach outperforms them in 4 out of 8 benchmarks. Source code is released at: https://github.com/kavehhassani/mvgrl

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple nodes with hyperedges, and better capturing the topology is essential for effective representation learning. Recent advances in generative self-supervised learning (SSL) suggest that hypergraph neural networks learned from generative self supervision have the potential to effectively encode the complex hypergraph topology. Designing a generative SSL strategy for hypergraphs, however, is not straightforward. Questions remain with regard to its generative SSL task, connection to downstream tasks, and empirical properties of learned representations. In light of the promises and challenges, we propose a novel generative SSL strategy for hypergraphs. We first formulate a generative SSL task on hypergraphs, hyperedge filling, and highlight its theoretical connection to node classification. Based on the generative SSL task, we propose a hypergraph SSL method, HypeBoy. HypeBoy learns effective general-purpose hypergraph representations, outperforming 16 baseline methods across 11 benchmark datasets.

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data is both challenging and time consuming. The core problem is that no machine learning method is capable of learning on multiple tables interconnected by primary-foreign key relations. Current methods can only learn from a single table, so the data must first be manually joined and aggregated into a single training table, the process known as feature engineering. Feature engineering is slow, error prone and leads to suboptimal models. Here we introduce an end-to-end deep representation learning approach to directly learn on data laid out across multiple tables. We name our approach Relational Deep Learning (RDL). The core idea is to view relational databases as a temporal, heterogeneous graph, with a node for each row in each table, and edges specified by primary-foreign key links. Message Passing Graph Neural Networks can then automatically learn across the graph to extract representations that leverage all input data, without any manual feature engineering. Relational Deep Learning leads to more accurate models that can be built much faster. To facilitate research in this area, we develop RelBench, a set of benchmark datasets and an implementation of Relational Deep Learning. The data covers a wide spectrum, from discussions on Stack Exchange to book reviews on the Amazon Product Catalog. Overall, we define a new research area that generalizes graph machine learning and broadens its applicability to a wide set of AI use cases.

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

Node features and structural information of a graph are both crucial for semi-supervised node classification problems. A variety of graph neural network (GNN) based approaches have been proposed to tackle these problems, which typically determine output labels through feature aggregation. This can be problematic, as it implies conditional independence of output nodes given hidden representations, despite their direct connections in the graph. To learn the direct influence among output nodes in a graph, we propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. To balance model complexity and expressivity, the pairwise factors have a shared component and a separate scaling coefficient for each edge. We apply the EM algorithm to train our model, and utilize a star-shaped piecewise likelihood for the tractable surrogate objective. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

We propose DyGFormer, a new Transformer-based architecture for dynamic graph learning. DyGFormer is conceptually simple and only needs to learn from nodes' historical first-hop interactions by: (1) a neighbor co-occurrence encoding scheme that explores the correlations of the source node and destination node based on their historical sequences; (2) a patching technique that divides each sequence into multiple patches and feeds them to Transformer, allowing the model to effectively and efficiently benefit from longer histories. We also introduce DyGLib, a unified library with standard training pipelines, extensible coding interfaces, and comprehensive evaluating protocols to promote reproducible, scalable, and credible dynamic graph learning research. By performing exhaustive experiments on thirteen datasets for dynamic link prediction and dynamic node classification tasks, we find that DyGFormer achieves state-of-the-art performance on most of the datasets, demonstrating its effectiveness in capturing nodes' correlations and long-term temporal dependencies. Moreover, some results of baselines are inconsistent with previous reports, which may be caused by their diverse but less rigorous implementations, showing the importance of DyGLib. All the used resources are publicly available at https://github.com/yule-BUAA/DyGLib.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

Designing a single model to address multiple tasks has been a long-standing objective in artificial intelligence. Recently, large language models have demonstrated exceptional capability in solving different tasks within the language domain. However, a unified model for various graph tasks remains underexplored, primarily due to the challenges unique to the graph learning domain. First, graph data from different areas carry distinct attributes and follow different distributions. Such discrepancy makes it hard to represent graphs in a single representation space. Second, tasks on graphs diversify into node, link, and graph tasks, requiring distinct embedding strategies. Finally, an appropriate graph prompting paradigm for in-context learning is unclear. We propose One for All (OFA), the first general framework that can use a single graph model to address the above challenges. Specifically, OFA proposes text-attributed graphs to unify different graph data by describing nodes and edges with natural language and uses language models to encode the diverse and possibly cross-domain text attributes to feature vectors in the same embedding space. Furthermore, OFA introduces the concept of nodes-of-interest to standardize different tasks with a single task representation. For in-context learning on graphs, OFA introduces a novel graph prompting paradigm that appends prompting substructures to the input graph, which enables it to address varied tasks without fine-tuning. We train the OFA model using graph data from multiple domains (including citation networks, molecular graphs, knowledge graphs, etc.) simultaneously and evaluate its ability in supervised, few-shot, and zero-shot learning scenarios. OFA performs well across different tasks, making it the first general-purpose across-domains classification model on graphs.

Molecular relational learning, whose goal is to learn the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. Recently, graph neural networks have recently shown great success in molecular relational learning by modeling a molecule as a graph structure, and considering atom-level interactions between two molecules. Despite their success, existing molecular relational learning methods tend to overlook the nature of chemistry, i.e., a chemical compound is composed of multiple substructures such as functional groups that cause distinctive chemical reactions. In this work, we propose a novel relational learning framework, called CGIB, that predicts the interaction behavior between a pair of graphs by detecting core subgraphs therein. The main idea is, given a pair of graphs, to find a subgraph from a graph that contains the minimal sufficient information regarding the task at hand conditioned on the paired graph based on the principle of conditional graph information bottleneck. We argue that our proposed method mimics the nature of chemical reactions, i.e., the core substructure of a molecule varies depending on which other molecule it interacts with. Extensive experiments on various tasks with real-world datasets demonstrate the superiority of CGIB over state-of-the-art baselines. Our code is available at https://github.com/Namkyeong/CGIB.

Rationale discovery is defined as finding a subset of the input data that maximally supports the prediction of downstream tasks. In graph machine learning context, graph rationale is defined to locate the critical subgraph in the given graph topology, which fundamentally determines the prediction results. In contrast to the rationale subgraph, the remaining subgraph is named the environment subgraph. Graph rationalization can enhance the model performance as the mapping between the graph rationale and prediction label is viewed as invariant, by assumption. To ensure the discriminative power of the extracted rationale subgraphs, a key technique named "intervention" is applied. The core idea of intervention is that given any changing environment subgraphs, the semantics from the rationale subgraph is invariant, which guarantees the correct prediction result. However, most, if not all, of the existing rationalization works on graph data develop their intervention strategies on the graph level, which is coarse-grained. In this paper, we propose well-tailored intervention strategies on graph data. Our idea is driven by the development of Transformer models, whose self-attention module provides rich interactions between input nodes. Based on the self-attention module, our proposed invariant graph Transformer (IGT) can achieve fine-grained, more specifically, node-level and virtual node-level intervention. Our comprehensive experiments involve 7 real-world datasets, and the proposed IGT shows significant performance advantages compared to 13 baseline methods.

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating both graph structure and feature information leads to complex models, and explaining predictions made by GNNs remains unsolved. Here we propose GNNExplainer, the first general, model-agnostic approach for providing interpretable explanations for predictions of any GNN-based model on any graph-based machine learning task. Given an instance, GNNExplainer identifies a compact subgraph structure and a small subset of node features that have a crucial role in GNN's prediction. Further, GNNExplainer can generate consistent and concise explanations for an entire class of instances. We formulate GNNExplainer as an optimization task that maximizes the mutual information between a GNN's prediction and distribution of possible subgraph structures. Experiments on synthetic and real-world graphs show that our approach can identify important graph structures as well as node features, and outperforms baselines by 17.1% on average. GNNExplainer provides a variety of benefits, from the ability to visualize semantically relevant structures to interpretability, to giving insights into errors of faulty GNNs.

In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Benefiting from the message passing mechanism, Graph Neural Networks (GNNs) have been successful on flourish tasks over graph data. However, recent studies have shown that attackers can catastrophically degrade the performance of GNNs by maliciously modifying the graph structure. A straightforward solution to remedy this issue is to model the edge weights by learning a metric function between pairwise representations of two end nodes, which attempts to assign low weights to adversarial edges. The existing methods use either raw features or representations learned by supervised GNNs to model the edge weights. However, both strategies are faced with some immediate problems: raw features cannot represent various properties of nodes (e.g., structure information), and representations learned by supervised GNN may suffer from the poor performance of the classifier on the poisoned graph. We need representations that carry both feature information and as mush correct structure information as possible and are insensitive to structural perturbations. To this end, we propose an unsupervised pipeline, named STABLE, to optimize the graph structure. Finally, we input the well-refined graph into a downstream classifier. For this part, we design an advanced GCN that significantly enhances the robustness of vanilla GCN without increasing the time complexity. Extensive experiments on four real-world graph benchmarks demonstrate that STABLE outperforms the state-of-the-art methods and successfully defends against various attacks.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: https://github.com/v18nguye/GLAD.

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences about the relationships between entities in a complex system, and to identify hidden patterns and trends. Despite the remarkable progress in automated reasoning with natural text, reasoning on graphs with large language models (LLMs) remains an understudied problem. In this work, we perform the first comprehensive study of encoding graph-structured data as text for consumption by LLMs. We show that LLM performance on graph reasoning tasks varies on three fundamental levels: (1) the graph encoding method, (2) the nature of the graph task itself, and (3) interestingly, the very structure of the graph considered. These novel results provide valuable insight on strategies for encoding graphs as text. Using these insights we illustrate how the correct choice of encoders can boost performance on graph reasoning tasks inside LLMs by 4.8% to 61.8%, depending on the task.

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.

In contrastive learning, the choice of ``view'' controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty. Furthermore, guided by structural entropy, we implement the anchor view, termed SEGA, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.

The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to images and audio. Despite this progress, a critical gap remains in empowering LLMs to proficiently understand and reason on graph data. Recent studies underscore LLMs' underwhelming performance on fundamental graph reasoning tasks. In this paper, we endeavor to unearth the obstacles that impede LLMs in graph reasoning, pinpointing the common practice of converting graphs into natural language descriptions (Graph2Text) as a fundamental bottleneck. To overcome this impediment, we introduce GraphLLM, a pioneering end-to-end approach that synergistically integrates graph learning models with LLMs. This synergy equips LLMs with the ability to proficiently interpret and reason on graph data, harnessing the superior expressive power of graph learning models. Our empirical evaluations across four fundamental graph reasoning tasks validate the effectiveness of GraphLLM. The results exhibit a substantial average accuracy enhancement of 54.44%, alongside a noteworthy context reduction of 96.45% across various graph reasoning tasks.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

Artificial General Intelligence (AGI) has revolutionized numerous fields, yet its integration with graph data, a cornerstone in our interconnected world, remains nascent. This paper presents a pioneering survey on the emerging domain of graph prompts in AGI, addressing key challenges and opportunities in harnessing graph data for AGI applications. Despite substantial advancements in AGI across natural language processing and computer vision, the application to graph data is relatively underexplored. This survey critically evaluates the current landscape of AGI in handling graph data, highlighting the distinct challenges in cross-modality, cross-domain, and cross-task applications specific to graphs. Our work is the first to propose a unified framework for understanding graph prompt learning, offering clarity on prompt tokens, token structures, and insertion patterns in the graph domain. We delve into the intrinsic properties of graph prompts, exploring their flexibility, expressiveness, and interplay with existing graph models. A comprehensive taxonomy categorizes over 100 works in this field, aligning them with pre-training tasks across node-level, edge-level, and graph-level objectives. Additionally, we present, ProG, a Python library, and an accompanying website, to support and advance research in graph prompting. The survey culminates in a discussion of current challenges and future directions, offering a roadmap for research in graph prompting within AGI. Through this comprehensive analysis, we aim to catalyze further exploration and practical applications of AGI in graph data, underlining its potential to reshape AGI fields and beyond. ProG and the website can be accessed by https://github.com/WxxShirley/Awesome-Graph-Prompt, and https://github.com/sheldonresearch/ProG, respectively.

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

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.~Our codes and datasets are available at: \url{https://github.com/XiaoxinHe/G-Retriever}

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links but also have semantics underlying their structure. Semantics is crucial in several downstream tasks, such as query answering or reasoning. We introduce the subgraph inference task, where a model has to generate likely and semantically valid subgraphs. We propose IntelliGraphs, a set of five new Knowledge Graph datasets. The IntelliGraphs datasets contain subgraphs with semantics expressed in logical rules for evaluating subgraph inference. We also present the dataset generator that produced the synthetic datasets. We designed four novel baseline models, which include three models based on traditional KGEs. We evaluate their expressiveness and show that these models cannot capture the semantics. We believe this benchmark will encourage the development of machine learning models that emphasize semantic understanding.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Graph representation learning is a fundamental research theme and can be generalized to benefit multiple downstream tasks from the node and link levels to the higher graph level. In practice, it is desirable to develop task-agnostic general graph representation learning methods that are typically trained in an unsupervised manner. Related research reveals that the power of graph representation learning methods depends on whether they can differentiate distinct graph structures as different embeddings and map isomorphic graphs to consistent embeddings (i.e., the isomorphic consistency of graph models). However, for task-agnostic general graph representation learning, existing unsupervised graph models, represented by the variational graph auto-encoders (VGAEs), can only keep the isomorphic consistency within the subgraphs of 1-hop neighborhoods and thus usually manifest inferior performance on the more difficult higher-level tasks. To overcome the limitations of existing unsupervised methods, in this paper, we propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for multi-level task-agnostic graph representation learning. We first devise a decoding scheme to provide a theoretical guarantee of keeping the isomorphic consistency under the settings of unsupervised learning. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization, which trains the model via reconstructing the GNN node embeddings with multi-hop neighborhood information, so as to maintain the high-order isomorphic consistency within the VGAE framework. We conduct extensive experiments on the representative graph learning tasks at different levels, including node classification, link prediction and graph classification, and the results verify that our proposed model generally outperforms both the state-of-the-art unsupervised methods and representative supervised methods.

In real-world scenarios, most of the data obtained from information retrieval (IR) system is unstructured. Converting natural language sentences into structured Knowledge Graphs (KGs) remains a critical challenge. The quality of constructed KGs may also impact the performance of some KG-dependent domains like GraphRAG systems and recommendation systems. Recently, Large Language Models (LLMs) have demonstrated impressive capabilities in addressing a wide range of natural language processing tasks. However, there are still challenges when utilizing LLMs to address the task of generating structured KGs. And we have identified three limitations with respect to existing KG construction methods. (1)There is a large amount of information and excessive noise in real-world documents, which could result in extracting messy information. (2)Native LLMs struggle to effectively extract accuracy knowledge from some domain-specific documents. (3)Hallucinations phenomenon cannot be overlooked when utilizing LLMs directly as an unsupervised method for constructing KGs. In this paper, we propose GraphJudger, a knowledge graph construction framework to address the aforementioned challenges. We introduce three innovative modules in our method, which are entity-centric iterative text denoising, knowledge aware instruction tuning and graph judgement, respectively. We seek to utilize the capacity of LLMs to function as a graph judger, a capability superior to their role only as a predictor for KG construction problems. Experiments conducted on two general text-graph pair datasets and one domain-specific text-graph pair dataset show superior performances compared to baseline methods. The code of our proposed method is available at https://github.com/hhy-huang/GraphJudger.

The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewire or infer a GNN's graph to maximize the GNN's predictive downstream performance, but it lacks solid theoretical foundations in terms of embedding-based representation guarantees. This paper addresses this issue by introducing a trainable deep learning architecture, coined neural snowflake, that can adaptively implement fractal-like metrics on R^d. We prove that any given finite weights graph can be isometrically embedded by a standard MLP encoder. Furthermore, when the latent graph can be represented in the feature space of a sufficiently regular kernel, we show that the combined neural snowflake and MLP encoder do not succumb to the curse of dimensionality by using only a low-degree polynomial number of parameters in the number of nodes. This implementation enables a low-dimensional isometric embedding of the latent graph. We conduct synthetic experiments to demonstrate the superior metric learning capabilities of neural snowflakes when compared to more familiar spaces like Euclidean space. Additionally, we carry out latent graph inference experiments on graph benchmarks. Consistently, the neural snowflake model achieves predictive performance that either matches or surpasses that of the state-of-the-art latent graph inference models. Importantly, this performance improvement is achieved without requiring random search for optimal latent geometry. Instead, the neural snowflake model achieves this enhancement in a differentiable manner.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Graph Contrastive Learning (GCL) has emerged as a popular training approach for learning node embeddings from augmented graphs without labels. Despite the key principle that maximizing the similarity between positive node pairs while minimizing it between negative node pairs is well established, some fundamental problems are still unclear. Considering the complex graph structure, are some nodes consistently well-trained and following this principle even with different graph augmentations? Or are there some nodes more likely to be untrained across graph augmentations and violate the principle? How to distinguish these nodes and further guide the training of GCL? To answer these questions, we first present experimental evidence showing that the training of GCL is indeed imbalanced across all nodes. To address this problem, we propose the metric "node compactness", which is the lower bound of how a node follows the GCL principle related to the range of augmentations. We further derive the form of node compactness theoretically through bound propagation, which can be integrated into binary cross-entropy as a regularization. To this end, we propose the PrOvable Training (POT) for GCL, which regularizes the training of GCL to encode node embeddings that follows the GCL principle better. Through extensive experiments on various benchmarks, POT consistently improves the existing GCL approaches, serving as a friendly plugin.

We study how to train personalized models for different tasks on decentralized devices with limited local data. We propose "Structured Cooperative Learning (SCooL)", in which a cooperation graph across devices is generated by a graphical model prior to automatically coordinate mutual learning between devices. By choosing graphical models enforcing different structures, we can derive a rich class of existing and novel decentralized learning algorithms via variational inference. In particular, we show three instantiations of SCooL that adopt Dirac distribution, stochastic block model (SBM), and attention as the prior generating cooperation graphs. These EM-type algorithms alternate between updating the cooperation graph and cooperative learning of local models. They can automatically capture the cross-task correlations among devices by only monitoring their model updating in order to optimize the cooperation graph. We evaluate SCooL and compare it with existing decentralized learning methods on an extensive set of benchmarks, on which SCooL always achieves the highest accuracy of personalized models and significantly outperforms other baselines on communication efficiency. Our code is available at https://github.com/ShuangtongLi/SCooL.

Advances in Visually Rich Document Understanding (VrDU) have enabled information extraction and question answering over documents with complex layouts. Two tropes of architectures have emerged -- transformer-based models inspired by LLMs, and Graph Neural Networks. In this paper, we introduce DocGraphLM, a novel framework that combines pre-trained language models with graph semantics. To achieve this, we propose 1) a joint encoder architecture to represent documents, and 2) a novel link prediction approach to reconstruct document graphs. DocGraphLM predicts both directions and distances between nodes using a convergent joint loss function that prioritizes neighborhood restoration and downweighs distant node detection. Our experiments on three SotA datasets show consistent improvement on IE and QA tasks with the adoption of graph features. Moreover, we report that adopting the graph features accelerates convergence in the learning process during training, despite being solely constructed through link prediction.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

To deduce new facts on a knowledge graph (KG), a link predictor learns from the graph structure and collects local evidence to find the answer to a given query. However, existing methods suffer from a severe scalability problem due to the utilization of the whole KG for prediction, which hinders their promise on large scale KGs and cannot be directly addressed by vanilla sampling methods. In this work, we propose the one-shot-subgraph link prediction to achieve efficient and adaptive prediction. The design principle is that, instead of directly acting on the whole KG, the prediction procedure is decoupled into two steps, i.e., (i) extracting only one subgraph according to the query and (ii) predicting on this single, query dependent subgraph. We reveal that the non-parametric and computation-efficient heuristics Personalized PageRank (PPR) can effectively identify the potential answers and supporting evidence. With efficient subgraph-based prediction, we further introduce the automated searching of the optimal configurations in both data and model spaces. Empirically, we achieve promoted efficiency and leading performances on five large-scale benchmarks. The code is publicly available at: https://github.com/tmlr-group/one-shot-subgraph.

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects -- graphon NNs for GNNs, and graphon NTKs for GNTKs -- , and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the directions of fastest learning which becomes relevant during early stopping, converges to the spectrum of the graphon NTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

Graph neural networks (GNNs) have been demonstrated to be powerful in modeling graph-structured data. However, training GNNs usually requires abundant task-specific labeled data, which is often arduously expensive to obtain. One effective way to reduce the labeling effort is to pre-train an expressive GNN model on unlabeled data with self-supervision and then transfer the learned model to downstream tasks with only a few labels. In this paper, we present the GPT-GNN framework to initialize GNNs by generative pre-training. GPT-GNN introduces a self-supervised attributed graph generation task to pre-train a GNN so that it can capture the structural and semantic properties of the graph. We factorize the likelihood of the graph generation into two components: 1) Attribute Generation and 2) Edge Generation. By modeling both components, GPT-GNN captures the inherent dependency between node attributes and graph structure during the generative process. Comprehensive experiments on the billion-scale Open Academic Graph and Amazon recommendation data demonstrate that GPT-GNN significantly outperforms state-of-the-art GNN models without pre-training by up to 9.1% across various downstream tasks.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

Masked graph autoencoders have emerged as a powerful graph self-supervised learning method that has yet to be fully explored. In this paper, we unveil that the existing discrete edge masking and binary link reconstruction strategies are insufficient to learn topologically informative representations, from the perspective of message propagation on graph neural networks. These limitations include blocking message flows, vulnerability to over-smoothness, and suboptimal neighborhood discriminability. Inspired by these understandings, we explore non-discrete edge masks, which are sampled from a continuous and dispersive probability distribution instead of the discrete Bernoulli distribution. These masks restrict the amount of output messages for each edge, referred to as "bandwidths". We propose a novel, informative, and effective topological masked graph autoencoder using bandwidth masking and a layer-wise bandwidth prediction objective. We demonstrate its powerful graph topological learning ability both theoretically and empirically. Our proposed framework outperforms representative baselines in both self-supervised link prediction (improving the discrete edge reconstructors by at most 20%) and node classification on numerous datasets, solely with a structure-learning pretext. Our implementation is available at https://github.com/Newiz430/Bandana.

Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.

Although Large Language Models (LLMs) have demonstrated potential in processing graphs, they struggle with comprehending graphical structure information through prompts of graph description sequences, especially as the graph size increases. We attribute this challenge to the uneven memory performance of LLMs across different positions in graph description sequences, known as ''positional biases''. To address this, we propose GraphInsight, a novel framework aimed at improving LLMs' comprehension of both macro- and micro-level graphical information. GraphInsight is grounded in two key strategies: 1) placing critical graphical information in positions where LLMs exhibit stronger memory performance, and 2) investigating a lightweight external knowledge base for regions with weaker memory performance, inspired by retrieval-augmented generation (RAG). Moreover, GraphInsight explores integrating these two strategies into LLM agent processes for composite graph tasks that require multi-step reasoning. Extensive empirical studies on benchmarks with a wide range of evaluation tasks show that GraphInsight significantly outperforms all other graph description methods (e.g., prompting techniques and reordering strategies) in understanding graph structures of varying sizes.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G^* while minimizing the number of interventions made. In our setting, we are additionally given side information about G^* as advice, e.g. a DAG G purported to be G^*. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G^* whose intervention cost is at most O(max{1, log psi}) times the cost for verifying G^*; here, psi is a distance measure between G and G^* that is upper bounded by the number of variables n, and is exactly 0 when G=G^*. Our approximation factor matches the state-of-the-art for the advice-less setting.

In this paper, the causal bandit problem is investigated, in which the objective is to select an optimal sequence of interventions on nodes in a causal graph. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. By exploiting the causal relationships between the nodes whose signals contribute to the reward, interventions are optimized. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed, which strongly reduces sample complexity relative to the prior art by learning sub-graphs. Under the assumption of Gaussian exogenous inputs and minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound based intervention selection to optimize the reward. To cope with non-stationary bandits, a sub-graph change detection mechanism is proposed, with high sample efficiency. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in both stationary and non-stationary settings. Compared to existing approaches, the proposed scheme takes 67% fewer samples to learn the causal structure and achieves an average reward gain of 85%.

Transferring latent structure from one environment or problem to another is a mechanism by which humans and animals generalize with very little data. Inspired by cognitive and neurobiological insights, we propose graph schemas as a mechanism of abstraction for transfer learning. Graph schemas start with latent graph learning where perceptually aliased observations are disambiguated in the latent space using contextual information. Latent graph learning is also emerging as a new computational model of the hippocampus to explain map learning and transitive inference. Our insight is that a latent graph can be treated as a flexible template -- a schema -- that models concepts and behaviors, with slots that bind groups of latent nodes to the specific observations or groundings. By treating learned latent graphs (schemas) as prior knowledge, new environments can be quickly learned as compositions of schemas and their newly learned bindings. We evaluate graph schemas on two previously published challenging tasks: the memory & planning game and one-shot StreetLearn, which are designed to test rapid task solving in novel environments. Graph schemas can be learned in far fewer episodes than previous baselines, and can model and plan in a few steps in novel variations of these tasks. We also demonstrate learning, matching, and reusing graph schemas in more challenging 2D and 3D environments with extensive perceptual aliasing and size variations, and show how different schemas can be composed to model larger and more complex environments. To summarize, our main contribution is a unified system, inspired and grounded in cognitive science, that facilitates rapid transfer learning of new environments using schemas via map-induction and composition that handles perceptual aliasing.

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at https://github.com/zknus/Hamiltonian-GNN.

We introduce a randomized topological augmentor based on Schur complements for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the technique generates unbiased approximations of its Schur complements and treats the corresponding graphs as augmented views. We discuss the benefits of our approach, provide theoretical justifications and present connections with graph diffusion. Unlike previous efforts, we study the empirical effectiveness of the augmentor in a controlled fashion by varying the design choices for subsequent GCL phases, such as encoding and contrasting. Extensive experiments on node and graph classification benchmarks demonstrate that our technique consistently outperforms pre-defined and adaptive augmentation approaches to achieve state-of-the-art results.

While Language Models have become workhorses for NLP, their interplay with textual knowledge graphs (KGs) - structured memories of general or domain knowledge - is actively researched. Current embedding methodologies for such graphs typically either (i) linearize graphs for embedding them using sequential Language Models (LMs), which underutilize structural information, or (ii) use Graph Neural Networks (GNNs) to preserve graph structure, while GNNs cannot represent textual features as well as a pre-trained LM could. In this work we introduce a novel language model, the Graph Language Model (GLM), that integrates the strengths of both approaches, while mitigating their weaknesses. The GLM parameters are initialized from a pretrained LM, to facilitate nuanced understanding of individual concepts and triplets. Simultaneously, its architectural design incorporates graph biases, thereby promoting effective knowledge distribution within the graph. Empirical evaluations on relation classification tasks on ConceptNet subgraphs reveal that GLM embeddings surpass both LM- and GNN-based baselines in supervised and zero-shot settings.

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.

We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.

We present POTATO, a task- and languageindependent framework for human-in-the-loop (HITL) learning of rule-based text classifiers using graph-based features. POTATO handles any type of directed graph and supports parsing text into Abstract Meaning Representations (AMR), Universal Dependencies (UD), and 4lang semantic graphs. A streamlit-based user interface allows users to build rule systems from graph patterns, provides real-time evaluation based on ground truth data, and suggests rules by ranking graph features using interpretable machine learning models. Users can also provide patterns over graphs using regular expressions, and POTATO can recommend refinements of such rules. POTATO is applied in projects across domains and languages, including classification tasks on German legal text and English social media data. All components of our system are written in Python, can be installed via pip, and are released under an MIT License on GitHub.

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic. In order to break this expressiveness barrier, GNNs have been enhanced with random node initialization (RNI), where the idea is to train and run the models with randomized initial node features. In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties. This universality result holds even with partially randomized initial node features, and preserves the invariance properties of GNNs in expectation. We then empirically analyze the effect of RNI on GNNs, based on carefully constructed datasets. Our empirical findings support the superior performance of GNNs with RNI over standard GNNs.

Graph representation learning is fundamental for analyzing graph-structured data. Exploring invariant graph representations remains a challenge for most existing graph representation learning methods. In this paper, we propose a cross-view graph consistency learning (CGCL) method that learns invariant graph representations for link prediction. First, two complementary augmented views are derived from an incomplete graph structure through a bidirectional graph structure augmentation scheme. This augmentation scheme mitigates the potential information loss that is commonly associated with various data augmentation techniques involving raw graph data, such as edge perturbation, node removal, and attribute masking. Second, we propose a CGCL model that can learn invariant graph representations. A cross-view training scheme is proposed to train the proposed CGCL model. This scheme attempts to maximize the consistency information between one augmented view and the graph structure reconstructed from the other augmented view. Furthermore, we offer a comprehensive theoretical CGCL analysis. This paper empirically and experimentally demonstrates the effectiveness of the proposed CGCL method, achieving competitive results on graph datasets in comparisons with several state-of-the-art algorithms.

Graph Neural Networks (GNNs) have greatly advanced the semi-supervised node classification task on graphs. The majority of existing GNNs are trained in an end-to-end manner that can be viewed as tackling a bi-level optimization problem. This process is often inefficient in computation and memory usage. In this work, we propose a new optimization framework for semi-supervised learning on graphs. The proposed framework can be conveniently solved by the alternating optimization algorithms, resulting in significantly improved efficiency. Extensive experiments demonstrate that the proposed method can achieve comparable or better performance with state-of-the-art baselines while it has significantly better computation and memory efficiency.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a "predictive" latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

Representation learning on heterogeneous graphs aims to obtain meaningful node representations to facilitate various downstream tasks, such as node classification and link prediction. Existing heterogeneous graph learning methods are primarily developed by following the propagation mechanism of node representations. There are few efforts on studying the role of relations for improving the learning of more fine-grained node representations. Indeed, it is important to collaboratively learn the semantic representations of relations and discern node representations with respect to different relation types. To this end, in this paper, we propose a novel Relation-aware Heterogeneous Graph Neural Network, namely R-HGNN, to learn node representations on heterogeneous graphs at a fine-grained level by considering relation-aware characteristics. Specifically, a dedicated graph convolution component is first designed to learn unique node representations from each relation-specific graph separately. Then, a cross-relation message passing module is developed to improve the interactions of node representations across different relations. Also, the relation representations are learned in a layer-wise manner to capture relation semantics, which are used to guide the node representation learning process. Moreover, a semantic fusing module is presented to aggregate relation-aware node representations into a compact representation with the learned relation representations. Finally, we conduct extensive experiments on a variety of graph learning tasks, and experimental results demonstrate that our approach consistently outperforms existing methods among all the tasks.

Large language models (LLMs) have achieved impressive success across several fields, but their proficiency in understanding and resolving complex graph problems is less explored. To bridge this gap, we introduce GraphInstruct, a novel and comprehensive instruction-tuning dataset designed to equip language models with the ability to tackle a broad spectrum of graph problems using explicit reasoning paths. Utilizing GraphInstruct, we build GraphWiz, an open-source language model capable of resolving various graph problem types while generating clear reasoning processes. To enhance the model's capability and reliability, we incorporate the Direct Preference Optimization (DPO) framework into the graph problem-solving context. The enhanced model, GraphWiz-DPO, achieves an average accuracy of 65% across nine tasks with different complexity levels, surpassing GPT-4 which has an average accuracy of 43.8%. Moreover, our research delves into the delicate balance between training data volume and model performance, highlighting the potential for overfitting with increased data. We also explore the transferability of the model's reasoning ability across different graph tasks, indicating the model's adaptability and practical application potential. Our investigation offers a new blueprint and valuable insights for developing LLMs specialized in graph reasoning and problem-solving.

Large language models (LLMs), while exhibiting exceptional performance, suffer from hallucinations, especially on knowledge-intensive tasks. Existing works propose to augment LLMs with individual text units retrieved from external knowledge corpora to alleviate the issue. However, in many domains, texts are interconnected (e.g., academic papers in a bibliographic graph are linked by citations and co-authorships) which form a (text-attributed) graph. The knowledge in such graphs is encoded not only in single texts/nodes but also in their associated connections. To facilitate the research of augmenting LLMs with graphs, we manually construct a Graph Reasoning Benchmark dataset called GRBench, containing 1,740 questions that can be answered with the knowledge from 10 domain graphs. Then, we propose a simple and effective framework called Graph Chain-of-thought (Graph-CoT) to augment LLMs with graphs by encouraging LLMs to reason on the graph iteratively. Each Graph-CoT iteration consists of three sub-steps: LLM reasoning, LLM-graph interaction, and graph execution. We conduct systematic experiments with three LLM backbones on GRBench, where Graph-CoT outperforms the baselines consistently. The code is available at https://github.com/PeterGriffinJin/Graph-CoT.

Pre-trained sequence-to-sequence language models have led to widespread success in many natural language generation tasks. However, there has been relatively less work on analyzing their ability to generate structured outputs such as graphs. Unlike natural language, graphs have distinct structural and semantic properties in the context of a downstream NLP task, e.g., generating a graph that is connected and acyclic can be attributed to its structural constraints, while the semantics of a graph can refer to how meaningfully an edge represents the relation between two node concepts. In this work, we study pre-trained language models that generate explanation graphs in an end-to-end manner and analyze their ability to learn the structural constraints and semantics of such graphs. We first show that with limited supervision, pre-trained language models often generate graphs that either violate these constraints or are semantically incoherent. Since curating large amount of human-annotated graphs is expensive and tedious, we propose simple yet effective ways of graph perturbations via node and edge edit operations that lead to structurally and semantically positive and negative graphs. Next, we leverage these graphs in different contrastive learning models with Max-Margin and InfoNCE losses. Our methods lead to significant improvements in both structural and semantic accuracy of explanation graphs and also generalize to other similar graph generation tasks. Lastly, we show that human errors are the best negatives for contrastive learning and also that automatically generating more such human-like negative graphs can lead to further improvements. Our code and models are publicly available at https://github.com/swarnaHub/ExplagraphGen

We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes sim 10\% of the number of parameters and sim 0.2\% of training samples compared with reinforcement learning or supervised learning methods.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

Electronic Health Records (EHR) are high-dimensional data with implicit connections among thousands of medical concepts. These connections, for instance, the co-occurrence of diseases and lab-disease correlations can be informative when only a subset of these variables is documented by the clinician. A feasible approach to improving the representation learning of EHR data is to associate relevant medical concepts and utilize these connections. Existing medical ontologies can be the reference for EHR structures, but they place numerous constraints on the data source. Recent progress on graph neural networks (GNN) enables end-to-end learning of topological structures for non-grid or non-sequential data. However, there are problems to be addressed on how to learn the medical graph adaptively and how to understand the effect of the medical graph on representation learning. In this paper, we propose a variationally regularized encoder-decoder graph network that achieves more robustness in graph structure learning by regularizing node representations. Our model outperforms the existing graph and non-graph based methods in various EHR predictive tasks based on both public data and real-world clinical data. Besides the improvements in empirical experiment performances, we provide an interpretation of the effect of variational regularization compared to standard graph neural network, using singular value analysis.

Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the property of the polynomial basis. Consequently, two natural and fundamental questions arise: Can we learn a suitable polynomial basis from the training data? Can we determine the optimal polynomial basis for a given graph and node features? In this paper, we propose two spectral GNN models that provide positive answers to the questions posed above. First, inspired by Favard's Theorem, we propose the FavardGNN model, which learns a polynomial basis from the space of all possible orthonormal bases. Second, we examine the supposedly unsolvable definition of optimal polynomial basis from Wang & Zhang (2022) and propose a simple model, OptBasisGNN, which computes the optimal basis for a given graph structure and graph signal. Extensive experiments are conducted to demonstrate the effectiveness of our proposed models.

Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods. However, they suffer from exponential computational costs or searching the matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we first prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. We can then yield an implementation of linear time complexity by the built-in tree-structured aggregation mechanism on graph neural networks. Moreover, circle structures and node attributes can be easily incorporated in D2Match to boost the matching performance. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed exploits the subtrees and differs from existing GNNs-based subgraph matching methods that depend on memorizing the data distribution divergence

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

The arXiv has collected 1.5 million pre-print articles over 28 years, hosting literature from scientific fields including Physics, Mathematics, and Computer Science. Each pre-print features text, figures, authors, citations, categories, and other metadata. These rich, multi-modal features, combined with the natural graph structure---created by citation, affiliation, and co-authorship---makes the arXiv an exciting candidate for benchmarking next-generation models. Here we take the first necessary steps toward this goal, by providing a pipeline which standardizes and simplifies access to the arXiv's publicly available data. We use this pipeline to extract and analyze a 6.7 million edge citation graph, with an 11 billion word corpus of full-text research articles. We present some baseline classification results, and motivate application of more exciting generative graph models.

Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly graphs. With the success of these graph neural networks (GNN) in the static setting, we approach further practical scenarios where the graph dynamically evolves. Existing approaches typically resort to node embeddings and use a recurrent neural network (RNN, broadly speaking) to regulate the embeddings and learn the temporal dynamics. These methods require the knowledge of a node in the full time span (including both training and testing) and are less applicable to the frequent change of the node set. In some extreme scenarios, the node sets at different time steps may completely differ. To resolve this challenge, we propose EvolveGCN, which adapts the graph convolutional network (GCN) model along the temporal dimension without resorting to node embeddings. The proposed approach captures the dynamism of the graph sequence through using an RNN to evolve the GCN parameters. Two architectures are considered for the parameter evolution. We evaluate the proposed approach on tasks including link prediction, edge classification, and node classification. The experimental results indicate a generally higher performance of EvolveGCN compared with related approaches. The code is available at https://github.com/IBM/EvolveGCN.

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adopting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and complex query answering tasks by learning representations of entities, relations, and queries. Still, most existing query answering methods rely on transductive entity embeddings and cannot generalize to KGs containing new entities without retraining the entity embeddings. In this work, we study the inductive query answering task where inference is performed on a graph containing new entities with queries over both seen and unseen entities. To this end, we devise two mechanisms leveraging inductive node and relational structure representations powered by graph neural networks (GNNs). Experimentally, we show that inductive models are able to perform logical reasoning at inference time over unseen nodes generalizing to graphs up to 500% larger than training ones. Exploring the efficiency--effectiveness trade-off, we find the inductive relational structure representation method generally achieves higher performance, while the inductive node representation method is able to answer complex queries in the inference-only regime without any training on queries and scales to graphs of millions of nodes. Code is available at https://github.com/DeepGraphLearning/InductiveQE.

Large Language Models (LLMs) have gained the ability to assimilate human knowledge and facilitate natural language interactions with both humans and other LLMs. However, despite their impressive achievements, LLMs have not made significant advancements in the realm of graph machine learning. This limitation arises because graphs encapsulate distinct relational data, making it challenging to transform them into natural language that LLMs understand. In this paper, we bridge this gap with a novel framework, GraphText, that translates graphs into natural language. GraphText derives a graph-syntax tree for each graph that encapsulates both the node attributes and inter-node relationships. Traversal of the tree yields a graph text sequence, which is then processed by an LLM to treat graph tasks as text generation tasks. Notably, GraphText offers multiple advantages. It introduces training-free graph reasoning: even without training on graph data, GraphText with ChatGPT can achieve on par with, or even surpassing, the performance of supervised-trained graph neural networks through in-context learning (ICL). Furthermore, GraphText paves the way for interactive graph reasoning, allowing both humans and LLMs to communicate with the model seamlessly using natural language. These capabilities underscore the vast, yet-to-be-explored potential of LLMs in the domain of graph machine learning.

A legal knowledge graph constructed from court cases, judgments, laws and other legal documents can enable a number of applications like question answering, document similarity, and search. While the use of knowledge graphs for distant supervision in NLP tasks is well researched, using knowledge graphs for downstream graph tasks like node similarity presents challenges in selecting node types and their features. In this demo, we describe our solution for predicting similar nodes in a case graph derived from our legal knowledge graph.

Since the pioneering work on the lottery ticket hypothesis for graph neural networks (GNNs) was proposed in Chen et al. (2021), the study on finding graph lottery tickets (GLT) has become one of the pivotal focus in the GNN community, inspiring researchers to discover sparser GLT while achieving comparable performance to original dense networks. In parallel, the graph structure has gained substantial attention as a crucial factor in GNN training dynamics, also elucidated by several recent studies. Despite this, contemporary studies on GLT, in general, have not fully exploited inherent pathways in the graph structure and identified tickets in an iterative manner, which is time-consuming and inefficient. To address these limitations, we introduce TEDDY, a one-shot edge sparsification framework that leverages structural information by incorporating edge-degree information. Following edge sparsification, we encourage the parameter sparsity during training via simple projected gradient descent on the ell_0 ball. Given the target sparsity levels for both the graph structure and the model parameters, our TEDDY facilitates efficient and rapid realization of GLT within a single training. Remarkably, our experimental results demonstrate that TEDDY significantly surpasses conventional iterative approaches in generalization, even when conducting one-shot sparsification that solely utilizes graph structures, without taking feature information into account.

The growing interest in machine learning problems over graphs with additional node information such as texts, images, or labels has popularized methods that require the costly operation of processing the entire graph. Yet, little effort has been made to the development of fast local methods (i.e. without accessing the entire graph) that extract useful information from such data. To that end, we propose a study of local graph clustering using noisy node labels as a proxy for additional node information. In this setting, nodes receive initial binary labels based on cluster affiliation: 1 if they belong to the target cluster and 0 otherwise. Subsequently, a fraction of these labels is flipped. We investigate the benefits of incorporating noisy labels for local graph clustering. By constructing a weighted graph with such labels, we study the performance of graph diffusion-based local clustering method on both the original and the weighted graphs. From a theoretical perspective, we consider recovering an unknown target cluster with a single seed node in a random graph with independent noisy node labels. We provide sufficient conditions on the label noise under which, with high probability, using diffusion in the weighted graph yields a more accurate recovery of the target cluster. This approach proves more effective than using the given labels alone or using diffusion in the label-free original graph. Empirically, we show that reliable node labels can be obtained with just a few samples from an attributed graph. Moreover, utilizing these labels via diffusion in the weighted graph leads to significantly better local clustering performance across several real-world datasets, improving F1 scores by up to 13%.

Graph neural networks (GNNs) emerged recently as a standard toolkit for learning from data on graphs. Current GNN designing works depend on immense human expertise to explore different message-passing mechanisms, and require manual enumeration to determine the proper message-passing depth. Inspired by the strong searching capability of neural architecture search (NAS) in CNN, this paper proposes Graph Neural Architecture Search (GNAS) with novel-designed search space. The GNAS can automatically learn better architecture with the optimal depth of message passing on the graph. Specifically, we design Graph Neural Architecture Paradigm (GAP) with tree-topology computation procedure and two types of fine-grained atomic operations (feature filtering and neighbor aggregation) from message-passing mechanism to construct powerful graph network search space. Feature filtering performs adaptive feature selection, and neighbor aggregation captures structural information and calculates neighbors' statistics. Experiments show that our GNAS can search for better GNNs with multiple message-passing mechanisms and optimal message-passing depth. The searched network achieves remarkable improvement over state-of-the-art manual designed and search-based GNNs on five large-scale datasets at three classical graph tasks. Codes can be found at https://github.com/phython96/GNAS-MP.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Self-supervised learning (SSL) has been extensively explored in recent years. Particularly, generative SSL has seen emerging success in natural language processing and other AI fields, such as the wide adoption of BERT and GPT. Despite this, contrastive learning-which heavily relies on structural data augmentation and complicated training strategies-has been the dominant approach in graph SSL, while the progress of generative SSL on graphs, especially graph autoencoders (GAEs), has thus far not reached the potential as promised in other fields. In this paper, we identify and examine the issues that negatively impact the development of GAEs, including their reconstruction objective, training robustness, and error metric. We present a masked graph autoencoder GraphMAE that mitigates these issues for generative self-supervised graph pretraining. Instead of reconstructing graph structures, we propose to focus on feature reconstruction with both a masking strategy and scaled cosine error that benefit the robust training of GraphMAE. We conduct extensive experiments on 21 public datasets for three different graph learning tasks. The results manifest that GraphMAE-a simple graph autoencoder with careful designs-can consistently generate outperformance over both contrastive and generative state-of-the-art baselines. This study provides an understanding of graph autoencoders and demonstrates the potential of generative self-supervised pre-training on graphs.

Self-supervised learning of graph neural networks (GNNs) aims to learn an accurate representation of the graphs in an unsupervised manner, to obtain transferable representations of them for diverse downstream tasks. Predictive learning and contrastive learning are the two most prevalent approaches for graph self-supervised learning. However, they have their own drawbacks. While the predictive learning methods can learn the contextual relationships between neighboring nodes and edges, they cannot learn global graph-level similarities. Contrastive learning, while it can learn global graph-level similarities, its objective to maximize the similarity between two differently perturbed graphs may result in representations that cannot discriminate two similar graphs with different properties. To tackle such limitations, we propose a framework that aims to learn the exact discrepancy between the original and the perturbed graphs, coined as Discrepancy-based Self-supervised LeArning (D-SLA). Specifically, we create multiple perturbations of the given graph with varying degrees of similarity, and train the model to predict whether each graph is the original graph or the perturbed one. Moreover, we further aim to accurately capture the amount of discrepancy for each perturbed graph using the graph edit distance. We validate our D-SLA on various graph-related downstream tasks, including molecular property prediction, protein function prediction, and link prediction tasks, on which ours largely outperforms relevant baselines.

Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake visual and auditory media has been delivering to society. Hence it is essential to regulate the prevalence of generated graphs. To tackle this problem, we pioneer the formulation of the generated graph detection problem to distinguish generated graphs from real ones. We propose the first framework to systematically investigate a set of sophisticated models and their performance in four classification scenarios. Each scenario switches between seen and unseen datasets/generators during testing to get closer to real-world settings and progressively challenge the classifiers. Extensive experiments evidence that all the models are qualified for generated graph detection, with specific models having advantages in specific scenarios. Resulting from the validated generality and oblivion of the classifiers to unseen datasets/generators, we draw a safe conclusion that our solution can sustain for a decent while to curb generated graph misuses.

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 GNN and Graphformer efforts encoding graphs as Euclidean vectors, recovering original graph from the vectors remains a challenge. We introduce GraphsGPT, featuring a Graph2Seq encoder that transforms non-Euclidean graphs into learnable graph words in a Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from graph words to ensure information equivalence. We pretrain GraphsGPT on 100M molecules and yield some interesting findings: (1) Pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on 8/9 graph classification and regression tasks. (2) Pretrained GraphGPT serves as a strong graph generator, demonstrated by its ability to perform both unconditional and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known non-Euclidean challenge. (4) Our proposed novel edge-centric GPT pretraining task is effective in graph fields, underscoring its success in both representation and generation.

Graph Neural Networks (GNNs) are widely deployed in vast fields, but they often struggle to maintain accurate representations as graphs evolve. We theoretically establish a lower bound, proving that under mild conditions, representation distortion inevitably occurs over time. To estimate the temporal distortion without human annotation after deployment, one naive approach is to pre-train a recurrent model (e.g., RNN) before deployment and use this model afterwards, but the estimation is far from satisfactory. In this paper, we analyze the representation distortion from an information theory perspective, and attribute it primarily to inaccurate feature extraction during evolution. Consequently, we introduce Smart, a straightforward and effective baseline enhanced by an adaptive feature extractor through self-supervised graph reconstruction. In synthetic random graphs, we further refine the former lower bound to show the inevitable distortion over time and empirically observe that Smart achieves good estimation performance. Moreover, we observe that Smart consistently shows outstanding generalization estimation on four real-world evolving graphs. The ablation studies underscore the necessity of graph reconstruction. For example, on OGB-arXiv dataset, the estimation metric MAPE deteriorates from 2.19% to 8.00% without reconstruction.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins, and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.

Contrastive learning is an effective unsupervised method in graph representation learning, and the key component of contrastive learning lies in the construction of positive and negative samples. Previous methods usually utilize the proximity of nodes in the graph as the principle. Recently, the data-augmentation-based contrastive learning method has advanced to show great power in the visual domain, and some works extended this method from images to graphs. However, unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which leaves much space for improvement. In this work, by introducing an adversarial graph view for data augmentation, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within reasonable constraints. We develop a new technique called information regularization for stable training and use subgraph sampling for scalability. We generalize our method from node-level contrastive learning to the graph level by treating each graph instance as a super-node. ARIEL consistently outperforms the current graph contrastive learning methods for both node-level and graph-level classification tasks on real-world datasets. We further demonstrate that ARIEL is more robust in the face of adversarial attacks.

Recent progress in Graph Neural Networks has resulted in wide adoption by many applications, including recommendation systems. The reason for Graph Neural Networks' superiority over other approaches is that many problems in recommendation systems can be naturally modeled as graphs, where nodes can be either users or items and edges represent preference relationships. In current Graph Neural Network approaches, nodes are represented with a static vector learned at training time. This static vector might only be suitable to capture some of the nuances of users or items they define. To overcome this limitation, we propose using a recently proposed model inspired by category theory: Sheaf Neural Networks. Sheaf Neural Networks, and its connected Laplacian, can address the previous problem by associating every node (and edge) with a vector space instead than a single vector. The vector space representation is richer and allows picking the proper representation at inference time. This approach can be generalized for different related tasks on graphs and achieves state-of-the-art performance in terms of F1-Score@N in collaborative filtering and Hits@20 in link prediction. For collaborative filtering, the approach is evaluated on the MovieLens 100K with a 5.1% improvement, on MovieLens 1M with a 5.4% improvement and on Book-Crossing with a 2.8% improvement, while for link prediction on the ogbl-ddi dataset with a 1.6% refinement with respect to the respective baselines.

Rule learning is critical to improving knowledge graph (KG) reasoning due to their ability to provide logical and interpretable explanations. Recently, Graph Neural Networks (GNNs) with tail entity scoring achieve the state-of-the-art performance on KG reasoning. However, the theoretical understandings for these GNNs are either lacking or focusing on single-relational graphs, leaving what the kind of rules these GNNs can learn an open problem. We propose to fill the above gap in this paper. Specifically, GNNs with tail entity scoring are unified into a common framework. Then, we analyze their expressivity by formally describing the rule structures they can learn and theoretically demonstrating their superiority. These results further inspire us to propose a novel labeling strategy to learn more rules in KG reasoning. Experimental results are consistent with our theoretical findings and verify the effectiveness of our proposed method. The code is publicly available at https://github.com/LARS-research/Rule-learning-expressivity.

Large language models (LLMs), such as ChatGPT and LLaMA, are creating significant advancements in natural language processing, due to their strong text encoding/decoding ability and newly found emergent capability (e.g., reasoning). While LLMs are mainly designed to process pure texts, there are many real-world scenarios where text data are associated with rich structure information in the form of graphs (e.g., academic networks, and e-commerce networks) or scenarios where graph data are paired with rich textual information (e.g., molecules with descriptions). Besides, although LLMs have shown their pure text-based reasoning ability, it is underexplored whether such ability can be generalized to graph scenarios (i.e., graph-based reasoning). In this paper, we provide a systematic review of scenarios and techniques related to large language models on graphs. We first summarize potential scenarios of adopting LLMs on graphs into three categories, namely pure graphs, text-rich graphs, and text-paired graphs. We then discuss detailed techniques for utilizing LLMs on graphs, including LLM as Predictor, LLM as Encoder, and LLM as Aligner, and compare the advantages and disadvantages of different schools of models. Furthermore, we mention the real-world applications of such methods and summarize open-source codes and benchmark datasets. Finally, we conclude with potential future research directions in this fast-growing field. The related source can be found at https://github.com/PeterGriffinJin/Awesome-Language-Model-on-Graphs.

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.

Text-attributed graphs have recently garnered significant attention due to their wide range of applications in web domains. Existing methodologies employ word embedding models for acquiring text representations as node features, which are subsequently fed into Graph Neural Networks (GNNs) for training. Recently, the advent of Large Language Models (LLMs) has introduced their powerful capabilities in information retrieval and text generation, which can greatly enhance the text attributes of graph data. Furthermore, the acquisition and labeling of extensive datasets are both costly and time-consuming endeavors. Consequently, few-shot learning has emerged as a crucial problem in the context of graph learning tasks. In order to tackle this challenge, we propose a lightweight paradigm called LLM4NG, which adopts a plug-and-play approach to empower text-attributed graphs through node generation using LLMs. Specifically, we utilize LLMs to extract semantic information from the labels and generate samples that belong to these categories as exemplars. Subsequently, we employ an edge predictor to capture the structural information inherent in the raw dataset and integrate the newly generated samples into the original graph. This approach harnesses LLMs for enhancing class-level information and seamlessly introduces labeled nodes and edges without modifying the raw dataset, thereby facilitating the node classification task in few-shot scenarios. Extensive experiments demonstrate the outstanding performance of our proposed paradigm, particularly in low-shot scenarios. For instance, in the 1-shot setting of the ogbn-arxiv dataset, LLM4NG achieves a 76% improvement over the baseline model.

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.