Graph Neural Networks (GNNs) have demonstrated strong performance across various tasks by leveraging the structural information inherent in graph-structured data. To address the challenge of edge heterophily, where connected nodes may have dissimilar labels or features, two main families of GNNs have emerged: Mixture-of-Experts (MoE) based spatial GNNs and frequency filtering based spectral GNNs. While MoE-based spatial GNNs intuitively assign experts to different hops without solid theoretical grounding, spectral GNNs are based on principled insights from graph signal processing but often rely on manually designed filters and global operators, limiting their scalability and adaptability. In this work, we identify an inherent connection between these two families by showing that the eigengraph components in spectral methods can be treated as experts within an MoE framework. Building on this insight, we propose MORGAN, a novel spectral GNN that integrates Mixture-of-Experts into the spectral domain. MORGAN performs eigen-decomposition of the graph Laplacian, partitions the spectrum into multiple frequency bands, and assigns a dedicated expert network to each band. A learnable gating function dynamically combines these experts based on the spectral characteristics of the input. To support scalable and inductive learning, we further develop MORGAN(L), which incorporates subgraph sampling to enable localized spectral filtering without requiring full access to the graph Laplacian. Extensive experiments on 16 real-world benchmark datasets show that MORGAN achieves competitive or superior performance compared to state-of-the-art baselines, particularly in inductive node classification under heterophilic settings.

While large language models (LLMs) have achieved impressive results across many tasks, they remain prone to hallucinations, particularly in domains requiring substantial background knowledge. A common way to mitigate this issue is to incorporate external knowledge, often through retrieval-augmented generation (RAG). However, most existing RAG approaches focus solely on textual data and neglect an important aspect: the connections between pieces of knowledge. In domains such as scientific publishing, entities like papers, authors, and citations form rich graphs, where meaning emerges not only from individual texts but also from their relationships. To address this, we propose Graph-MCTS, a framework that enhances LLM reasoning by leveraging graph structures. Graph-MCTS uses Monte Carlo Tree Search (MCTS) to guide the model through structured exploration of graph-based knowledge. We evaluate Graph-MCTS across multiple LLM architectures and find that it consistently outperforms existing augmentation methods. These findings highlight the importance of structured, relational knowledge for improving the reasoning capabilities of LLMs. Code is available at https://github.com/lihuiliullh/Graph-MCTS

Knowledge graphs (KGs) are essential in many AI applications but often suffer from incompleteness, limiting their utility. Many relations in KGs have only a few examples, making it challenging to train accurate models. Few-shot learning offers a promising direction by enabling KG completion with only a small number of training triplets. However, most existing approaches treat each relation independently and fail to leverage shared information across tasks. In this paper, we introduce TransNet, a transfer learning method for few-shot KG completion that captures task relationships and reuses knowledge from related tasks. TransNet further incorporates meta-learning to effectively handle unseen relations. Experiments on standard benchmarks demonstrate that TransNet achieves strong performance compared to prior methods. Code and data will be released upon acceptance.

Graph Self-Supervised Learning (SSL) has emerged as a pivotal area of research in recent years. By engaging in pretext tasks to learn the intricate topological structures and properties of graphs using unlabeled data, these graph SSL models achieve enhanced performance, improved generalization, and heightened robustness. Despite the remarkable achievements of these graph SSL methods, their current implementation poses significant challenges for beginners and practitioners due to the complex nature of graph structures, inconsistent evaluation metrics, and concerns regarding reproducibility hinder further progress in this field. Recognizing the growing interest within the research community, there is an urgent need for a comprehensive, beginner-friendly, and accessible toolkit consisting of the most representative graph SSL algorithms. To address these challenges, we present a Graph SSL toolkit named PyG-SSL, which is built upon PyTorch and is compatible with various deep learning and scientific computing backends. Within the toolkit, we offer a unified framework encompassing dataset loading, hyper-parameter configuration, model training, and comprehensive performance evaluation for diverse downstream tasks. Moreover, we provide beginner-friendly tutorials and the best hyper-parameters of each graph SSL algorithm on different graph datasets, facilitating the reproduction of results. The GitHub repository of the library is https://github.com/iDEA-iSAIL-Lab-UIUC/pyg-ssl.

Knowledge graphs (KGs) enable reasoning tasks such as link prediction, question answering, and knowledge discovery.However, real-world KGs are often incomplete, making link prediction both essential and challenging.Existing methods, including embeddingbased and path-based approaches, rely on Euclidean embeddings, which struggle to capture hierarchical structures.GNN-based methods aggregate information through message passing in Euclidean space, but they struggle to effectively encode the recursive treelike structures that emerge in multi-hop reasoning.To address these challenges, instead of learning static entity and relation embeddings, we propose a hyperbolic GNN framework (HYPERKGR) that embeds recursive learning trees in dynamic query-specific hyperbolic space.By incorporating hierarchical message passing, our method naturally aligns with reasoning paths and dynamically adapts to queries, improving prediction accuracy.Unlike static embedding-based approaches, our model learns context-aware embeddings tailored to each query.Experiments on multiple benchmark datasets show that our approach consistently outperforms state-of-the-art methods, demonstrating its effectiveness in KG reasoning.The code can be found in https: //github.com/lihuiliullh/HyperKGR

Graph learning has been crucial to many real-world tasks, but they are often studied with a closed-world assumption, with all possible labels of data known a priori. To enable effective graph learning in an open and noisy environment, it is critical to inform the model users when the model makes a wrong prediction to in-distribution data of a known class, i.e., misclassification detection or when the model encounters out-of-distribution from novel classes, i.e., out-of-distribution detection. This paper introduces Evidential Reasoning Network (EVINET), a framework that addresses these two challenges by integrating Beta embedding within a subjective logic framework. EVINET includes two key modules: Dissonance Reasoning for misclassification detection and Vacuity Reasoning for out-of-distribution detection. Extensive experiments demonstrate that EVINET outperforms state-of-the-art methods across multiple metrics in the tasks of in-distribution classification, misclassification detection, and out-of-distribution detection. EVINET demonstrates the necessity of uncertainty estimation and logical reasoning for misclassification detection and out-of-distribution detection and paves the way for open-world graph learning. Our code and data are available at https://github.com/SSSKJ/EviNET.

The contextual bandit has been identified as a powerful framework to formulate the recommendation process as a sequential decision-making process, where each item is regarded as an arm and the objective is to minimize the regret of T rounds. In this paper, we study a new problem, Clustering of Neural Bandits, by extending previous work to the arbitrary reward function, to strike a balance between user heterogeneity and user correlations in the recommender system. To solve this problem, we propose a novel algorithm called M-CNB, which utilizes a meta-learner to represent and rapidly adapt to dynamic clusters, along with an informative Upper Confidence Bound (UCB)-based exploration strategy. We provide an instance-dependent performance guarantee for the proposed algorithm that withstands the adversarial context, and we further prove the guarantee is at least as good as state-of-the-art (SOTA) approaches under the same assumptions. In extensive experiments conducted in both recommendation and online classification scenarios, M-CNB outperforms SOTA baselines. This shows the effectiveness of the proposed approach in improving online recommendation and online classification performance.

Accessibility and openness are two of the most important factors in motivating AI and Web research. One example is as costs to train and deploy large Knowledge Graph (KG) systems increases, valuable auxiliary features such as visualization, explainability, and automation are often overlooked, diminishing impact and popularity. Furthermore, current KG research has undergone a vicissitude to become convoluted and abstract, dissuading collaboration. To this end, we present Ginkgo-P, a platform to automatically illustrate any KG algorithm with nothing but a script and a data file. Additionally, Ginkgo-P elucidates modern KG research on the UMLS dataset with interactive demonstrations on four categories: KG Node Recommendation, KG Completion, KG Question Answering, and KG Reinforcement Learning. These categories and their many applications are increasingly ubiquitous yet lack both introductory and advanced resources to accelerate interest and contributions: with just a few clicks, our demonstration addresses this by providing an open platform for users to integrate individual KG algorithms. The source code for Ginkgo-P is available: we hope that it will propel future KG systems to become more accessible as an open source project.

Network embedding plays an important role in a variety of social network applications. Existing network embedding methods, explicitly or implicitly, can be categorized into positional embedding (PE) methods or structural embedding (SE) methods. Specifically, PE methods encode the positional information and obtain similar embeddings for adjacent/close nodes, while SE methods aim to learn identical representations for nodes with the same local structural patterns, even if the two nodes are far away from each other. The disparate designs of the two types of methods lead to an apparent dilemma in that no embedding could perfectly capture both positional and structural information. In this paper, we seek to demystify the underlying relationship between positional embedding and structural embedding. We first point out that the positional embedding can produce the structural embedding with simple transformations, while the opposite direction cannot hold. Based on this finding, a novel network embedding model PACER is proposed, which optimizes the positional embedding with the help of random walk with restart (RWR) proximity distribution, and such positional embedding is then used to seamlessly obtain the structural embedding with simple transformations. Furthermore, two variants of PACER are proposed to handle node classification task on homophilic and heterophilic graphs. Extensive experiments on 17 datasets show that PACER achieves comparable or better performance than the state-of-the-arts.

Given an evolving tensor time series and multiple time ranges, how can we compute Tucker decomposition for each time range efficiently and accurately? Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. For example, Tucker decomposition on air pollution data allows us to analyze and compare air pollution patterns between different locations during different periods of time. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor time series are typically evolving in the time dimension. Such needs call for a data structure that can efficiently and accurately support range queries of Tucker decomposition and stream updates. Unfortunately, existing methods do not support either range queries or stream updates. For methods that do not support range queries, they have to re-compute from scratch for each query. Not until 2021 has a data structure called Zoom-Tucker been proposed to support range queries via block-wise preprocessing. However, Zoom-Tucker does not support stream updates and, more critically, suffers from a reluctant efficiency-accuracy tradeoff --- a large block size causes inaccuracy, while a small block size leads to inefficiency. This challenging problem has remained open for years prior to our work. To solve this challenging problem, we propose TUCKET, a data structure that can efficiently and accurately handle both range queries and stream updates. Our key idea is to design a new data structure that we call a stream segment tree by generalizing the segment tree , a data structure that was originally invented for computational geometry. For a range query of length L , our TUCKET can find O (log L ) nodes (called the hit set ) from the tree and efficiently stitch their preprocessed decompositions to answer the range query. We also propose an algorithm to optimally prune the hit set via an approximation of subtensor decomposition. For the T -th stream update, our TUCKET modifies only amortized O (1) nodes and only O (log T ) nodes in the worst case. Extensive evaluation demonstrates that our TUCKET consistently achieves the highest efficiency and accuracy across four large-scale datasets. Our TUCKET achieves at least 3 times lower latency and at least 1.4 times smaller reconstruction error than Zoom-Tucker on all datasets. The full version can be found at https://github.com/q-rz/TUCKET/blob/main/TUCKET-Full.pdf.

The use of knowledge graphs has gained significant traction in a wide variety of applications, ranging from recommender systems and question answering to fact checking. By leveraging the wealth of information contained within knowledge graphs, it is possible to greatly enhance various downstream tasks, making reasoning over knowledge graphs an area of increasing interest. However, despite its popularity, knowledge graph reasoning remains a challenging problem. The first major challenge of knowledge graph reasoning lies in the nature of knowledge graphs themselves. Most knowledge graphs are incomplete, meaning that they may not capture all the relevant knowledge required for reasoning. As a result, reasoning on incomplete knowledge graphs can be difficult. Additionally, real-world knowledge graphs often evolve over time, which presents an additional challenge. The second challenge of knowledge graph reasoning pertains to the input data. In some KG reasoning applications, users may be unfamiliar with the background knowledge graph, leading to the possibility of asking ambiguous questions that can make KG reasoning tasks more challenging. Moreover, some applications require iterative reasoning, where users ask several related questions in sequence, further increasing the complexity of the task. The third challenge of knowledge graph reasoning concerns the algorithmic aspect. Due to the varied properties of relations in knowledge graphs, such as transitivity, symmetry, and asymmetry, designing an all-round KG reasoning model that fits all these properties can be challenging. Furthermore, most KG reasoning models tend to focus on solving a specific problem, lacking the generalization ability required to apply to other tasks. This tutorial aims to comprehensively review different aspects of knowledge graph reasoning applications and highlight open challenges and future directions. It is intended to benefit researchers and practitioners in the fields of data mining, artificial intelligence, and social science.

Network embedding plays a significant role in a variety of applications. To capture the topology of the network, most of the existing network embedding algorithms follow a sampling training procedure, which maximizes the similarity (e.g., embedding vectors' dot product) between positively sampled node pairs and minimizes the similarity between negatively sampled node pairs in the embedding space. Typically, close node pairs function as positive samples while distant node pairs are usually considered as negative samples. However, under different or even competing sampling strategies, some methods champion sampling distant node pairs as positive samples to encapsulate longer distance information in link prediction, whereas others advocate adding close nodes into the negative sample set to boost the performance of node recommendation. In this paper, we seek to understand the intrinsic relationships between these competing strategies. To this end, we identify two properties (discrimination and monotonicity) that given any node pair proximity distribution, node embeddings should embrace. Moreover, we quantify the empirical error of the trained similarity score w.r.t. the sampling strategy, which leads to an important finding that the discrimination property and the monotonicity property for all node pairs can not be satisfied simultaneously in real-world applications. Guided by such analysis, a simple yet novel model (SENSEI) is proposed, which seamlessly fulfills the discrimination property and the partial monotonicity within the top-$K$ ranking list. Extensive experiments show that SENSEI outperforms the state-of-the-arts in plain network embedding.

Knowledge graph question answering aims to identify answers of the query according to the facts in the knowledge graph. In the vast majority of the existing works, the input queries are considered perfect and can precisely express the user’s query intention. However, in reality, input queries might be ambiguous and elusive which only contain a limited amount of information. Directly answering these ambiguous queries may yield unwanted answers and deteriorate user experience. In this paper, we propose PReFNet which focuses on answering ambiguous queries with pseudo relevance feedback on knowledge graphs. In order to leverage the hidden (pseudo) relevance information existed in the results that are initially returned from a given query, PReFNet treats the top-k returned candidate answers as a set of most relevant answers, and uses variational Bayesian inference to infer user’s query intention. To boost the quality of the inferred queries, a neighborhood embedding based VGAE model is used to prune inferior inferred queries. The inferred high quality queries will be returned to the users to help them search with ease. Moreover, all the high-quality candidate nodes will be re-ranked according to the inferred queries. The experiment results show that our proposed method can recommend high-quality query graphs to users and improve the question answering accuracy.

Knowledge graph has been widely used in fact checking, owing to its capability to provide crucial background knowledge to help verify claims. Traditional fact checking works mainly focus on analyzing a single claim but have largely ignored analysis on the semantic consistency of pair-wise claims, despite its key importance in the real-world applications, e.g., multimodal fake news detection. This paper proposes a graph neural network based model INSPECTOR for pair-wise fact checking. Given a pair of claims, INSPECTOR aims to detect the potential semantic inconsistency of the input claims. The main idea of INSPECTOR is to use a graph attention neural network to learn a graph embedding for each claim in the pair, then use a tensor neural network to classify this pair of claims as consistent vs. inconsistent. The experiment results show that our algorithm outperforms state-of-the-art methods, with a higher accuracy and a lower variance.

Knowledge graph is ubiquitous and plays an important role in many real-world applications, including recommender systems, question answering, fact-checking, and so on. However, most of the knowledge graphs are incomplete which can hamper their practical usage. Fortunately, knowledge graph completion (KGC) can mitigate this problem by inferring missing edges in the knowledge graph according to the existing information. In this paper, we propose a novel KGC method named ABM (Attention-Based Message passing) which focuses on predicting the relation between any two entities in a knowledge graph. The proposed ABM consists of three integral parts, including (1) context embedding, (2) structure embedding, and (3) path embedding. In the context embedding, the proposed ABM generalizes the existing message passing neural network to update the node embedding and the edge embedding to assimilate the knowledge of nodes' neighbors, which captures the relative role information of the edge that we want to predict. In the structure embedding, the proposed method overcomes the shortcomings of the existing GNN method (i.e., most methods ignore the structural similarity between nodes.) by assigning different attention weights to different nodes while doing the aggregation. Path embedding generates paths between any two entities and treats these paths as sequences. Then, the sequence can be used as the input of the Transformer to update the embedding of the knowledge graph to gather the global role of the missing edges. By utilizing these three mutually complementary strategies, the proposed ABM is able to capture both the local and global information which in turn leads to a superb performance. Experiment results show that ABM outperforms baseline methods on a wide range of datasets.

Knowledge graph reasoning plays a pivotal role in many real-world applications, such as network alignment, computational fact-checking, recommendation, and many more. Among these applications, knowledge graph completion (KGC) and multi-hop question answering over knowledge graph (Multi-hop KGQA) are two representative reasoning tasks. In the vast majority of the existing works, the two tasks are considered separately with different models or algorithms. However, we envision that KGC and Multi-hop KGQA are closely related to each other. Therefore, the two tasks will benefit from each other if they are approached adequately. In this work, we propose a neural model named BiNet to jointly handle KGC and multi-hop KGQA, and formulate it as a multi-task learning problem. Specifically, our proposed model leverages a shared embedding space and an answer scoring module, which allows the two tasks to automatically share latent features and learn the interactions between natural language question decoder and answer scoring module. Compared to the existing methods, the proposed BiNet model addresses both multi-hop KGQA and KGC tasks simultaneously with superior performance. Experiment results show that BiNet outperforms state-of-the-art methods on a wide range of KGQA and KGC benchmark datasets.

Knowledge graph (KG for short) alignment aims at building a complete KG by linking the shared entities across complementary KGs. Existing approaches assume that KGs are static, despite the fact that almost every KG evolves over time. In this paper, we introduce the task of dynamic knowledge graph alignment, the main challenge of which is how to efficiently update entity embeddings for the evolving graph topology. Our key insight is to view the parameter matrix of GCN as a feature transformation operator and decouple the transformation process from the aggregation process. Based on that, we first propose a novel base algorithm (DINGAL-B) with topology-invariant mask gate and highway gate, which consistently outperforms 14 existing knowledge graph alignment methods in the static setting. More importantly, it naturally leads to two effective and efficient algorithms to align dynamic knowledge graph, including (1) DINGAL-O which leverages previous parameter matrices to update the embeddings of affected entities; and (2) DINGAL-U which resorts to newly obtained anchor links to fine-tune parameter matrices. Compared with their static counterpart (DINGAL-B), DINGAL-U and DINGAL-O are 10× and 100× faster respectively, with little alignment accuracy loss.

How can we identify the same or similar users from a collection of social network platforms (e.g., Facebook, Twitter, LinkedIn, etc.)? Which restaurant shall we recommend to a given user at the right time at the right location? Given a disease, which genes and drugs are most relevant? Multi-way association, which identifies strongly correlated node sets from multiple input networks, is the key to answering these questions. Despite its importance, very few multi-way association methods exist due to its high complexity. In this paper, we formulate multi-way association as a convex optimization problem, whose optimal solution can be obtained by a Sylvester tensor equation. Furthermore, we propose two fast algorithms to solve the Sylvester tensor equation, with a linear time and space complexity. We further provide theoretic analysis in terms of the sensitivity of the Sylvester tensor equation solution. Empirical evaluations demonstrate the efficacy of the proposed method.

Reasoning is a fundamental capability for harnessing valuable insight, knowledge and patterns from knowledge graphs. Existing work has primarily been focusing on point-wise reasoning, including search, link prediction, entity prediction, subgraph matching and so on. This paper introduces comparative reasoning over knowledge graphs, which aims to infer the commonality and inconsistency with respect to multiple pieces of clues. We envision that the comparative reasoning will complement and expand the existing point-wise reasoning over knowledge graphs. In detail, we develop KompaRe, the first of its kind prototype system that provides comparative reasoning capability over large knowledge graphs. We present both the system architecture and its core algorithms, including knowledge segment extraction, pairwise reasoning and collective reasoning. Empirical evaluations demonstrate the efficacy of the proposed KompaRe.

Logical queries constitute an important subset of questions posed in knowledge graph question answering systems. Yet, effectively answering logical queries on large knowledge graphs remains a highly challenging problem. Traditional subgraph matching based methods might suffer from the noise and incompleteness of the underlying knowledge graph, often with a prolonged online response time. Recently, an alternative type of method has emerged whose key idea is to embed knowledge graph entities and the query in an embedding space so that the embedding of answer entities is close to that of the query. Compared with subgraph matching based methods, it can better handle the noisy or missing information in knowledge graph, with a faster online response. Promising as it might be, several fundamental limitations still exist, including the linear transformation assumption for modeling relations and the inability to answer complex queries with multiple variable nodes. In this paper, we propose an embedding based method (NewLook) to address these limitations. Our proposed method offers three major advantages. First (Applicability), it supports four types of logical operations and can answer queries with multiple variable nodes. Second (Effectiveness), the proposed NewLook goes beyond the linear transformation assumption, and thus consistently outperforms the existing methods. Third (Efficiency), compared with subgraph matching based methods, NewLook is at least 3 times faster in answering the queries; compared with the existing embed-ding based methods, NewLook bears a comparable or even faster online response and offline training time.

Networks are natural representations in modeling adversarial activities, such as smuggling, human trafficking, and illegal arms dealing. However, such activities are often covert and embedded across multiple domains and sources. They are generally not detectable and recognizable from the perspective of an isolated network, and only become apparent when multiple networks are analyzed in a unified m anner. T o t his e nd, we propose Complex Analytics of Network of Networks (CANON), a mathematical and computational framework for modeling adversarial activities from large-scale, multi-sourced data inputs. Central to our framework is a network-of-networks model, where nodes and edges can be defined across different domains and at multiple resolutions. Based on this model, we address the key challenges in modeling adversarial activities via four technical components, including optimization-based network alignment, network embedding and conditioning, approximate subgraph matching, and investigative subgraph discovery.In this paper, we describe the design and implementation of the individual components as well as integrating these components into a unified system using a modular microservice architecture. Extensive experiments have been conducted in both synthetics and real-world datasets to demonstrate the effectiveness of our proposed system under the DARPA Modeling Adversarial Activity (MAA) program.

Subgraph matching is a core primitive across a number of disciplines, ranging from data mining, databases, information retrieval, computer vision to natural language processing. Despite decades of efforts, it is still highly challenging to balance between the matching accuracy and the computational efficiency, especially when the query graph and/or the data graph are large. In this paper, we propose an index-based algorithm (G-FINDER) to find the top-k approximate matching subgraphs. At the heart of the proposed algorithm are two techniques, including (1) a novel auxiliary data structure (LOOKUP-TABLE) in conjunction with a neighborhood expansion method to effectively and efficiently index candidate vertices, and (2) a dynamic filtering and refinement strategy to prune the false candidates at an early stage. The proposed G-FINDER bears some distinctive features, including (1) generality, being able to handle different types of inexact matching (e.g., missing nodes, missing edges, intermediate vertices) on node attributed and/or edge attributed graphs or multigraphs; (2) effectiveness, achieving up to 30% Fl-Score improvement over the best known competitor; and (3) efficiency, scaling near-linearly w.r.t. the size of the data graph as well as the query graph.

When running data intensive scientific workflow in multiple data centers environment, it is inevitable that massive data movement will be caused. The emergence of cloud computing technologies offers a new way to develop scientific workflow systems, and using dataset replicas to reduce data transfer among data centers is an import issue. In this paper, we propose a group based genetic algorithm which can make full use of dataset replicas to reduce data transmission in cloud. We compare the performance of our proposed algorithm with that of random algorithm and K-means algorithm. The results show that our proposed algorithm can effectively reduce data movements among data centers and improve the performance of data intensive scientific workflow.

In a cloud distributed system, machine failure or region failure is a very common scenario. Data replication is a key technique for ensuring data availability. However, Objects are usually assumed independently by distributed systems, despite, a user-level task typically requests multiple data objects. This paper studies the effect of data placement on the availability of user-level tasks from a theoretical perspective, and finds the best and the worst placements which can provide the highest and the lowest availability for user-level tasks in a cloud distributed system. This paper also gives a novel algorithm called SPOverlap (S Parts Overlap), which provides a tradeoff between task availability and other system performance.