Daily Papers

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.

This paper presents OG-RAG, an Ontology-Grounded Retrieval Augmented Generation method designed to enhance LLM-generated responses by anchoring retrieval processes in domain-specific ontologies. While LLMs are widely used for tasks like question answering and search, they struggle to adapt to specialized knowledge, such as industrial workflows or knowledge work, without expensive fine-tuning or sub-optimal retrieval methods. Existing retrieval-augmented models, such as RAG, offer improvements but fail to account for structured domain knowledge, leading to suboptimal context generation. Ontologies, which conceptually organize domain knowledge by defining entities and their interrelationships, offer a structured representation to address this gap. OG-RAG constructs a hypergraph representation of domain documents, where each hyperedge encapsulates clusters of factual knowledge grounded using domain-specific ontology. An optimization algorithm then retrieves the minimal set of hyperedges that constructs a precise, conceptually grounded context for the LLM. This method enables efficient retrieval while preserving the complex relationships between entities. OG-RAG applies to domains where fact-based reasoning is essential, particularly in tasks that require workflows or decision-making steps to follow predefined rules and procedures. These include industrial workflows in healthcare, legal, and agricultural sectors, as well as knowledge-driven tasks such as news journalism, investigative research, consulting and more. Our evaluations demonstrate that OG-RAG increases the recall of accurate facts by 55% and improves response correctness by 40% across four different LLMs. Additionally, OG-RAG enables 30% faster attribution of responses to context and boosts fact-based reasoning accuracy by 27% compared to baseline methods.

The drug development pipeline for a new compound can last 10-20 years and cost over 10 billion. Drug repurposing offers a more time- and cost-effective alternative. Computational approaches based on biomedical knowledge graph representations have recently yielded new drug repurposing hypotheses. In this study, we present a novel, disease-specific hypergraph representation learning technique to derive contextual embeddings of biological pathways of various lengths but that all start at any given drug and all end at the disease of interest. Further, we extend this method to multi-disease hypergraphs. To determine the repurposing potential of each of the 1,522 drugs, we derive drug-specific distributions of cosine similarity values and ultimately consider the median for ranking. Cosine similarity values are computed between (1) all biological pathways starting at the considered drug and ending at the disease of interest and (2) all biological pathways starting at drugs currently prescribed against that disease and ending at the disease of interest. We illustrate our approach with Alzheimer's disease (AD) and two of its risk factors: hypertension (HTN) and type 2 diabetes (T2D). We compare each drug's rank across four hypergraph settings (single- or multi-disease): AD only, AD + HTN, AD + T2D, and AD + HTN + T2D. Notably, our framework led to the identification of two promising drugs whose repurposing potential was significantly higher in hypergraphs combining two diseases: dapagliflozin (antidiabetic; moved up, from top 32% to top 7%, across all considered drugs) and debrisoquine (antihypertensive; moved up, from top 76% to top 23%). Our approach serves as a hypothesis generation tool, to be paired with a validation pipeline relying on laboratory experiments and semi-automated parsing of the biomedical literature.

This paper studies the topic modeling problem of tagged documents and images. Higher-order relations among tagged documents and images are major and ubiquitous characteristics, and play positive roles in extracting reliable and interpretable topics. In this paper, we propose the tag-topic models (TTM) to depict such higher-order topic structural dependencies within the Markov random field (MRF) framework. First, we use the novel factor graph representation of latent Dirichlet allocation (LDA)-based topic models from the MRF perspective, and present an efficient loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Second, we propose the factor hypergraph representation of TTM, and focus on both pairwise and higher-order relation modeling among tagged documents and images. Efficient loopy BP algorithm is developed to learn TTM, which encourages the topic labeling smoothness among tagged documents and images. Extensive experimental results confirm the incorporation of higher-order relations to be effective in enhancing the overall topic modeling performance, when compared with current state-of-the-art topic models, in many text and image mining tasks of broad interests such as word and link prediction, document classification, and tag recommendation.

Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary relations, as each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n >= 2) in real-world knowledge. In this work, we propose HyperGraphRAG, a novel hypergraph-based RAG method that represents n-ary relational facts via hyperedges, and consists of knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality.

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.

Language models pretrained on large collections of tabular data have demonstrated their effectiveness in several downstream tasks. However, many of these models do not take into account the row/column permutation invariances, hierarchical structure, etc. that exist in tabular data. To alleviate these limitations, we propose HYTREL, a tabular language model, that captures the permutation invariances and three more structural properties of tabular data by using hypergraphs - where the table cells make up the nodes and the cells occurring jointly together in each row, column, and the entire table are used to form three different types of hyperedges. We show that HYTREL is maximally invariant under certain conditions for tabular data, i.e., two tables obtain the same representations via HYTREL iff the two tables are identical up to permutations. Our empirical results demonstrate that HYTREL consistently outperforms other competitive baselines on four downstream tasks with minimal pretraining, illustrating the advantages of incorporating the inductive biases associated with tabular data into the representations. Finally, our qualitative analyses showcase that HYTREL can assimilate the table structures to generate robust representations for the cells, rows, columns, and the entire table.

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.

Temporal hypergraphs provide a powerful paradigm for modeling time-dependent, higher-order interactions in complex systems. Representation learning for hypergraphs is essential for extracting patterns of the higher-order interactions that are critically important in real-world problems in social network analysis, neuroscience, finance, etc. However, existing methods are typically designed only for specific tasks or static hypergraphs. We present CAT-Walk, an inductive method that learns the underlying dynamic laws that govern the temporal and structural processes underlying a temporal hypergraph. CAT-Walk introduces a temporal, higher-order walk on hypergraphs, SetWalk, that extracts higher-order causal patterns. CAT-Walk uses a novel adaptive and permutation invariant pooling strategy, SetMixer, along with a set-based anonymization process that hides the identity of hyperedges. Finally, we present a simple yet effective neural network model to encode hyperedges. Our evaluation on 10 hypergraph benchmark datasets shows that CAT-Walk attains outstanding performance on temporal hyperedge prediction benchmarks in both inductive and transductive settings. It also shows competitive performance with state-of-the-art methods for node classification. (https://github.com/ubc-systopia/CATWalk)

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, bioinformatics and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making them well-suited for modeling complex molecular systems. In this work, we introduce EquiHGNN, an Equivariant HyperGraph Neural Network framework that integrates symmetry-aware representations to improve molecular modeling. By enforcing the equivariance under relevant transformation groups, our approach preserves geometric and topological properties, leading to more robust and physically meaningful representations. We examine a range of equivariant architectures and demonstrate that integrating symmetry constraints leads to notable performance gains on large-scale molecular datasets. Experiments on both small and large molecules show that high-order interactions offer limited benefits for small molecules but consistently outperform 2D graphs on larger ones. Adding geometric features to these high-order structures further improves the performance, emphasizing the value of spatial information in molecular learning. Our source code is available at https://github.com/HySonLab/EquiHGNN/

The YOLO series models reign supreme in real-time object detection due to their superior accuracy and computational efficiency. However, both the convolutional architectures of YOLO11 and earlier versions and the area-based self-attention mechanism introduced in YOLOv12 are limited to local information aggregation and pairwise correlation modeling, lacking the capability to capture global multi-to-multi high-order correlations, which limits detection performance in complex scenarios. In this paper, we propose YOLOv13, an accurate and lightweight object detector. To address the above-mentioned challenges, we propose a Hypergraph-based Adaptive Correlation Enhancement (HyperACE) mechanism that adaptively exploits latent high-order correlations and overcomes the limitation of previous methods that are restricted to pairwise correlation modeling based on hypergraph computation, achieving efficient global cross-location and cross-scale feature fusion and enhancement. Subsequently, we propose a Full-Pipeline Aggregation-and-Distribution (FullPAD) paradigm based on HyperACE, which effectively achieves fine-grained information flow and representation synergy within the entire network by distributing correlation-enhanced features to the full pipeline. Finally, we propose to leverage depthwise separable convolutions to replace vanilla large-kernel convolutions, and design a series of blocks that significantly reduce parameters and computational complexity without sacrificing performance. We conduct extensive experiments on the widely used MS COCO benchmark, and the experimental results demonstrate that our method achieves state-of-the-art performance with fewer parameters and FLOPs. Specifically, our YOLOv13-N improves mAP by 3.0\% over YOLO11-N and by 1.5\% over YOLOv12-N. The code and models of our YOLOv13 model are available at: https://github.com/iMoonLab/yolov13.

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.

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.

Hypergraphs offer a powerful framework for modeling higher-order interactions that traditional pairwise graphs cannot fully capture. However, practical constraints often lead to their simplification into projected graphs, resulting in substantial information loss and ambiguity in representing higher-order relationships. In this work, we propose MARIOH, a supervised approach for reconstructing the original hypergraph from its projected graph by leveraging edge multiplicity. To overcome the difficulties posed by the large search space, MARIOH integrates several key ideas: (a) identifying provable size-2 hyperedges, which reduces the candidate search space, (b) predicting the likelihood of candidates being hyperedges by utilizing both structural and multiplicity-related features, and (c) not only targeting promising hyperedge candidates but also examining less confident ones to explore alternative possibilities. Together, these ideas enable MARIOH to efficiently and effectively explore the search space. In our experiments using 10 real-world datasets, MARIOH achieves up to 74.51% higher reconstruction accuracy compared to state-of-the-art methods.

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%uparrow in prediction accuracy over four datasets therein.

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

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.

E-commerce platforms should provide detailed product descriptions (attribute values) for effective product search and recommendation. However, attribute value information is typically not available for new products. To predict unseen attribute values, large quantities of labeled training data are needed to train a traditional supervised learning model. Typically, it is difficult, time-consuming, and costly to manually label large quantities of new product profiles. In this paper, we propose a novel method to efficiently and effectively extract unseen attribute values from new products in the absence of labeled data (zero-shot setting). We propose HyperPAVE, a multi-label zero-shot attribute value extraction model that leverages inductive inference in heterogeneous hypergraphs. In particular, our proposed technique constructs heterogeneous hypergraphs to capture complex higher-order relations (i.e. user behavior information) to learn more accurate feature representations for graph nodes. Furthermore, our proposed HyperPAVE model uses an inductive link prediction mechanism to infer future connections between unseen nodes. This enables HyperPAVE to identify new attribute values without the need for labeled training data. We conduct extensive experiments with ablation studies on different categories of the MAVE dataset. The results demonstrate that our proposed HyperPAVE model significantly outperforms existing classification-based, generation-based large language models for attribute value extraction in the zero-shot setting.

Hypergraph Neural Networks (HGNNs) have recently attracted much attention and exhibited satisfactory performance due to their superiority in high-order correlation modeling. However, it is noticed that the high-order modeling capability of hypergraph also brings increased computation complexity, which hinders its practical industrial deployment. In practice, we find that one key barrier to the efficient deployment of HGNNs is the high-order structural dependencies during inference. In this paper, we propose to bridge the gap between the HGNNs and inference-efficient Multi-Layer Perceptron (MLPs) to eliminate the hypergraph dependency of HGNNs and thus reduce computational complexity as well as improve inference speed. Specifically, we introduce LightHGNN and LightHGNN^+ for fast inference with low complexity. LightHGNN directly distills the knowledge from teacher HGNNs to student MLPs via soft labels, and LightHGNN^+ further explicitly injects reliable high-order correlations into the student MLPs to achieve topology-aware distillation and resistance to over-smoothing. Experiments on eight hypergraph datasets demonstrate that even without hypergraph dependency, the proposed LightHGNNs can still achieve competitive or even better performance than HGNNs and outperform vanilla MLPs by 16.3 on average. Extensive experiments on three graph datasets further show the average best performance of our LightHGNNs compared with all other methods. Experiments on synthetic hypergraphs with 5.5w vertices indicate LightHGNNs can run 100times faster than HGNNs, showcasing their ability for latency-sensitive deployments.

The burgeoning presence of multimodal content-sharing platforms propels the development of personalized recommender systems. Previous works usually suffer from data sparsity and cold-start problems, and may fail to adequately explore semantic user-product associations from multimodal data. To address these issues, we propose a novel Multi-Modal Hypergraph Contrastive Learning (MMHCL) framework for user recommendation. For a comprehensive information exploration from user-product relations, we construct two hypergraphs, i.e. a user-to-user (u2u) hypergraph and an item-to-item (i2i) hypergraph, to mine shared preferences among users and intricate multimodal semantic resemblance among items, respectively. This process yields denser second-order semantics that are fused with first-order user-item interaction as complementary to alleviate the data sparsity issue. Then, we design a contrastive feature enhancement paradigm by applying synergistic contrastive learning. By maximizing/minimizing the mutual information between second-order (e.g. shared preference pattern for users) and first-order (information of selected items for users) embeddings of the same/different users and items, the feature distinguishability can be effectively enhanced. Compared with using sparse primary user-item interaction only, our MMHCL obtains denser second-order hypergraphs and excavates more abundant shared attributes to explore the user-product associations, which to a certain extent alleviates the problems of data sparsity and cold-start. Extensive experiments have comprehensively demonstrated the effectiveness of our method. Our code is publicly available at: https://github.com/Xu107/MMHCL.

Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for predicting novel structural knowledge. Few approaches have integrated learning and inference with both modalities and these existing ones could only partially exploit the interaction of structural and textual knowledge. In our approach, we build on existing strong representations of single modalities and we use hypercomplex algebra to represent both, (i), single-modality embedding as well as, (ii), the interaction between different modalities and their complementary means of knowledge representation. More specifically, we suggest Dihedron and Quaternion representations of 4D hypercomplex numbers to integrate four modalities namely structural knowledge graph embedding, word-level representations (e.g.\ Word2vec, Fasttext), sentence-level representations (Sentence transformer), and document-level representations (sentence transformer, Doc2vec). Our unified vector representation scores the plausibility of labelled edges via Hamilton and Dihedron products, thus modeling pairwise interactions between different modalities. Extensive experimental evaluation on standard benchmark datasets shows the superiority of our two new models using abundant textual information besides sparse structural knowledge to enhance performance in link prediction tasks.

Most existing zero-shot learning approaches exploit transfer learning via an intermediate-level semantic representation shared between an annotated auxiliary dataset and a target dataset with different classes and no annotation. A projection from a low-level feature space to the semantic representation space is learned from the auxiliary dataset and is applied without adaptation to the target dataset. In this paper we identify two inherent limitations with these approaches. First, due to having disjoint and potentially unrelated classes, the projection functions learned from the auxiliary dataset/domain are biased when applied directly to the target dataset/domain. We call this problem the projection domain shift problem and propose a novel framework, transductive multi-view embedding, to solve it. The second limitation is the prototype sparsity problem which refers to the fact that for each target class, only a single prototype is available for zero-shot learning given a semantic representation. To overcome this problem, a novel heterogeneous multi-view hypergraph label propagation method is formulated for zero-shot learning in the transductive embedding space. It effectively exploits the complementary information offered by different semantic representations and takes advantage of the manifold structures of multiple representation spaces in a coherent manner. We demonstrate through extensive experiments that the proposed approach (1) rectifies the projection shift between the auxiliary and target domains, (2) exploits the complementarity of multiple semantic representations, (3) significantly outperforms existing methods for both zero-shot and N-shot recognition on three image and video benchmark datasets, and (4) enables novel cross-view annotation tasks.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex hierarchical relationships in images with remarkably small dimensionality. To demonstrate hyperbolic embeddings' competence, we introduce a light-weight hyperbolic graph neural network for image segmentation, encompassing patch-level features in a very small embedding size. Our solution, Seg-HGNN, surpasses the current best unsupervised method by 2.5\%, 4\% on VOC-07, VOC-12 for localization, and by 0.8\%, 1.3\% on CUB-200, ECSSD for segmentation, respectively. With less than 7.5k trainable parameters, Seg-HGNN delivers effective and fast (approx 2 images/second) results on very standard GPUs like the GTX1650. This empirical evaluation presents compelling evidence of the efficacy and potential of hyperbolic representations for vision tasks.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

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.

The shared topology of human skeletons motivated the recent investigation of graph convolutional network (GCN) solutions for action recognition. However, the existing GCNs rely on the binary connection of two neighbouring vertices (joints) formed by an edge (bone), overlooking the potential of constructing multi-vertex convolution structures. In this paper we address this oversight and explore the merits of a hyper-graph convolutional network (Hyper-GCN) to achieve the aggregation of rich semantic information conveyed by skeleton vertices. In particular, our Hyper-GCN adaptively optimises multi-scale hyper-graphs during training, revealing the action-driven multi-vertex relations. Besides, virtual connections are often designed to support efficient feature aggregation, implicitly extending the spectrum of dependencies within the skeleton. By injecting virtual connections into hyper-graphs, the semantic clues of diverse action categories can be highlighted. The results of experiments conducted on the NTU-60, NTU-120, and NW-UCLA datasets, demonstrate the merits of our Hyper-GCN, compared to the state-of-the-art methods. Specifically, we outperform the existing solutions on NTU-120, achieving 90.2\% and 91.4\% in terms of the top-1 recognition accuracy on X-Sub and X-Set.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

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.

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.

Few-shot models aim at making predictions using a minimal number of labeled examples from a given task. The main challenge in this area is the one-shot setting where only one element represents each class. We propose HyperShot - the fusion of kernels and hypernetwork paradigm. Compared to reference approaches that apply a gradient-based adjustment of the parameters, our model aims to switch the classification module parameters depending on the task's embedding. In practice, we utilize a hypernetwork, which takes the aggregated information from support data and returns the classifier's parameters handcrafted for the considered problem. Moreover, we introduce the kernel-based representation of the support examples delivered to hypernetwork to create the parameters of the classification module. Consequently, we rely on relations between embeddings of the support examples instead of direct feature values provided by the backbone models. Thanks to this approach, our model can adapt to highly different tasks.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Given a massive graph, how can we exploit its hierarchical structure for concisely but exactly summarizing the graph? By exploiting the structure, can we achieve better compression rates than state-of-the-art graph summarization methods? The explosive proliferation of the Web has accelerated the emergence of large graphs, such as online social networks and hyperlink networks. Consequently, graph compression has become increasingly important to process such large graphs without expensive I/O over the network or to disk. Among a number of approaches, graph summarization, which in essence combines similar nodes into a supernode and describe their connectivity concisely, protrudes with several advantages. However, we note that it fails to exploit pervasive hierarchical structures of real-world graphs as its underlying representation model enforces supernodes to be disjoint. In this work, we propose the hierarchical graph summarization model, which is an expressive graph representation model that includes the previous one proposed by Navlakha et al. as a special case. The new model represents an unweighted graph using positive and negative edges between hierarchical supernodes, each of which can contain others. Then, we propose Slugger, a scalable heuristic for concisely and exactly representing a given graph under our new model. Slugger greedily merges nodes into supernodes while maintaining and exploiting their hierarchy, which is later pruned. Slugger significantly accelerates this process by sampling, approximation, and memoization. Our experiments on 16 real-world graphs show that Slugger is (a) Effective: yielding up to 29.6% more concise summary than state-of-the-art lossless summarization methods, (b) Fast: summarizing a graph with 0.8 billion edges in a few hours, and (c) Scalable: scaling linearly with the number of edges in the input graph.

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.

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.

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.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Hyper-relational knowledge graphs (HKGs) extend standard knowledge graphs by associating attribute-value qualifiers to triples, which effectively represent additional fine-grained information about its associated triple. Hyper-relational knowledge graph completion (HKGC) aims at inferring unknown triples while considering its qualifiers. Most existing approaches to HKGC exploit a global-level graph structure to encode hyper-relational knowledge into the graph convolution message passing process. However, the addition of multi-hop information might bring noise into the triple prediction process. To address this problem, we propose HyperFormer, a model that considers local-level sequential information, which encodes the content of the entities, relations and qualifiers of a triple. More precisely, HyperFormer is composed of three different modules: an entity neighbor aggregator module allowing to integrate the information of the neighbors of an entity to capture different perspectives of it; a relation qualifier aggregator module to integrate hyper-relational knowledge into the corresponding relation to refine the representation of relational content; a convolution-based bidirectional interaction module based on a convolutional operation, capturing pairwise bidirectional interactions of entity-relation, entity-qualifier, and relation-qualifier. realize the depth perception of the content related to the current statement. Furthermore, we introduce a Mixture-of-Experts strategy into the feed-forward layers of HyperFormer to strengthen its representation capabilities while reducing the amount of model parameters and computation. Extensive experiments on three well-known datasets with four different conditions demonstrate HyperFormer's effectiveness. Datasets and code are available at https://github.com/zhiweihu1103/HKGC-HyperFormer.

The vast, complex, and dynamic nature of social message data has posed challenges to social event detection (SED). Despite considerable effort, these challenges persist, often resulting in inadequately expressive message representations (ineffective) and prolonged learning durations (inefficient). In response to the challenges, this work introduces an unsupervised framework, HyperSED (Hyperbolic SED). Specifically, the proposed framework first models social messages into semantic-based message anchors, and then leverages the structure of the anchor graph and the expressiveness of the hyperbolic space to acquire structure- and geometry-aware anchor representations. Finally, HyperSED builds the partitioning tree of the anchor message graph by incorporating differentiable structural information as the reflection of the detected events. Extensive experiments on public datasets demonstrate HyperSED's competitive performance, along with a substantial improvement in efficiency compared to the current state-of-the-art unsupervised paradigm. Statistically, HyperSED boosts incremental SED by an average of 2%, 2%, and 25% in NMI, AMI, and ARI, respectively; enhancing efficiency by up to 37.41 times and at least 12.10 times, illustrating the advancement of the proposed framework. Our code is publicly available at https://github.com/XiaoyanWork/HyperSED.

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.

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination of two optimization objectives, we propose a novel semantic graph representation (SGR) method to formulate the joint optimization of the two heterogeneous sources into a common high-order proximity based framework. Concretely, we first construct an auxiliary weighted graph, where the complex homogeneous and heterogeneous relations among nodes and attributes in the original graph are comprehensively encoded. Conventional embedding methods that consider high-order topology proximities can then be easily applied to the newly constructed graph to learn the representations of both node and attribute while capturing the nonlinear high-order intrinsic correlation inside or among graph structure and semantic. The learned attribute embeddings can also effectively support some semantic-oriented inference tasks (e.g., semantic community detection), helping to reveal the graph's deep semantic. The effectiveness of SGR is further verified on a series of real graphs, where it achieves impressive performance over other baselines.

For robots to perform a wide variety of tasks, they require a 3D representation of the world that is semantically rich, yet compact and efficient for task-driven perception and planning. Recent approaches have attempted to leverage features from large vision-language models to encode semantics in 3D representations. However, these approaches tend to produce maps with per-point feature vectors, which do not scale well in larger environments, nor do they contain semantic spatial relationships between entities in the environment, which are useful for downstream planning. In this work, we propose ConceptGraphs, an open-vocabulary graph-structured representation for 3D scenes. ConceptGraphs is built by leveraging 2D foundation models and fusing their output to 3D by multi-view association. The resulting representations generalize to novel semantic classes, without the need to collect large 3D datasets or finetune models. We demonstrate the utility of this representation through a number of downstream planning tasks that are specified through abstract (language) prompts and require complex reasoning over spatial and semantic concepts. (Project page: https://concept-graphs.github.io/ Explainer video: https://youtu.be/mRhNkQwRYnc )

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

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}

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 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.

The label-embedded dictionary learning (DL) algorithms generate influential dictionaries by introducing discriminative information. However, there exists a limitation: All the label-embedded DL methods rely on the labels due that this way merely achieves ideal performances in supervised learning. While in semi-supervised and unsupervised learning, it is no longer sufficient to be effective. Inspired by the concept of self-supervised learning (e.g., setting the pretext task to generate a universal model for the downstream task), we propose a Self-Supervised Dictionary Learning (SSDL) framework to address this challenge. Specifically, we first design a p-Laplacian Attention Hypergraph Learning (pAHL) block as the pretext task to generate pseudo soft labels for DL. Then, we adopt the pseudo labels to train a dictionary from a primary label-embedded DL method. We evaluate our SSDL on two human activity recognition datasets. The comparison results with other state-of-the-art methods have demonstrated the efficiency of SSDL.

Assistive drawing aims to facilitate the creative process by providing intelligent guidance to artists. Existing solutions often fail to effectively model intricate stroke details or adequately address the temporal aspects of drawing. We introduce hyperstroke, a novel stroke representation designed to capture precise fine stroke details, including RGB appearance and alpha-channel opacity. Using a Vector Quantization approach, hyperstroke learns compact tokenized representations of strokes from real-life drawing videos of artistic drawing. With hyperstroke, we propose to model assistive drawing via a transformer-based architecture, to enable intuitive and user-friendly drawing applications, which are experimented in our exploratory evaluation.

Conventional representation learning algorithms for knowledge graphs (KG) map each entity to a unique embedding vector. Such a shallow lookup results in a linear growth of memory consumption for storing the embedding matrix and incurs high computational costs when working with real-world KGs. Drawing parallels with subword tokenization commonly used in NLP, we explore the landscape of more parameter-efficient node embedding strategies with possibly sublinear memory requirements. To this end, we propose NodePiece, an anchor-based approach to learn a fixed-size entity vocabulary. In NodePiece, a vocabulary of subword/sub-entity units is constructed from anchor nodes in a graph with known relation types. Given such a fixed-size vocabulary, it is possible to bootstrap an encoding and embedding for any entity, including those unseen during training. Experiments show that NodePiece performs competitively in node classification, link prediction, and relation prediction tasks while retaining less than 10% of explicit nodes in a graph as anchors and often having 10x fewer parameters. To this end, we show that a NodePiece-enabled model outperforms existing shallow models on a large OGB WikiKG 2 graph having 70x fewer parameters.

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.

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.

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.

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.

We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being local, global or relative. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges O(N+E) by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework GraphGPS that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current HNNs in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, a fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression. {Experiments on standard vision tasks demonstrate the promising performance of our HCNN framework in both hybrid and fully hyperbolic settings.} Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV.

Abstract meaning representation (AMR) highlights the core semantic information of text in a graph structure. Recently, pre-trained language models (PLMs) have advanced tasks of AMR parsing and AMR-to-text generation, respectively. However, PLMs are typically pre-trained on textual data, thus are sub-optimal for modeling structural knowledge. To this end, we investigate graph self-supervised training to improve the structure awareness of PLMs over AMR graphs. In particular, we introduce two graph auto-encoding strategies for graph-to-graph pre-training and four tasks to integrate text and graph information during pre-training. We further design a unified framework to bridge the gap between pre-training and fine-tuning tasks. Experiments on both AMR parsing and AMR-to-text generation show the superiority of our model. To our knowledge, we are the first to consider pre-training on semantic graphs.

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.

We design a new technique for the distributional semantic modeling with a neural network-based approach to learn distributed term representations (or term embeddings) - term vector space models as a result, inspired by the recent ontology-related approach (using different types of contextual knowledge such as syntactic knowledge, terminological knowledge, semantic knowledge, etc.) to the identification of terms (term extraction) and relations between them (relation extraction) called semantic pre-processing technology - SPT. Our method relies on automatic term extraction from the natural language texts and subsequent formation of the problem-oriented or application-oriented (also deeply annotated) text corpora where the fundamental entity is the term (includes non-compositional and compositional terms). This gives us an opportunity to changeover from distributed word representations (or word embeddings) to distributed term representations (or term embeddings). This transition will allow to generate more accurate semantic maps of different subject domains (also, of relations between input terms - it is useful to explore clusters and oppositions, or to test your hypotheses about them). The semantic map can be represented as a graph using Vec2graph - a Python library for visualizing word embeddings (term embeddings in our case) as dynamic and interactive graphs. The Vec2graph library coupled with term embeddings will not only improve accuracy in solving standard NLP tasks, but also update the conventional concept of automated ontology development. The main practical result of our work is the development kit (set of toolkits represented as web service APIs and web application), which provides all necessary routines for the basic linguistic pre-processing and the semantic pre-processing of the natural language texts in Ukrainian for future training of term vector space models.

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

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.

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.

In recent years, graph representation learning has undergone a paradigm shift, driven by the emergence and proliferation of graph neural networks (GNNs) and their heterogeneous counterparts. Heterogeneous GNNs have shown remarkable success in extracting low-dimensional embeddings from complex graphs that encompass diverse entity types and relationships. While meta-path-based techniques have long been recognized for their ability to capture semantic affinities among nodes, their dependence on manual specification poses a significant limitation. In contrast, matrix-focused methods accelerate processing by utilizing structural cues but often overlook contextual richness. In this paper, we challenge the current paradigm by introducing ontology as a fundamental semantic primitive within complex graphs. Our goal is to integrate the strengths of both matrix-centric and meta-path-based approaches into a unified framework. We propose perturbation Ontology-based Graph Attention Networks (POGAT), a novel methodology that combines ontology subgraphs with an advanced self-supervised learning paradigm to achieve a deep contextual understanding. The core innovation of POGAT lies in our enhanced homogeneous perturbing scheme designed to generate rigorous negative samples, encouraging the model to explore minimal contextual features more thoroughly. Through extensive empirical evaluations, we demonstrate that POGAT significantly outperforms state-of-the-art baselines, achieving a groundbreaking improvement of up to 10.78\% in F1-score for the critical task of link prediction and 12.01\% in Micro-F1 for the critical task of node classification.

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.

Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in complex scenarios. Recent studies integrating Vision-Language Models (VLMs) with class hierarchies have shown promise, yet they fall short of fully exploiting the hierarchical relationships. These efforts are constrained by their inability to perform effectively across varied granularity of categories. To tackle this issue, we propose a novel framework (HGCLIP) that effectively combines CLIP with a deeper exploitation of the Hierarchical class structure via Graph representation learning. We explore constructing the class hierarchy into a graph, with its nodes representing the textual or image features of each category. After passing through a graph encoder, the textual features incorporate hierarchical structure information, while the image features emphasize class-aware features derived from prototypes through the attention mechanism. Our approach demonstrates significant improvements on 11 diverse visual recognition benchmarks. Our codes are fully available at https://github.com/richard-peng-xia/HGCLIP.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

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.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

We present hyper-connections, a simple yet effective method that can serve as an alternative to residual connections. This approach specifically addresses common drawbacks observed in residual connection variants, such as the seesaw effect between gradient vanishing and representation collapse. Theoretically, hyper-connections allow the network to adjust the strength of connections between features at different depths and dynamically rearrange layers. We conduct experiments focusing on the pre-training of large language models, including dense and sparse models, where hyper-connections show significant performance improvements over residual connections. Additional experiments conducted on vision tasks also demonstrate similar improvements. We anticipate that this method will be broadly applicable and beneficial across a wide range of AI problems.

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.

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot product function. In this paper, we propose a new representation learning framework for dense retrieval. Instead of learning a vector for each query and document, our framework learns a multivariate distribution and uses negative multivariate KL divergence to compute the similarity between distributions. For simplicity and efficiency reasons, we assume that the distributions are multivariate normals and then train large language models to produce mean and variance vectors for these distributions. We provide a theoretical foundation for the proposed framework and show that it can be seamlessly integrated into the existing approximate nearest neighbor algorithms to perform retrieval efficiently. We conduct an extensive suite of experiments on a wide range of datasets, and demonstrate significant improvements compared to competitive dense retrieval models.

We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections between the words in a sequence. Such architecture does not leverage the graph connectivity inductive bias, and can perform poorly when the graph topology is important and has not been encoded into the node features. We introduce a graph transformer with four new properties compared to the standard model. First, the attention mechanism is a function of the neighborhood connectivity for each node in the graph. Second, the positional encoding is represented by the Laplacian eigenvectors, which naturally generalize the sinusoidal positional encodings often used in NLP. Third, the layer normalization is replaced by a batch normalization layer, which provides faster training and better generalization performance. Finally, the architecture is extended to edge feature representation, which can be critical to tasks s.a. chemistry (bond type) or link prediction (entity relationship in knowledge graphs). Numerical experiments on a graph benchmark demonstrate the performance of the proposed graph transformer architecture. This work closes the gap between the original transformer, which was designed for the limited case of line graphs, and graph neural networks, that can work with arbitrary graphs. As our architecture is simple and generic, we believe it can be used as a black box for future applications that wish to consider transformer and graphs.

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.

Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hypergraphs and simplicial complexes. While the increased expressivity of these models can indeed lead to a better classification performance and a more faithful representation of the underlying system, the computational cost of these higher-order models can increase dramatically. To this end, we here explore a simplicial complex neural network learning architecture based on random walks and fast 1D convolutions (SCRaWl), in which we can adjust the increase in computational cost by varying the length and number of random walks considered while accounting for higher-order relationships. Importantly, due to the random walk-based design, the expressivity of the proposed architecture is provably incomparable to that of existing message-passing simplicial neural networks. We empirically evaluate SCRaWl on real-world datasets and show that it outperforms other simplicial neural networks.

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.

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.

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via composition. However, notwithstanding the potential performance benefit, the syntactically-aware DSMs proposed to date have huge numbers of parameters (compared to conventional DSMs) and suffer from data sparsity. Furthermore, the encoding of the SyG links (i.e., the syntactic relations) has been largely limited to linear maps. The knowledge graphs' literature, on the other hand, has proposed light-weight models employing different geometric transformations (GTs) to encode edges in a knowledge graph (KG). Our work explores the possibility of adopting this family of models to encode SyGs. Furthermore, we investigate which GT better encodes syntactic relations, so that these representations can be used to enhance phrase-level composition via syntactic contextualisation.

The vast majority of retrieval models depend on vector inner products to produce a relevance score between a query and a document. This naturally limits the expressiveness of the relevance score that can be employed. We propose a new paradigm, instead of producing a vector to represent the query we produce a small neural network which acts as a learned relevance function. This small neural network takes in a representation of the document, in this paper we use a single vector, and produces a scalar relevance score. To produce the little neural network we use a hypernetwork, a network that produce the weights of other networks, as our query encoder or as we call it a Hypencoder. Experiments on in-domain search tasks show that Hypencoder is able to significantly outperform strong dense retrieval models and has higher metrics then reranking models and models an order of magnitude larger. Hypencoder is also shown to generalize well to out-of-domain search tasks. To assess the extent of Hypencoder's capabilities, we evaluate on a set of hard retrieval tasks including tip-of-the-tongue retrieval and instruction-following retrieval tasks and find that the performance gap widens substantially compared to standard retrieval tasks. Furthermore, to demonstrate the practicality of our method we implement an approximate search algorithm and show that our model is able to search 8.8M documents in under 60ms.

Dense retrieval has achieved impressive advances in first-stage retrieval from a large-scale document collection, which is built on bi-encoder architecture to produce single vector representation of query and document. However, a document can usually answer multiple potential queries from different views. So the single vector representation of a document is hard to match with multi-view queries, and faces a semantic mismatch problem. This paper proposes a multi-view document representation learning framework, aiming to produce multi-view embeddings to represent documents and enforce them to align with different queries. First, we propose a simple yet effective method of generating multiple embeddings through viewers. Second, to prevent multi-view embeddings from collapsing to the same one, we further propose a global-local loss with annealed temperature to encourage the multiple viewers to better align with different potential queries. Experiments show our method outperforms recent works and achieves state-of-the-art results.

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 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.

Recent progress in Sign Language Translation (SLT) has focussed primarily on improving the representational capacity of large language models to incorporate Sign Language features. This work explores an alternative direction: enhancing the geometric properties of skeletal representations themselves. We propose Geo-Sign, a method that leverages the properties of hyperbolic geometry to model the hierarchical structure inherent in sign language kinematics. By projecting skeletal features derived from Spatio-Temporal Graph Convolutional Networks (ST-GCNs) into the Poincar\'e ball model, we aim to create more discriminative embeddings, particularly for fine-grained motions like finger articulations. We introduce a hyperbolic projection layer, a weighted Fr\'echet mean aggregation scheme, and a geometric contrastive loss operating directly in hyperbolic space. These components are integrated into an end-to-end translation framework as a regularisation function, to enhance the representations within the language model. This work demonstrates the potential of hyperbolic geometry to improve skeletal representations for Sign Language Translation, improving on SOTA RGB methods while preserving privacy and improving computational efficiency. Code available here: https://github.com/ed-fish/geo-sign.

The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer.

This paper introduces layout-aware graph modeling for multimodal RAG. Different from traditional RAG methods that mostly deal with flat text chunks, the proposed method takes into account the relationship of multimodalities by using a graph structure. To do that, a graph modeling structure is defined based on document layout parsing. The structure of an input document is retained with the connection of text chunks, tables, and figures. This representation allows the method to handle complex questions that require information from multimodalities. To confirm the efficiency of the graph modeling, a flexible RAG pipeline is developed using robust components. Experimental results on four benchmark test sets confirm the contribution of the layout-aware modeling for performance improvement of the RAG pipeline.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Relation extraction has the potential for large-scale knowledge graph construction, but current methods do not consider the qualifier attributes for each relation triplet, such as time, quantity or location. The qualifiers form hyper-relational facts which better capture the rich and complex knowledge graph structure. For example, the relation triplet (Leonard Parker, Educated At, Harvard University) can be factually enriched by including the qualifier (End Time, 1967). Hence, we propose the task of hyper-relational extraction to extract more specific and complete facts from text. To support the task, we construct HyperRED, a large-scale and general-purpose dataset. Existing models cannot perform hyper-relational extraction as it requires a model to consider the interaction between three entities. Hence, we propose CubeRE, a cube-filling model inspired by table-filling approaches and explicitly considers the interaction between relation triplets and qualifiers. To improve model scalability and reduce negative class imbalance, we further propose a cube-pruning method. Our experiments show that CubeRE outperforms strong baselines and reveal possible directions for future research. Our code and data are available at github.com/declare-lab/HyperRED.

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and consistently deliver state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present hyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, hyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.

We introduce a novel graph-based Retrieval-Augmented Generation (RAG) framework specifically designed for the medical domain, called MedGraphRAG, aimed at enhancing Large Language Model (LLM) capabilities and generating evidence-based results, thereby improving safety and reliability when handling private medical data. Our comprehensive pipeline begins with a hybrid static-semantic approach to document chunking, significantly improving context capture over traditional methods. Extracted entities are used to create a three-tier hierarchical graph structure, linking entities to foundational medical knowledge sourced from medical papers and dictionaries. These entities are then interconnected to form meta-graphs, which are merged based on semantic similarities to develop a comprehensive global graph. This structure supports precise information retrieval and response generation. The retrieval process employs a U-retrieve method to balance global awareness and indexing efficiency of the LLM. Our approach is validated through a comprehensive ablation study comparing various methods for document chunking, graph construction, and information retrieval. The results not only demonstrate that our hierarchical graph construction method consistently outperforms state-of-the-art models on multiple medical Q\&A benchmarks, but also confirms that the responses generated include source documentation, significantly enhancing the reliability of medical LLMs in practical applications. Code will be at: https://github.com/MedicineToken/Medical-Graph-RAG/tree/main

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.

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar\'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar\'e 2D convolutions up to Poincar\'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr\'echet mean calculations in hyperbolic space. We introduce Poincar\'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar\'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

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.

This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the relationship between a genotype - the hypernetwork - and a phenotype - the main network. Though they are also reminiscent of HyperNEAT in evolution, our hypernetworks are trained end-to-end with backpropagation and thus are usually faster. The focus of this work is to make hypernetworks useful for deep convolutional networks and long recurrent networks, where hypernetworks can be viewed as relaxed form of weight-sharing across layers. Our main result is that hypernetworks can generate non-shared weights for LSTM and achieve near state-of-the-art results on a variety of sequence modelling tasks including character-level language modelling, handwriting generation and neural machine translation, challenging the weight-sharing paradigm for recurrent networks. Our results also show that hypernetworks applied to convolutional networks still achieve respectable results for image recognition tasks compared to state-of-the-art baseline models while requiring fewer learnable parameters.

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.

Named entity recognition is a fundamental task in natural language processing, identifying the span and category of entities in unstructured texts. The traditional sequence labeling methodology ignores the nested entities, i.e. entities included in other entity mentions. Many approaches attempt to address this scenario, most of which rely on complex structures or have high computation complexity. The representation learning of the heterogeneous star graph containing text nodes and type nodes is investigated in this paper. In addition, we revise the graph attention mechanism into a hybrid form to address its unreasonableness in specific topologies. The model performs the type-supervised sequence labeling after updating nodes in the graph. The annotation scheme is an extension of the single-layer sequence labeling and is able to cope with the vast majority of nested entities. Extensive experiments on public NER datasets reveal the effectiveness of our model in extracting both flat and nested entities. The method achieved state-of-the-art performance on both flat and nested datasets. The significant improvement in accuracy reflects the superiority of the multi-layer labeling strategy.

Deep learning has proven itself as a successful set of models for learning useful semantic representations of data. These, however, are mostly implicitly learned as part of a classification task. In this paper we propose the triplet network model, which aims to learn useful representations by distance comparisons. A similar model was defined by Wang et al. (2014), tailor made for learning a ranking for image information retrieval. Here we demonstrate using various datasets that our model learns a better representation than that of its immediate competitor, the Siamese network. We also discuss future possible usage as a framework for unsupervised learning.

Structured representations like graphs and parse trees play a crucial role in many Natural Language Processing systems. In recent years, the advancements in multi-turn user interfaces necessitate the need for controlling and updating these structured representations given new sources of information. Although there have been many efforts focusing on improving the performance of the parsers that map text to graphs or parse trees, very few have explored the problem of directly manipulating these representations. In this paper, we explore the novel problem of graph modification, where the systems need to learn how to update an existing scene graph given a new user's command. Our novel models based on graph-based sparse transformer and cross attention information fusion outperform previous systems adapted from the machine translation and graph generation literature. We further contribute our large graph modification datasets to the research community to encourage future research for this new problem.

Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns, exhibiting local node-level homophilic and heterophilic structures. However, existing works are only devoted to designing better HGNN backbones or architectures for node classification tasks on heterophilic and homophilic graph benchmarks simultaneously, and their analyses of HGNN performance with respect to nodes are only based on the determined data distribution without exploring the effect caused by this structural difference between training and testing nodes. How to learn invariant node representations on heterophilic graphs to handle this structure difference or distribution shifts remains unexplored. In this paper, we first discuss the limitations of previous graph-based invariant learning methods from the perspective of data augmentation. Then, we propose HEI, a framework capable of generating invariant node representations through incorporating heterophily information to infer latent environments without augmentation, which are then used for invariant prediction, under heterophilic graph structure distribution shifts. We theoretically show that our proposed method can achieve guaranteed performance under heterophilic graph structure distribution shifts. Extensive experiments on various benchmarks and backbones can also demonstrate the effectiveness of our method compared with existing state-of-the-art baselines.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

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-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.

HAL (Hyper Articles en Ligne) is the French national publication repository, used by most higher education and research organizations for their open science policy. As a digital library, it is a rich repository of scholarly documents, but its potential for advanced research has been underutilized. We present HALvest, a unique dataset that bridges the gap between citation networks and the full text of papers submitted on HAL. We craft our dataset by filtering HAL for scholarly publications, resulting in approximately 700,000 documents, spanning 34 languages across 13 identified domains, suitable for language model training, and yielding approximately 16.5 billion tokens (with 8 billion in French and 7 billion in English, the most represented languages). We transform the metadata of each paper into a citation network, producing a directed heterogeneous graph. This graph includes uniquely identified authors on HAL, as well as all open submitted papers, and their citations. We provide a baseline for authorship attribution using the dataset, implement a range of state-of-the-art models in graph representation learning for link prediction, and discuss the usefulness of our generated knowledge graph structure.

When reading a document, glancing at the spatial layout of a document is an initial step to understand it roughly. Traditional document layout analysis (DLA) methods, however, offer only a superficial parsing of documents, focusing on basic instance detection and often failing to capture the nuanced spatial and logical relations between instances. These limitations hinder DLA-based models from achieving a gradually deeper comprehension akin to human reading. In this work, we propose a novel graph-based Document Structure Analysis (gDSA) task. This task requires that model not only detects document elements but also generates spatial and logical relations in form of a graph structure, allowing to understand documents in a holistic and intuitive manner. For this new task, we construct a relation graph-based document structure analysis dataset (GraphDoc) with 80K document images and 4.13M relation annotations, enabling training models to complete multiple tasks like reading order, hierarchical structures analysis, and complex inter-element relation inference. Furthermore, a document relation graph generator (DRGG) is proposed to address the gDSA task, which achieves performance with 57.6% at mAP_g@0.5 for a strong benchmark baseline on this novel task and dataset. We hope this graphical representation of document structure can mark an innovative advancement in document structure analysis and understanding. The new dataset and code will be made publicly available at https://yufanchen96.github.io/projects/GraphDoc.

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.

Document retrieval is a core component of question-answering systems, as it enables conditioning answer generation on new and large-scale corpora. While effective, the standard practice of encoding documents into high-dimensional embeddings for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. In this paper, we propose a tree-based method for organizing and representing reference documents at various granular levels, which offers the flexibility to balance cost and utility, and eases the inspection of the corpus content and retrieval operations. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches, hence directly optimizing for retrieval performance. Our evaluations show that ReTreever generally preserves full representation accuracy. Its hierarchical structure further provides strong coarse representations and enhances transparency by indirectly learning meaningful semantic groupings. Among hierarchical retrieval methods, ReTreever achieves the best retrieval accuracy at the lowest latency, proving that this family of techniques can be viable in practical applications.

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.

Vector space word representations are learned from distributional information of words in large corpora. Although such statistics are semantically informative, they disregard the valuable information that is contained in semantic lexicons such as WordNet, FrameNet, and the Paraphrase Database. This paper proposes a method for refining vector space representations using relational information from semantic lexicons by encouraging linked words to have similar vector representations, and it makes no assumptions about how the input vectors were constructed. Evaluated on a battery of standard lexical semantic evaluation tasks in several languages, we obtain substantial improvements starting with a variety of word vector models. Our refinement method outperforms prior techniques for incorporating semantic lexicons into the word vector training algorithms.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Due to the mutual occlusion, severe scale variation, and complex spatial distribution, the current multi-person mesh recovery methods cannot produce accurate absolute body poses and shapes in large-scale crowded scenes. To address the obstacles, we fully exploit crowd features for reconstructing groups of people from a monocular image. A novel hypergraph relational reasoning network is proposed to formulate the complex and high-order relation correlations among individuals and groups in the crowd. We first extract compact human features and location information from the original high-resolution image. By conducting the relational reasoning on the extracted individual features, the underlying crowd collectiveness and interaction relationship can provide additional group information for the reconstruction. Finally, the updated individual features and the localization information are used to regress human meshes in camera coordinates. To facilitate the network training, we further build pseudo ground-truth on two crowd datasets, which may also promote future research on pose estimation and human behavior understanding in crowded scenes. The experimental results show that our approach outperforms other baseline methods both in crowded and common scenarios. The code and datasets are publicly available at https://github.com/boycehbz/GroupRec.

Visual spatial description (VSD) aims to generate texts that describe the spatial relations of the given objects within images. Existing VSD work merely models the 2D geometrical vision features, thus inevitably falling prey to the problem of skewed spatial understanding of target objects. In this work, we investigate the incorporation of 3D scene features for VSD. With an external 3D scene extractor, we obtain the 3D objects and scene features for input images, based on which we construct a target object-centered 3D spatial scene graph (Go3D-S2G), such that we model the spatial semantics of target objects within the holistic 3D scenes. Besides, we propose a scene subgraph selecting mechanism, sampling topologically-diverse subgraphs from Go3D-S2G, where the diverse local structure features are navigated to yield spatially-diversified text generation. Experimental results on two VSD datasets demonstrate that our framework outperforms the baselines significantly, especially improving on the cases with complex visual spatial relations. Meanwhile, our method can produce more spatially-diversified generation. Code is available at https://github.com/zhaoyucs/VSD.

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.

Associating unstructured data with structured information is crucial for real-world tasks that require relevance search. However, existing graph learning benchmarks often overlook the rich semantic information associate with each node. To bridge such gap, we introduce the Multimodal Graph Benchmark (MM-GRAPH), the first comprehensive multi-modal graph benchmark that incorporates both textual and visual information. MM-GRAPH surpasses previous efforts, which have primarily focused on text-attributed graphs with various connectivity patterns. MM-GRAPH consists of five graph learning datasets of various scales that are appropriate for different learning tasks. Their multimodal node features, enabling a more comprehensive evaluation of graph learning algorithms in real-world scenarios. To facilitate research on multimodal graph learning, we further provide an extensive study on the performance of various graph neural networks in the presence of features from various modalities. MM-GRAPH aims to foster research on multimodal graph learning and drive the development of more advanced and robust graph learning algorithms. By providing a diverse set of datasets and benchmarks, MM-GRAPH enables researchers to evaluate and compare their models in realistic settings, ultimately leading to improved performance on real-world applications that rely on multimodal graph data.

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.

Captions that describe or explain charts help improve recall and comprehension of the depicted data and provide a more accessible medium for people with visual disabilities. However, current approaches for automatically generating such captions struggle to articulate the perceptual or cognitive features that are the hallmark of charts (e.g., complex trends and patterns). In response, we introduce VisText: a dataset of 12,441 pairs of charts and captions that describe the charts' construction, report key statistics, and identify perceptual and cognitive phenomena. In VisText, a chart is available as three representations: a rasterized image, a backing data table, and a scene graph -- a hierarchical representation of a chart's visual elements akin to a web page's Document Object Model (DOM). To evaluate the impact of VisText, we fine-tune state-of-the-art language models on our chart captioning task and apply prefix-tuning to produce captions that vary the semantic content they convey. Our models generate coherent, semantically rich captions and perform on par with state-of-the-art chart captioning models across machine translation and text generation metrics. Through qualitative analysis, we identify six broad categories of errors that our models make that can inform future work.

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.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

While Retrieval-Augmented Generation (RAG) enhances the accuracy and relevance of responses by generative language models, it falls short in graph-based contexts where both textual and topological information are important. Naive RAG approaches inherently neglect the structural intricacies of textual graphs, resulting in a critical gap in the generation process. To address this challenge, we introduce Graph Retrieval-Augmented Generation (GRAG), which significantly enhances both the retrieval and generation processes by emphasizing the importance of subgraph structures. Unlike RAG approaches that focus solely on text-based entity retrieval, GRAG maintains an acute awareness of graph topology, which is crucial for generating contextually and factually coherent responses. Our GRAG approach consists of four main stages: indexing of k-hop ego-graphs, graph retrieval, soft pruning to mitigate the impact of irrelevant entities, and generation with pruned textual subgraphs. GRAG's core workflow-retrieving textual subgraphs followed by soft pruning-efficiently identifies relevant subgraph structures while avoiding the computational infeasibility typical of exhaustive subgraph searches, which are NP-hard. Moreover, we propose a novel prompting strategy that achieves lossless conversion from textual subgraphs to hierarchical text descriptions. Extensive experiments on graph multi-hop reasoning benchmarks demonstrate that in scenarios requiring multi-hop reasoning on textual graphs, our GRAG approach significantly outperforms current state-of-the-art RAG methods while effectively mitigating hallucinations.

Knowledge Graphs (KG) are of vital importance for multiple applications on the web, including information retrieval, recommender systems, and metadata annotation. Regardless of whether they are built manually by domain experts or with automatic pipelines, KGs are often incomplete. Recent work has begun to explore the use of textual descriptions available in knowledge graphs to learn vector representations of entities in order to preform link prediction. However, the extent to which these representations learned for link prediction generalize to other tasks is unclear. This is important given the cost of learning such representations. Ideally, we would prefer representations that do not need to be trained again when transferring to a different task, while retaining reasonable performance. In this work, we propose a holistic evaluation protocol for entity representations learned via a link prediction objective. We consider the inductive link prediction and entity classification tasks, which involve entities not seen during training. We also consider an information retrieval task for entity-oriented search. We evaluate an architecture based on a pretrained language model, that exhibits strong generalization to entities not observed during training, and outperforms related state-of-the-art methods (22% MRR improvement in link prediction on average). We further provide evidence that the learned representations transfer well to other tasks without fine-tuning. In the entity classification task we obtain an average improvement of 16% in accuracy compared with baselines that also employ pre-trained models. In the information retrieval task, we obtain significant improvements of up to 8.8% in NDCG@10 for natural language queries. We thus show that the learned representations are not limited KG-specific tasks, and have greater generalization properties than evaluated in previous work.

Multimodal Attributed Graphs (MAGs) are ubiquitous in real-world applications, encompassing extensive knowledge through multimodal attributes attached to nodes (e.g., texts and images) and topological structure representing node interactions. Despite its potential to advance diverse research fields like social networks and e-commerce, MAG representation learning (MAGRL) remains underexplored due to the lack of standardized datasets and evaluation frameworks. In this paper, we first propose MAGB, a comprehensive MAG benchmark dataset, featuring curated graphs from various domains with both textual and visual attributes. Based on MAGB dataset, we further systematically evaluate two mainstream MAGRL paradigms: GNN-as-Predictor, which integrates multimodal attributes via Graph Neural Networks (GNNs), and VLM-as-Predictor, which harnesses Vision Language Models (VLMs) for zero-shot reasoning. Extensive experiments on MAGB reveal following critical insights: (i) Modality significances fluctuate drastically with specific domain characteristics. (ii) Multimodal embeddings can elevate the performance ceiling of GNNs. However, intrinsic biases among modalities may impede effective training, particularly in low-data scenarios. (iii) VLMs are highly effective at generating multimodal embeddings that alleviate the imbalance between textual and visual attributes. These discoveries, which illuminate the synergy between multimodal attributes and graph topologies, contribute to reliable benchmarks, paving the way for future MAG research. The MAGB dataset and evaluation pipeline are publicly available at https://github.com/sktsherlock/MAGB.

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.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

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.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

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.

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.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Scientific knowledge is growing rapidly, making it challenging to track progress and high-level conceptual links across broad disciplines. While existing tools like citation networks and search engines make it easy to access a few related papers, they fundamentally lack the flexible abstraction needed to represent the density of activity in various scientific subfields. We motivate SCIENCE HIERARCHOGRAPHY, the goal of organizing scientific literature into a high-quality hierarchical structure that allows for the categorization of scientific work across varying levels of abstraction, from very broad fields to very specific studies. Such a representation can provide insights into which fields are well-explored and which are under-explored. To achieve the goals of SCIENCE HIERARCHOGRAPHY, we develop a range of algorithms. Our primary approach combines fast embedding-based clustering with LLM-based prompting to balance the computational efficiency of embedding methods with the semantic precision offered by LLM prompting. We demonstrate that this approach offers the best trade-off between quality and speed compared to methods that heavily rely on LLM prompting, such as iterative tree construction with LLMs. To better reflect the interdisciplinary and multifaceted nature of research papers, our hierarchy captures multiple dimensions of categorization beyond simple topic labels. We evaluate the utility of our framework by assessing how effectively an LLM-based agent can locate target papers using the hierarchy. Results show that this structured approach enhances interpretability, supports trend discovery, and offers an alternative pathway for exploring scientific literature beyond traditional search methods. Code, data and demo: https://github.com/JHU-CLSP/science-hierarchography{https://github.com/JHU-CLSP/science-hierarchography}

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures. Code can be found at https://github.com/hamed1375/Exphormer.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the 1-dimensional Weisfeiler--Leman algorithm (1-WL). Here, the 1-WL is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the 1-WL. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the 1-WL and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.

A vector database is used to store high-dimensional data that cannot be characterized by traditional DBMS. Although there are not many articles describing existing or introducing new vector database architectures, the approximate nearest neighbor search problem behind vector databases has been studied for a long time, and considerable related algorithmic articles can be found in the literature. This article attempts to comprehensively review relevant algorithms to provide a general understanding of this booming research area. The basis of our framework categorises these studies by the approach of solving ANNS problem, respectively hash-based, tree-based, graph-based and quantization-based approaches. Then we present an overview of existing challenges for vector databases. Lastly, we sketch how vector databases can be combined with large language models and provide new possibilities.