Daily Papers

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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)

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.

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.

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.

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)

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.

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.

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.

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.

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.

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

Neural architecture search (NAS) automatically finds the best task-specific neural network topology, outperforming many manual architecture designs. However, it can be prohibitively expensive as the search requires training thousands of different networks, while each can last for hours. In this work, we propose the Graph HyperNetwork (GHN) to amortize the search cost: given an architecture, it directly generates the weights by running inference on a graph neural network. GHNs model the topology of an architecture and therefore can predict network performance more accurately than regular hypernetworks and premature early stopping. To perform NAS, we randomly sample architectures and use the validation accuracy of networks with GHN generated weights as the surrogate search signal. GHNs are fast -- they can search nearly 10 times faster than other random search methods on CIFAR-10 and ImageNet. GHNs can be further extended to the anytime prediction setting, where they have found networks with better speed-accuracy tradeoff than the state-of-the-art manual designs.

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.

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.

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.

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

Graph-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.

Deep learning has been successful in automating the design of features in machine learning pipelines. However, the algorithms optimizing neural network parameters remain largely hand-designed and computationally inefficient. We study if we can use deep learning to directly predict these parameters by exploiting the past knowledge of training other networks. We introduce a large-scale dataset of diverse computational graphs of neural architectures - DeepNets-1M - and use it to explore parameter prediction on CIFAR-10 and ImageNet. By leveraging advances in graph neural networks, we propose a hypernetwork that can predict performant parameters in a single forward pass taking a fraction of a second, even on a CPU. The proposed model achieves surprisingly good performance on unseen and diverse networks. For example, it is able to predict all 24 million parameters of a ResNet-50 achieving a 60% accuracy on CIFAR-10. On ImageNet, top-5 accuracy of some of our networks approaches 50%. Our task along with the model and results can potentially lead to a new, more computationally efficient paradigm of training networks. Our model also learns a strong representation of neural architectures enabling their analysis.

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.

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.

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.

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.

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.

Hypernetworks, or hypernets in short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility, adaptability, dynamism, faster training, information sharing, and model compression etc. Hypernets have shown promising results in a variety of deep learning problems, including continual learning, causal inference, transfer learning, weight pruning, uncertainty quantification, zero-shot learning, natural language processing, and reinforcement learning etc. Despite their success across different problem settings, currently, there is no review available to inform the researchers about the developments and to help in utilizing hypernets. To fill this gap, we review the progress in hypernets. We present an illustrative example to train deep neural networks using hypernets and propose categorizing hypernets based on five design criteria as inputs, outputs, variability of inputs and outputs, and architecture of hypernets. We also review applications of hypernets across different deep learning problem settings, followed by a discussion of general scenarios where hypernets can be effectively employed. Finally, we discuss the challenges and future directions that remain under-explored in the field of hypernets. We believe that hypernetworks have the potential to revolutionize the field of deep learning. They offer a new way to design and train neural networks, and they have the potential to improve the performance of deep learning models on a variety of tasks. Through this review, we aim to inspire further advancements in deep learning through hypernetworks.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

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.

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.

A good initialization of deep learning models is essential since it can help them converge better and faster. However, pretraining large models is unaffordable for many researchers, which makes a desired prediction for initial parameters more necessary nowadays. Graph HyperNetworks (GHNs), one approach to predicting model parameters, have recently shown strong performance in initializing large vision models. Unfortunately, predicting parameters of very wide networks relies on copying small chunks of parameters multiple times and requires an extremely large number of parameters to support full prediction, which greatly hinders its adoption in practice. To address this limitation, we propose LoGAH (Low-rank GrAph Hypernetworks), a GHN with a low-rank parameter decoder that expands to significantly wider networks without requiring as excessive increase of parameters as in previous attempts. LoGAH allows us to predict the parameters of 774-million large neural networks in a memory-efficient manner. We show that vision and language models (i.e., ViT and GPT-2) initialized with LoGAH achieve better performance than those initialized randomly or using existing hypernetworks. Furthermore, we show promising transfer learning results w.r.t. training LoGAH on small datasets and using the predicted parameters to initialize for larger tasks. We provide the codes in https://github.com/Blackzxy/LoGAH .

Recently, a new Continual Learning (CL) paradigm was presented to control catastrophic forgetting, called Interval Continual Learning (InterContiNet), which relies on enforcing interval constraints on the neural network parameter space. Unfortunately, InterContiNet training is challenging due to the high dimensionality of the weight space, making intervals difficult to manage. To address this issue, we introduce HyperInterval, a technique that employs interval arithmetic within the embedding space and utilizes a hypernetwork to map these intervals to the target network parameter space. We train interval embeddings for consecutive tasks and train a hypernetwork to transform these embeddings into weights of the target network. An embedding for a given task is trained along with the hypernetwork, preserving the response of the target network for the previous task embeddings. Interval arithmetic works with a more manageable, lower-dimensional embedding space rather than directly preparing intervals in a high-dimensional weight space. Our model allows faster and more efficient training. Furthermore, HyperInterval maintains the guarantee of not forgetting. At the end of training, we can choose one universal embedding to produce a single network dedicated to all tasks. In such a framework, hypernetwork is used only for training and can be seen as a meta-trainer. HyperInterval obtains significantly better results than InterContiNet and gives SOTA results on several benchmarks.

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.

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.

Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial topologies; they are able to represent human phenomena such as epidemic processes, the dynamics of populations, and the urbanization of cities. The investigation of complex networks has been extrapolated to many fields of science, with particular emphasis on computing techniques, including artificial intelligence. In such a case, the analysis of the interaction between entities of interest is transposed to the internal learning of algorithms, a paradigm whose investigation is able to expand the state of the art in Computer Science. By exploring this paradigm, this thesis puts together complex networks and machine learning techniques to improve the understanding of the human phenomena observed in pandemics, pendular migration, and street networks. Accordingly, we contribute with: (i) a new neural network architecture capable of modeling dynamic processes observed in spatial and temporal data with applications in epidemics propagation, weather forecasting, and patient monitoring in intensive care units; (ii) a machine-learning methodology for analyzing and predicting links in the scope of human mobility between all the cities of Brazil; and, (iii) techniques for identifying inconsistencies in the urban planning of cities while tracking the most influential vertices, with applications over Brazilian and worldwide cities. We obtained results sustained by sound evidence of advances to the state of the art in artificial intelligence, rigorous formalisms, and ample experimentation. Our findings rely upon real-world applications in a range of domains, demonstrating the applicability of our methodologies.

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. Recent findings suggest that fixing the routers can achieve competitive performance by alleviating the collapsing problem, where all experts eventually learn similar representations. However, this strategy has two key limitations: (i) the policy derived from random routers might be sub-optimal, and (ii) it requires extensive resources during training and evaluation, leading to limited efficiency gains. This work introduces \HyperRout, which dynamically generates the router's parameters through a fixed hypernetwork and trainable embeddings to achieve a balance between training the routers and freezing them to learn an improved routing policy. Extensive experiments across a wide range of tasks demonstrate the superior performance and efficiency gains of \HyperRouter compared to existing routing methods. Our implementation is publicly available at {{https://github.com/giangdip2410/HyperRouter}}.

For a broad range of research, governmental and commercial applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich relational data in digital social networks (the social graph). As social media data sets are very large, most approaches make use of distributed computing systems for this purpose. Distributing graph processing requires solving many difficult engineering problems, which has lead some researchers to look at single-machine solutions that are faster and easier to maintain. In this article, we present a single-machine real-time system for large-scale graph processing that allows analysts to interactively explore graph structures. The key idea is that the aggregate actions of large numbers of users can be compressed into a data structure that encapsulates user similarities while being robust to noise and queryable in real-time. We achieve single machine real-time performance by compressing the neighbourhood of each vertex using minhash signatures and facilitate rapid queries through Locality Sensitive Hashing. These techniques reduce query times from hours using industrial desktop machines operating on the full graph to milliseconds on standard laptops. Our method allows exploration of strongly associated regions (i.e. communities) of large graphs in real-time on a laptop. It has been deployed in software that is actively used by social network analysts and offers another channel for media owners to monetise their data, helping them to continue to provide free services that are valued by billions of people globally.

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.

The topology of the hyperlink graph among pages expressing different opinions may influence the exposure of readers to diverse content. Structural bias may trap a reader in a polarized bubble with no access to other opinions. We model readers' behavior as random walks. A node is in a polarized bubble if the expected length of a random walk from it to a page of different opinion is large. The structural bias of a graph is the sum of the radii of highly-polarized bubbles. We study the problem of decreasing the structural bias through edge insertions. Healing all nodes with high polarized bubble radius is hard to approximate within a logarithmic factor, so we focus on finding the best k edges to insert to maximally reduce the structural bias. We present RePBubLik, an algorithm that leverages a variant of the random walk closeness centrality to select the edges to insert. RePBubLik obtains, under mild conditions, a constant-factor approximation. It reduces the structural bias faster than existing edge-recommendation methods, including some designed to reduce the polarization of a graph.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-of-the-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

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

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified communities and connectivities, and evaluated clustering coefficients and betweenness centrality of pivotal nodes, uncovering fascinating knowledge architectures. The graph has an inherently scale-free nature, is highly connected, and can be used for graph reasoning by taking advantage of transitive and isomorphic properties that reveal unprecedented interdisciplinary relationships that can be used to answer queries, identify gaps in knowledge, propose never-before-seen material designs, and predict material behaviors. We compute deep node embeddings for combinatorial node similarity ranking for use in a path sampling strategy links dissimilar concepts that have previously not been related. One comparison revealed structural parallels between biological materials and Beethoven's 9th Symphony, highlighting shared patterns of complexity through isomorphic mapping. In another example, the algorithm proposed a hierarchical mycelium-based composite based on integrating path sampling with principles extracted from Kandinsky's 'Composition VII' painting. The resulting material integrates an innovative set of concepts that include a balance of chaos/order, adjustable porosity, mechanical strength, and complex patterned chemical functionalization. We uncover other isomorphisms across science, technology and art, revealing a nuanced ontology of immanence that reveal a context-dependent heterarchical interplay of constituents. Graph-based generative AI achieves a far higher degree of novelty, explorative capacity, and technical detail, than conventional approaches and establishes a widely useful framework for innovation by revealing hidden connections.

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

Federated learning is an active research topic since it enables several participants to jointly train a model without sharing local data. Currently, cross-silo federated learning is a popular training setting that utilizes a few hundred reliable data silos with high-speed access links to training a model. While this approach has been widely applied in real-world scenarios, designing a robust topology to reduce the training time remains an open problem. In this paper, we present a new multigraph topology for cross-silo federated learning. We first construct the multigraph using the overlay graph. We then parse this multigraph into different simple graphs with isolated nodes. The existence of isolated nodes allows us to perform model aggregation without waiting for other nodes, hence effectively reducing the training time. Intensive experiments on three public datasets show that our proposed method significantly reduces the training time compared with recent state-of-the-art topologies while maintaining the accuracy of the learned model. Our code can be found at https://github.com/aioz-ai/MultigraphFL

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

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.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

Semi-transitive graphs, defined in hps98 as examples where ``uniform percolation" holds whenever p>p_c, are a large class of graphs more general than quasi-transitive graphs. Let G be a semi-transitive graph with one end which can be properly embedded into the plane with uniformly bounded face degree for finite faces and minimal vertex degree at least 7. We show that p_u^{site}(G) +p_c^{site}(G_*)=1, where G_* denotes the matching graph of G. This fulfils and extends an observation of Sykes and Essam in 1964 (SE64) to semi-transitive graphs.

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

The volume of scientific output is creating an urgent need for automated tools to help scientists keep up with developments in their field. Semantic Scholar (S2) is an open data platform and website aimed at accelerating science by helping scholars discover and understand scientific literature. We combine public and proprietary data sources using state-of-the-art techniques for scholarly PDF content extraction and automatic knowledge graph construction to build the Semantic Scholar Academic Graph, the largest open scientific literature graph to-date, with 200M+ papers, 80M+ authors, 550M+ paper-authorship edges, and 2.4B+ citation edges. The graph includes advanced semantic features such as structurally parsed text, natural language summaries, and vector embeddings. In this paper, we describe the components of the S2 data processing pipeline and the associated APIs offered by the platform. We will update this living document to reflect changes as we add new data offerings and improve existing services.

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.

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.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

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.

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.

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.

Reconstructing both objects and hands in 3D from a single RGB image is complex. Existing methods rely on manually defined hand-object constraints in Euclidean space, leading to suboptimal feature learning. Compared with Euclidean space, hyperbolic space better preserves the geometric properties of meshes thanks to its exponentially-growing space distance, which amplifies the differences between the features based on similarity. In this work, we propose the first precise hand-object reconstruction method in hyperbolic space, namely Dynamic Hyperbolic Attention Network (DHANet), which leverages intrinsic properties of hyperbolic space to learn representative features. Our method that projects mesh and image features into a unified hyperbolic space includes two modules, ie. dynamic hyperbolic graph convolution and image-attention hyperbolic graph convolution. With these two modules, our method learns mesh features with rich geometry-image multi-modal information and models better hand-object interaction. Our method provides a promising alternative for fine hand-object reconstruction in hyperbolic space. Extensive experiments on three public datasets demonstrate that our method outperforms most state-of-the-art methods.

Node classification is a classical graph machine learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datasets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs

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.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Text-Attributed Graphs (TAGs) augment graph structures with natural language descriptions, facilitating detailed depictions of data and their interconnections across various real-world settings. However, existing TAG datasets predominantly feature textual information only at the nodes, with edges typically represented by mere binary or categorical attributes. This lack of rich textual edge annotations significantly limits the exploration of contextual relationships between entities, hindering deeper insights into graph-structured data. To address this gap, we introduce Textual-Edge Graphs Datasets and Benchmark (TEG-DB), a comprehensive and diverse collection of benchmark textual-edge datasets featuring rich textual descriptions on nodes and edges. The TEG-DB datasets are large-scale and encompass a wide range of domains, from citation networks to social networks. In addition, we conduct extensive benchmark experiments on TEG-DB to assess the extent to which current techniques, including pre-trained language models, graph neural networks, and their combinations, can utilize textual node and edge information. Our goal is to elicit advancements in textual-edge graph research, specifically in developing methodologies that exploit rich textual node and edge descriptions to enhance graph analysis and provide deeper insights into complex real-world networks. The entire TEG-DB project is publicly accessible as an open-source repository on Github, accessible at https://github.com/Zhuofeng-Li/TEG-Benchmark.

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.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

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

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

Retrieval-augmented generation (RAG) is a powerful technique that enhances downstream task execution by retrieving additional information, such as knowledge, skills, and tools from external sources. Graph, by its intrinsic "nodes connected by edges" nature, encodes massive heterogeneous and relational information, making it a golden resource for RAG in tremendous real-world applications. As a result, we have recently witnessed increasing attention on equipping RAG with Graph, i.e., GraphRAG. However, unlike conventional RAG, where the retriever, generator, and external data sources can be uniformly designed in the neural-embedding space, the uniqueness of graph-structured data, such as diverse-formatted and domain-specific relational knowledge, poses unique and significant challenges when designing GraphRAG for different domains. Given the broad applicability, the associated design challenges, and the recent surge in GraphRAG, a systematic and up-to-date survey of its key concepts and techniques is urgently desired. Following this motivation, we present a comprehensive and up-to-date survey on GraphRAG. Our survey first proposes a holistic GraphRAG framework by defining its key components, including query processor, retriever, organizer, generator, and data source. Furthermore, recognizing that graphs in different domains exhibit distinct relational patterns and require dedicated designs, we review GraphRAG techniques uniquely tailored to each domain. Finally, we discuss research challenges and brainstorm directions to inspire cross-disciplinary opportunities. Our survey repository is publicly maintained at https://github.com/Graph-RAG/GraphRAG/.

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.

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

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

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.

Heterogeneous graph learning aims to capture complex relationships and diverse relational semantics among entities in a heterogeneous graph to obtain meaningful representations for nodes and edges. Recent advancements in heterogeneous graph neural networks (HGNNs) have achieved state-of-the-art performance by considering relation heterogeneity and using specialized message functions and aggregation rules. However, existing frameworks for heterogeneous graph learning have limitations in generalizing across diverse heterogeneous graph datasets. Most of these frameworks follow the "pre-train" and "fine-tune" paradigm on the same dataset, which restricts their capacity to adapt to new and unseen data. This raises the question: "Can we generalize heterogeneous graph models to be well-adapted to diverse downstream learning tasks with distribution shifts in both node token sets and relation type heterogeneity?'' To tackle those challenges, we propose HiGPT, a general large graph model with Heterogeneous graph instruction-tuning paradigm. Our framework enables learning from arbitrary heterogeneous graphs without the need for any fine-tuning process from downstream datasets. To handle distribution shifts in heterogeneity, we introduce an in-context heterogeneous graph tokenizer that captures semantic relationships in different heterogeneous graphs, facilitating model adaptation. We incorporate a large corpus of heterogeneity-aware graph instructions into our HiGPT, enabling the model to effectively comprehend complex relation heterogeneity and distinguish between various types of graph tokens. Furthermore, we introduce the Mixture-of-Thought (MoT) instruction augmentation paradigm to mitigate data scarcity by generating diverse and informative instructions. Through comprehensive evaluations, our proposed framework demonstrates exceptional performance in terms of generalization performance.

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.

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.

Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are essential, making prior methods potentially unsuitable in such contexts. Moreover, while trivial adaptations are available, empirical investigations reveal their limited efficacy as they do not properly model the interplay among graph components. To address this, we propose a joint score-based model of nodes and edges for graph generation that considers all graph components. Our approach offers two key novelties: (i) node and edge attributes are combined in an attention module that generates samples based on the two ingredients; and (ii) node, edge and adjacency information are mutually dependent during the graph diffusion process. We evaluate our method on challenging benchmarks involving real-world and synthetic datasets in which edge features are crucial. Additionally, we introduce a new synthetic dataset that incorporates edge values. Furthermore, we propose a novel application that greatly benefits from the method due to its nature: the generation of traffic scenes represented as graphs. Our method outperforms other graph generation methods, demonstrating a significant advantage in edge-related measures.

Despite significant advances in large-scale text-to-image models, achieving hyper-realistic human image generation remains a desirable yet unsolved task. Existing models like Stable Diffusion and DALL-E 2 tend to generate human images with incoherent parts or unnatural poses. To tackle these challenges, our key insight is that human image is inherently structural over multiple granularities, from the coarse-level body skeleton to fine-grained spatial geometry. Therefore, capturing such correlations between the explicit appearance and latent structure in one model is essential to generate coherent and natural human images. To this end, we propose a unified framework, HyperHuman, that generates in-the-wild human images of high realism and diverse layouts. Specifically, 1) we first build a large-scale human-centric dataset, named HumanVerse, which consists of 340M images with comprehensive annotations like human pose, depth, and surface normal. 2) Next, we propose a Latent Structural Diffusion Model that simultaneously denoises the depth and surface normal along with the synthesized RGB image. Our model enforces the joint learning of image appearance, spatial relationship, and geometry in a unified network, where each branch in the model complements to each other with both structural awareness and textural richness. 3) Finally, to further boost the visual quality, we propose a Structure-Guided Refiner to compose the predicted conditions for more detailed generation of higher resolution. Extensive experiments demonstrate that our framework yields the state-of-the-art performance, generating hyper-realistic human images under diverse scenarios. Project Page: https://snap-research.github.io/HyperHuman/

We present a distributed data structure, which we call the rainbow skip graph. To our knowledge, this is the first peer-to-peer data structure that simultaneously achieves high fault tolerance, constant-sized nodes, and fast update and query times for ordered data. It is a non-trivial adaptation of the SkipNet/skip-graph structures of Harvey et al. and Aspnes and Shah, so as to provide fault-tolerance as these structures do, but to do so using constant-sized nodes, as in the family tree structure of Zatloukal and Harvey. It supports successor queries on a set of n items using O(log n) messages with high probability, an improvement over the expected O(log n) messages of the family tree.

We propose SAM-Road, an adaptation of the Segment Anything Model (SAM) for extracting large-scale, vectorized road network graphs from satellite imagery. To predict graph geometry, we formulate it as a dense semantic segmentation task, leveraging the inherent strengths of SAM. The image encoder of SAM is fine-tuned to produce probability masks for roads and intersections, from which the graph vertices are extracted via simple non-maximum suppression. To predict graph topology, we designed a lightweight transformer-based graph neural network, which leverages the SAM image embeddings to estimate the edge existence probabilities between vertices. Our approach directly predicts the graph vertices and edges for large regions without expensive and complex post-processing heuristics, and is capable of building complete road network graphs spanning multiple square kilometers in a matter of seconds. With its simple, straightforward, and minimalist design, SAM-Road achieves comparable accuracy with the state-of-the-art method RNGDet++, while being 40 times faster on the City-scale dataset. We thus demonstrate the power of a foundational vision model when applied to a graph learning task. The code is available at https://github.com/htcr/sam_road.

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}

Knowledge graphs have been proven extremely useful in powering diverse applications in semantic search and natural language understanding. In this paper, we present GraphGen4Code, a toolkit to build code knowledge graphs that can similarly power various applications such as program search, code understanding, bug detection, and code automation. GraphGen4Code uses generic techniques to capture code semantics with the key nodes in the graph representing classes, functions, and methods. Edges indicate function usage (e.g., how data flows through function calls, as derived from program analysis of real code), and documentation about functions (e.g., code documentation, usage documentation, or forum discussions such as StackOverflow). Our toolkit uses named graphs in RDF to model graphs per program, or can output graphs as JSON. We show the scalability of the toolkit by applying it to 1.3 million Python files drawn from GitHub, 2,300 Python modules, and 47 million forum posts. This results in an integrated code graph with over 2 billion triples. We make the toolkit to build such graphs as well as the sample extraction of the 2 billion triples graph publicly available to the community for use.

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

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.

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.

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.

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

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.

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

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.

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

Realistic graphs contain both (1) rich self-features of nodes and (2) informative structures of neighborhoods, jointly handled by a Graph Neural Network (GNN) in the typical setup. We propose to decouple the two modalities by Mixture of weak and strong experts (Mowst), where the weak expert is a light-weight Multi-layer Perceptron (MLP), and the strong expert is an off-the-shelf GNN. To adapt the experts' collaboration to different target nodes, we propose a "confidence" mechanism based on the dispersion of the weak expert's prediction logits. The strong expert is conditionally activated in the low-confidence region when either the node's classification relies on neighborhood information, or the weak expert has low model quality. We reveal interesting training dynamics by analyzing the influence of the confidence function on loss: our training algorithm encourages the specialization of each expert by effectively generating soft splitting of the graph. In addition, our "confidence" design imposes a desirable bias toward the strong expert to benefit from GNN's better generalization capability. Mowst is easy to optimize and achieves strong expressive power, with a computation cost comparable to a single GNN. Empirically, Mowst on 4 backbone GNN architectures show significant accuracy improvement on 6 standard node classification benchmarks, including both homophilous and heterophilous graphs (https://github.com/facebookresearch/mowst-gnn).

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

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

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

Graph 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.

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques are often employed to map multiple entities to the same embedding and thus reduce the size of the embedding tables. Concurrently, graph-based collaborative signals have emerged as powerful tools in recommender systems, yet their potential for optimizing embedding table reduction remains unexplored. This paper introduces GraphHash, the first graph-based approach that leverages modularity-based bipartite graph clustering on user-item interaction graphs to reduce embedding table sizes. We demonstrate that the modularity objective has a theoretical connection to message-passing, which provides a foundation for our method. By employing fast clustering algorithms, GraphHash serves as a computationally efficient proxy for message-passing during preprocessing and a plug-and-play graph-based alternative to traditional ID hashing. Extensive experiments show that GraphHash substantially outperforms diverse hashing baselines on both retrieval and click-through-rate prediction tasks. In particular, GraphHash achieves on average a 101.52% improvement in recall when reducing the embedding table size by more than 75%, highlighting the value of graph-based collaborative information for model reduction. Our code is available at https://github.com/snap-research/GraphHash.

Acceleration of graph applications on GPUs has found large interest due to the ubiquitous use of graph processing in various domains. The inherent irregularity in graph applications leads to several challenges for parallelization. A key challenge, which we address in this paper, is that of load-imbalance. If the work-assignment to threads uses node-based graph partitioning, it can result in skewed task-distribution, leading to poor load-balance. In contrast, if the work-assignment uses edge-based graph partitioning, the load-balancing is better, but the memory requirement is relatively higher. This makes it unsuitable for large graphs. In this work, we propose three techniques for improved load-balancing of graph applications on GPUs. Each technique brings in unique advantages, and a user may have to employ a specific technique based on the requirement. Using Breadth First Search and Single Source Shortest Paths as our processing kernels, we illustrate the effectiveness of each of the proposed techniques in comparison to the existing node-based and edge-based mechanisms.

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.

Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of their capability are scarce, despite their empirical effectiveness in state-of-the-art recommender models. Recently, research has explored the expressiveness of GNNs in general, demonstrating that message passing GNNs are at most as powerful as the Weisfeiler-Lehman test, and that GNNs combined with random node initialization are universal. Nevertheless, the concept of "expressiveness" for GNNs remains vaguely defined. Most existing works adopt the graph isomorphism test as the metric of expressiveness, but this graph-level task may not effectively assess a model's ability in recommendation, where the objective is to distinguish nodes of different closeness. In this paper, we provide a comprehensive theoretical analysis of the expressiveness of GNNs in recommendation, considering three levels of expressiveness metrics: graph isomorphism (graph-level), node automorphism (node-level), and topological closeness (link-level). We propose the topological closeness metric to evaluate GNNs' ability to capture the structural distance between nodes, which aligns closely with the objective of recommendation. To validate the effectiveness of this new metric in evaluating recommendation performance, we introduce a learning-less GNN algorithm that is optimal on the new metric and can be optimal on the node-level metric with suitable modification. We conduct extensive experiments comparing the proposed algorithm against various types of state-of-the-art GNN models to explore the explainability of the new metric in the recommendation task. For reproducibility, implementation codes are available at https://github.com/HKUDS/GTE.

Hyperspectral sensors have enjoyed widespread use in the realm of remote sensing; however, they must be adapted to a format in which they can be operated onboard mobile robots. In this work, we introduce a first-of-its-kind system architecture with snapshot hyperspectral cameras and point spectrometers to efficiently generate composite datacubes from a robotic base. Our system collects and registers datacubes spanning the visible to shortwave infrared (660-1700 nm) spectrum while simultaneously capturing the ambient solar spectrum reflected off a white reference tile. We collect and disseminate a large dataset of more than 500 labeled datacubes from on-road and off-road terrain compliant with the ATLAS ontology to further the integration and demonstration of hyperspectral imaging (HSI) as beneficial in terrain class separability. Our analysis of this data demonstrates that HSI is a significant opportunity to increase understanding of scene composition from a robot-centric context. All code and data are open source online: https://river-lab.github.io/hyper_drive_data

Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at the origin of the hyperbolic space. This hybrid method greatly limits the modeling ability of networks. In this paper, we propose a fully hyperbolic framework to build hyperbolic networks based on the Lorentz model by adapting the Lorentz transformations (including boost and rotation) to formalize essential operations of neural networks. Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the capabilities of existing hyperbolic networks. The experimental results on four NLP tasks show that our method has better performance for building both shallow and deep networks. Our code will be released to facilitate follow-up research.

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.

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.

With the widespread use of mobile devices and the rapid growth of micro-video platforms such as TikTok and Kwai, the demand for personalized micro-video recommendation systems has significantly increased. Micro-videos typically contain diverse information, such as textual metadata, visual cues (e.g., cover images), and dynamic video content, significantly affecting user interaction and engagement patterns. However, most existing approaches often suffer from the problem of over-smoothing, which limits their ability to capture comprehensive interaction information effectively. Additionally, cold-start scenarios present ongoing challenges due to sparse interaction data and the underutilization of available interaction signals. To address these issues, we propose a Multi-view Hypergraph-based Contrastive learning model for cold-start micro-video Recommendation (MHCR). MHCR introduces a multi-view multimodal feature extraction layer to capture interaction signals from various perspectives and incorporates multi-view self-supervised learning tasks to provide additional supervisory signals. Through extensive experiments on two real-world datasets, we show that MHCR significantly outperforms existing video recommendation models and effectively mitigates cold-start challenges. Our code is available at https://github.com/sisuolv/MHCR.

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.

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

The success of deep learning notoriously requires larger amounts of costly annotated data. This has led to the development of self-supervised learning (SSL) that aims to alleviate this limitation by creating domain specific pretext tasks on unlabeled data. Simultaneously, there are increasing interests in generalizing deep learning to the graph domain in the form of graph neural networks (GNNs). GNNs can naturally utilize unlabeled nodes through the simple neighborhood aggregation that is unable to thoroughly make use of unlabeled nodes. Thus, we seek to harness SSL for GNNs to fully exploit the unlabeled data. Different from data instances in the image and text domains, nodes in graphs present unique structure information and they are inherently linked indicating not independent and identically distributed (or i.i.d.). Such complexity is a double-edged sword for SSL on graphs. On the one hand, it determines that it is challenging to adopt solutions from the image and text domains to graphs and dedicated efforts are desired. On the other hand, it provides rich information that enables us to build SSL from a variety of perspectives. Thus, in this paper, we first deepen our understandings on when, why, and which strategies of SSL work with GNNs by empirically studying numerous basic SSL pretext tasks on graphs. Inspired by deep insights from the empirical studies, we propose a new direction SelfTask to build advanced pretext tasks that are able to achieve state-of-the-art performance on various real-world datasets. The specific experimental settings to reproduce our results can be found in https://github.com/ChandlerBang/SelfTask-GNN.

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 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.

Recently, a series of diffusion-aware distillation algorithms have emerged to alleviate the computational overhead associated with the multi-step inference process of Diffusion Models (DMs). Current distillation techniques often dichotomize into two distinct aspects: i) ODE Trajectory Preservation; and ii) ODE Trajectory Reformulation. However, these approaches suffer from severe performance degradation or domain shifts. To address these limitations, we propose Hyper-SD, a novel framework that synergistically amalgamates the advantages of ODE Trajectory Preservation and Reformulation, while maintaining near-lossless performance during step compression. Firstly, we introduce Trajectory Segmented Consistency Distillation to progressively perform consistent distillation within pre-defined time-step segments, which facilitates the preservation of the original ODE trajectory from a higher-order perspective. Secondly, we incorporate human feedback learning to boost the performance of the model in a low-step regime and mitigate the performance loss incurred by the distillation process. Thirdly, we integrate score distillation to further improve the low-step generation capability of the model and offer the first attempt to leverage a unified LoRA to support the inference process at all steps. Extensive experiments and user studies demonstrate that Hyper-SD achieves SOTA performance from 1 to 8 inference steps for both SDXL and SD1.5. For example, Hyper-SDXL surpasses SDXL-Lightning by +0.68 in CLIP Score and +0.51 in Aes Score in the 1-step inference.

Solving image-to-3D from a single view is an ill-posed problem, and current neural reconstruction methods addressing it through diffusion models still rely on scene-specific optimization, constraining their generalization capability. To overcome the limitations of existing approaches regarding generalization and consistency, we introduce a novel neural rendering technique. Our approach employs the signed distance function as the surface representation and incorporates generalizable priors through geometry-encoding volumes and HyperNetworks. Specifically, our method builds neural encoding volumes from generated multi-view inputs. We adjust the weights of the SDF network conditioned on an input image at test-time to allow model adaptation to novel scenes in a feed-forward manner via HyperNetworks. To mitigate artifacts derived from the synthesized views, we propose the use of a volume transformer module to improve the aggregation of image features instead of processing each viewpoint separately. Through our proposed method, dubbed as Hyper-VolTran, we avoid the bottleneck of scene-specific optimization and maintain consistency across the images generated from multiple viewpoints. Our experiments show the advantages of our proposed approach with consistent results and rapid generation.

Long-context language models (LCLM), characterized by their extensive context window, is becoming increasingly popular. Meanwhile, many long-context benchmarks present challenging tasks that even the most advanced LCLMs struggle to complete. However, the underlying sources of various challenging long-context tasks have seldom been studied. To bridge this gap, we conduct experiments to indicate their difficulty stems primarily from two basic issues: "multi-matching retrieval," which requires the simultaneous retrieval of multiple items, and "logic-based retrieval," which necessitates logical judgment within retrieval criteria. These two problems, while seemingly straightforward, actually exceed the capabilities of LCLMs because they are proven to be hyper-multi-step (demanding numerous steps to solve) in nature. This finding could explain why LLMs struggle with more advanced long-context tasks, providing a more accurate perspective for rethinking solutions for them.

Massively multilingual models are promising for transfer learning across tasks and languages. However, existing methods are unable to fully leverage training data when it is available in different task-language combinations. To exploit such heterogeneous supervision, we propose Hyper-X, a single hypernetwork that unifies multi-task and multilingual learning with efficient adaptation. This model generates weights for adapter modules conditioned on both tasks and language embeddings. By learning to combine task and language-specific knowledge, our model enables zero-shot transfer for unseen languages and task-language combinations. Our experiments on a diverse set of languages demonstrate that Hyper-X achieves the best or competitive gain when a mixture of multiple resources is available, while being on par with strong baselines in the standard scenario. Hyper-X is also considerably more efficient in terms of parameters and resources compared to methods that train separate adapters. Finally, Hyper-X consistently produces strong results in few-shot scenarios for new languages, showing the versatility of our approach beyond zero-shot transfer.

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.

As a natural disaster, landslide often brings tremendous losses to human lives, so it urgently demands reliable detection of landslide risks. When detecting old landslides that present important information for landslide risk warning, problems such as visual blur and small-sized dataset cause great challenges when using remote sensing data. To extract accurate semantic features, a hyper-pixel-wise contrastive learning augmented segmentation network (HPCL-Net) is proposed, which augments the local salient feature extraction from boundaries of landslides through HPCL-Net and fuses heterogeneous infromation in the semantic space from high-resolution remote sensing images and digital elevation model data. For full utilization of precious samples, a global hyper-pixel-wise sample pair queues-based contrastive learning method is developed, which includes the construction of global queues that store hyper-pixel-wise samples and the updating scheme of a momentum encoder, reliably enhancing the extraction ability of semantic features. The proposed HPCL-Net is evaluated on the Loess Plateau old landslide dataset and experimental results verify that the proposed HPCL-Net greatly outperforms existing models, where the mIoU is increased from 0.620 to 0.651, the Landslide IoU is improved from 0.334 to 0.394 and the F1score is enhanced from 0.501 to 0.565.

Graph Neural Networks (GNNs) have shown great potential in the field of graph representation learning. Standard GNNs define a local message-passing mechanism which propagates information over the whole graph domain by stacking multiple layers. This paradigm suffers from two major limitations, over-squashing and poor long-range dependencies, that can be solved using global attention but significantly increases the computational cost to quadratic complexity. In this work, we propose an alternative approach to overcome these structural limitations by leveraging the ViT/MLP-Mixer architectures introduced in computer vision. We introduce a new class of GNNs, called Graph ViT/MLP-Mixer, that holds three key properties. First, they capture long-range dependency and mitigate the issue of over-squashing as demonstrated on Long Range Graph Benchmark and TreeNeighbourMatch datasets. Second, they offer better speed and memory efficiency with a complexity linear to the number of nodes and edges, surpassing the related Graph Transformer and expressive GNN models. Third, they show high expressivity in terms of graph isomorphism as they can distinguish at least 3-WL non-isomorphic graphs. We test our architecture on 4 simulated datasets and 7 real-world benchmarks, and show highly competitive results on all of them. The source code is available for reproducibility at: https://github.com/XiaoxinHe/Graph-ViT-MLPMixer.

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.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

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

Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

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.

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the k-dimensional Weisfeiler-Leman (kWL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the kWL test. A central focus of research in this field revolves around determining the least dimensionality k, for which kWL can discern graphs with different number of occurrences of a pattern graph P. We refer to such a least k as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern P. We additionally demonstrate that in cases where the kWL test distinguishes between graphs with varying occurrences of a pattern P, the exact number of occurrences of P can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern P, answering an open question from previous work.

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.

Hypercomplex neural networks have proven to reduce the overall number of parameters while ensuring valuable performance by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by involving efficient parameterized Kronecker products. In this paper, we define the parameterization of hypercomplex convolutional layers and introduce the family of parameterized hypercomplex neural networks (PHNNs) that are lightweight and efficient large-scale models. Our method grasps the convolution rules and the filter organization directly from data without requiring a rigidly predefined domain structure to follow. PHNNs are flexible to operate in any user-defined or tuned domain, from 1D to nD regardless of whether the algebra rules are preset. Such a malleability allows processing multidimensional inputs in their natural domain without annexing further dimensions, as done, instead, in quaternion neural networks for 3D inputs like color images. As a result, the proposed family of PHNNs operates with 1/n free parameters as regards its analog in the real domain. We demonstrate the versatility of this approach to multiple domains of application by performing experiments on various image datasets as well as audio datasets in which our method outperforms real and quaternion-valued counterparts. Full code is available at: https://github.com/eleGAN23/HyperNets.