Daily Papers

Companies, including market rivals, have long collaborated on the development of open source software (OSS), resulting in a tangle of co-operation and competition known as "open source co-opetition". While prior work investigates open source co-opetition in OSS projects that are hosted by vendor-neutral foundations, we have a limited understanding thereof in OSS projects that are hosted and governed by one company. Given their prevalence, it is timely to investigate open source co-opetition in such contexts. Towards this end, we conduct a mixed-methods analysis of three company-hosted OSS projects in the artificial intelligence (AI) industry: Meta's PyTorch (prior to its donation to the Linux Foundation), Google's TensorFlow, and Hugging Face's Transformers. We contribute three key findings. First, while the projects exhibit similar code authorship patterns between host and external companies (80%/20% of commits), collaborations are structured differently (e.g., decentralised vs. hub-and-spoke networks). Second, host and external companies engage in strategic, non-strategic, and contractual collaborations, with varying incentives and collaboration practices. Some of the observed collaborations are specific to the AI industry (e.g., hardware-software optimizations or AI model integrations), while others are typical of the broader software industry (e.g., bug fixing or task outsourcing). Third, single-vendor governance creates a power imbalance that influences open source co-opetition practices and possibilities, from the host company's singular decision-making power (e.g., the risk of license change) to their community involvement strategy (e.g., from over-control to over-delegation). We conclude with recommendations for future research.

This study addresses challenges in reverse logistics, a frequently overlooked but essential component of last-mile delivery, particularly in disaster relief scenarios where infrastructure disruptions demand adaptive solutions. While hub-and-spoke logistics networks excel at long-distance scalability, they often fail to optimize closely spaced spokes reliant on distant hubs, introducing inefficiencies in transit times and resource allocation. Using 20 Apple AirTags embedded in packages, this research provides empirical insights into logistical flows, capturing granular spatial and temporal data through Bluetooth LE (BLE) 5 trackers integrated with the Apple Find My network. These trackers demonstrated their value in monitoring dynamic cargo movements, enabling real-time adjustments in mobile hub placement and route optimization, particularly in disaster relief contexts like Hurricane Helene. A novel application of discrete event simulation (DES) further explored the saddle point in hub-spoke configurations, where excessive hub reliance clashes with diminishing spoke interaction demand. By coupling simulation results with empirical AirTag tracking, the study highlights the potential of BLE technology to refine reverse logistics, reduce delays, and improve operational flexibility in both routine and crisis-driven delivery networks.

Communication costs within Federated learning hinder the system scalability for reaching more data from more clients. The proposed FL adopts a hub-and-spoke network topology. All clients communicate through the central server. Hence, reducing communication overheads via techniques such as data compression has been proposed to mitigate this issue. Another challenge of federated learning is unbalanced data distribution, data on each client are not independent and identically distributed (non-IID) in a typical federated learning setting. In this paper, we proposed a new compression compensation scheme called Global Momentum Fusion (GMF) which reduces communication overheads between FL clients and the server and maintains comparable model accuracy in the presence of non-IID data. GitHub repository: https://github.com/tony92151/global-momentum-fusion-fl

Multimodal representation learning seeks shared representations for cross-modal retrieval and knowledge transfer. Hub-based binding reduces pairwise supervision costs, but separate hub connections cannot guarantee reliable alignment between modalities without direct joint training. We introduce Hub-Spectral Activation (HSA), a closed-form method for recovering and activating the hub-readable component of latent multimodal knowledge in frozen representations. We formalize this knowledge as source-induced cross-modal dependence and characterize the component determined by the second-order statistics of two trained hub edges. Under a second-order source model, we establish conditions for exact recovery of the complete source-induced relation and bound the dimension of its hub-readable component by the hub covariance rank. HSA composes and standardizes hub-edge statistics, extracts paired spectral directions, and combines reliability-weighted matching evidence with source-gated candidate resolution for bidirectional retrieval and prototype classification. HSA requires no target-pair supervision, gradient optimization, or backbone updates. Across 19 retrieval and 11 prototype-classification relations on ImageBind and LanguageBind, HSA raises mean bidirectional Recall@10 from 18.27% to 31.15% and mean macro Top-1 accuracy from 29.01% to 52.43%, respectively. Controlled analyses further identify valid hub-edge correspondence and leading spectral directions as key sources of retrieval gains, demonstrating the utility of latent multimodal knowledge beyond native similarity scores. Code and models are publicly available at https://github.com/Luo1Yan/HSA.

Modern language models can process inputs across diverse languages and modalities. We hypothesize that models acquire this capability through learning a shared representation space across heterogeneous data types (e.g., different languages and modalities), which places semantically similar inputs near one another, even if they are from different modalities/languages. We term this the semantic hub hypothesis, following the hub-and-spoke model from neuroscience (Patterson et al., 2007) which posits that semantic knowledge in the human brain is organized through a transmodal semantic "hub" which integrates information from various modality-specific "spokes" regions. We first show that model representations for semantically equivalent inputs in different languages are similar in the intermediate layers, and that this space can be interpreted using the model's dominant pretraining language via the logit lens. This tendency extends to other data types, including arithmetic expressions, code, and visual/audio inputs. Interventions in the shared representation space in one data type also predictably affect model outputs in other data types, suggesting that this shared representations space is not simply a vestigial byproduct of large-scale training on broad data, but something that is actively utilized by the model during input processing.

We present an agentic, autonomous graph expansion framework that iteratively structures and refines knowledge in situ. Unlike conventional knowledge graph construction methods relying on static extraction or single-pass learning, our approach couples a reasoning-native large language model with a continually updated graph representation. At each step, the system actively generates new concepts and relationships, merges them into a global graph, and formulates subsequent prompts based on its evolving structure. Through this feedback-driven loop, the model organizes information into a scale-free network characterized by hub formation, stable modularity, and bridging nodes that link disparate knowledge clusters. Over hundreds of iterations, new nodes and edges continue to appear without saturating, while centrality measures and shortest path distributions evolve to yield increasingly distributed connectivity. Our analysis reveals emergent patterns, such as the rise of highly connected 'hub' concepts and the shifting influence of 'bridge' nodes, indicating that agentic, self-reinforcing graph construction can yield open-ended, coherent knowledge structures. Applied to materials design problems, we present compositional reasoning experiments by extracting node-specific and synergy-level principles to foster genuinely novel knowledge synthesis, yielding cross-domain ideas that transcend rote summarization and strengthen the framework's potential for open-ended scientific discovery. We discuss other applications in scientific discovery and outline future directions for enhancing scalability and interpretability.

Semantic representations of text, i.e. representations of natural language which capture meaning by geometry, are essential for areas such as information retrieval and document grouping. High-dimensional trained dense vectors have received much attention in recent years as such representations. We investigate the structure of semantic spaces that arise from embeddings made with Sentence-BERT and find that the representations suffer from a well-known problem in high dimensions called hubness. Hubness results in asymmetric neighborhood relations, such that some texts (the hubs) are neighbours of many other texts while most texts (so-called anti-hubs), are neighbours of few or no other texts. We quantify the semantic quality of the embeddings using hubness scores and error rate of a neighbourhood based classifier. We find that when hubness is high, we can reduce error rate and hubness using hubness reduction methods. We identify a combination of two methods as resulting in the best reduction. For example, on one of the tested pretrained models, this combined method can reduce hubness by about 75% and error rate by about 9%. Thus, we argue that mitigating hubness in the embedding space provides better semantic representations of text.

Human mobility has a significant impact on several layers of society, from infrastructural planning and economics to the spread of diseases and crime. Representing the system as a complex network, in which nodes are assigned to regions (e.g., a city) and links indicate the flow of people between two of them, physics-inspired models have been proposed to quantify the number of people migrating from one city to the other. Despite the advances made by these models, our ability to predict the number of commuters and reconstruct mobility networks remains limited. Here, we propose an alternative approach using machine learning and 22 urban indicators to predict the flow of people and reconstruct the intercity commuters network. Our results reveal that predictions based on machine learning algorithms and urban indicators can reconstruct the commuters network with 90.4% of accuracy and describe 77.6% of the variance observed in the flow of people between cities. We also identify essential features to recover the network structure and the urban indicators mostly related to commuting patterns. As previously reported, distance plays a significant role in commuting, but other indicators, such as Gross Domestic Product (GDP) and unemployment rate, are also driven-forces for people to commute. We believe that our results shed new lights on the modeling of migration and reinforce the role of urban indicators on commuting patterns. Also, because link-prediction and network reconstruction are still open challenges in network science, our results have implications in other areas, like economics, social sciences, and biology, where node attributes can give us information about the existence of links connecting entities in the network.

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.

Multilingual embedding models are deployed under the assumption that cross-lingual retrieval is symmetric: if a query in language A retrieves its translation in language B, the reverse should also hold. In practice it does not. Using a parallel corpus of 6,518 idiomatic and proverbial expressions in English, Bangla, Hindi, and Arabic, embedded by five production-grade encoders (Gemini, Mistral, OpenAI-L, OpenAI-S, Qwen), we formalise this failure as a deficit in mutual nearest-neighbour reciprocity and test a single mechanistic claim: among the geometric pathologies of multilingual spaces, hubness, not anisotropy, centroid drift, or magnitude, is the dominant causal driver. Across five pre-registered experiments with falsification conditions specified in advance, hub mass dominates a joint regression on reciprocity (49.5% dominance share, 1.68x the next predictor; partial R^2 = 0.302 versus 0.003 for anisotropy), while a hub-aware score correction (CSLS) closes 63.5% of the worst-to-best reciprocity gap and yields a mean within-model effect size 130x larger than surgical hub-vector ablation. The latter contrast pinpoints the mechanism: hubness is a pathology of the similarity metric, not of individual hub vectors. We resolve the well-known anisotropy-hubness paradox by showing the two are statistically dissociable, and we recommend replacing cosine similarity with CSLS as the default retrieval metric for multilingual embedding pipelines.

Hypergraphs are widely being employed to represent complex higher-order relations in real-world applications. Most existing research on hypergraph learning focuses on node-level or edge-level tasks. A practically relevant and more challenging task, edge-dependent node classification (ENC), is still under-explored. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node features unique to each hyperedge. The state-of-the-art ENC solution, WHATsNet, only outputs single node and edge representations, leading to the limitations of entangled edge-specific features and non-adaptive representation sizes when applied to ENC. Additionally, WHATsNet suffers from the common oversmoothing issue in most HGNNs. To address these limitations, we propose CoNHD, a novel HGNN architecture specifically designed to model edge-specific features for ENC. Instead of learning separate representations for nodes and edges, CoNHD reformulates within-edge and within-node interactions as a hypergraph diffusion process over node-edge co-representations. We develop a neural implementation of the proposed diffusion process, leveraging equivariant networks as diffusion operators to effectively learn the diffusion dynamics from data. Extensive experiments demonstrate that CoNHD achieves the best performance across all benchmark ENC datasets and several downstream tasks without sacrificing efficiency. Our implementation is available at https://github.com/zhengyijia/CoNHD.

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

Recent advances in agent-mediated systems have enabled a new paradigm of social network simulation, where AI agents interact with human-like autonomy. This evolution has fostered the emergence of agent-driven social networks such as Moltbook, a Reddit-like platform populated entirely by AI agents. Despite these developments, empirical comparisons between agent-driven and human-driven social networks remain scarce, limiting our understanding of how their network topologies might diverge. This paper presents the first comparative analysis of network topology on Moltbook, utilizing a comment network comprising 33,577 nodes and 697,688 edges. To provide a benchmark, we curated a parallel dataset from Reddit consisting of 7.8 million nodes and 51.8 million edges. We examine key structural differences between agent-drive and human-drive networks, specifically focusing on topological patterns and the edge formation efficacy of their respective posts. Our findings provide a foundational profile of AI-driven social structures, serving as a preliminary step toward developing more robust and authentic agent-mediated social systems.

Complex networks provide a means to describe cities through their street mesh, expressing characteristics that refer to the structure and organization of an urban zone. Although other studies have used complex networks to model street meshes, we observed a lack of methods to characterize the relationship between cities by using their topological features. Accordingly, this paper aims to describe interactions between cities by using vectors of topological features extracted from their street meshes represented as complex networks. The methodology of this study is based on the use of digital maps. Over the computational representation of such maps, we extract global complex-network features that embody the characteristics of the cities. These vectors allow for the use of multidimensional projection and clustering techniques, enabling a similarity-based comparison of the street meshes. We experiment with 645 cities from the Brazilian state of Sao Paulo. Our results show how the joint of global features describes urban indicators that are deep-rooted in the network's topology and how they reveal characteristics and similarities among sets of cities that are separated from each other.

Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can be effectively modeled through temporal k-cores. This paper introduces a novel decentralized and incremental algorithm for computing the core decomposition of temporal networks. Decentralized solutions leverage the ability of network nodes to communicate and coordinate locally, addressing complex problems in a scalable, adaptive, and timely manner. By leveraging previously computed coreness values, our approach significantly reduces the activation of nodes and the volume of message exchanges when the network changes over time. This enables scalability with only a minimal trade-off in precision. Experimental evaluations on large real-world networks under varying levels of dynamism demonstrate the efficiency of our solution compared to a state-of-the-art approach, particularly in terms of active nodes, communication overhead, and convergence speed.

Inferring the full transportation network, including sidewalks and cycleways, is crucial for many automated systems, including autonomous driving, multi-modal navigation, trip planning, mobility simulations, and freight management. Many transportation decisions can be informed based on an accurate pedestrian network, its interactions, and connectivity with the road networks of other modes of travel. A connected pedestrian path network is vital to transportation activities, as sidewalks and crossings connect pedestrians to other modes of transportation. However, information about these paths' location and connectivity is often missing or inaccurate in city planning systems and wayfinding applications, causing severe information gaps and errors for planners and pedestrians. This work begins to address this problem at scale by introducing a novel dataset of aerial satellite imagery, street map imagery, and rasterized annotations of sidewalks, crossings, and corner bulbs in urban cities. The dataset spans 2,700 km^2 land area, covering select regions from 6 different cities. It can be used for various learning tasks related to segmenting and understanding pedestrian environments. We also present an end-to-end process for inferring a connected pedestrian path network map using street network information and our proposed dataset. The process features the use of a multi-input segmentation network trained on our dataset to predict important classes in the pedestrian environment and then generate a connected pedestrian path network. Our results demonstrate that the dataset is sufficiently large to train common segmentation models yielding accurate, robust pedestrian path networks.

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.

Smart cities will be characterized by a variety of intelligent and networked services, each with specific requirements for the underlying network infrastructure. While smart city architectures and services have been studied extensively, little attention has been paid to the network technology. The KIGLIS research project, consisting of a consortium of companies, universities and research institutions, focuses on artificial intelligence for optimizing fiber-optic networks of a smart city, with a special focus on future mobility applications, such as automated driving. In this paper, we present early results on our process of collecting smart city requirements for communication networks, which will lead towards reference infrastructure and architecture solutions. Finally, we suggest directions in which artificial intelligence will improve smart city networks.

Traffic prediction is essential for the progression of Intelligent Transportation Systems (ITS) and the vision of smart cities. While Spatial-Temporal Graph Neural Networks (STGNNs) have shown promise in this domain by leveraging Graph Neural Networks (GNNs) integrated with either RNNs or Transformers, they present challenges such as computational complexity, gradient issues, and resource-intensiveness. This paper addresses these challenges, advocating for three main solutions: a node-embedding approach, time series decomposition, and periodicity learning. We introduce STLinear, a minimalist model architecture designed for optimized efficiency and performance. Unlike traditional STGNNs, STlinear operates fully locally, avoiding inter-node data exchanges, and relies exclusively on linear layers, drastically cutting computational demands. Our empirical studies on real-world datasets confirm STLinear's prowess, matching or exceeding the accuracy of leading STGNNs, but with significantly reduced complexity and computation overhead (more than 95% reduction in MACs per epoch compared to state-of-the-art STGNN baseline published in 2023). In summary, STLinear emerges as a potent, efficient alternative to conventional STGNNs, with profound implications for the future of ITS and smart city initiatives.

From cells to cities, ecosystems to economies, complex networks exhibit peak intensities that define their empirical limit. Estimating these limits traditionally requires domain-specific knowledge. We demonstrate that a wide range of complex networks share a capacity frontier that constrains these maxima. We formalize this regularity by proposing Structural Capacity Theory for Network Substrate Structured Systems. These systems couple a fixed network substrate with an observable dynamical process. The frontier is learned from a vector representation of the network substrate and modulated log-additively by a vector representation of the dynamical process. Frontiers trained on one set of domains reliably bound empirical maxima of entirely different ones without observing their peak intensities or simulating their dynamics. Independent learning paradigms converge on consistent upper bounds. Frontier performance is stable under perturbation, yet degrades under deliberate falsification, with no performance gain under ablation. These findings support the capacity frontier as a generalizable constraint that describes how network structure bounds dynamical processes across otherwise unrelated systems.

Recent advancements in large language models (LLMs) and their multimodal variants have led to remarkable progress across various domains, demonstrating impressive capabilities and unprecedented potential. In the era of ubiquitous connectivity, leveraging communication networks to distribute intelligence is a transformative concept, envisioning AI-powered services accessible at the network edge. However, pushing large models from the cloud to resource-constrained environments faces critical challenges. Model inference on low-end devices leads to excessive latency and performance bottlenecks, while raw data transmission over limited bandwidth networks causes high communication overhead. This article presents AI Flow, a framework that streamlines the inference process by jointly leveraging the heterogeneous resources available across devices, edge nodes, and cloud servers, making intelligence flow across networks. To facilitate cooperation among multiple computational nodes, the proposed framework explores a paradigm shift in the design of communication network systems from transmitting information flow to intelligence flow, where the goal of communications is task-oriented and folded into the inference process. Experimental results demonstrate the effectiveness of the proposed framework through an image captioning use case, showcasing the ability to reduce response latency while maintaining high-quality captions. This article serves as a position paper for identifying the motivation, challenges, and principles of AI Flow.

Information flows by routes inside the network via mechanisms implemented in the model. These routes can be represented as graphs where nodes correspond to token representations and edges to operations inside the network. We automatically build these graphs in a top-down manner, for each prediction leaving only the most important nodes and edges. In contrast to the existing workflows relying on activation patching, we do this through attribution: this allows us to efficiently uncover existing circuits with just a single forward pass. Additionally, the applicability of our method is far beyond patching: we do not need a human to carefully design prediction templates, and we can extract information flow routes for any prediction (not just the ones among the allowed templates). As a result, we can talk about model behavior in general, for specific types of predictions, or different domains. We experiment with Llama 2 and show that the role of some attention heads is overall important, e.g. previous token heads and subword merging heads. Next, we find similarities in Llama 2 behavior when handling tokens of the same part of speech. Finally, we show that some model components can be specialized on domains such as coding or multilingual texts.

Despite the impressive advancements of Large Language Models (LLMs) in generating text, they are often limited by the knowledge contained in the input and prone to producing inaccurate or hallucinated content. To tackle these issues, Retrieval-augmented Generation (RAG) is employed as an effective strategy to enhance the available knowledge base and anchor the responses in reality by pulling additional texts from external databases. In real-world applications, texts are often linked through entities within a graph, such as citations in academic papers or comments in social networks. This paper exploits these topological relationships to guide the retrieval process in RAG. Specifically, we explore two kinds of topological connections: proximity-based, focusing on closely connected nodes, and role-based, which looks at nodes sharing similar subgraph structures. Our empirical research confirms their relevance to text relationships, leading us to develop a Topology-aware Retrieval-augmented Generation framework. This framework includes a retrieval module that selects texts based on their topological relationships and an aggregation module that integrates these texts into prompts to stimulate LLMs for text generation. We have curated established text-attributed networks and conducted comprehensive experiments to validate the effectiveness of this framework, demonstrating its potential to enhance RAG with topological awareness.

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

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

Graph Neural Networks (GNNs) have become vital in applications like document classification in citation networks, epidemic forecasting, viral marketing, user recommendation in social networks, and network monitoring. However, their deployment faces three key challenges: feature oversmoothing in deep architectures, poor handling of heterogeneous relationships, and monolithic feature aggregation. To address these, we introduce AxelGNN, a novel architecture based on Axelrod's cultural dissemination model that incorporates three key innovations: (1) similarity-gated interactions that adaptively promote convergence or divergence based on feature similarity, (2) segment-wise feature copying that enables fine-grained aggregation of semantic feature groups rather than monolithic vectors, and (3) global polarization that maintains multiple distinct representation clusters to prevent oversmoothing. This model demonstrates empirically the capability to handle both homophilic and heterophilic graphs within a single architecture, without requiring specialized model selection based on graph characteristics. Our experiments demonstrate that AxelGNN achieves competitive or superior performance compared to existing methods in node classification and influence estimation while maintaining computational efficiency.

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.

Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in short-term traffic forecasting, their performance in long-term predictions remains limited. This challenge arises from over-squashing problem, where bottlenecks and limited receptive fields restrict information flow and hinder the modeling of global dependencies. To address these challenges, this study introduces a novel framework that incorporates virtual nodes, which are additional nodes added to the graph and connected to existing nodes, in order to aggregate information across the entire graph within a single GNN layer. Our proposed model incorporates virtual nodes by constructing a semi-adaptive adjacency matrix. This matrix integrates distance-based and adaptive adjacency matrices, allowing the model to leverage geographical information while also learning task-specific features from data. Experimental results demonstrate that the inclusion of virtual nodes significantly enhances long-term prediction accuracy while also improving layer-wise sensitivity to mitigate the over-squashing problem. Virtual nodes also offer enhanced explainability by focusing on key intersections and high-traffic areas, as shown by the visualization of their adjacency matrix weights on road network heat maps. Our advanced approach enhances the understanding and management of urban traffic systems, making it particularly well-suited for real-world applications.

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

Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While Large Language Models (LLMs) offer inferential capabilities, they often depend on retrieval-augmented contexts that lack structural depth. Traditional Knowledge Graphs (KGs) attempt to bridge this gap, yet their pairwise constraints fail to capture the irreducible higher-order interactions that govern emergent physical behavior. To address this, we introduce a methodology for constructing hypergraph-based knowledge representations that faithfully encode multi-entity relationships. Applied to a corpus of ~1,100 manuscripts on biocomposite scaffolds, our framework constructs a global hypergraph of 161,172 nodes and 320,201 hyperedges, revealing a scale-free topology (power law exponent ~1.23) organized around highly connected conceptual hubs. This representation prevents the combinatorial explosion typical of pairwise expansions and explicitly preserves the co-occurrence context of scientific formulations. We further demonstrate that equipping agentic systems with hypergraph traversal tools, specifically using node-intersection constraints, enables them to bridge semantically distant concepts. By exploiting these higher-order pathways, the system successfully generates grounded mechanistic hypotheses for novel composite materials, such as linking cerium oxide to PCL scaffolds via chitosan intermediates. This work establishes a "teacherless" agentic reasoning system where hypergraph topology acts as a verifiable guardrail, accelerating scientific discovery by uncovering relationships obscured by traditional graph methods.

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

Graph Convolutional Neural Networks (GCNs) possess strong capabilities for processing graph data in non-grid domains. They can capture the topological logical structure and node features in graphs and integrate them into nodes' final representations. GCNs have been extensively studied in various fields, such as recommendation systems, social networks, and protein molecular structures. With the increasing application of graph neural networks, research has focused on improving their performance while compressing their size. In this work, a plug-in module named Graph Knowledge Enhancement and Distillation Module (GKEDM) is proposed. GKEDM can enhance node representations and improve the performance of GCNs by extracting and aggregating graph information via multi-head attention mechanism. Furthermore, GKEDM can serve as an auxiliary transferor for knowledge distillation. With a specially designed attention distillation method, GKEDM can distill the knowledge of large teacher models into high-performance and compact student models. Experiments on multiple datasets demonstrate that GKEDM can significantly improve the performance of various GCNs with minimal overhead. Furthermore, it can efficiently transfer distilled knowledge from large teacher networks to small student networks via attention distillation.

We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics (e.g. number of common friends) enter the link formation equation, while the mapping from model primitives to equilibrium network structure is generally intractable. Our approach sidesteps this difficulty using a ``bounding-by-c'' technique that treats endogenous covariates as random variables and exploits monotonicity restrictions to obtain identifying information. A central contribution is to develop a spectrum of fixed-effects handling strategies based on subnetwork configurations: tetrad-based restrictions that difference out all individual fixed effects, triad-based and weighted restrictions that combine ``difference-out'' and ``integrate-out'' steps by differencing out some fixed effects and profiling over the remainder conditional on observed characteristics, and general weighted cycle-based restrictions that unify these cases. We also provide point identification results. Preliminary simulations show that the approach can deliver informative bounds on the structural parameters.

Cross-modal retrieval aims to bridge the semantic gap between different modalities, such as visual and textual data, enabling accurate retrieval across them. Despite significant advancements with models like CLIP that align cross-modal representations, a persistent challenge remains: the hubness problem, where a small subset of samples (hubs) dominate as nearest neighbors, leading to biased representations and degraded retrieval accuracy. Existing methods often mitigate hubness through post-hoc normalization techniques, relying on prior data distributions that may not be practical in real-world scenarios. In this paper, we directly mitigate hubness during training and introduce NeighborRetr, a novel method that effectively balances the learning of hubs and adaptively adjusts the relations of various kinds of neighbors. Our approach not only mitigates the hubness problem but also enhances retrieval performance, achieving state-of-the-art results on multiple cross-modal retrieval benchmarks. Furthermore, NeighborRetr demonstrates robust generalization to new domains with substantial distribution shifts, highlighting its effectiveness in real-world applications. We make our code publicly available at: https://github.com/zzezze/NeighborRetr .

We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating walks as the equivalent of sentences. We demonstrate DeepWalk's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube. Our results show that DeepWalk outperforms challenging baselines which are allowed a global view of the network, especially in the presence of missing information. DeepWalk's representations can provide F_1 scores up to 10% higher than competing methods when labeled data is sparse. In some experiments, DeepWalk's representations are able to outperform all baseline methods while using 60% less training data. DeepWalk is also scalable. It is an online learning algorithm which builds useful incremental results, and is trivially parallelizable. These qualities make it suitable for a broad class of real world applications such as network classification, and anomaly detection.

Graph Neural Networks (GNNs) are popular models for machine learning on graphs that typically follow the message-passing paradigm, whereby the feature of a node is updated recursively upon aggregating information over its neighbors. While exchanging messages over the input graph endows GNNs with a strong inductive bias, it can also make GNNs susceptible to over-squashing, thereby preventing them from capturing long-range interactions in the given graph. To rectify this issue, graph rewiring techniques have been proposed as a means of improving information flow by altering the graph connectivity. In this work, we identify three desiderata for graph-rewiring: (i) reduce over-squashing, (ii) respect the locality of the graph, and (iii) preserve the sparsity of the graph. We highlight fundamental trade-offs that occur between spatial and spectral rewiring techniques; while the former often satisfy (i) and (ii) but not (iii), the latter generally satisfy (i) and (iii) at the expense of (ii). We propose a novel rewiring framework that satisfies all of (i)--(iii) through a locality-aware sequence of rewiring operations. We then discuss a specific instance of such rewiring framework and validate its effectiveness on several real-world benchmarks, showing that it either matches or significantly outperforms existing rewiring approaches.

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms -- learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space (d_{space} = 64), requiring 80% fewer routing parameters than standard linear routers. Through 62 controlled experiments on WikiText-103 at 76--84M parameters trained to convergence (50K steps, 1.64B tokens), we find that routing topology does not determine asymptotic perplexity (PPL): five cosine-routing variants are statistically equivalent within a 1-PPL margin (Two One-Sided Tests [TOST], p < 0.05 for all 10 pairwise comparisons; 15 runs across 3 seeds, observed range 33.93--34.72). The finding extends to hash, random-fixed, and top-1 routing (single-seed; graceful 1.1--2.2 PPL degradation) and replicates on OpenWebText (0.03 PPL gap, 6 runs, 3 seeds each). A standard linear router with 5.3times more routing parameters reaches PPL 32.76, but iso-parameter cosine routing closes 67% of this gap -- the true mechanism advantage is sim1.2%. The mechanistic explanation is convergent redundancy: multi-hop updates are collinear (cos(Δh_0, Δh_1) = 0.805), implementing magnitude amplification rather than compositional reasoning; a single learnable scalar replicates multi-hop performance. As a practical payoff, zero-shot relative-norm halting saves 25% of MoE FLOPs at +0.12% PPL. Expert-level specialization and causal controllability -- which coexist with topology-level equifinality -- are explored in a companion paper.

Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes. However, a major issue of those generalizations is that the calculation of such paths is computationally expensive. Addressing this issue, we study the application of De Bruijn Graph Neural Networks (DBGNN), a causality-aware graph neural network architecture, to predict temporal path-based centralities in time series data. We experimentally evaluate our approach in 13 temporal graphs from biological and social systems and show that it considerably improves the prediction of both betweenness and closeness centrality compared to a static Graph Convolutional Neural Network.

Graph neural networks (GNNs) have shown great potential in learning on graphs, but they are known to perform sub-optimally on link prediction tasks. Existing GNNs are primarily designed to learn node-wise representations and usually fail to capture pairwise relations between target nodes, which proves to be crucial for link prediction. Recent works resort to learning more expressive edge-wise representations by enhancing vanilla GNNs with structural features such as labeling tricks and link prediction heuristics, but they suffer from high computational overhead and limited scalability. To tackle this issue, we propose to learn structural link representations by augmenting the message-passing framework of GNNs with Bloom signatures. Bloom signatures are hashing-based compact encodings of node neighborhoods, which can be efficiently merged to recover various types of edge-wise structural features. We further show that any type of neighborhood overlap-based heuristic can be estimated by a neural network that takes Bloom signatures as input. GNNs with Bloom signatures are provably more expressive than vanilla GNNs and also more scalable than existing edge-wise models. Experimental results on five standard link prediction benchmarks show that our proposed model achieves comparable or better performance than existing edge-wise GNN models while being 3-200 times faster and more memory-efficient for online inference.

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.

Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across most datasets.

Graphs are ubiquitous structures found in numerous real-world applications, such as drug discovery, recommender systems, and social network analysis. To model graph-structured data, graph neural networks (GNNs) have become a popular tool. However, existing GNN architectures encounter challenges in cross-graph learning where multiple graphs have different feature spaces. To address this, recent approaches introduce text-attributed graphs (TAGs), where each node is associated with a textual description, which can be projected into a unified feature space using textual encoders. While promising, this method relies heavily on the availability of text-attributed graph data, which is difficult to obtain in practice. To bridge this gap, we propose a novel method named Topology-Aware Node description Synthesis (TANS), leveraging large language models (LLMs) to convert existing graphs into text-attributed graphs. The key idea is to integrate topological information into LLMs to explain how graph topology influences node semantics. We evaluate our TANS on text-rich, text-limited, and text-free graphs, demonstrating its applicability. Notably, on text-free graphs, our method significantly outperforms existing approaches that manually design node features, showcasing the potential of LLMs for preprocessing graph-structured data in the absence of textual information. The code and data are available at https://github.com/Zehong-Wang/TANS.

Understanding where people go after visiting one business is crucial for urban planning, retail analytics, and location-based services. However, predicting these co-visitation patterns across millions of venues remains challenging due to extreme data sparsity and the complex interplay between spatial proximity and business relationships. Traditional approaches using only geographic distance fail to capture why coffee shops attract different customer flows than fine dining restaurants, even when co-located. We introduce NAICS-aware GraphSAGE, a novel graph neural network that integrates business taxonomy knowledge through learnable embeddings to predict population-scale co-visitation patterns. Our key insight is that business semantics, captured through detailed industry codes, provide crucial signals that pure spatial models cannot explain. The approach scales to massive datasets (4.2 billion potential venue pairs) through efficient state-wise decomposition while combining spatial, temporal, and socioeconomic features in an end-to-end framework. Evaluated on our POI-Graph dataset comprising 94.9 million co-visitation records across 92,486 brands and 48 US states, our method achieves significant improvements over state-of-the-art baselines: the R-squared value increases from 0.243 to 0.625 (a 157 percent improvement), with strong gains in ranking quality (32 percent improvement in NDCG at 10).

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

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Graph Neural Networks (GNNs) are powerful tools for processing relational data but often struggle to generalize to unseen graphs, giving rise to the development of Graph Foundational Models (GFMs). However, current GFMs are challenged by the extreme heterogeneity of graph data, where each graph can possess a unique feature space, label set, and topology. To address this, two main paradigms have emerged. The first leverages Large Language Models (LLMs), but is fundamentally text-dependent, thus struggles to handle the numerical features in vast graphs. The second pre-trains a structure-based model, but the adaptation to new tasks typically requires a costly, per-graph tuning stage, creating a critical efficiency bottleneck. In this work, we move beyond these limitations and introduce Graph In-context Learning Transformer (GILT), a framework built on an LLM-free and tuning-free architecture. GILT introduces a novel token-based framework for in-context learning (ICL) on graphs, reframing classification tasks spanning node, edge and graph levels in a unified framework. This mechanism is the key to handling heterogeneity, as it is designed to operate on generic numerical features. Further, its ability to understand class semantics dynamically from the context enables tuning-free adaptation. Comprehensive experiments show that GILT achieves stronger few-shot performance with significantly less time than LLM-based or tuning-based baselines, validating the effectiveness of our approach. Our code is available at: https://github.com/yiming421/inductnode/.

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

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.

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.

This study examines cross-asset connectedness in an international financial network of major exchange rates, gold futures, and Bitcoin. Moving beyond the conventional net transmitter--receiver classification, we characterize asset roles through three complementary dimensions: direct spillover transmission, stationary source-tracing dynamics, and multistep upstream connectivity. Return spillovers are estimated using VAR generalized forecast-error variance decomposition (VAR-GFEVD). The positive pairwise net-spillover structure is then mapped into a row-stochastic Markov kernel whose transitions trace dominant net-spillover sources in the reverse direction of the original transmission edges. A stationary departure flux describes long-run movement in this source-tracing chain, while Viral Centrality is evaluated by the deterministic probability-propagation algorithm of Fink et al. to approximate multistep upstream reach. Empirically, gold futures emerge as the dominant direct net transmitter and the leading stationary source-tracing node, but do not have the largest Viral Centrality. Several exchange-rate nodes classified as direct net receivers have relatively high Viral Centrality, indicating broad conditional access to upstream source nodes. Bitcoin occupies an intermediate role. An auxiliary specification including the U.S. Dollar Index yields qualitatively similar role differentiation. The results show that direct connectedness, stationary source tracing, and approximate multistep upstream reach cannot be inferred from NET spillovers alone. All diffusion interpretations are descriptive and conditional on the estimated network, row normalization, and restart closure.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis (TDA) paradigm, of which real-world data exhibits multi-scale patterns, we construct several graphs using Persistent Homology Filtration -- a mathematical framework describing the multiscale structural properties of data points. Then, we use the constructed graphs as an input to create an ensemble of Graph Neural Networks. The ensemble aggregates the signals from the individual learners via an attention-based routing mechanism, thus systematically encoding the inherent multiscale structures of data. Four different real-world experiments on seismic activity prediction and traffic forecasting (PEMS-BAY, METR-LA) demonstrate that our approach consistently outperforms single-graph baselines while providing interpretable insights.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

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.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.

Large populations of AI agents are increasingly embedded in online environments, yet little is known about how their collective interaction patterns compare to human social systems. Here, we analyze the full interaction network of Moltbook, a platform where AI agents and humans coexist, and systematically compare its structure to well-characterized human communication networks. Although Moltbook follows the same node-edge scaling relationship observed in human systems, indicating comparable global growth constraints, its internal organization diverges markedly. The network exhibits extreme attention inequality, heavy-tailed and asymmetric degree distributions, suppressed reciprocity, and a global under-representation of connected triadic structures. Community analysis reveals a structured modular architecture with elevated modularity and comparatively lower community size inequality relative to degree-preserving null models. Together, these findings show that AI-agent societies can reproduce global structural regularities of human networks while exhibiting fundamentally different internal organizing principles, highlighting that key features of human social organization are not universal but depend on the nature of the interacting agents.

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

Traffic forecasting has emerged as a core component of intelligent transportation systems. However, timely accurate traffic forecasting, especially long-term forecasting, still remains an open challenge due to the highly nonlinear and dynamic spatial-temporal dependencies of traffic flows. In this paper, we propose a novel paradigm of Spatial-Temporal Transformer Networks (STTNs) that leverages dynamical directed spatial dependencies and long-range temporal dependencies to improve the accuracy of long-term traffic forecasting. Specifically, we present a new variant of graph neural networks, named spatial transformer, by dynamically modeling directed spatial dependencies with self-attention mechanism to capture realtime traffic conditions as well as the directionality of traffic flows. Furthermore, different spatial dependency patterns can be jointly modeled with multi-heads attention mechanism to consider diverse relationships related to different factors (e.g. similarity, connectivity and covariance). On the other hand, the temporal transformer is utilized to model long-range bidirectional temporal dependencies across multiple time steps. Finally, they are composed as a block to jointly model the spatial-temporal dependencies for accurate traffic prediction. Compared to existing works, the proposed model enables fast and scalable training over a long range spatial-temporal dependencies. Experiment results demonstrate that the proposed model achieves competitive results compared with the state-of-the-arts, especially forecasting long-term traffic flows on real-world PeMS-Bay and PeMSD7(M) datasets.

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only manually define a single-value edge to describe the connectivity or strength of association between a pair of vertices, task-specific and crucial relationship cues may be disregarded by such manually defined topology and single-value edge features. In this paper, we propose the first general graph representation learning framework (called GRATIS) which can generate a strong graph representation with a task-specific topology and task-specific multi-dimensional edge features from any arbitrary input. To learn each edge's presence and multi-dimensional feature, our framework takes both of the corresponding vertices pair and their global contextual information into consideration, enabling the generated graph representation to have a globally optimal message passing mechanism for different down-stream tasks. The principled investigation results achieved for various graph analysis tasks on 11 graph and non-graph datasets show that our GRATIS can not only largely enhance pre-defined graphs but also learns a strong graph representation for non-graph data, with clear performance improvements on all tasks. In particular, the learned topology and multi-dimensional edge features provide complementary task-related cues for graph analysis tasks. Our framework is effective, robust and flexible, and is a plug-and-play module that can be combined with different backbones and Graph Neural Networks (GNNs) to generate a task-specific graph representation from various graph and non-graph data. Our code is made publicly available at https://github.com/SSYSteve/Learning-Graph-Representation-with-Task-specific-Topology-and-Multi-dimensional-Edge-Features.

Text-attributed graphs (TAGs) present unique challenges in representation learning by requiring models to capture both the semantic richness of node-associated texts and the structural dependencies of the graph. While graph neural networks (GNNs) excel at modeling topological information, they lack the capacity to process unstructured text. Conversely, large language models (LLMs) are proficient in text understanding but are typically unaware of graph structure. In this work, we propose BiGTex (Bidirectional Graph Text), a novel architecture that tightly integrates GNNs and LLMs through stacked Graph-Text Fusion Units. Each unit allows for mutual attention between textual and structural representations, enabling information to flow in both directions, text influencing structure and structure guiding textual interpretation. The proposed architecture is trained using parameter-efficient fine-tuning (LoRA), keeping the LLM frozen while adapting to task-specific signals. Extensive experiments on five benchmark datasets demonstrate that BiGTex achieves state-of-the-art performance in node classification and generalizes effectively to link prediction. An ablation study further highlights the importance of soft prompting and bi-directional attention in the model's success.

Multi-scenario route ranking (MSRR) is crucial in many industrial mapping systems. However, the industrial community mainly adopts interactive interfaces to encourage users to select pre-defined scenarios, which may hinder the downstream ranking performance. In addition, in the academic community, the multi-scenario ranking works only come from other fields, and there are no works specifically focusing on route data due to lacking a publicly available MSRR dataset. Moreover, all the existing multi-scenario works still fail to address the three specific challenges of MSRR simultaneously, i.e. explosion of scenario number, high entanglement, and high-capacity demand. Different from the prior, to address MSRR, our key idea is to factorize the complicated scenario in route ranking into several disentangled factor scenario patterns. Accordingly, we propose a novel method, Disentangled Scenario Factorization Network (DSFNet), which flexibly composes scenario-dependent parameters based on a high-capacity multi-factor-scenario-branch structure. Then, a novel regularization is proposed to induce the disentanglement of factor scenarios. Furthermore, two extra novel techniques, i.e. scenario-aware batch normalization and scenario-aware feature filtering, are developed to improve the network awareness of scenario representation. Additionally, to facilitate MSRR research in the academic community, we propose MSDR, the first large-scale publicly available annotated industrial Multi-Scenario Driving Route dataset. Comprehensive experimental results demonstrate the superiority of our DSFNet, which has been successfully deployed in AMap to serve the major online traffic.

Training large and highly accurate deep learning (DL) models is computationally costly. This cost is in great part due to the excessive number of trained parameters, which are well-known to be redundant and compressible for the execution phase. This paper proposes a novel transformation which changes the topology of the DL architecture such that it reaches an optimal cross-layer connectivity. This transformation leverages our important observation that for a set level of accuracy, convergence is fastest when network topology reaches the boundary of a Small-World Network. Small-world graphs are known to possess a specific connectivity structure that enables enhanced signal propagation among nodes. Our small-world models, called SWNets, provide several intriguing benefits: they facilitate data (gradient) flow within the network, enable feature-map reuse by adding long-range connections and accommodate various network architectures/datasets. Compared to densely connected networks (e.g., DenseNets), SWNets require a substantially fewer number of training parameters while maintaining a similar level of classification accuracy. We evaluate our networks on various DL model architectures and image classification datasets, namely, CIFAR10, CIFAR100, and ILSVRC (ImageNet). Our experiments demonstrate an average of ~2.1x improvement in convergence speed to the desired accuracy

The ongoing development of Lean 4's Mathlib has produced a macroscopic structural complexity that interweaves logical, mathematical, and infrastructural dependencies. We present a network analysis of this library, extracting its dependency structure into a multilayer graph of 308,129 declarations, 8.4 million edges, and 7,563 modules. By introducing graph decompositions that isolate explicit edges from those synthesized by the compiler or driven by proofs, we quantify the structural properties of formalized mathematics. Our analysis reveals three findings. First, taxonomies designed by humans diverge from logical structures, exhibiting a 50.9% coupling across namespaces. Second, developers utilize a median of 1.6% of the imported scope. Third, formalization compresses semantic hierarchies, with network centrality capturing language infrastructure rather than mathematical relevance.

In this paper, we present a new MTL framework that searches for structures optimized for multiple tasks with diverse graph topologies and shares features among tasks. We design a restricted DAG-based central network with read-in/read-out layers to build topologically diverse task-adaptive structures while limiting search space and time. We search for a single optimized network that serves as multiple task adaptive sub-networks using our three-stage training process. To make the network compact and discretized, we propose a flow-based reduction algorithm and a squeeze loss used in the training process. We evaluate our optimized network on various public MTL datasets and show ours achieves state-of-the-art performance. An extensive ablation study experimentally validates the effectiveness of the sub-module and schemes in our framework.

The R-Learner is a powerful, theoretically-grounded framework for estimating heterogeneous treatment effects, prized for its robustness to nuisance model errors. However, its application to network data, where causal heterogeneity is often graph-dependent, presents a critical challenge to its core assumption of a well-specified final-stage model. In this paper, we conduct a large-scale empirical study to systematically dissect the R-Learner framework on graphs. We provide the first rigorous evidence that the primary driver of performance is the inductive bias of the final-stage CATE estimator, an effect that dominates the choice of nuisance models. Our central finding is the quantification of a catastrophic "representation bottleneck": we prove with overwhelming statistical significance (p < 0.001) that R-Learners with a graph-blind final stage fail completely (MSE > 4.0), even when paired with powerful GNN nuisance models. Conversely, our proposed end-to-end Graph R-Learner succeeds and significantly outperforms a strong, non-DML GNN T-Learner baseline. Furthermore, we identify and provide a mechanistic explanation for a subtle, topology-dependent "nuisance bottleneck," linking it to GNN over-squashing via a targeted "Hub-Periphery Trade-off" analysis. Our findings are validated across diverse synthetic and semi-synthetic benchmarks. We release our code as a reproducible benchmark to facilitate future research on this critical "final-stage bottleneck."

Signed networks allow us to model conflicting relationships and interactions, such as friend/enemy and support/oppose. These signed interactions happen in real-time. Modeling such dynamics of signed networks is crucial to understanding the evolution of polarization in the network and enabling effective prediction of the signed structure (i.e., link signs and signed weights) in the future. However, existing works have modeled either (static) signed networks or dynamic (unsigned) networks but not dynamic signed networks. Since both sign and dynamics inform the graph structure in different ways, it is non-trivial to model how to combine the two features. In this work, we propose a new Graph Neural Network (GNN)-based approach to model dynamic signed networks, named SEMBA: Signed link's Evolution using Memory modules and Balanced Aggregation. Here, the idea is to incorporate the signs of temporal interactions using separate modules guided by balance theory and to evolve the embeddings from a higher-order neighborhood. Experiments on 4 real-world datasets and 4 different tasks demonstrate that SEMBA consistently and significantly outperforms the baselines by up to 80% on the tasks of predicting signs of future links while matching the state-of-the-art performance on predicting the existence of these links in the future. We find that this improvement is due specifically to the superior performance of SEMBA on the minority negative class.

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.

Modeling networks as different graph types and researching on route finding strategies, to avoid congestion in dense subnetworks via graph-theoretic approaches, contributes to overall blocking probability reduction in networks. Our main focus is to study methods for modeling congested subnetworks and graph density measures, in order to identify routes that avoid dense subgraphs for global congestion avoidance, along with covering related algorithmic issues.

Modeling and estimating mixed memberships for overlapping unipartite un-weighted networks has been well studied in recent years. However, to our knowledge, there is no model for a more general case, the overlapping bipartite weighted networks. To close this gap, we introduce a novel model, the Bipartite Mixed Membership Distribution-Free (BiMMDF) model. Our model allows an adjacency matrix to follow any distribution as long as its expectation has a block structure related to node membership. In particular, BiMMDF can model overlapping bipartite signed networks and it is an extension of many previous models, including the popular mixed membership stochastic blcokmodels. An efficient algorithm with a theoretical guarantee of consistent estimation is applied to fit BiMMDF. We then obtain the separation conditions of BiMMDF for different distributions. Furthermore, we also consider missing edges for sparse networks. The advantage of BiMMDF is demonstrated in extensive synthetic networks and eight real-world networks.

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

Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

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

We introduce TravelFraudBench (TFG), a configurable benchmark for evaluating graph neural networks (GNNs) on fraud ring detection in travel platform graphs. Existing benchmarks--YelpChi, Amazon-Fraud, Elliptic, PaySim--cover single node types or domain-generic patterns with no mechanism to evaluate across structurally distinct fraud ring topologies. TFG simulates three travel-specific ring types--ticketing fraud (star topology with shared device/IP clusters), ghost hotel schemes (reviewer x hotel bipartite cliques), and account takeover rings (loyalty transfer chains)--in a heterogeneous graph with 9 node types and 12 edge types. Ring size, count, fraud rate, scale (500 to 200,000 nodes), and composition are fully configurable. We evaluate six methods--MLP, GraphSAGE, RGCN-proj, HAN, RGCN, and PC-GNN--under a ring-based split where each ring appears entirely in one partition, eliminating transductive label leakage. GraphSAGE achieves AUC=0.992 and RGCN-proj AUC=0.987, outperforming the MLP baseline (AUC=0.938) by 5.5 and 5.0 pp, confirming graph structure adds substantial discriminative power. HAN (AUC=0.935) is a negative result, matching the MLP baseline. On the ring recovery task (>=80% of ring members flagged simultaneously), GraphSAGE achieves 100% recovery across all ring types; MLP recovers only 17-88%. The edge-type ablation shows device and IP co-occurrence are the primary signals: removing uses_device drops AUC by 5.2 pp. TFG is released as an open-source Python package (MIT license) with PyG, DGL, and NetworkX exporters and pre-generated datasets at https://huggingface.co/datasets/bsajja7/travel-fraud-graphs, with Croissant metadata including Responsible AI fields.

Graph neural networks (GNNs) excel at aggregating neighbor information for classification, yet their performance is hindered by graph structural entanglement, where spurious correlations from semantically irrelevant neighbors contaminate node embeddings. This challenge is most acute for nodes near class boundaries in the embedding space, where amplified structural noise blurs decision boundaries and destabilizes predictions. Existing robust GNN methods largely treat all nodes uniformly, ignoring boundary vulnerabilities. In this paper, to improve classification performance, we tackle graph structural disentanglement by identifying boundary-region entanglement as the primary bottleneck and propose Boundary Embedding Shaping (BES), an adaptive contrastive learning GNN plug-in module that selectively suppresses spurious structural noise at decision boundaries with minimal model parameter perturbation. Extensive experiments demonstrate that BES consistently improves boundary discrimination and outperforms existing leading methods. Notably, BES boosts GCN performance by an average of 3.3% in node classification (up to 5.0% on WikiCS) and achieves superior accuracy in link prediction.

In this paper, we present the findings of our Project ALPINE which stands for ``Autoregressive Learning for Planning In NEtworks." Project ALPINE initiates a theoretical investigation into the development of planning capabilities in Transformer-based language models through their autoregressive learning mechanisms, aiming to identify any potential limitations in their planning abilities. We abstract planning as a network path-finding task where the objective is to generate a valid path from a specified source node to a designated target node. In terms of expressiveness, we show that the Transformer is capable of executing path-finding by embedding the adjacency and reachability matrices within its weights. Our theoretical analysis of the gradient-based learning dynamic of the Transformer reveals that the Transformer is capable of learning both the adjacency matrix and a limited form of the reachability matrix. These theoretical insights are then validated through experiments, which demonstrate that the Transformer indeed learns the adjacency matrix and an incomplete reachability matrix, which aligns with the predictions made in our theoretical analysis. Additionally, when applying our methodology to a real-world planning benchmark, called Blocksworld, our observations remain consistent. Our theoretical and empirical analyses further unveil a potential limitation of Transformer in path-finding: it cannot identify reachability relationships through transitivity, and thus would fail when path concatenation is needed to generate a path. In summary, our findings shed new light on how the internal mechanisms of autoregressive learning enable planning in networks. This study may contribute to our understanding of the general planning capabilities in other related domains.

Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.

Knowledge graph (KG) link prediction aims to infer new facts based on existing facts in the KG. Recent studies have shown that using the graph neighborhood of a node via graph neural networks (GNNs) provides more useful information compared to just using the query information. Conventional GNNs for KG link prediction follow the standard message-passing paradigm on the entire KG, which leads to superfluous computation, over-smoothing of node representations, and also limits their expressive power. On a large scale, it becomes computationally expensive to aggregate useful information from the entire KG for inference. To address the limitations of existing KG link prediction frameworks, we propose a novel retrieve-and-read framework, which first retrieves a relevant subgraph context for the query and then jointly reasons over the context and the query with a high-capacity reader. As part of our exemplar instantiation for the new framework, we propose a novel Transformer-based GNN as the reader, which incorporates graph-based attention structure and cross-attention between query and context for deep fusion. This simple yet effective design enables the model to focus on salient context information relevant to the query. Empirical results on two standard KG link prediction datasets demonstrate the competitive performance of the proposed method. Furthermore, our analysis yields valuable insights for designing improved retrievers within the framework.

Modeling complex spatial and temporal correlations in the correlated time series data is indispensable for understanding the traffic dynamics and predicting the future status of an evolving traffic system. Recent works focus on designing complicated graph neural network architectures to capture shared patterns with the help of pre-defined graphs. In this paper, we argue that learning node-specific patterns is essential for traffic forecasting while the pre-defined graph is avoidable. To this end, we propose two adaptive modules for enhancing Graph Convolutional Network (GCN) with new capabilities: 1) a Node Adaptive Parameter Learning (NAPL) module to capture node-specific patterns; 2) a Data Adaptive Graph Generation (DAGG) module to infer the inter-dependencies among different traffic series automatically. We further propose an Adaptive Graph Convolutional Recurrent Network (AGCRN) to capture fine-grained spatial and temporal correlations in traffic series automatically based on the two modules and recurrent networks. Our experiments on two real-world traffic datasets show AGCRN outperforms state-of-the-art by a significant margin without pre-defined graphs about spatial connections.

Agent-native social platforms such as Moltbook are rapidly emerging, yet they inherit and amplify classical influence and abuse attacks, where coordinated agents strategically comment and upvote to manipulate visibility and propagate narratives across communities. However, rigorous measurement and learning-based monitoring remain constrained by the absence of longitudinal, graph-native datasets for agentic social networks that jointly capture heterogeneous interactions, temporal drift, and visibility signals needed to connect coordination behavior to downstream exposure. We introduce MoltGraph as a realistic longitudinal agentic social-network graph dataset for studying how agents behave, coordinate, and evolve in the wild, enabling reproducible measurement on emerging multi-agent social ecosystems. Using MoltGraph, we provide the first graph-centric characterization of Moltbook as a dynamic network: (i) heavy-tailed connectivity with power-law exponents in the range alpha in [1.86, 2.72], (ii) accelerating hub formation and attention centralization where the top 1% agents account for 29.00% of engagements, (iii) bursty, short-lived coordination episodes, 98.33% last under 24 hours, and (iv) measurable exposure effects across submolts. In matched analyses, posts receiving coordinated engagement exhibit 506.35% higher early interaction rates (within H=5 days) and 242.63% higher downstream exposure in feeds than non-coordinated controls.

Heterogeneous information network (HIN) embedding aims to find the representations of nodes that preserve the proximity between entities of different nature. A family of approaches that are wildly adopted applies random walk to generate a sequence of heterogeneous context, from which the embedding is learned. However, due to the multipartite graph structure of HIN, hub nodes tend to be over-represented in the sampled sequence, giving rise to imbalanced samples of the network. Here we propose a new embedding method CoarSAS2hvec. The self-avoid short sequence sampling with the HIN coarsening procedure (CoarSAS) is utilized to better collect the rich information in HIN. An optimized loss function is used to improve the performance of the HIN structure embedding. CoarSAS2hvec outperforms nine other methods in two different tasks on four real-world data sets. The ablation study confirms that the samples collected by CoarSAS contain richer information of the network compared with those by other methods, which is characterized by a higher information entropy. Hence, the traditional loss function applied to samples by CoarSAS can also yield improved results. Our work addresses a limitation of the random-walk-based HIN embedding that has not been emphasized before, which can shed light on a range of problems in HIN analyses.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Natural data is redundant yet predominant architectures tile computation uniformly across their input and output space. We propose the Recurrent Interface Networks (RINs), an attention-based architecture that decouples its core computation from the dimensionality of the data, enabling adaptive computation for more scalable generation of high-dimensional data. RINs focus the bulk of computation (i.e. global self-attention) on a set of latent tokens, using cross-attention to read and write (i.e. route) information between latent and data tokens. Stacking RIN blocks allows bottom-up (data to latent) and top-down (latent to data) feedback, leading to deeper and more expressive routing. While this routing introduces challenges, this is less problematic in recurrent computation settings where the task (and routing problem) changes gradually, such as iterative generation with diffusion models. We show how to leverage recurrence by conditioning the latent tokens at each forward pass of the reverse diffusion process with those from prior computation, i.e. latent self-conditioning. RINs yield state-of-the-art pixel diffusion models for image and video generation, scaling to 1024X1024 images without cascades or guidance, while being domain-agnostic and up to 10X more efficient than 2D and 3D U-Nets.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

Traffic forecasting represents a crucial problem within intelligent transportation systems. In recent research, Large Language Models (LLMs) have emerged as a promising method, but their intrinsic design, tailored primarily for sequential token processing, introduces notable challenges in effectively capturing spatial dependencies. Specifically, the inherent limitations of LLMs in modeling spatial relationships and their architectural incompatibility with graph-structured spatial data remain largely unaddressed. To overcome these limitations, we introduce ST-LINK, a novel framework that enhances the capability of Large Language Models to capture spatio-temporal dependencies. Its key components are Spatially-Enhanced Attention (SE-Attention) and the Memory Retrieval Feed-Forward Network (MRFFN). SE-Attention extends rotary position embeddings to integrate spatial correlations as direct rotational transformations within the attention mechanism. This approach maximizes spatial learning while preserving the LLM's inherent sequential processing structure. Meanwhile, MRFFN dynamically retrieves and utilizes key historical patterns to capture complex temporal dependencies and improve the stability of long-term forecasting. Comprehensive experiments on benchmark datasets demonstrate that ST-LINK surpasses conventional deep learning and LLM approaches, and effectively captures both regular traffic patterns and abrupt changes.

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such metrics are expensive in terms of computational resources when running real-time applications or massive real world networks. Thus, approximation techniques have been developed and used to compute the measures in such scenarios. In this paper, we demonstrate and analyze the use of neural network learning algorithms to tackle such task and compare their performance in terms of solution quality and computation time with other techniques from the literature. Our work offers several contributions. We highlight both the pros and cons of approximating centralities though neural learning. By empirical means and statistics, we then show that the regression model generated with a feedforward neural networks trained by the Levenberg-Marquardt algorithm is not only the best option considering computational resources, but also achieves the best solution quality for relevant applications and large-scale networks. Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models, Machine Learning, Regression Model

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.

Sparse Mixture-of-Experts (SMoE) models enable scaling language models efficiently, but training them remains challenging, as routing can collapse onto few experts and auxiliary load-balancing losses can reduce specialization. Motivated by these hurdles, we study how routing decisions in SMoEs are formed mechanistically. First, we reveal a geometric coupling between routers and their corresponding experts. For a given token, the router weights for the selected expert and the expert weights processing it receive gradients along the same input direction, differing only in scalar coefficients. Thus, matched router--expert directions accumulate the same routed token history. This theoretical coupling also appears empirically in routing dynamics. In a 1B SMoE trained from scratch, higher router scores predict stronger expert neuron activations, showing that routing decisions are mirrored inside the selected expert. Next, we analyze the effects of auxiliary load balancing on the router--expert geometric coupling, showing that such losses break this structure by spreading input-directed gradients across router weights, making distinct router directions nearly three times more similar to each other. Last, we demonstrate the centrality of geometric coupling for effective routing with a parameter-free online K-Means router, in which each expert maintains a running average of the hidden states routed to it and tokens are assigned based on cosine similarity. Compared with auxiliary-loss and loss-free balancing, this router achieves the lowest load imbalance with only a modest perplexity increase, indicating that geometric coupling captures a substantial part of what the router learns. Overall, our results explain how routers form assignment geometry that supports an effective division of labor.

Foundation models like ChatGPT and GPT-4 have revolutionized artificial intelligence, exhibiting remarkable abilities to generalize across a wide array of tasks and applications beyond their initial training objectives. However, graph learning has predominantly focused on single-graph models, tailored to specific tasks or datasets, lacking the ability to transfer learned knowledge to different domains. This limitation stems from the inherent complexity and diversity of graph structures, along with the different feature and label spaces specific to graph data. In this paper, we recognize text as an effective unifying medium and employ Text-Attributed Graphs (TAGs) to leverage this potential. We present our UniGraph framework, designed to learn a foundation model for TAGs, which is capable of generalizing to unseen graphs and tasks across diverse domains. Unlike single-graph models that use pre-computed node features of varying dimensions as input, our approach leverages textual features for unifying node representations, even for graphs such as molecular graphs that do not naturally have textual features. We propose a novel cascaded architecture of Language Models (LMs) and Graph Neural Networks (GNNs) as backbone networks. Additionally, we propose the first pre-training algorithm specifically designed for large-scale self-supervised learning on TAGs, based on Masked Graph Modeling. We introduce graph instruction tuning using Large Language Models (LLMs) to enable zero-shot prediction ability. Our comprehensive experiments across various graph learning tasks and domains demonstrate the model's effectiveness in self-supervised representation learning on unseen graphs, few-shot in-context transfer, and zero-shot transfer, even surpassing or matching the performance of GNNs that have undergone supervised training on target datasets.

Graph mining is an important area in data mining and machine learning that involves extracting valuable information from graph-structured data. In recent years, significant progress has been made in this field through the development of graph neural networks (GNNs). However, GNNs are still deficient in generalizing to diverse graph data. Aiming to this issue, Large Language Models (LLMs) could provide new solutions for graph mining tasks with their superior semantic understanding. In this review, we systematically review the combination and application techniques of LLMs and GNNs and present a novel taxonomy for research in this interdisciplinary field, which involves three main categories: GNN-driving-LLM, LLM-driving-GNN, and GNN-LLM-co-driving. Within this framework, we reveal the capabilities of LLMs in enhancing graph feature extraction as well as improving the effectiveness of downstream tasks such as node classification, link prediction, and community detection. Although LLMs have demonstrated their great potential in handling graph-structured data, their high computational requirements and complexity remain challenges. Future research needs to continue to explore how to efficiently fuse LLMs and GNNs to achieve more powerful graph learning and reasoning capabilities and provide new impetus for the development of graph mining techniques.

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to high-quality, large-scale real-world hypergraph data. Yet, compared to traditional pairwise graphs, real hypergraph datasets remain scarce in both scale and diversity. This shortage significantly limits the development and evaluation of advanced hypergraph learning algorithms. Therefore, how to quickly generate large-scale hypergraphs that conform to the characteristics of real networks is a crucial task that has not received sufficient attention. Motivated by recent advances in large language models (LLMs), particularly their capabilities in semantic reasoning, structured generation, and simulating human behavior, we investigate whether LLMs can facilitate hypergraph generation from a fundamentally new perspective. We introduce HyperLLM, a novel LLM-driven hypergraph generator that simulates the formation and evolution of hypergraphs through a multi-agent collaboration. The framework integrates prompts and structural feedback mechanisms to ensure that the generated hypergraphs reflect key real-world patterns. Extensive experiments across diverse datasets demonstrate that HyperLLM achieves superior fidelity to structural and temporal hypergraph patterns, while requiring minimal statistical priors. Our findings suggest that LLM-based frameworks offer a promising new direction for hypergraph modeling.

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. We uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention nor fixed connectivity is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: https://github.com/millioniron/LLM_exploration{LLM4Exploration}

In this work, we present a new network design paradigm. Our goal is to help advance the understanding of network design and discover design principles that generalize across settings. Instead of focusing on designing individual network instances, we design network design spaces that parametrize populations of networks. The overall process is analogous to classic manual design of networks, but elevated to the design space level. Using our methodology we explore the structure aspect of network design and arrive at a low-dimensional design space consisting of simple, regular networks that we call RegNet. The core insight of the RegNet parametrization is surprisingly simple: widths and depths of good networks can be explained by a quantized linear function. We analyze the RegNet design space and arrive at interesting findings that do not match the current practice of network design. The RegNet design space provides simple and fast networks that work well across a wide range of flop regimes. Under comparable training settings and flops, the RegNet models outperform the popular EfficientNet models while being up to 5x faster on GPUs.

High-dimensional vector spaces, particularly embedding spaces with dense semantic structure, are often interpreted primarily leveraging solely geometric relationships. In this work, we show that they can also be viewed as spectral energy networks induced by the topology of their underlying feature-space manifold with relevant improvements for downstream tasks. Building on this perspective, we introduce Graph Wiring, a general framework for exploiting feature-space spectral structure, together with Spectral Indexing, its task-specific instantiation for vector search. By coupling geometric similarity with spectral information, the proposed method improves Head-Tail coherence and semantic alignment relative to purely geometric retrieval methods. It further supports adaptive search behavior through tau-modulation, providing the flexibility increasingly required by modern Retrieval-Augmented Generation (RAG) pipelines. We present the complete algorithmic pipeline, establish its theoretical foundation through epiplexity, and evaluate the approach across benchmark and industrial settings using the open-source arrowspace library.

As economics scales, a key bottleneck is representing what papers claim in a comparable, aggregable form. We introduce evidence-annotated claim graphs that map each paper into a directed network of standardized economic concepts (nodes) and stated relationships (edges), with each edge labeled by evidentiary basis, including whether it is supported by causal inference designs or by non-causal evidence. Using a structured multi-stage AI workflow, we construct claim graphs for 44,852 economics papers from 1980-2023. The share of causal edges rises from 7.7% in 1990 to 31.7% in 2020. Measures of causal narrative structure and causal novelty are positively associated with top-five publication and long-run citations, whereas non-causal counterparts are weakly related or negative.

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. However, existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. In particular, we demonstrate that some random walk statistics can be informative features to characterize node identities and positions while supporting the inductive embedding inference. Experiments validate the superior performance of IRWE beyond various baselines for the transductive and inductive inference of identity and position embeddings.

Knowledge graphs enable a wide variety of applications, including question answering and information retrieval. Despite the great effort invested in their creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata) remain incomplete. We introduce Relational Graph Convolutional Networks (R-GCNs) and apply them to two standard knowledge base completion tasks: Link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes). R-GCNs are related to a recent class of neural networks operating on graphs, and are developed specifically to deal with the highly multi-relational data characteristic of realistic knowledge bases. We demonstrate the effectiveness of R-GCNs as a stand-alone model for entity classification. We further show that factorization models for link prediction such as DistMult can be significantly improved by enriching them with an encoder model to accumulate evidence over multiple inference steps in the relational graph, demonstrating a large improvement of 29.8% on FB15k-237 over a decoder-only baseline.

Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none at all. We show experimentally that triangle centrality is broadly applicable to many different types of networks. Our empirical results demonstrate that 30% of the time triangle centrality identified central vertices that differed with those found by five well-known centrality measures, which suggests novelty without being overly specialized. It is also asymptotically faster to compute on sparse graphs than all but the most trivial of these other measures. We introduce optimal algorithms that compute triangle centrality in O(mbarδ) time and O(m+n) space, where barδle O(m) is the average degeneracy introduced by Burkhardt, Faber, and Harris (2020). In practical applications, barδ is much smaller than m so triangle centrality can be computed in nearly linear time. On a Concurrent Read Exclusive Write (CREW) Parallel Random Access Machine (PRAM), we give a near work-optimal parallel algorithm that takes O(log n) time using O(mm) CREW PRAM processors. In MapReduce, we show it takes four rounds using O(mm) communication bits and is therefore optimal. We also derive a linear algebraic formulation of triangle centrality which can be computed in O(mbarδ) time on sparse graphs.

Conventional community detection requires centralized network data, making it unsuitable for distributed or privacy-preserving systems. In this paper, we demonstrate that macroscopic graph partitioning can emerge purely from strictly local, privacy preserving interactions driven by social learning. By reframing clustering as a symmetry-breaking process within nonlinear opinion dynamics, we show that exchanging saturated state dependent signal (like public actions) forces a network to naturally fracture along its sparsest cuts. We mathematically establish the spectral conditions under which dense core communities lock into stable, polarized states, robustly resisting external influence. To apply this mechanism, we propose three decentralized algorithms, leading up to the Score-based Edge Reliability (SER) framework. By evaluating network ties across multiple independent discussion topics, SER statistically bypasses the errors of traditional greedy bisections and naturally isolates structurally ambiguous frontier nodes. Validations on the ABCD benchmark and the real-world Ngogo chimpanzee network confirm that our fully decentralized approach matches the accuracy of globally optimized heuristics (e.g., Louvain, Leiden) up to a theoretical limit of detectable graphs.

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor.

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

Personalizing language models by effectively incorporating user interaction history remains a central challenge in the development of adaptive AI systems. While large language models (LLMs), combined with Retrieval-Augmented Generation (RAG), have improved factual accuracy, they often lack structured memory and fail to scale in complex, long-term interactions. To address this, we propose a flexible external memory framework based on a knowledge graph that is constructed and updated automatically by the LLM. Building upon the AriGraph architecture, we introduce a novel hybrid graph design that supports both standard edges and two types of hyper-edges, enabling rich and dynamic semantic and temporal representations. Our framework also supports diverse retrieval mechanisms, including A*, WaterCircles traversal, beam search, and hybrid methods, making it adaptable to different datasets and LLM capacities. We evaluate our system on TriviaQA, HotpotQA, DiaASQ benchmarks and demonstrate that different memory and retrieval configurations yield optimal performance depending on the task. Additionally, we extend the DiaASQ benchmark with temporal annotations and internally contradictory statements, showing that our system remains robust and effective in managing temporal dependencies and context-aware reasoning

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.

In recent years, large language models (LLMs) have demonstrated remarkable generalization capabilities across various natural language processing (NLP) tasks. Similarly, graph foundation models (GFMs) have emerged as a promising direction in graph learning, aiming to generalize across diverse datasets through large-scale pre-training. However, unlike language models that rely on explicit token representations, graphs lack a well-defined unit for generalization, making it challenging to design effective pre-training strategies. In this work, we propose REEF, a novel framework that leverages relation tokens as the basic units for GFMs. Inspired by the token vocabulary in LLMs, we construct a relation vocabulary of relation tokens to store relational information within graphs. To accommodate diverse relations, we introduce two hypernetworks that adaptively generate the parameters of aggregators and classifiers in graph neural networks based on relation tokens. In addition, we design another hypernetwork to construct dataset-specific projectors and incorporate a dataset-level feature bias into the initial node representations, enhancing flexibility across different datasets with the same relation. Further, we adopt graph data augmentation and a mixed-dataset pre-training strategy, allowing REEF to capture relational diversity more effectively and exhibit strong generalization capabilities. Extensive experiments show that REEF significantly outperforms existing methods on both pre-training and transfer learning tasks, underscoring its potential as a powerful foundation model for graph-based applications.

Complex networks can be used for modeling street meshes and urban agglomerates. With such a model, many aspects of a city can be investigated to promote a better quality of life to its citizens. Along these lines, this paper proposes a set of distance-based pattern-discovery algorithmic instruments to improve urban structures modeled as complex networks, detecting nodes that lack access from/to points of interest in a given city. Furthermore, we introduce a greedy algorithm that is able to recommend improvements to the structure of a city by suggesting where points of interest are to be placed. We contribute to a thorough process to deal with complex networks, including mathematical modeling and algorithmic innovation. The set of our contributions introduces a systematic manner to treat a recurrent problem of broad interest in cities.

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

The Dragonfly network, with its high-radix and low-diameter structure, is a leading interconnect in high-performance computing. A major challenge is workload interference on shared network links. Parallel discrete event simulation (PDES) is commonly used to analyze workload interference. However, high-fidelity PDES is computationally expensive, making it impractical for large-scale or real-time scenarios. Hybrid simulation that incorporates data-driven surrogate models offers a promising alternative, especially for forecasting application runtime, a task complicated by the dynamic behavior of network traffic. We present \ourmodel, a surrogate model that combines graph neural networks (GNNs) and large language models (LLMs) to capture both spatial and temporal patterns from port level router data. \ourmodel outperforms existing statistical and machine learning baselines, enabling accurate runtime prediction and supporting efficient hybrid simulation of Dragonfly networks.

Large language models have been extensively studied as neural knowledge bases for their knowledge access, editability, reasoning, and explainability. However, few works focus on the structural patterns of their knowledge. Motivated by this gap, we investigate these structural patterns from a graph perspective. We quantify the knowledge of LLMs at both the triplet and entity levels, and analyze how it relates to graph structural properties such as node degree. Furthermore, we uncover the knowledge homophily, where topologically close entities exhibit similar levels of knowledgeability, which further motivates us to develop graph machine learning models to estimate entity knowledge based on its local neighbors. This model further enables valuable knowledge checking by selecting triplets less known to LLMs. Empirical results show that using selected triplets for fine-tuning leads to superior performance.

Pioneered by the foundational information theory by Claude Shannon and the visionary framework of machine intelligence by Alan Turing, the convergent evolution of information and communication technologies (IT/CT) has created an unbroken wave of connectivity and computation. This synergy has sparked a technological revolution, now reaching its peak with large artificial intelligence (AI) models that are reshaping industries and redefining human-machine collaboration. However, the realization of ubiquitous intelligence faces considerable challenges due to substantial resource consumption in large models and high communication bandwidth demands. To address these challenges, AI Flow has been introduced as a multidisciplinary framework that integrates cutting-edge IT and CT advancements, with a particular emphasis on the following three key points. First, device-edge-cloud framework serves as the foundation, which integrates end devices, edge servers, and cloud clusters to optimize scalability and efficiency for low-latency model inference. Second, we introduce the concept of familial models, which refers to a series of different-sized models with aligned hidden features, enabling effective collaboration and the flexibility to adapt to varying resource constraints and dynamic scenarios. Third, connectivity- and interaction-based intelligence emergence is a novel paradigm of AI Flow. By leveraging communication networks to enhance connectivity, the collaboration among AI models across heterogeneous nodes achieves emergent intelligence that surpasses the capability of any single model. The innovations of AI Flow provide enhanced intelligence, timely responsiveness, and ubiquitous accessibility to AI services, paving the way for the tighter fusion of AI techniques and communication systems.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. Temporal-first approaches build per-node temporal embeddings and only afterwards perform spatial aggregation, whereas Spatial-first approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; concretely, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's past trajectory. This paper introduces SiST-GNN (Simultaneous Spatial-Temporal GNN), which fuses the two signals inside a single message-passing operation rather than chaining them. Concretely, at each snapshot we maintain a recurrent hidden state per node that summarises its history, pair it with the node's current feature vector, and treat the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. Our empirical study spans nine public baselines and fourteen model-dataset combinations, covering both fixed-split and live-update evaluation regimes. Across every public benchmark, SiST-GNN sets a new state of the art in link prediction task over the strongest prior method by 109--277% in the fixed-split setting and by 68--194% in the live-update setting. We additionally construct three dynamic node-classification tasks by discretising the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7--22% and matches continuous-time (CTDG) methods that consume the raw events directly.

Centrality measures are widely used to rank nodes in networked data, but fairness interventions for graph centrality typically target global score mass or modify the centrality operator rather than controlling who appears in the displayed top-k ranking. We study this top-k setting for Katz centrality. Given a target group proportion, an admissible set of directed edge additions, and a fairness tolerance, the goal is to find the smallest edit set whose resulting Katz top-k ranking satisfies the target representation constraint. We formalize this problem as Fair Top-k Katz Centrality Design and show that the minimum-edit objective is strongly inapproximable, ruling out worst-case polynomial-time approximation guarantees unless P = NP. We then derive closed-form Katz sensitivity expressions showing that useful edits are boundary-driven: they must help promotable nodes outside the top-k set overtake opposing nodes inside it. Based on this structure, we develop BLADE, a scalable boundary-link algorithm that avoids dense Katz-kernel maintenance by using score-based direct-target batches and warm-started Katz updates. Experiments on synthetic and real-world networks show that BLADE reaches the desired top-k representation using far fewer edits than natural baselines, while scaling to large real-world graphs and preserving the original ranking structure.

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

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

This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs) that focuses on hidden representations analysis rather than pure downstream task performance. Different from existing efforts, we analyze the models through a three-part evaluation: Embedding Geometry Analysis to assess representation space utilization, Metric Alignment Assessment to measure correspondence with domain-expert features, and Causal Sensitivity Testing to evaluate robustness to protocol perturbations. Using five diverse network datasets spanning controlled and real-world environments, we evaluate four state-of-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns, an inability to separate the high-level context, payload dependency, and other properties. Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance (by up to +0.35 F_1 score without architectural changes).

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.

We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .

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.

Accurate real-time traffic forecast is critical for intelligent transportation systems (ITS) and it serves as the cornerstone of various smart mobility applications. Though this research area is dominated by deep learning, recent studies indicate that the accuracy improvement by developing new model structures is becoming marginal. Instead, we envision that the improvement can be achieved by transferring the "forecasting-related knowledge" across cities with different data distributions and network topologies. To this end, this paper aims to propose a novel transferable traffic forecasting framework: Domain Adversarial Spatial-Temporal Network (DASTNet). DASTNet is pre-trained on multiple source networks and fine-tuned with the target network's traffic data. Specifically, we leverage the graph representation learning and adversarial domain adaptation techniques to learn the domain-invariant node embeddings, which are further incorporated to model the temporal traffic data. To the best of our knowledge, we are the first to employ adversarial multi-domain adaptation for network-wide traffic forecasting problems. DASTNet consistently outperforms all state-of-the-art baseline methods on three benchmark datasets. The trained DASTNet is applied to Hong Kong's new traffic detectors, and accurate traffic predictions can be delivered immediately (within one day) when the detector is available. Overall, this study suggests an alternative to enhance the traffic forecasting methods and provides practical implications for cities lacking historical traffic data.

In this work, we present a post-processing solution to address the hubness problem in cross-modal retrieval, a phenomenon where a small number of gallery data points are frequently retrieved, resulting in a decline in retrieval performance. We first theoretically demonstrate the necessity of incorporating both the gallery and query data for addressing hubness as hubs always exhibit high similarity with gallery and query data. Second, building on our theoretical results, we propose a novel framework, Dual Bank Normalization (DBNorm). While previous work has attempted to alleviate hubness by only utilizing the query samples, DBNorm leverages two banks constructed from the query and gallery samples to reduce the occurrence of hubs during inference. Next, to complement DBNorm, we introduce two novel methods, dual inverted softmax and dual dynamic inverted softmax, for normalizing similarity based on the two banks. Specifically, our proposed methods reduce the similarity between hubs and queries while improving the similarity between non-hubs and queries. Finally, we present extensive experimental results on diverse language-grounded benchmarks, including text-image, text-video, and text-audio, demonstrating the superior performance of our approaches compared to previous methods in addressing hubness and boosting retrieval performance. Our code is available at https://github.com/yimuwangcs/Better_Cross_Modal_Retrieval.

Router is the cornerstone component to the Mixture-of-Experts models. Serving as expert proxies, the rows of the router matrix compute their similarity to the MoE inputs to determine which subset of experts is activated. Ideally, each router row is designed to encode the expert matrix into this representative vector, such that its dot-product with token can better reflect token-expert affinity. However, there exists no design principles to enforce this condensation. In this paper, we propose to align each router row with the principal singular direction of the associated expert, as this direction provides the most expressive mathematical description of a matrix. Based on this principle, we propose a router redesign with Manifold Power Iteration (MPI). Specifically, it introduces a "Power-then-Retract" paradigm, where a power iteration step is performed on the router weights, followed by a retraction to impose a norm constraint to ensure both efficiency and stability. Theoretically, we show that MPI drives router rows to converge toward the principal singular directions of associated experts. Empirically, we pretrain MoE model across scales from 1B to 11B parameters to confirm that this alignment facilitates more effective MoE models.