Daily Papers

Retrieval-augmented generation (RAG) based on large language models often falters on narrative documents with inherent temporal structures. Standard unstructured RAG methods rely solely on embedding-similarity matching and lack any general mechanism to encode or exploit chronological information, while knowledge graph RAG (KG-RAG) frameworks collapse every mention of an entity into a single node, erasing the evolving context that drives many queries. To formalize this challenge and draw the community's attention, we construct ChronoQA, a robust and discriminative QA benchmark that measures temporal, causal, and character consistency understanding in narrative documents (e.g., novels) under the RAG setting. We then introduce Entity-Event RAG (E^2RAG), a dual-graph framework that keeps separate entity and event subgraphs linked by a bipartite mapping, thereby preserving the temporal and causal facets needed for fine-grained reasoning. Across ChronoQA, our approach outperforms state-of-the-art unstructured and KG-based RAG baselines, with notable gains on causal and character consistency queries. E^2RAG therefore offers a practical path to more context-aware retrieval for tasks that require precise answers grounded in chronological information.

Recently, integrating external tools with Large Language Models (LLMs) has gained significant attention as an effective strategy to mitigate the limitations inherent in their pre-training data. However, real-world systems often incorporate a wide array of tools, making it impractical to input all tools into LLMs due to length limitations and latency constraints. Therefore, to fully exploit the potential of tool-augmented LLMs, it is crucial to develop an effective tool retrieval system. Existing tool retrieval methods primarily focus on semantic matching between user queries and tool descriptions, frequently leading to the retrieval of redundant, similar tools. Consequently, these methods fail to provide a complete set of diverse tools necessary for addressing the multifaceted problems encountered by LLMs. In this paper, we propose a novel modelagnostic COllaborative Learning-based Tool Retrieval approach, COLT, which captures not only the semantic similarities between user queries and tool descriptions but also takes into account the collaborative information of tools. Specifically, we first fine-tune the PLM-based retrieval models to capture the semantic relationships between queries and tools in the semantic learning stage. Subsequently, we construct three bipartite graphs among queries, scenes, and tools and introduce a dual-view graph collaborative learning framework to capture the intricate collaborative relationships among tools during the collaborative learning stage. Extensive experiments on both the open benchmark and the newly introduced ToolLens dataset show that COLT achieves superior performance. Notably, the performance of BERT-mini (11M) with our proposed model framework outperforms BERT-large (340M), which has 30 times more parameters. Furthermore, we will release ToolLens publicly to facilitate future research on tool retrieval.

Retrieval-Augmented Generation (RAG) has emerged as a fundamental paradigm for expanding Large Language Models beyond their static training limitations. However, a critical misalignment exists between current RAG capabilities and real-world information environments. Modern knowledge repositories are inherently multimodal, containing rich combinations of textual content, visual elements, structured tables, and mathematical expressions. Yet existing RAG frameworks are limited to textual content, creating fundamental gaps when processing multimodal documents. We present RAG-Anything, a unified framework that enables comprehensive knowledge retrieval across all modalities. Our approach reconceptualizes multimodal content as interconnected knowledge entities rather than isolated data types. The framework introduces dual-graph construction to capture both cross-modal relationships and textual semantics within a unified representation. We develop cross-modal hybrid retrieval that combines structural knowledge navigation with semantic matching. This enables effective reasoning over heterogeneous content where relevant evidence spans multiple modalities. RAG-Anything demonstrates superior performance on challenging multimodal benchmarks, achieving significant improvements over state-of-the-art methods. Performance gains become particularly pronounced on long documents where traditional approaches fail. Our framework establishes a new paradigm for multimodal knowledge access, eliminating the architectural fragmentation that constrains current systems. Our framework is open-sourced at: https://github.com/HKUDS/RAG-Anything.

The advancement of large language models (LLMs) is critically dependent on the availability of high-quality datasets for Supervised Fine-Tuning (SFT), alignment tasks like Direct Preference Optimization (DPO), etc. In this work, we present a comprehensive synthetic data generation framework that facilitates scalable, configurable, and high-fidelity generation of synthetic data tailored for these training paradigms. Our approach employs a modular and configuration-based pipeline capable of modeling complex dialogue flows with minimal manual intervention. This framework uses a dual-stage quality tagging mechanism, combining heuristic rules and LLM-based evaluations, to automatically filter and score data extracted from OASST-formatted conversations, ensuring the curation of high-quality dialogue samples. The resulting datasets are structured under a flexible schema supporting both SFT and DPO use cases, enabling seamless integration into diverse training workflows. Together, these innovations offer a robust solution for generating and managing synthetic conversational data at scale, significantly reducing the overhead of data preparation in LLM training pipelines.

Graph neural network (GNN), as a powerful representation learning model on graph data, attracts much attention across various disciplines. However, recent studies show that GNN is vulnerable to adversarial attacks. How to make GNN more robust? What are the key vulnerabilities in GNN? How to address the vulnerabilities and defense GNN against the adversarial attacks? In this paper, we propose DefNet, an effective adversarial defense framework for GNNs. In particular, we first investigate the latent vulnerabilities in every layer of GNNs and propose corresponding strategies including dual-stage aggregation and bottleneck perceptron. Then, to cope with the scarcity of training data, we propose an adversarial contrastive learning method to train the GNN in a conditional GAN manner by leveraging the high-level graph representation. Extensive experiments on three public datasets demonstrate the effectiveness of DefNet in improving the robustness of popular GNN variants, such as Graph Convolutional Network and GraphSAGE, under various types of adversarial attacks.

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

Multimodal recommendation systems typically integrates user behavior with multimodal data from items, thereby capturing more accurate user preferences. Concurrently, with the rise of large models (LMs), multimodal recommendation is increasingly leveraging their strengths in semantic understanding and contextual reasoning. However, LM representations are inherently optimized for general semantic tasks, while recommendation models rely heavily on sparse user/item unique identity (ID) features. Existing works overlook the fundamental representational divergence between large models and recommendation systems, resulting in incompatible multimodal representations and suboptimal recommendation performance. To bridge this gap, we propose RecGOAT, a novel yet simple dual semantic alignment framework for LLM-enhanced multimodal recommendation, which offers theoretically guaranteed alignment capability. RecGOAT first employs graph attention networks to enrich collaborative semantics by modeling item-item, user-item, and user-user relationships, leveraging user/item LM representations and interaction history. Furthermore, we design a dual-granularity progressive multimodality-ID alignment framework, which achieves instance-level and distribution-level semantic alignment via cross-modal contrastive learning (CMCL) and optimal adaptive transport (OAT), respectively. Theoretically, we demonstrate that the unified representations derived from our alignment framework exhibit superior semantic consistency and comprehensiveness. Extensive experiments on three public benchmarks show that our RecGOAT achieves state-of-the-art performance, empirically validating our theoretical insights. Additionally, the deployment on a large-scale online advertising platform confirms the model's effectiveness and scalability in industrial recommendation scenarios. Code available at https://github.com/6lyc/RecGOAT-LLM4Rec.

Retrieval-Augmented Generation (RAG) and Graph-based RAG has become the important paradigm for enhancing Large Language Models (LLMs) with external knowledge. However, existing approaches face a fundamental trade-off. While graph-based methods are inherently dependent on high-quality graph structures, they face significant practical constraints: manually constructed knowledge graphs are prohibitively expensive to scale, while automatically extracted graphs from corpora are limited by the performance of the underlying LLM extractors, especially when using smaller, local-deployed models. This paper presents Think-on-Graph 3.0 (ToG-3), a novel framework that introduces Multi-Agent Context Evolution and Retrieval (MACER) mechanism to overcome these limitations. Our core innovation is the dynamic construction and refinement of a Chunk-Triplets-Community heterogeneous graph index, which pioneeringly incorporates a dual-evolution mechanism of Evolving Query and Evolving Sub-Graph for precise evidence retrieval. This approach addresses a critical limitation of prior Graph-based RAG methods, which typically construct a static graph index in a single pass without adapting to the actual query. A multi-agent system, comprising Constructor, Retriever, Reflector, and Responser agents, collaboratively engages in an iterative process of evidence retrieval, answer generation, sufficiency reflection, and, crucially, evolving query and subgraph. This dual-evolving multi-agent system allows ToG-3 to adaptively build a targeted graph index during reasoning, mitigating the inherent drawbacks of static, one-time graph construction and enabling deep, precise reasoning even with lightweight LLMs. Extensive experiments demonstrate that ToG-3 outperforms compared baselines on both deep and broad reasoning benchmarks, and ablation studies confirm the efficacy of the components of MACER framework.

We present MG-Nav (Memory-Guided Navigation), a dual-scale framework for zero-shot visual navigation that unifies global memory-guided planning with local geometry-enhanced control. At its core is the Sparse Spatial Memory Graph (SMG), a compact, region-centric memory where each node aggregates multi-view keyframe and object semantics, capturing both appearance and spatial structure while preserving viewpoint diversity. At the global level, the agent is localized on SMG and a goal-conditioned node path is planned via an image-to-instance hybrid retrieval, producing a sequence of reachable waypoints for long-horizon guidance. At the local level, a navigation foundation policy executes these waypoints in point-goal mode with obstacle-aware control, and switches to image-goal mode when navigating from the final node towards the visual target. To further enhance viewpoint alignment and goal recognition, we introduce VGGT-adapter, a lightweight geometric module built on the pre-trained VGGT model, which aligns observation and goal features in a shared 3D-aware space. MG-Nav operates global planning and local control at different frequencies, using periodic re-localization to correct errors. Experiments on HM3D Instance-Image-Goal and MP3D Image-Goal benchmarks demonstrate that MG-Nav achieves state-of-the-art zero-shot performance and remains robust under dynamic rearrangements and unseen scene conditions.

Ear biometrics offer a stable and contactless modality for identity recognition, yet their effectiveness remains limited by the scarcity of annotated data and significant intra-class variability. Existing methods typically extract identity features from individual impressions in isolation, restricting their ability to capture consistent and discriminative representations. To overcome these limitations, a few-shot learning framework, ProtoN, is proposed to jointly process multiple impressions of an identity using a graph-based approach. Each impression is represented as a node in a class-specific graph, alongside a learnable prototype node that encodes identity-level information. This graph is processed by a Prototype Graph Neural Network (PGNN) layer, specifically designed to refine both impression and prototype representations through a dual-path message-passing mechanism. To further enhance discriminative power, the PGNN incorporates a cross-graph prototype alignment strategy that improves class separability by enforcing intra-class compactness while maintaining inter-class distinction. Additionally, a hybrid loss function is employed to balance episodic and global classification objectives, thereby improving the overall structure of the embedding space. Extensive experiments on five benchmark ear datasets demonstrate that ProtoN achieves state-of-the-art performance, with Rank-1 identification accuracy of up to 99.60% and an Equal Error Rate (EER) as low as 0.025, showing the effectiveness for few-shot ear recognition under limited data conditions.

Diffusion models have demonstrated exceptional generative capabilities but are computationally intensive, posing significant challenges for deployment in resource-constrained or latency-sensitive environments. Quantization offers an effective means to reduce model size and computational cost, with post-training quantization (PTQ) being particularly appealing due to its compatibility with pre-trained models without requiring retraining or training data. However, existing PTQ methods for diffusion models often rely on architecture-specific heuristics that limit their generalizability and hinder integration with industrial deployment pipelines. To address these limitations, we propose SegQuant, a unified quantization framework that adaptively combines complementary techniques to enhance cross-model versatility. SegQuant consists of a segment-aware, graph-based quantization strategy (SegLinear) that captures structural semantics and spatial heterogeneity, along with a dual-scale quantization scheme (DualScale) that preserves polarity-asymmetric activations, which is crucial for maintaining visual fidelity in generated outputs. SegQuant is broadly applicable beyond Transformer-based diffusion models, achieving strong performance while ensuring seamless compatibility with mainstream deployment tools.

Industrial-scale recommender systems rely on a cascade pipeline in which the retrieval stage must return a high-recall candidate set from billions of items under tight latency. Existing solutions ei- ther (i) suffer from limited expressiveness in capturing fine-grained user-item interactions, as seen in decoupled dual-tower architectures that rely on separate encoders, or generative models that lack precise target-aware matching capabilities, or (ii) build structured indices (tree, graph, quantization) whose item-centric topologies struggle to incorporate dynamic user preferences and incur prohibitive construction and maintenance costs. We present GRank, a novel structured-index-free retrieval paradigm that seamlessly unifies target-aware learning with user-centric retrieval. Our key innovations include: (1) A target-aware Generator trained to perform personalized candidate generation via GPU-accelerated MIPS, eliminating semantic drift and maintenance costs of structured indexing; (2) A lightweight but powerful Ranker that performs fine-grained, candidate-specific inference on small subsets; (3) An end-to-end multi-task learning framework that ensures semantic consistency between generation and ranking objectives. Extensive experiments on two public benchmarks and a billion-item production corpus demonstrate that GRank improves Recall@500 by over 30% and 1.7times the P99 QPS of state-of-the-art tree- and graph-based retrievers. GRank has been fully deployed in production in our recommendation platform since Q2 2025, serving 400 million active users with 99.95% service availability. Online A/B tests confirm significant improvements in core engagement metrics, with Total App Usage Time increasing by 0.160% in the main app and 0.165% in the Lite version.

Protein language models (pLMs) pre-trained on vast protein sequence databases excel at various downstream tasks but lack the structural knowledge essential for many biological applications. To address this, we integrate structural insights from pre-trained protein graph neural networks (pGNNs) into pLMs through a latent-level contrastive learning task. This task aligns residue representations from pLMs with those from pGNNs across multiple proteins, enriching pLMs with inter-protein structural knowledge. Additionally, we incorporate a physical-level task that infuses intra-protein structural knowledge by optimizing pLMs to predict structural tokens. The proposed dual-task framework effectively incorporates both inter-protein and intra-protein structural knowledge into pLMs. Given the variability in the quality of protein structures in PDB, we further introduce a residue loss selection module, which uses a small model trained on high-quality structures to select reliable yet challenging residue losses for the pLM to learn. Applying our structure alignment method to the state-of-the-art ESM2 and AMPLIFY results in notable performance gains across a wide range of tasks, including a 12.7% increase in ESM2 contact prediction. The data, code, and resulting SaESM2 and SaAMPLIFY models will be released on Hugging Face.

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.

Video Question Answering (VideoQA) based on Large Language Models (LLMs) has shown potential in general video understanding but faces significant challenges when applied to the inherently complex domain of sports videos. In this work, we propose FineQuest, the first training-free framework that leverages dual-mode reasoning inspired by cognitive science: i) Reactive Reasoning for straightforward sports queries and ii) Deliberative Reasoning for more complex ones. To bridge the knowledge gap between general-purpose models and domain-specific sports understanding, FineQuest incorporates SSGraph, a multimodal sports knowledge scene graph spanning nine sports, which encodes both visual instances and domain-specific terminology to enhance reasoning accuracy. Furthermore, we introduce two new sports VideoQA benchmarks, Gym-QA and Diving-QA, derived from the FineGym and FineDiving datasets, enabling diverse and comprehensive evaluation. FineQuest achieves state-of-the-art performance on these benchmarks as well as the existing SPORTU dataset, while maintains strong general VideoQA capabilities.

Gaussian splatting has emerged as a powerful tool for high-fidelity reconstruction of dynamic scenes. However, existing methods primarily rely on implicit motion representations, such as encoding motions into neural networks or per-Gaussian parameters, which makes it difficult to further manipulate the reconstructed motions. This lack of explicit controllability limits existing methods to replaying recorded motions only, which hinders a wider application in robotics. To address this, we propose Motion Blender Gaussian Splatting (MBGS), a novel framework that uses motion graphs as an explicit and sparse motion representation. The motion of a graph's links is propagated to individual Gaussians via dual quaternion skinning, with learnable weight painting functions that determine the influence of each link. The motion graphs and 3D Gaussians are jointly optimized from input videos via differentiable rendering. Experiments show that MBGS achieves state-of-the-art performance on the highly challenging iPhone dataset while being competitive on HyperNeRF. We demonstrate the application potential of our method in animating novel object poses, synthesizing real robot demonstrations, and predicting robot actions through visual planning. The source code, models, video demonstrations can be found at http://mlzxy.github.io/motion-blender-gs.

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

We introduce a method for the generation of images from an input scene graph. The method separates between a layout embedding and an appearance embedding. The dual embedding leads to generated images that better match the scene graph, have higher visual quality, and support more complex scene graphs. In addition, the embedding scheme supports multiple and diverse output images per scene graph, which can be further controlled by the user. We demonstrate two modes of per-object control: (i) importing elements from other images, and (ii) navigation in the object space, by selecting an appearance archetype. Our code is publicly available at https://www.github.com/ashual/scene_generation

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

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

Medical Dialogue Generation serves a critical role in telemedicine by facilitating the dissemination of medical expertise to patients. Existing studies focus on incorporating textual representations, which have limited their ability to represent the semantics of text, such as ignoring important medical entities. To enhance the model's understanding of the textual semantics and the medical knowledge including entities and relations, we introduce the use of Abstract Meaning Representations (AMR) to construct graphical representations that delineate the roles of language constituents and medical entities within the dialogues. In this paper, We propose a novel framework that models dialogues between patients and healthcare professionals using AMR graphs, where the neural networks incorporate textual and graphical knowledge with a dual attention mechanism. Experimental results show that our framework outperforms strong baseline models in medical dialogue generation, demonstrating the effectiveness of AMR graphs in enhancing the representations of medical knowledge and logical relationships. Furthermore, to support future research in this domain, we provide the corresponding source code at https://github.com/Bernard-Yang/MedDiaAMR.

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

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.

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

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.

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

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

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

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

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.

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.

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

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.

Unsupervised Multiplex Graph Learning (UMGL) aims to learn node representations on various edge types without manual labeling. However, existing research overlooks a key factor: the reliability of the graph structure. Real-world data often exhibit a complex nature and contain abundant task-irrelevant noise, severely compromising UMGL's performance. Moreover, existing methods primarily rely on contrastive learning to maximize mutual information across different graphs, limiting them to multiplex graph redundant scenarios and failing to capture view-unique task-relevant information. In this paper, we focus on a more realistic and challenging task: to unsupervisedly learn a fused graph from multiple graphs that preserve sufficient task-relevant information while removing task-irrelevant noise. Specifically, our proposed Information-aware Unsupervised Multiplex Graph Fusion framework (InfoMGF) uses graph structure refinement to eliminate irrelevant noise and simultaneously maximizes view-shared and view-unique task-relevant information, thereby tackling the frontier of non-redundant multiplex graph. Theoretical analyses further guarantee the effectiveness of InfoMGF. Comprehensive experiments against various baselines on different downstream tasks demonstrate its superior performance and robustness. Surprisingly, our unsupervised method even beats the sophisticated supervised approaches. The source code and datasets are available at https://github.com/zxlearningdeep/InfoMGF.

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

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

The application of video captioning models aims at translating the content of videos by using accurate natural language. Due to the complex nature inbetween object interaction in the video, the comprehensive understanding of spatio-temporal relations of objects remains a challenging task. Existing methods often fail in generating sufficient feature representations of video content. In this paper, we propose a video captioning model based on dual graphs and gated fusion: we adapt two types of graphs to generate feature representations of video content and utilize gated fusion to further understand these different levels of information. Using a dual-graphs model to generate appearance features and motion features respectively can utilize the content correlation in frames to generate various features from multiple perspectives. Among them, dual-graphs reasoning can enhance the content correlation in frame sequences to generate advanced semantic features; The gated fusion, on the other hand, aggregates the information in multiple feature representations for comprehensive video content understanding. The experiments conducted on worldly used datasets MSVD and MSR-VTT demonstrate state-of-the-art performance of our proposed approach.

Relational reasoning lies at the core of many NLP tasks, drawing on complementary signals from text and graphs. While prior research has investigated how to leverage this dual complementarity, a detailed and systematic understanding of text-graph interplay and its effect on hybrid models remains underexplored. We take an analysis-driven approach to investigate text-graph representation complementarity via a unified architecture that supports knowledge co-distillation (CoD). We explore five tasks involving relational reasoning that differ in how text and graph structures encode the information needed to solve that task. By tracking how these dual representations evolve during training, we uncover interpretable patterns of alignment and divergence, and provide insights into when and why their integration is beneficial.

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

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

Graph representation learning is crucial for many real-world applications (e.g. social relation analysis). A fundamental problem for graph representation learning is how to effectively learn representations without human labeling, which is usually costly and time-consuming. Graph contrastive learning (GCL) addresses this problem by pulling the positive node pairs (or similar nodes) closer while pushing the negative node pairs (or dissimilar nodes) apart in the representation space. Despite the success of the existing GCL methods, they primarily sample node pairs based on the node-level proximity yet the community structures have rarely been taken into consideration. As a result, two nodes from the same community might be sampled as a negative pair. We argue that the community information should be considered to identify node pairs in the same communities, where the nodes insides are semantically similar. To address this issue, we propose a novel Graph Communal Contrastive Learning (gCooL) framework to jointly learn the community partition and learn node representations in an end-to-end fashion. Specifically, the proposed gCooL consists of two components: a Dense Community Aggregation (DeCA) algorithm for community detection and a Reweighted Self-supervised Cross-contrastive (ReSC) training scheme to utilize the community information. Additionally, the real-world graphs are complex and often consist of multiple views. In this paper, we demonstrate that the proposed gCooL can also be naturally adapted to multiplex graphs. Finally, we comprehensively evaluate the proposed gCooL on a variety of real-world graphs. The experimental results show that the gCooL outperforms the state-of-the-art methods.

Graph Retrieval-Augmented Generation (GraphRAG) enhances factual reasoning in LLMs by structurally modeling knowledge through graph-based representations. However, existing GraphRAG approaches face two core limitations: shallow retrieval that fails to surface all critical evidence, and inefficient utilization of pre-constructed structural graph data, which hinders effective reasoning from complex queries. To address these challenges, we propose GraphSearch, a novel agentic deep searching workflow with dual-channel retrieval for GraphRAG. GraphSearch organizes the retrieval process into a modular framework comprising six modules, enabling multi-turn interactions and iterative reasoning. Furthermore, GraphSearch adopts a dual-channel retrieval strategy that issues semantic queries over chunk-based text data and relational queries over structural graph data, enabling comprehensive utilization of both modalities and their complementary strengths. Experimental results across six multi-hop RAG benchmarks demonstrate that GraphSearch consistently improves answer accuracy and generation quality over the traditional strategy, confirming GraphSearch as a promising direction for advancing graph retrieval-augmented generation.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

Modeling dynamic graphs, such as those found in social networks, recommendation systems, and e-commerce platforms, is crucial for capturing evolving relationships and delivering relevant insights over time. Traditional approaches primarily rely on graph neural networks with temporal components or sequence generation models, which often focus narrowly on the historical context of target nodes. This limitation restricts the ability to adapt to new and emerging patterns in dynamic graphs. To address this challenge, we propose a novel framework, Retrieval-Augmented Generation for Dynamic Graph modeling (RAG4DyG), which enhances dynamic graph predictions by incorporating contextually and temporally relevant examples from broader graph structures. Our approach includes a time- and context-aware contrastive learning module to identify high-quality demonstrations and a graph fusion strategy to effectively integrate these examples with historical contexts. The proposed framework is designed to be effective in both transductive and inductive scenarios, ensuring adaptability to previously unseen nodes and evolving graph structures. Extensive experiments across multiple real-world datasets demonstrate the effectiveness of RAG4DyG in improving predictive accuracy and adaptability for dynamic graph modeling. The code and datasets are publicly available at https://github.com/YuxiaWu/RAG4DyG.

Relational databases (RDBs) are composed of interconnected tables, where relationships between them are defined through foreign keys. Recent research on applying machine learning to RDBs has explored graph-based representations of RDBs, where rows of tables are modeled as nodes, and foreign key relationships are modeled as edges. RDB-to-graph modeling helps capture cross-table dependencies, ultimately leading to enhanced performance across diverse tasks. However, there are numerous ways to model RDBs as graphs, and performance varies significantly depending on the chosen graph model. In our analysis, applying a common heuristic rule for graph modeling leads to up to a 10% drop in performance compared to the best-performing graph model, which remains non-trivial to identify. To foster research on intelligent RDB-to-graph modeling, we introduce RDB2G-Bench, the first benchmark framework for evaluating such methods. We construct extensive datasets covering 5 real-world RDBs and 12 predictive tasks, resulting in around 50k graph-performance pairs for efficient and reproducible evaluations. Thanks to our precomputed datasets, we were able to benchmark 9 automatic RDB-to-graph modeling methods on the 12 tasks over 600x faster than on-the-fly evaluation, which requires repeated model training. Our analysis of the datasets and benchmark results reveals key structural patterns affecting graph model effectiveness, along with practical implications for effective graph modeling.

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

Existing foundation models, such as CLIP, aim to learn a unified embedding space for multimodal data, enabling a wide range of downstream web-based applications like search, recommendation, and content classification. However, these models often overlook the inherent graph structures in multimodal datasets, where entities and their relationships are crucial. Multimodal graphs (MMGs) represent such graphs where each node is associated with features from different modalities, while the edges capture the relationships between these entities. On the other hand, existing graph foundation models primarily focus on text-attributed graphs (TAGs) and are not designed to handle the complexities of MMGs. To address these limitations, we propose UniGraph2, a novel cross-domain graph foundation model that enables general representation learning on MMGs, providing a unified embedding space. UniGraph2 employs modality-specific encoders alongside a graph neural network (GNN) to learn a unified low-dimensional embedding space that captures both the multimodal information and the underlying graph structure. We propose a new cross-domain multi-graph pre-training algorithm at scale to ensure effective transfer learning across diverse graph domains and modalities. Additionally, we adopt a Mixture of Experts (MoE) component to align features from different domains and modalities, ensuring coherent and robust embeddings that unify the information across modalities. Extensive experiments on a variety of multimodal graph tasks demonstrate that UniGraph2 significantly outperforms state-of-the-art models in tasks such as representation learning, transfer learning, and multimodal generative tasks, offering a scalable and flexible solution for learning on MMGs.

The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a high-dimensional optimization challenge. Existing approaches often rely on a single model or fixed tool-calling logic, failing to exploit the performance variations across heterogeneous model-tool pairs. In this paper, we present ATLAS (Adaptive Tool-LLM Alignment and Synergistic Invocation), a dual-path framework for dynamic tool usage in cross-domain complex reasoning. ATLAS operates via a dual-path approach: (1) training-free cluster-based routing that exploits empirical priors for domain-specific alignment, and (2) RL-based multi-step routing that explores autonomous trajectories for out-of-distribution generalization. Extensive experiments across 15 benchmarks demonstrate that our method outperforms closed-source models like GPT-4o, surpassing existing routing methods on both in-distribution (+10.1%) and out-of-distribution (+13.1%) tasks. Furthermore, our framework shows significant gains in visual reasoning by orchestrating specialized multi-modal tools.

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

Large Language Models (LLMs) have demonstrated their potential in hardware design tasks, such as Hardware Description Language (HDL) generation and debugging. Yet, their performance in real-world, repository-level HDL projects with thousands or even tens of thousands of code lines is hindered. To this end, we propose HDLxGraph, a novel framework that integrates Graph Retrieval Augmented Generation (Graph RAG) with LLMs, introducing HDL-specific graph representations by incorporating Abstract Syntax Trees (ASTs) and Data Flow Graphs (DFGs) to capture both code graph view and hardware graph view. HDLxGraph utilizes a dual-retrieval mechanism that not only mitigates the limited recall issues inherent in similarity-based semantic retrieval by incorporating structural information, but also enhances its extensibility to various real-world tasks by a task-specific retrieval finetuning. Additionally, to address the lack of comprehensive HDL search benchmarks, we introduce HDLSearch, a multi-granularity evaluation dataset derived from real-world repository-level projects. Experimental results demonstrate that HDLxGraph significantly improves average search accuracy, debugging efficiency and completion quality by 12.04%, 12.22% and 5.04% compared to similarity-based RAG, respectively. The code of HDLxGraph and collected HDLSearch benchmark are available at https://github.com/Nick-Zheng-Q/HDLxGraph.

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

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

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

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

Learning vector representations (aka. embeddings) of users and items lies at the core of modern recommender systems. Ranging from early matrix factorization to recently emerged deep learning based methods, existing efforts typically obtain a user's (or an item's) embedding by mapping from pre-existing features that describe the user (or the item), such as ID and attributes. We argue that an inherent drawback of such methods is that, the collaborative signal, which is latent in user-item interactions, is not encoded in the embedding process. As such, the resultant embeddings may not be sufficient to capture the collaborative filtering effect. In this work, we propose to integrate the user-item interactions -- more specifically the bipartite graph structure -- into the embedding process. We develop a new recommendation framework Neural Graph Collaborative Filtering (NGCF), which exploits the user-item graph structure by propagating embeddings on it. This leads to the expressive modeling of high-order connectivity in user-item graph, effectively injecting the collaborative signal into the embedding process in an explicit manner. We conduct extensive experiments on three public benchmarks, demonstrating significant improvements over several state-of-the-art models like HOP-Rec and Collaborative Memory Network. Further analysis verifies the importance of embedding propagation for learning better user and item representations, justifying the rationality and effectiveness of NGCF. Codes are available at https://github.com/xiangwang1223/neural_graph_collaborative_filtering.

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the academics and industries. However, analyses of large directed networks are often time-consuming and expensive because the complexities of a lot of graph algorithms are often polynomial with the size of the graph. Hence, sampling algorithms that can generate graphs preserving properties of original graph are of great importance because they can speed up the analysis process. We propose a promising framework to sample directed graphs: Construct a sample graph with linearly rescaled Joint Degree Matrix (JDM) and Degree Correlation Matrix (DCM). Previous work shows that graphs with the same JDM and DCM will have a range of very similar graph properties. We also conduct experiments on real-world datasets to show that the numbers of non-zero entries in JDM and DCM are quite small compared to the number of edges and nodes. Adopting this framework, we propose a novel graph sampling algorithm that can provably preserves in-degree and out-degree distributions, which are two most fundamental properties of a graph. We also prove the upper bound for deviations in the joint degree distribution and degree correlation distribution, which correspond to JDM and DCM. Besides, we prove that the deviations in these distributions are negatively correlated with the sparsity of the JDM and DCM. Considering that these two matrices are always quite sparse, we believe that proposed algorithm will have a better-than-theory performance on real-world large directed networks.

Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive generative capabilities that have been used to correct corruptions in images, and the similarities between "in-painting" and filling in missing nodes and edges conditioned on the observed graph, we propose a novel graph generative framework, SGDM, which is based on subgraph diffusion. Our framework not only improves the scalability and fidelity of graph diffusion models, but also leverages the reverse process to perform novel, conditional generation tasks. In particular, through extensive empirical analysis and a set of novel metrics, we demonstrate that our proposed model effectively supports the following refinement tasks for partially observable networks: T1: denoising extraneous subgraphs, T2: expanding existing subgraphs and T3: performing "style" transfer by regenerating a particular subgraph to match the characteristics of a different node or subgraph.

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

Knowledge Graphs (KGs) have been used to support a wide range of applications, from web search to personal assistant. In this paper, we describe three generations of knowledge graphs: entity-based KGs, which have been supporting general search and question answering (e.g., at Google and Bing); text-rich KGs, which have been supporting search and recommendations for products, bio-informatics, etc. (e.g., at Amazon and Alibaba); and the emerging integration of KGs and LLMs, which we call dual neural KGs. We describe the characteristics of each generation of KGs, the crazy ideas behind the scenes in constructing such KGs, and the techniques developed over time to enable industry impact. In addition, we use KGs as examples to demonstrate a recipe to evolve research ideas from innovations to production practice, and then to the next level of innovations, to advance both science and business.

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

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

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.

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.

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

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

This paper studies learning on text-attributed graphs (TAGs), where each node is associated with a text description. An ideal solution for such a problem would be integrating both the text and graph structure information with large language models and graph neural networks (GNNs). However, the problem becomes very challenging when graphs are large due to the high computational complexity brought by training large language models and GNNs together. In this paper, we propose an efficient and effective solution to learning on large text-attributed graphs by fusing graph structure and language learning with a variational Expectation-Maximization (EM) framework, called GLEM. Instead of simultaneously training large language models and GNNs on big graphs, GLEM proposes to alternatively update the two modules in the E-step and M-step. Such a procedure allows training the two modules separately while simultaneously allowing the two modules to interact and mutually enhance each other. Extensive experiments on multiple data sets demonstrate the efficiency and effectiveness of the proposed approach.

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

We propose a novel framework that leverages LLMs for full causal graph discovery. While previous LLM-based methods have used a pairwise query approach, this requires a quadratic number of queries which quickly becomes impractical for larger causal graphs. In contrast, the proposed framework uses a breadth-first search (BFS) approach which allows it to use only a linear number of queries. We also show that the proposed method can easily incorporate observational data when available, to improve performance. In addition to being more time and data-efficient, the proposed framework achieves state-of-the-art results on real-world causal graphs of varying sizes. The results demonstrate the effectiveness and efficiency of the proposed method in discovering causal relationships, showcasing its potential for broad applicability in causal graph discovery tasks across different domains.

The Text-to-SQL task, aiming to translate the natural language of the questions into SQL queries, has drawn much attention recently. One of the most challenging problems of Text-to-SQL is how to generalize the trained model to the unseen database schemas, also known as the cross-domain Text-to-SQL task. The key lies in the generalizability of (i) the encoding method to model the question and the database schema and (ii) the question-schema linking method to learn the mapping between words in the question and tables/columns in the database schema. Focusing on the above two key issues, we propose a Structure-Aware Dual Graph Aggregation Network (SADGA) for cross-domain Text-to-SQL. In SADGA, we adopt the graph structure to provide a unified encoding model for both the natural language question and database schema. Based on the proposed unified modeling, we further devise a structure-aware aggregation method to learn the mapping between the question-graph and schema-graph. The structure-aware aggregation method is featured with Global Graph Linking, Local Graph Linking, and Dual-Graph Aggregation Mechanism. We not only study the performance of our proposal empirically but also achieved 3rd place on the challenging Text-to-SQL benchmark Spider at the time of writing.

Graph neural networks (GNNs) have become compelling models designed to perform learning and inference on graph-structured data. However, little work has been done to understand the fundamental limitations of GNNs for scaling to larger graphs and generalizing to out-of-distribution (OOD) inputs. In this paper, we use a random graph generator to systematically investigate how the graph size and structural properties affect the predictive performance of GNNs. We present specific evidence that the average node degree is a key feature in determining whether GNNs can generalize to unseen graphs, and that the use of multiple node update functions can improve the generalization performance of GNNs when dealing with graphs of multimodal degree distributions. Accordingly, we propose a multi-module GNN framework that allows the network to adapt flexibly to new graphs by generalizing a single canonical nonlinear transformation over aggregated inputs. Our results show that the multi-module GNNs improve the OOD generalization on a variety of inference tasks in the direction of diverse structural features.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

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.

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

Recent advancements in graph diffusion models (GDMs) have enabled the synthesis of realistic network structures, yet ensuring fairness in the generated data remains a critical challenge. Existing solutions attempt to mitigate bias by re-training the GDMs with ad-hoc fairness constraints. Conversely, with this work, we propose FAROS, a novel FAir graph geneRatiOn framework leveraging attribute Switching mechanisms and directly running in the generation process of the pre-trained GDM. Technically, our approach works by altering nodes' sensitive attributes during the generation. To this end, FAROS calculates the optimal fraction of switching nodes, and selects the diffusion step to perform the switch by setting tailored multi-criteria constraints to preserve the node-topology profile from the original distribution (a proxy for accuracy) while ensuring the edge independence on the sensitive attributes for the generated graph (a proxy for fairness). Our experiments on benchmark datasets for link prediction demonstrate that the proposed approach effectively reduces fairness discrepancies while maintaining comparable (or even higher) accuracy performance to other similar baselines. Noteworthy, FAROS is also able to strike a better accuracy-fairness trade-off than other competitors in some of the tested settings under the Pareto optimality concept, demonstrating the effectiveness of the imposed multi-criteria constraints.

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

Real-world databases are predominantly relational, comprising multiple interlinked tables that contain complex structural and statistical dependencies. Learning generative models on relational data has shown great promise in generating synthetic data and imputing missing values. However, existing methods often struggle to capture this complexity, typically reducing relational data to conditionally generated flat tables and imposing limiting structural assumptions. To address these limitations, we introduce RelDiff, a novel diffusion generative model that synthesizes complete relational databases by explicitly modeling their foreign key graph structure. RelDiff combines a joint graph-conditioned diffusion process across all tables for attribute synthesis, and a 2K+SBM graph generator based on the Stochastic Block Model for structure generation. The decomposition of graph structure and relational attributes ensures both high fidelity and referential integrity, both of which are crucial aspects of synthetic relational database generation. Experiments on 11 benchmark datasets demonstrate that RelDiff consistently outperforms prior methods in producing realistic and coherent synthetic relational databases. Code is available at https://github.com/ValterH/RelDiff.

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

Generalizable, transferrable, and robust representation learning on graph-structured data remains a challenge for current graph neural networks (GNNs). Unlike what has been developed for convolutional neural networks (CNNs) for image data, self-supervised learning and pre-training are less explored for GNNs. In this paper, we propose a graph contrastive learning (GraphCL) framework for learning unsupervised representations of graph data. We first design four types of graph augmentations to incorporate various priors. We then systematically study the impact of various combinations of graph augmentations on multiple datasets, in four different settings: semi-supervised, unsupervised, and transfer learning as well as adversarial attacks. The results show that, even without tuning augmentation extents nor using sophisticated GNN architectures, our GraphCL framework can produce graph representations of similar or better generalizability, transferrability, and robustness compared to state-of-the-art methods. We also investigate the impact of parameterized graph augmentation extents and patterns, and observe further performance gains in preliminary experiments. Our codes are available at https://github.com/Shen-Lab/GraphCL.

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.

Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations suitable for extensive parallelization. By advocating graph as the central programming abstraction, DGL can perform optimizations transparently. By cautiously adopting a framework-neutral design, DGL allows users to easily port and leverage the existing components across multiple deep learning frameworks. Our evaluation shows that DGL significantly outperforms other popular GNN-oriented frameworks in both speed and memory consumption over a variety of benchmarks and has little overhead for small scale workloads.

Multi-modal recommender system focuses on utilizing rich modal information ( i.e., images and textual descriptions) of items to improve recommendation performance. The current methods have achieved remarkable success with the powerful structure modeling capability of graph neural networks. However, these methods are often hindered by sparse data in real-world scenarios. Although contrastive learning and homography ( i.e., homogeneous graphs) are employed to address the data sparsity challenge, existing methods still suffer two main limitations: 1) Simple multi-modal feature contrasts fail to produce effective representations, causing noisy modal-shared features and loss of valuable information in modal-unique features; 2) The lack of exploration of the homograph relations between user interests and item co-occurrence results in incomplete mining of user-item interplay. To address the above limitations, we propose a novel framework for REfining multi-modAl contRastive learning and hoMography relations (REARM). Specifically, we complement multi-modal contrastive learning by employing meta-network and orthogonal constraint strategies, which filter out noise in modal-shared features and retain recommendation-relevant information in modal-unique features. To mine homogeneous relationships effectively, we integrate a newly constructed user interest graph and an item co-occurrence graph with the existing user co-occurrence and item semantic graphs for graph learning. The extensive experiments on three real-world datasets demonstrate the superiority of REARM to various state-of-the-art baselines. Our visualization further shows an improvement made by REARM in distinguishing between modal-shared and modal-unique features. Code is available https://github.com/MrShouxingMa/REARM{here}.

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

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

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

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

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.

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5% gap of the best results in less than 0.5% of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

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.

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

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional 'Pre-train & Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates SIX pre-training methods and FIVE state-of-the-art graph prompt techniques, evaluated across FIFTEEN diverse datasets to assess performance, flexibility, and efficiency. We also present 'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques. The code is available at: https://github.com/sheldonresearch/ProG.

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

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

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

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

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

Unsupervised representation learning for dynamic graphs has attracted a lot of research attention in recent years. Compared with static graph, the dynamic graph is a comprehensive embodiment of both the intrinsic stable characteristics of nodes and the time-related dynamic preference. However, existing methods generally mix these two types of information into a single representation space, which may lead to poor explanation, less robustness, and a limited ability when applied to different downstream tasks. To solve the above problems, in this paper, we propose a novel disenTangled representation learning framework for discrete-time Dynamic graphs, namely DyTed. We specially design a temporal-clips contrastive learning task together with a structure contrastive learning to effectively identify the time-invariant and time-varying representations respectively. To further enhance the disentanglement of these two types of representation, we propose a disentanglement-aware discriminator under an adversarial learning framework from the perspective of information theory. Extensive experiments on Tencent and five commonly used public datasets demonstrate that DyTed, as a general framework that can be applied to existing methods, achieves state-of-the-art performance on various downstream tasks, as well as be more robust against noise.

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.

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests refactoring them into a unified design space for graph matching networks. Existing methods occupy only a few isolated patches in this space, which remains largely uncharted. We undertake the first comprehensive exploration of this space, featuring such axes as attention-based vs. soft permutation-based interaction between query and corpus graphs, aligning nodes vs. edges, and the form of the final scoring network that integrates neural representations of the graphs. Our extensive experiments reveal that judicious and hitherto-unexplored combinations of choices in this space lead to large performance benefits. Beyond better performance, our study uncovers valuable insights and establishes general design principles for neural graph representation and interaction, which may be of wider interest.

Multimodal recommender systems utilizing multimodal features (e.g., images and textual descriptions) typically show better recommendation accuracy than general recommendation models based solely on user-item interactions. Generally, prior work fuses multimodal features into item ID embeddings to enrich item representations, thus failing to capture the latent semantic item-item structures. In this context, LATTICE proposes to learn the latent structure between items explicitly and achieves state-of-the-art performance for multimodal recommendations. However, we argue the latent graph structure learning of LATTICE is both inefficient and unnecessary. Experimentally, we demonstrate that freezing its item-item structure before training can also achieve competitive performance. Based on this finding, we propose a simple yet effective model, dubbed as FREEDOM, that FREEzes the item-item graph and DenOises the user-item interaction graph simultaneously for Multimodal recommendation. Theoretically, we examine the design of FREEDOM through a graph spectral perspective and demonstrate that it possesses a tighter upper bound on the graph spectrum. In denoising the user-item interaction graph, we devise a degree-sensitive edge pruning method, which rejects possibly noisy edges with a high probability when sampling the graph. We evaluate the proposed model on three real-world datasets and show that FREEDOM can significantly outperform current strongest baselines. Compared with LATTICE, FREEDOM achieves an average improvement of 19.07% in recommendation accuracy while reducing its memory cost up to 6times on large graphs. The source code is available at: https://github.com/enoche/FREEDOM.

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

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

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

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

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

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

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

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

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

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.

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

Developing models capable of complex, multi-step reasoning is a central goal in artificial intelligence. While representing problems as graphs is a powerful approach, Graph Neural Networks (GNNs) are fundamentally constrained by their message-passing mechanism, which imposes a local bottleneck that limits global, holistic reasoning. We argue that dynamic programming (DP), which solves problems by iteratively refining a global state, offers a more powerful and suitable learning paradigm. We introduce FloydNet, a new architecture that embodies this principle. In contrast to local message passing, FloydNet maintains a global, all-pairs relationship tensor and learns a generalized DP operator to progressively refine it. This enables the model to develop a task-specific relational calculus, providing a principled framework for capturing long-range dependencies. Theoretically, we prove that FloydNet achieves 3-WL (2-FWL) expressive power, and its generalized form aligns with the k-FWL hierarchy. FloydNet demonstrates state-of-the-art performance across challenging domains: it achieves near-perfect scores (often >99\%) on the CLRS-30 algorithmic benchmark, finds exact optimal solutions for the general Traveling Salesman Problem (TSP) at rates significantly exceeding strong heuristics, and empirically matches the 3-WL test on the BREC benchmark. Our results establish this learned, DP-style refinement as a powerful and practical alternative to message passing for high-level graph reasoning.

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

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.

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.

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

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

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.