Daily Papers

Diagram-to-graph topology extraction aims to extract a graph of entities and their connections from a structural diagram. This task remains challenging for current vision-language models because it requires both fine-grained perceptual grounding and topology-aware reasoning with global consistency. We present TopoBench-180, a human-verified benchmark for diagram-to-graph topology extraction, and TopoAgent, a structure-aware perception-to-reasoning framework for reliable topology extraction using large vision-language models. TopoBench-180 contains 180 structural diagrams spanning Web-style and Network-style categories, paired with canonical graph annotations. TopoAgent progressively extracts the target graph by combining grounded perception, global structural priors, canonical node inventory construction, node-centric local-to-global relation reasoning, and topological consistency enforcement. Experiments on TopoBench-180 show that TopoAgent outperforms strong vision-language model baselines and recent visual reasoning frameworks, especially on edge extraction. More broadly, this work fills an important gap in multimodal structured understanding by establishing a benchmark and framework for diagram-to-graph topology extraction. The benchmark and associated resources will be publicly released at https://huggingface.co/datasets/WayneGuo0011/TopoBench-180.

Foundation models have demonstrated remarkable capabilities across various domains, but developing analogous models for knowledge graphs presents unique challenges due to their dynamic nature and the need for cross-domain reasoning. To address these issues, we introduce \textsc{GraphOracle}, a relation-centric foundation model that unifies reasoning across knowledge graphs by converting them into Relation-Dependency Graphs (RDG), explicitly encoding compositional patterns with fewer edges than prior methods. A query-dependent attention mechanism is further developed to learn inductive representations for both relations and entities. Pre-training on diverse knowledge graphs, followed by minutes-level fine-tuning, enables effective generalization to unseen entities, relations, and entire graphs. Through comprehensive experiments on 31 diverse benchmarks spanning transductive, inductive, and cross-domain settings, we demonstrate consistent state-of-the-art performance with minimal adaptation, improving the prediction performance by up to 35\% compared to the strongest baselines.

Knowledge Graph-based Question Answering (KGQA) plays a pivotal role in complex reasoning tasks but remains constrained by two persistent challenges: the structural heterogeneity of Knowledge Graphs(KGs) often leads to semantic mismatch during retrieval, while existing reasoning path retrieval methods lack a global structural perspective. To address these issues, we propose Structure-Tracing Evidence Mining (STEM), a novel framework that reframes multi-hop reasoning as a schema-guided graph search task. First, we design a Semantic-to-Structural Projection pipeline that leverages KG structural priors to decompose queries into atomic relational assertions and construct an adaptive query schema graph. Subsequently, we execute globally-aware node anchoring and subgraph retrieval to obtain the final evidence reasoning graph from KG. To more effectively integrate global structural information during the graph construction process, we design a Triple-Dependent GNN (Triple-GNN) to generate a Global Guidance Subgraph (Guidance Graph) that guides the construction. STEM significantly improves both the accuracy and evidence completeness of multi-hop reasoning graph retrieval, and achieves State-of-the-Art performance on multiple multi-hop benchmarks.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and complex query answering tasks by learning representations of entities, relations, and queries. Still, most existing query answering methods rely on transductive entity embeddings and cannot generalize to KGs containing new entities without retraining the entity embeddings. In this work, we study the inductive query answering task where inference is performed on a graph containing new entities with queries over both seen and unseen entities. To this end, we devise two mechanisms leveraging inductive node and relational structure representations powered by graph neural networks (GNNs). Experimentally, we show that inductive models are able to perform logical reasoning at inference time over unseen nodes generalizing to graphs up to 500% larger than training ones. Exploring the efficiency--effectiveness trade-off, we find the inductive relational structure representation method generally achieves higher performance, while the inductive node representation method is able to answer complex queries in the inference-only regime without any training on queries and scales to graphs of millions of nodes. Code is available at https://github.com/DeepGraphLearning/InductiveQE.

Generalizing to unseen graph tasks without task-pecific supervision remains challenging. Graph Neural Networks (GNNs) are limited by fixed label spaces, while Large Language Models (LLMs) lack structural inductive biases. Recent advances in Large Reasoning Models (LRMs) provide a zero-shot alternative via explicit, long chain-of-thought reasoning. Inspired by this, we propose a GNN-free approach that reformulates graph tasks--node classification, link prediction, and graph classification--as textual reasoning problems solved by LRMs. We introduce the first datasets with detailed reasoning traces for these tasks and develop Graph-R1, a reinforcement learning framework that leverages task-specific rethink templates to guide reasoning over linearized graphs. Experiments demonstrate that Graph-R1 outperforms state-of-the-art baselines in zero-shot settings, producing interpretable and effective predictions. Our work highlights the promise of explicit reasoning for graph learning and provides new resources for future research.

Reasoning over text-attributed graphs (TAGs) requires large language models (LLMs) to combine a node's text with evidence distributed across its neighbourhood. Existing methods fix the set of accessible neighbours before generation, forcing reasoning to operate over a static context and preventing the model from acquiring missing evidence during inference. We argue that neighbour selection should itself be part of the reasoning process. To this end, we propose Call Neighbours Yourself (CNY), a framework that enables LLMs to proactively explore graph neighbourhoods through topology-constrained graph-walk actions. Instead of reasoning over a pre-selected neighbour set, CNY exposes lightweight neighbour previews and learns when to expand candidate neighbours for additional evidence. To address the delayed-credit challenge of neighbour exploration, we introduce destination-conditioned on-policy self-distillation, which retrospectively evaluates a selected neighbour after its content is revealed and converts the resulting change in action preference into an action-level training signal. Experiments on standard TAG reasoning benchmarks under a unified raw-text setting show that CNY consistently outperforms fixed-context post-training baselines. Furthermore, the learned exploration policy transfers to unseen graphs and to a graph-level task not encountered during training. Code is available at https://github.com/superallen13/CNY.

Graph neural networks (GNNs) have shown promising performance for knowledge graph reasoning. A recent variant of GNN called progressive relational graph neural network (PRGNN), utilizes relational rules to infer missing knowledge in relational digraphs and achieves notable results. However, during reasoning with PRGNN, two important properties are often overlooked: (1) the sequentiality of relation composition, where the order of combining different relations affects the semantics of the relational rules, and (2) the lagged entity information propagation, where the transmission speed of required information lags behind the appearance speed of new entities. Ignoring these properties leads to incorrect relational rule learning and decreased reasoning accuracy. To address these issues, we propose a novel knowledge graph reasoning approach, the Relational rUle eNhanced Graph Neural Network (RUN-GNN). Specifically, RUN-GNN employs a query related fusion gate unit to model the sequentiality of relation composition and utilizes a buffering update mechanism to alleviate the negative effect of lagged entity information propagation, resulting in higher-quality relational rule learning. Experimental results on multiple datasets demonstrate the superiority of RUN-GNN is superior on both transductive and inductive link prediction tasks.

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

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

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

Large Language Models (LLMs) have made remarkable strides in reasoning tasks, yet their performance often falters on novel and complex problems. Domain-specific continued pretraining (CPT) methods, such as those tailored for mathematical reasoning, have shown promise but lack transferability to broader reasoning tasks. In this work, we pioneer the use of Graph Problem Reasoning (GPR) to enhance the general reasoning capabilities of LLMs. GPR tasks, spanning pathfinding, network analysis, numerical computation, and topological reasoning, require sophisticated logical and relational reasoning, making them ideal for teaching diverse reasoning patterns. To achieve this, we introduce GraphPile, the first large-scale corpus specifically designed for CPT using GPR data. Spanning 10.9 billion tokens across 23 graph tasks, the dataset includes chain-of-thought, program-of-thought, trace of execution, and real-world graph data. Using GraphPile, we train GraphMind on popular base models Llama 3 and 3.1, as well as Gemma 2, achieving up to 4.9 percent higher accuracy in mathematical reasoning and up to 21.2 percent improvement in non-mathematical reasoning tasks such as logical and commonsense reasoning. By being the first to harness GPR for enhancing reasoning patterns and introducing the first dataset of its kind, our work bridges the gap between domain-specific pretraining and universal reasoning capabilities, advancing the adaptability and robustness of LLMs.

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.

This work aims to tackle the challenging heterogeneous graph encoding problem in the text-to-SQL task. Previous methods are typically node-centric and merely utilize different weight matrices to parameterize edge types, which 1) ignore the rich semantics embedded in the topological structure of edges, and 2) fail to distinguish local and non-local relations for each node. To this end, we propose a Line Graph Enhanced Text-to-SQL (LGESQL) model to mine the underlying relational features without constructing meta-paths. By virtue of the line graph, messages propagate more efficiently through not only connections between nodes, but also the topology of directed edges. Furthermore, both local and non-local relations are integrated distinctively during the graph iteration. We also design an auxiliary task called graph pruning to improve the discriminative capability of the encoder. Our framework achieves state-of-the-art results (62.8% with Glove, 72.0% with Electra) on the cross-domain text-to-SQL benchmark Spider at the time of writing.

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins, and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.

Large language models have shown strong performance in natural language generation and downstream reasoning tasks, but they still struggle with logical consistency, factual grounding, and interpretability in complex multi-step reasoning. To address these limitations, this paper proposes SGR, a stepwise reasoning enhancement framework that integrates large language models with external knowledge graphs through query-relevant subgraph generation. Given an input question, SGR first extracts key entities, relations, and constraints to construct a structured schema, then retrieves compact subgraphs from a knowledge graph using schema-guided querying. The generated subgraphs provide explicit relational evidence that guides the language model through step-by-step reasoning. In addition, SGR combines direct Cypher-based reasoning with collaborative reasoning integration, allowing candidate answers from multiple reasoning paths to be validated and aggregated according to both model confidence and graph consistency. Experiments on benchmark datasets including CWQ, WebQSP, GrailQA, and KQA Pro demonstrate that SGR improves reasoning accuracy and Hits@1 performance over standard prompting and several knowledge-enhanced baselines. Ablation studies further show that schema guidance and Neo4j-based retrieval are both crucial to the effectiveness of the framework. These results indicate that dynamically generated external subgraphs can improve the accuracy, robustness, and interpretability of LLM-based reasoning.

Large language models (LLMs) excel at reasoning but struggle with knowledge-intensive questions due to limited context and parametric knowledge. However, existing methods that rely on finetuned LLMs or GNN retrievers are limited by dataset-specific tuning and scalability on large or unseen graphs. We propose the LLM-KGFR collaborative framework, where an LLM works with a structured retriever, the Knowledge Graph Foundation Retriever (KGFR). KGFR encodes relations using LLM-generated descriptions and initializes entities based on their roles in the question, enabling zero-shot generalization to unseen KGs. To handle large graphs efficiently, it employs Asymmetric Progressive Propagation (APP)- a stepwise expansion that selectively limits high-degree nodes while retaining informative paths. Through node-, edge-, and path-level interfaces, the LLM iteratively requests candidate answers, supporting facts, and reasoning paths, forming a controllable reasoning loop. Experiments demonstrate that LLM-KGFR achieves strong performance while maintaining scalability and generalization, providing a practical solution for KG-augmented reasoning.

Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to embed entities in vector space for logical query operations, but they suffer from subpar performance on complex queries and dataset-specific representations. In this paper, we propose a novel decoupled approach, Language-guided Abstract Reasoning over Knowledge graphs (LARK), that formulates complex KG reasoning as a combination of contextual KG search and logical query reasoning, to leverage the strengths of graph extraction algorithms and large language models (LLM), respectively. Our experiments demonstrate that the proposed approach outperforms state-of-the-art KG reasoning methods on standard benchmark datasets across several logical query constructs, with significant performance gain for queries of higher complexity. Furthermore, we show that the performance of our approach improves proportionally to the increase in size of the underlying LLM, enabling the integration of the latest advancements in LLMs for logical reasoning over KGs. Our work presents a new direction for addressing the challenges of complex KG reasoning and paves the way for future research in this area.

Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through large-scale pretraining and generalization, extending these capabilities to graphs -- characterized by non-Euclidean structures and complex relational semantics -- poses unique challenges and opens new opportunities. To this end, Graph Foundation Models (GFMs) aim to bring scalable, general-purpose intelligence to structured data, enabling broad transfer across graph-centric tasks and domains. This survey provides a comprehensive overview of GFMs, unifying diverse efforts under a modular framework comprising three key components: backbone architectures, pretraining strategies, and adaptation mechanisms. We categorize GFMs by their generalization scope -- universal, task-specific, and domain-specific -- and review representative methods, key innovations, and theoretical insights within each category. Beyond methodology, we examine theoretical foundations including transferability and emergent capabilities, and highlight key challenges such as structural alignment, heterogeneity, scalability, and evaluation. Positioned at the intersection of graph learning and general-purpose AI, GFMs are poised to become foundational infrastructure for open-ended reasoning over structured data. This survey consolidates current progress and outlines future directions to guide research in this rapidly evolving field. Resources are available at https://github.com/Zehong-Wang/Awesome-Foundation-Models-on-Graphs.

Recent advances in search-augmented large reasoning models (LRMs) enable the retrieval of external knowledge to reduce hallucinations in multistep reasoning. However, their ability to operate on graph-structured data, prevalent in domains such as e-commerce, social networks, and scientific citations, remains underexplored. Unlike plain text corpora, graphs encode rich topological signals that connect related entities and can serve as valuable priors for retrieval, enabling more targeted search and improved reasoning efficiency. Yet, effectively leveraging such structure poses unique challenges, including the difficulty of generating graph-expressive queries and ensuring reliable retrieval that balances structural and semantic relevance. To address this gap, we introduce GraphSearch, the first framework that extends search-augmented reasoning to graph learning, enabling zero-shot graph learning without task-specific fine-tuning. GraphSearch combines a Graph-aware Query Planner, which disentangles search space (e.g., 1-hop, multi-hop, or global neighbors) from semantic queries, with a Graph-aware Retriever, which constructs candidate sets based on topology and ranks them using a hybrid scoring function. We further instantiate two traversal modes: GraphSearch-R, which recursively expands neighborhoods hop by hop, and GraphSearch-F, which flexibly retrieves across local and global neighborhoods without hop constraints. Extensive experiments across diverse benchmarks show that GraphSearch achieves competitive or even superior performance compared to supervised graph learning methods, setting state-of-the-art results in zero-shot node classification and link prediction. These findings position GraphSearch as a flexible and generalizable paradigm for agentic reasoning over graphs.

Large language models (LLMs) excel at complex reasoning but remain limited by static and incomplete parametric knowledge. Retrieval-augmented generation (RAG) mitigates this by incorporating external knowledge, yet existing RAGs struggle with knowledge-intensive tasks due to fragmented information and weak modeling of knowledge structure. Graphs offer a natural way to model relationships within knowledge, but LLMs are inherently unstructured and cannot effectively reason over graph-structured data. Recent graph-enhanced RAG (GraphRAG) attempts to bridge this gap by constructing tailored graphs and enabling LLMs to reason on them. However, these methods often depend on ad-hoc graph designs, heuristic search, or costly agent pipelines, which hinder scalability and generalization. To address these challenges, we present G-reasoner, a unified framework that integrates graph and language foundation models for scalable reasoning over diverse graph-structured knowledge. Central to our approach is QuadGraph, a standardized four-layer abstraction that unifies heterogeneous knowledge sources into a common graph representation. Building on this, we introduce a 34M-parameter graph foundation model (GFM) that jointly captures graph topology and textual semantics, and is integrated with LLMs to enhance reasoning in downstream applications. To ensure scalability and efficiency, mixed-precision training and distributed message-passing are implemented to scale GFM with more GPUs. Extensive experiments on six benchmarks show that G-reasoner consistently outperforms state-of-the-art baselines, significantly enhances LLM reasoning, and achieves strong efficiency and cross-graph generalization.

Representation learning on heterogeneous graphs aims to obtain meaningful node representations to facilitate various downstream tasks, such as node classification and link prediction. Existing heterogeneous graph learning methods are primarily developed by following the propagation mechanism of node representations. There are few efforts on studying the role of relations for improving the learning of more fine-grained node representations. Indeed, it is important to collaboratively learn the semantic representations of relations and discern node representations with respect to different relation types. To this end, in this paper, we propose a novel Relation-aware Heterogeneous Graph Neural Network, namely R-HGNN, to learn node representations on heterogeneous graphs at a fine-grained level by considering relation-aware characteristics. Specifically, a dedicated graph convolution component is first designed to learn unique node representations from each relation-specific graph separately. Then, a cross-relation message passing module is developed to improve the interactions of node representations across different relations. Also, the relation representations are learned in a layer-wise manner to capture relation semantics, which are used to guide the node representation learning process. Moreover, a semantic fusing module is presented to aggregate relation-aware node representations into a compact representation with the learned relation representations. Finally, we conduct extensive experiments on a variety of graph learning tasks, and experimental results demonstrate that our approach consistently outperforms existing methods among all the tasks.

Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs can understand. In contrast, many real-world relational patterns do not naturally conform to the pairwise-edge assumption, and are better modeled as high-order associations in hypergraphs. For hypergraph structures, existing methods often fail to preserve the native semantics that multiple objects are jointly connected by the same high-order relation, limiting their ability to exploit complex structures. To address this limitation, we put forth the "Hypergraph as Language" perspective and propose Hyper-Align, a hypergraph-native alignment framework for large language models. Hyper-Align compiles the query-object-centered hypergraph context into hypergraph tokens directly consumable by a base LLM. Specifically, we introduce Hypergraph Incidence Detail Template with Overview (HIDT-O), which serializes high-order association structures into a fixed-shape hybrid template combining local incidence details and overview-level summaries. We then design a Hypergraph Incidence Projector (HIP), which maps native high-order incidence structures into the LLM token space through explicit semantic-structural decoupling and bidirectional message passing between vertices and hyperedges. We further define a concrete Hypergraph-as-Language input protocol, which jointly feeds hypergraph tokens and textual prompts into a frozen base LLM, supporting both vertex-level and hyperedge-level tasks under a unified question-answering paradigm. To systematically evaluate different methods in hypergraph structural modeling, we introduce HyperAlign-Bench. Extensive experiments show that Hyper-Align significantly outperforms existing methods across in-domain and zero-shot evaluations.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

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

Large language models (LLMs) are capable of answering knowledge-intensive complex questions with chain-of-thought (CoT) reasoning. However, they tend to generate factually incorrect reasoning steps when the required knowledge is not available or up-to-date in models' parameters. Recent works turn to retrieving external knowledge to augment CoT reasoning. Despite being promising, these chain-based methods suffer from: 1) Negative retrieval. Unnecessary or incorrect retrieval may mislead the reasoning; 2) Limited sight. Lacking the ability to look backward or forward, a local error in one step will propagate along the chain. In this paper, we propose a novel approach: Probabilistic Tree-of-thought Reasoning (ProbTree). First, LLMs translate a complex question into a query tree, in which each non-root node denotes a sub-question of its parent node. Then, probabilistic reasoning is conducted over the tree, by solving questions from leaf to root considering the confidence of both question decomposing and answering. During reasoning, for leaf nodes, LLMs choose a more confident answer from Closed-book QA that employs parametric knowledge and Open-book QA that employs retrieved external knowledge, thus eliminating the negative retrieval problem. For non-leaf nodes, with the hierarchical structure, LLMs have broader sights and are able to globally reason with the information from child nodes, thus recovering from local errors. The experiments on three Complex QA datasets under the open-domain setting show that our approach outperforms SOTA methods significantly, demonstrating the effect of probabilistic tree-of-thought reasoning.

Attention mechanisms have been widely used to capture long-range dependencies among nodes in Graph Transformers. Bottlenecked by the quadratic computational cost, attention mechanisms fail to scale in large graphs. Recent improvements in computational efficiency are mainly achieved by attention sparsification with random or heuristic-based graph subsampling, which falls short in data-dependent context reasoning. State space models (SSMs), such as Mamba, have gained prominence for their effectiveness and efficiency in modeling long-range dependencies in sequential data. However, adapting SSMs to non-sequential graph data presents a notable challenge. In this work, we introduce Graph-Mamba, the first attempt to enhance long-range context modeling in graph networks by integrating a Mamba block with the input-dependent node selection mechanism. Specifically, we formulate graph-centric node prioritization and permutation strategies to enhance context-aware reasoning, leading to a substantial improvement in predictive performance. Extensive experiments on ten benchmark datasets demonstrate that Graph-Mamba outperforms state-of-the-art methods in long-range graph prediction tasks, with a fraction of the computational cost in both FLOPs and GPU memory consumption. The code and models are publicly available at https://github.com/bowang-lab/Graph-Mamba.

Large Language Models (LLMs) demonstrate an impressive capacity to recall a vast range of factual knowledge. However, understanding their underlying reasoning and internal mechanisms in exploiting this knowledge remains a key research area. This work unveils the factual information an LLM represents internally for sentence-level claim verification. We propose an end-to-end framework to decode factual knowledge embedded in token representations from a vector space to a set of ground predicates, showing its layer-wise evolution using a dynamic knowledge graph. Our framework employs activation patching, a vector-level technique that alters a token representation during inference, to extract encoded knowledge. Accordingly, we neither rely on training nor external models. Using factual and common-sense claims from two claim verification datasets, we showcase interpretability analyses at local and global levels. The local analysis highlights entity centrality in LLM reasoning, from claim-related information and multi-hop reasoning to representation errors causing erroneous evaluation. On the other hand, the global reveals trends in the underlying evolution, such as word-based knowledge evolving into claim-related facts. By interpreting semantics from LLM latent representations and enabling graph-related analyses, this work enhances the understanding of the factual knowledge resolution process.

While large language models (LLMs) have made significant progress in processing and reasoning over knowledge graphs, current methods suffer from a high non-retrieval rate. This limitation reduces the accuracy of answering questions based on these graphs. Our analysis reveals that the combination of greedy search and forward reasoning is a major contributor to this issue. To overcome these challenges, we introduce the concept of super-relations, which enables both forward and backward reasoning by summarizing and connecting various relational paths within the graph. This holistic approach not only expands the search space, but also significantly improves retrieval efficiency. In this paper, we propose the ReKnoS framework, which aims to Reason over Knowledge Graphs with Super-Relations. Our framework's key advantages include the inclusion of multiple relation paths through super-relations, enhanced forward and backward reasoning capabilities, and increased efficiency in querying LLMs. These enhancements collectively lead to a substantial improvement in the successful retrieval rate and overall reasoning performance. We conduct extensive experiments on nine real-world datasets to evaluate ReKnoS, and the results demonstrate the superior performance of ReKnoS over existing state-of-the-art baselines, with an average accuracy gain of 2.92%.

We present an approach to modifying Transformer architectures by integrating graph-aware relational reasoning into the attention mechanism, merging concepts from graph neural networks and language modeling. Building on the inherent connection between attention and graph theory, we reformulate the Transformer's attention mechanism as a graph operation and propose Graph-Aware Isomorphic Attention. This method leverages advanced graph modeling strategies, including Graph Isomorphism Networks (GIN) and Principal Neighborhood Aggregation (PNA), to enrich the representation of relational structures. Our approach captures complex dependencies and generalizes across tasks, as evidenced by a reduced generalization gap and improved learning performance. Additionally, we expand the concept of graph-aware attention to introduce Sparse GIN-Attention, a fine-tuning approach that employs sparse GINs. By interpreting attention matrices as sparse adjacency graphs, this technique enhances the adaptability of pre-trained foundational models with minimal computational overhead, endowing them with graph-aware capabilities. Sparse GIN-Attention fine-tuning achieves improved training dynamics and better generalization compared to alternative methods like low-rank adaption (LoRA). We discuss latent graph-like structures within traditional attention mechanisms, offering a new lens through which Transformers can be understood. By evolving Transformers as hierarchical GIN models for relational reasoning. This perspective suggests profound implications for foundational model development, enabling the design of architectures that dynamically adapt to both local and global dependencies. Applications in bioinformatics, materials science, language modeling, and beyond could benefit from this synthesis of relational and sequential data modeling, setting the stage for interpretable and generalizable modeling strategies.

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.

In this work, we seek new insights into the underlying challenges of the Scene Graph Generation (SGG) task. Quantitative and qualitative analysis of the Visual Genome dataset implies -- 1) Ambiguity: even if inter-object relationship contains the same object (or predicate), they may not be visually or semantically similar, 2) Asymmetry: despite the nature of the relationship that embodied the direction, it was not well addressed in previous studies, and 3) Higher-order contexts: leveraging the identities of certain graph elements can help to generate accurate scene graphs. Motivated by the analysis, we design a novel SGG framework, Local-to-Global Interaction Networks (LOGIN). Locally, interactions extract the essence between three instances of subject, object, and background, while baking direction awareness into the network by explicitly constraining the input order of subject and object. Globally, interactions encode the contexts between every graph component (i.e., nodes and edges). Finally, Attract & Repel loss is utilized to fine-tune the distribution of predicate embeddings. By design, our framework enables predicting the scene graph in a bottom-up manner, leveraging the possible complementariness. To quantify how much LOGIN is aware of relational direction, a new diagnostic task called Bidirectional Relationship Classification (BRC) is also proposed. Experimental results demonstrate that LOGIN can successfully distinguish relational direction than existing methods (in BRC task), while showing state-of-the-art results on the Visual Genome benchmark (in SGG task).

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

Knowledge Graphs (KGs) are valuable tools for representing relationships between entities in a structured format. Traditionally, these knowledge bases are queried to extract specific information. However, question-answering (QA) over such KGs poses a challenge due to the intrinsic complexity of natural language compared to the structured format and the size of these graphs. Despite these challenges, the structured nature of KGs can provide a solid foundation for grounding the outputs of Large Language Models (LLMs), offering organizations increased reliability and control. Recent advancements in LLMs have introduced reasoning methods at inference time to improve their performance and maximize their capabilities. In this work, we propose integrating these reasoning strategies with KGs to anchor every step or "thought" of the reasoning chains in KG data. Specifically, we evaluate both agentic and automated search methods across several reasoning strategies, including Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT), using GRBench, a benchmark dataset for graph reasoning with domain-specific graphs. Our experiments demonstrate that this approach consistently outperforms baseline models, highlighting the benefits of grounding LLM reasoning processes in structured KG data.

Relational reasoning is a central component of generally intelligent behavior, but has proven difficult for neural networks to learn. In this paper we describe how to use Relation Networks (RNs) as a simple plug-and-play module to solve problems that fundamentally hinge on relational reasoning. We tested RN-augmented networks on three tasks: visual question answering using a challenging dataset called CLEVR, on which we achieve state-of-the-art, super-human performance; text-based question answering using the bAbI suite of tasks; and complex reasoning about dynamic physical systems. Then, using a curated dataset called Sort-of-CLEVR we show that powerful convolutional networks do not have a general capacity to solve relational questions, but can gain this capacity when augmented with RNs. Our work shows how a deep learning architecture equipped with an RN module can implicitly discover and learn to reason about entities and their relations.

Large Language Models (LLMs) often struggle with inherent knowledge boundaries and hallucinations, limiting their reliability in knowledge-intensive tasks. While Retrieval-Augmented Generation (RAG) mitigates these issues, it frequently overlooks structural interdependencies essential for multi-hop reasoning. Graph-based RAG approaches attempt to bridge this gap, yet they typically face trade-offs between accuracy and efficiency due to challenges such as costly graph traversals and semantic noise in LLM-generated summaries. In this paper, we propose HyperNode Expansion and Logical Path-Guided Evidence Localization strategies for GraphRAG (HELP), a novel framework designed to balance accuracy with practical efficiency through two core strategies: 1) HyperNode Expansion, which iteratively chains knowledge triplets into coherent reasoning paths abstracted as HyperNodes to capture complex structural dependencies and ensure retrieval accuracy; and 2) Logical Path-Guided Evidence Localization, which leverages precomputed graph-text correlations to map these paths directly to the corpus for superior efficiency. HELP avoids expensive random walks and semantic distortion, preserving knowledge integrity while drastically reducing retrieval latency. Extensive experiments demonstrate that HELP achieves competitive performance across multiple simple and multi-hop QA benchmarks and up to a 28.8times speedup over leading Graph-based RAG baselines.

We propose Reasoning to Ground (R2G), a neural symbolic model that grounds the target objects within 3D scenes in a reasoning manner. In contrast to prior works, R2G explicitly models the 3D scene with a semantic concept-based scene graph; recurrently simulates the attention transferring across object entities; thus makes the process of grounding the target objects with the highest probability interpretable. Specifically, we respectively embed multiple object properties within the graph nodes and spatial relations among entities within the edges, utilizing a predefined semantic vocabulary. To guide attention transferring, we employ learning or prompting-based methods to analyze the referential utterance and convert it into reasoning instructions within the same semantic space. In each reasoning round, R2G either (1) merges current attention distribution with the similarity between the instruction and embedded entity properties or (2) shifts the attention across the scene graph based on the similarity between the instruction and embedded spatial relations. The experiments on Sr3D/Nr3D benchmarks show that R2G achieves a comparable result with the prior works while maintaining improved interpretability, breaking a new path for 3D language grounding.

Large Language Models (LLMs) show strong reasoning ability in open-domain question answering, yet their reasoning processes are typically linear and often logically inconsistent. In contrast, real-world reasoning requires integrating multiple premises and solving subproblems in parallel. Existing methods, such as Chain-of-Thought (CoT), express reasoning in a linear textual form, which may appear coherent but frequently leads to inconsistent conclusions. Recent approaches rely on externally provided graphs and do not explore how LLMs can construct and use their own graph-structured reasoning, particularly in open-domain QA. To fill this gap, we novelly explore graph-structured reasoning of LLMs in general-domain question answering. We propose Self-Graph Reasoning (SGR), a framework that enables LLMs to explicitly represent their reasoning process as a structured graph before producing the final answer. We further construct a graph-structured reasoning dataset that merges multiple candidate reasoning graphs into refined graph structures for model training. Experiments on five QA benchmarks across both general and specialized domains show that SGR consistently improves reasoning consistency and yields a 17.74% gain over the base model. The LLaMA-3.3-70B model fine-tuned with SGR performs comparably to GPT-4o and surpasses Claude-3.5-Haiku, demonstrating the effectiveness of graph-structured reasoning.

Graph retrieval-augmented generation (GraphRAG) has effectively enhanced large language models in complex reasoning by organizing fragmented knowledge into explicitly structured graphs. Prior efforts have been made to improve either graph construction or graph retrieval in isolation, yielding suboptimal performance, especially when domain shifts occur. In this paper, we propose a vertically unified agentic paradigm, Youtu-GraphRAG, to jointly connect the entire framework as an intricate integration. Specifically, (i) a seed graph schema is introduced to bound the automatic extraction agent with targeted entity types, relations and attribute types, also continuously expanded for scalability over unseen domains; (ii) To obtain higher-level knowledge upon the schema, we develop novel dually-perceived community detection, fusing structural topology with subgraph semantics for comprehensive knowledge organization. This naturally yields a hierarchical knowledge tree that supports both top-down filtering and bottom-up reasoning with community summaries; (iii) An agentic retriever is designed to interpret the same graph schema to transform complex queries into tractable and parallel sub-queries. It iteratively performs reflection for more advanced reasoning; (iv) To alleviate the knowledge leaking problem in pre-trained LLM, we propose a tailored anonymous dataset and a novel 'Anonymity Reversion' task that deeply measures the real performance of the GraphRAG frameworks. Extensive experiments across six challenging benchmarks demonstrate the robustness of Youtu-GraphRAG, remarkably moving the Pareto frontier with up to 90.71% saving of token costs and 16.62% higher accuracy over state-of-the-art baselines. The results indicate our adaptability, allowing seamless domain transfer with minimal intervention on schema.

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.

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

Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the computational feasibility of the global attention mechanism is possible. The next goal is to scale up these architectures to handle very large graphs on the scale of millions or even billions of nodes. With large-scale graphs, global attention learning is proven impractical due to its quadratic complexity w.r.t. the number of nodes. On the other hand, neighborhood sampling techniques become essential to manage large graph sizes, yet finding the optimal trade-off between speed and accuracy with sampling techniques remains challenging. This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints for developing scalable graph transformer (GT) architectures. We argue such GT requires layers that can adeptly learn both local and global graph representations while swiftly sampling the graph topology. As such, a key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism that encompasses a 4-hop reception field, but achieved through just 2-hop operations. This local node embedding is then integrated with a global node embedding, acquired via another self-attention layer with an approximate global codebook, before finally sent through a downstream layer for node predictions. The proposed GT framework, named LargeGT, overcomes previous computational bottlenecks and is validated on three large-scale node classification benchmarks. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-papers100M with a 5.9% performance improvement.

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.

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

Large language models (LLMs) have recently been applied to 3D vision-language (3D-VL) tasks, which require spatial reasoning to identify target objects relative to anchors. Scene graphs are commonly employed to represent such relations, but reasoning over complete graphs incurs high token costs and computational inefficiencies, motivating the need for pruning. Existing pruning methods primarily rely on spatial proximity and often remove task-relevant relations, thereby undermining reliable spatial reasoning. To address these limitations, we derive a key requirement for scene graph pruning: preserving spatial relations that are most pertinent to the specific 3D-VL task. Guided by this insight, we propose the Conceptual-Adjacent Scene Graph Pruner (CAPruner). CAPruner integrates fuzzy semantic relevance with spatial proximity to estimate the importance of relations, enabling the selection of critical relations in a task-specific context. Moreover, to avoid costly relation-level annotations, CAPruner is trained by supervising the aggregated scores of each node's incident edges. Extensive experiments demonstrate that CAPruner effectively preserves relations essential for spatial reasoning, leading to substantial performance improvements of LLMs on 3D-VL tasks. Code is available at https://github.com/fz-zsl/CAPruner.

Link prediction, a fundamental task on graphs, has proven indispensable in various applications, e.g., friend recommendation, protein analysis, and drug interaction prediction. However, since datasets span a multitude of domains, they could have distinct underlying mechanisms of link formation. Evidence in existing literature underscores the absence of a universally best algorithm suitable for all datasets. In this paper, we endeavor to explore principles of link prediction across diverse datasets from a data-centric perspective. We recognize three fundamental factors critical to link prediction: local structural proximity, global structural proximity, and feature proximity. We then unearth relationships among those factors where (i) global structural proximity only shows effectiveness when local structural proximity is deficient. (ii) The incompatibility can be found between feature and structural proximity. Such incompatibility leads to GNNs for Link Prediction (GNN4LP) consistently underperforming on edges where the feature proximity factor dominates. Inspired by these new insights from a data perspective, we offer practical instruction for GNN4LP model design and guidelines for selecting appropriate benchmark datasets for more comprehensive evaluations.

Graphs are a fundamental data structure for representing relationships in real-world scenarios. With the success of Large Language Models (LLMs) across various natural language processing (NLP) tasks, there has been growing interest in integrating LLMs for graph learning. However, applying LLMs to graph-related tasks poses significant challenges, as these models are not inherently designed to capture the complex structural information present in graphs. Existing approaches address this challenge through two strategies: the chain of tasks approach, which uses Graph Neural Networks (GNNs) to encode the graph structure so that LLMs are relieved from understanding spatial positions; and Graph-to-Text Conversion, which translates graph structures into semantic text representations that LLMs can process. Despite their progress, these methods often struggle to fully preserve the topological information of graphs or require extensive computational resources, limiting their practical applicability. In this work, we introduce Node Tokenizer for Large Language Models (NT-LLM), a novel framework that efficiently encodes graph structures by selecting key nodes as anchors and representing each node based on its relative distance to these anchors. This position-anchored encoding effectively captures the graph topology, enabling enhanced reasoning capabilities in LLMs over graph data. Additionally, we implement a task-specific tuning procedure to further improve structural understanding within LLMs. Through extensive empirical evaluations, NT-LLM demonstrates significant performance improvements across a variety of graph-related tasks.

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

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.

Long-range dependencies are critical for effective graph representation learning, yet most existing datasets focus on small graphs tailored to inductive tasks, offering limited insight into long-range interactions. Current evaluations primarily compare models employing global attention (e.g., graph transformers) with those using local neighborhood aggregation (e.g., message-passing neural networks) without a direct measurement of long-range dependency. In this work, we introduce City-Networks, a novel large-scale transductive learning dataset derived from real-world city roads. This dataset features graphs with over 10^5 nodes and significantly larger diameters than those in existing benchmarks, naturally embodying long-range information. We annotate the graphs using an eccentricity-based approach, ensuring that the classification task inherently requires information from distant nodes. Furthermore, we propose a model-agnostic measurement based on the Jacobians of neighbors from distant hops, offering a principled quantification of long-range dependencies. Finally, we provide theoretical justifications for both our dataset design and the proposed measurement - particularly by focusing on over-smoothing and influence score dilution - which establishes a robust foundation for further exploration of long-range interactions in graph neural networks.

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.

The growing demand for automated graph algorithm reasoning has attracted increasing attention in the large language model (LLM) community. Recent LLM-based graph reasoning methods typically decouple task descriptions from graph data, generate executable code augmented by retrieval from technical documentation, and refine the code through debugging. However, we identify two key limitations in existing approaches: (i) they treat technical documentation as flat text collections and ignore its hierarchical structure, leading to noisy retrieval that degrades code generation quality; and (ii) their debugging mechanisms focus primarily on runtime errors, yet ignore more critical logical errors. To address them, we propose {\method}, an agentic hierarchical retrieval-augmented coding framework that exploits the document hierarchy through top-down traversal and early pruning, together with a self-debugging coding agent that iteratively refines code using automatically generated small-scale test cases. To enable comprehensive evaluation of complex graph reasoning, we introduce a new dataset, {\dataset}, covering small-scale, large-scale, and composite graph reasoning tasks. Extensive experiments demonstrate that our method achieves higher task accuracy and lower inference cost compared to baselinesThe code is available at \href{https://github.com/FairyFali/GraphSkill{blue{https://github.com/FairyFali/GraphSkill}}.}.

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

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

Our collective attention span is shortened by the flood of online information. With FarFetched, we address the need for automated claim validation based on the aggregated evidence derived from multiple online news sources. We introduce an entity-centric reasoning framework in which latent connections between events, actions, or statements are revealed via entity mentions and represented in a graph database. Using entity linking and semantic similarity, we offer a way for collecting and combining information from diverse sources in order to generate evidence relevant to the user's claim. Then, we leverage textual entailment recognition to quantitatively determine whether this assertion is credible, based on the created evidence. Our approach tries to fill the gap in automated claim validation for less-resourced languages and is showcased on the Greek language, complemented by the training of relevant semantic textual similarity (STS) and natural language inference (NLI) models that are evaluated on translated versions of common benchmarks.

The Non-Local Network (NLNet) presents a pioneering approach for capturing long-range dependencies, via aggregating query-specific global context to each query position. However, through a rigorous empirical analysis, we have found that the global contexts modeled by non-local network are almost the same for different query positions within an image. In this paper, we take advantage of this finding to create a simplified network based on a query-independent formulation, which maintains the accuracy of NLNet but with significantly less computation. We further observe that this simplified design shares similar structure with Squeeze-Excitation Network (SENet). Hence we unify them into a three-step general framework for global context modeling. Within the general framework, we design a better instantiation, called the global context (GC) block, which is lightweight and can effectively model the global context. The lightweight property allows us to apply it for multiple layers in a backbone network to construct a global context network (GCNet), which generally outperforms both simplified NLNet and SENet on major benchmarks for various recognition tasks. The code and configurations are released at https://github.com/xvjiarui/GCNet.

Graph neural networks (GNNs) have become an indispensable tool for analyzing relational data. In the literature, classical GNNs may be classified into three variants: convolutional, attentional, and message-passing. While the standard message-passing variant is highly expressive, its typical pair-wise messages nevertheless only consider the features of the center node and each neighboring node individually. This design fails to incorporate the rich contextual information contained within the broader local neighborhood, potentially hindering its ability to learn complex relationships within the entire set of neighboring nodes. To address this limitation, this work first formalizes the concept of neighborhood-contextualization, rooted in a key property of the attentional variant. This then serves as the foundation for generalizing the message-passing variant to the proposed neighborhood-contextualized message-passing (NCMP) framework. To demonstrate its utility, a simple, practical, and efficient method to parametrize and operationalize NCMP is presented, leading to the development of the proposed Soft-Isomorphic Neighborhood-Contextualized Graph Convolution Network (SINC-GCN). A preliminary analysis on a synthetic binary node classification problem then underscores both the expressivity and efficiency of the proposed GNN architecture. Overall, the paper lays the foundation for the novel NCMP framework as a practical path toward further enhancing the graph representational power of classical GNNs.

Social relation reasoning aims to identify relation categories such as friends, spouses, and colleagues from images. While current methods adopt the paradigm of training a dedicated network end-to-end using labeled image data, they are limited in terms of generalizability and interpretability. To address these issues, we first present a simple yet well-crafted framework named {\name}, which combines the perception capability of Vision Foundation Models (VFMs) and the reasoning capability of Large Language Models (LLMs) within a modular framework, providing a strong baseline for social relation recognition. Specifically, we instruct VFMs to translate image content into a textual social story, and then utilize LLMs for text-based reasoning. {\name} introduces systematic design principles to adapt VFMs and LLMs separately and bridge their gaps. Without additional model training, it achieves competitive zero-shot results on two databases while offering interpretable answers, as LLMs can generate language-based explanations for the decisions. The manual prompt design process for LLMs at the reasoning phase is tedious and an automated prompt optimization method is desired. As we essentially convert a visual classification task into a generative task of LLMs, automatic prompt optimization encounters a unique long prompt optimization issue. To address this issue, we further propose the Greedy Segment Prompt Optimization (GSPO), which performs a greedy search by utilizing gradient information at the segment level. Experimental results show that GSPO significantly improves performance, and our method also generalizes to different image styles. The code is available at https://github.com/Mengzibin/SocialGPT.

The Non-Local Network (NLNet) presents a pioneering approach for capturing long-range dependencies within an image, via aggregating query-specific global context to each query position. However, through a rigorous empirical analysis, we have found that the global contexts modeled by the non-local network are almost the same for different query positions. In this paper, we take advantage of this finding to create a simplified network based on a query-independent formulation, which maintains the accuracy of NLNet but with significantly less computation. We further replace the one-layer transformation function of the non-local block by a two-layer bottleneck, which further reduces the parameter number considerably. The resulting network element, called the global context (GC) block, effectively models global context in a lightweight manner, allowing it to be applied at multiple layers of a backbone network to form a global context network (GCNet). Experiments show that GCNet generally outperforms NLNet on major benchmarks for various recognition tasks. The code and network configurations are available at https://github.com/xvjiarui/GCNet.

Graph Foundation Models (GFMs) have achieved remarkable success in generalizing across diverse domains. However, they mainly focus on Text-Attributed Graphs (TAGs), leaving Multimodal-Attributed Graphs (MAGs) largely untapped. Developing Multimodal Graph Foundation Models (MGFMs) allows for leveraging the rich multimodal information in MAGs, and extends applicability to broader types of downstream tasks. While recent MGFMs integrate diverse modality information, our empirical investigation reveals two fundamental limitations of existing MGFMs: (1)they fail to explicitly model modality interaction, essential for capturing intricate cross-modal semantics beyond simple aggregation, and (2)they exhibit sub-optimal modality alignment, which is critical for bridging the significant semantic disparity between distinct modal spaces. To address these challenges, we propose PLANET (graPh topoLogy-aware modAlity iNteraction and alignmEnT), a novel framework employing a Divide-and-Conquer strategy to decouple modality interaction and alignment across distinct granularities. At the embedding granularity, (1)Embedding-wise Domain Gating (EDG) performs local semantic enrichment by adaptively infusing topology-aware cross-modal context, achieving modality interaction. At the node granularity, (2)Node-wise Discretization Retrieval (NDR) ensures global modality alignment by constructing a Discretized Semantic Representation Space (DSRS) to bridge modality gaps. Extensive experiments demonstrate that PLANET significantly outperforms state-of-the-art baselines across diverse graph-centric and multimodal generative tasks.

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample complexity) if its individual components align well with the target algorithm. Specifically, GNNs are claimed to align with dynamic programming (DP), a general problem-solving strategy which expresses many polynomial-time algorithms. However, has this alignment truly been demonstrated and theoretically quantified? Here we show, using methods from category theory and abstract algebra, that there exists an intricate connection between GNNs and DP, going well beyond the initial observations over individual algorithms such as Bellman-Ford. Exposing this connection, we easily verify several prior findings in the literature, produce better-grounded GNN architectures for edge-centric tasks, and demonstrate empirical results on the CLRS algorithmic reasoning benchmark. We hope our exposition will serve as a foundation for building stronger algorithmically aligned GNNs.

Knowledge Graph Foundation Models (KGFMs) have shown promise in enabling zero-shot reasoning over unseen graphs by learning transferable patterns. However, most existing KGFMs rely solely on graph structure, overlooking the rich semantic signals encoded in textual attributes. We introduce SEMMA, a dual-module KGFM that systematically integrates transferable textual semantics alongside structure. SEMMA leverages Large Language Models (LLMs) to enrich relation identifiers, generating semantic embeddings that subsequently form a textual relation graph, which is fused with the structural component. Across 54 diverse KGs, SEMMA outperforms purely structural baselines like ULTRA in fully inductive link prediction. Crucially, we show that in more challenging generalization settings, where the test-time relation vocabulary is entirely unseen, structural methods collapse while SEMMA is 2x more effective. Our findings demonstrate that textual semantics are critical for generalization in settings where structure alone fails, highlighting the need for foundation models that unify structural and linguistic signals in knowledge reasoning.

Answering complex real-world questions often requires accurate retrieval from textual knowledge graphs (TKGs). The scarcity of annotated data, along with intricate topological structures, makes this task particularly challenging. As the nature of relational path information could enhance the inference ability of Large Language Models (LLMs), efficiently retrieving more complex relational path information from TKGs presents another key challenge. To tackle these challenges, we first develop a Dataset for LLMs Complex Reasoning over Textual Knowledge Graphs (RiTeK) with a broad topological structure coverage.We synthesize realistic user queries that integrate diverse topological structures, relational information, and complex textual descriptions. We conduct rigorous expert evaluation to validate the quality of our synthesized queries. And then, we introduce an enhanced Monte Carlo Tree Search (MCTS) method, Relational MCTS, to automatically extract relational path information from textual graphs for specific queries. Our dataset mainly covers the medical domain as the relation types and entity are complex and publicly available. Experimental results indicate that RiTeK poses significant challenges for current retrieval and LLM systems, while the proposed Relational MCTS method enhances LLM inference ability and achieves state-of-the-art performance on RiTeK.

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models often focus on structured inputs such as tables, graphs, or synthetic tasks, and do not isolate the difficulty introduced by higher-arity relational binding. We study this problem through the lens of Relational Complexity (RC), which we define as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty while controlling for confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Across frontier LLMs, performance degrades consistently and monotonically as RC increases, even when the total number of entities is held fixed. This failure mode persists with increased test-time compute and in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than to insufficient inference steps or lack of exposure to examples. Our results identify a regime of higher-arity reasoning in which current models struggle, and motivate re-examining benchmarks through the lens of relational complexity.

Relational Deep Learning (RDL) models multi-tabular databases as temporal heterogeneous graphs for end-to-end representation learning. While RDL is evolving rapidly, existing approaches face significant generalization obstacles. They are either schema-specific, requiring training from scratch for every new database, or they rely on monolithic architectures that entangle feature encoding with graph message-passing. Analyzing these limitations, we establish four core pillars for building foundational relational models: semantic granularity, structural topology, temporal causality, and unified optimization. Addressing these pillars, we propose a modular approach that decouples row encoding from graph message-passing. We introduce the Universal Row Encoder, a transformer-based module that integrates raw cell data with schema metadata-including column semantics, table names, and global distribution statistics-to produce table-width invariant row embeddings. By explicitly feeding global statistics to an intra-row self-attention mechanism, the encoder natively contextualizes unseen features and handles sparse data. Serving as a flexible "backend" for any downstream graph architecture, our pretrained encoder enhances cross-database knowledge transfer on the established RelBench benchmarks while improving learning convergence and memory footprint.

Graph Attention Network (GAT) focuses on modelling simple undirected and single relational graph data only. This limits its ability to deal with more general and complex multi-relational graphs that contain entities with directed links of different labels (e.g., knowledge graphs). Therefore, directly applying GAT on multi-relational graphs leads to sub-optimal solutions. To tackle this issue, we propose r-GAT, a relational graph attention network to learn multi-channel entity representations. Specifically, each channel corresponds to a latent semantic aspect of an entity. This enables us to aggregate neighborhood information for the current aspect using relation features. We further propose a query-aware attention mechanism for subsequent tasks to select useful aspects. Extensive experiments on link prediction and entity classification tasks show that our r-GAT can model multi-relational graphs effectively. Also, we show the interpretability of our approach by case study.

Neural link predictors are immensely useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries that arise in a number of domains, such as queries using logical conjunctions (land), disjunctions (lor) and existential quantifiers (exists), while accounting for missing edges. In this work, we propose a framework for efficiently answering complex queries on incomplete Knowledge Graphs. We translate each query into an end-to-end differentiable objective, where the truth value of each atom is computed by a pre-trained neural link predictor. We then analyse two solutions to the optimisation problem, including gradient-based and combinatorial search. In our experiments, the proposed approach produces more accurate results than state-of-the-art methods -- black-box neural models trained on millions of generated queries -- without the need of training on a large and diverse set of complex queries. Using orders of magnitude less training data, we obtain relative improvements ranging from 8% up to 40% in Hits@3 across different knowledge graphs containing factual information. Finally, we demonstrate that it is possible to explain the outcome of our model in terms of the intermediate solutions identified for each of the complex query atoms. All our source code and datasets are available online, at https://github.com/uclnlp/cqd.

Graph-structured data exhibit substantial heterogeneity in where their predictive signals originate: in some domains, node-level semantics dominate, while in others, structural patterns play a central role. This structure-semantics heterogeneity implies that no graph learning model with a fixed inductive bias can generalize optimally across diverse graph domains. However, most existing methods address this challenge from the model side by incrementally injecting new inductive biases, which remains fundamentally limited given the open-ended diversity of real-world graphs. In this work, we take a data-centric perspective and treat node semantics as a task-adaptive variable. We propose a Data-Adaptive Semantic Refinement framework DAS for graph representation learning, which couples a fixed graph neural network (GNN) and a large language model (LLM) in a closed feedback loop. The GNN provides implicit supervisory signals to guide the semantic refinement of LLM, and the refined semantics are fed back to update the same graph learner. We evaluate our approach on both text-rich and text-free graphs. Results show consistent improvements on structure-dominated graphs while remaining competitive on semantics-rich graphs, demonstrating the effectiveness of data-centric semantic adaptation under structure-semantics heterogeneity.

Reasoning-acting frameworks enhance large language models (LLMs) by interleaving reasoning with actions for dynamic information acquisition. However, extending this paradigm to graph learning remains underexplored. Graph data is inherently structured, with information distributed across nodes and edges and encoded through both topology and latent representations. As a result, effective reasoning over graphs requires not only retrieving informative evidence from the graph, but also progressively refining the accumulated context during multi-step inference. In this work, we propose GraphReAct, a graph reasoning-acting framework that enables step-by-step inference over graph-structured data. Specifically, we design a graph-based action space with two complementary retrieval actions: topological retrieval, which captures local structural dependencies, and semantic retrieval, which accesses non-local but relevant evidence in the representation space. These actions dynamically expand the reasoning context. To further support multi-step reasoning, we introduce another type of action, context refinement, which distills and reorganizes accumulated information into a compact representation. By interleaving reasoning with both retrieval and refinement actions, our framework enables a progressive transition from context expansion to compression. Extensive experiments on six benchmark datasets demonstrate that GraphReAct consistently outperforms state-of-the-art methods, validating the effectiveness of reasoning-acting for graph learning.

This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational network, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]'s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty-CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

The prevalence of relation networks in computer vision is in stark contrast to underexplored point-based methods. In this paper, we explore the possibilities of local relation operators and survey their feasibility. We propose a scalable and efficient module, called group relation aggregator. The module computes a feature of a group based on the aggregation of the features of the inner-group points weighted by geometric relations and semantic relations. We adopt this module to design our RPNet. We further verify the expandability of RPNet, in terms of both depth and width, on the tasks of classification and segmentation. Surprisingly, empirical results show that wider RPNet fits for classification, while deeper RPNet works better on segmentation. RPNet achieves state-of-the-art for classification and segmentation on challenging benchmarks. We also compare our local aggregator with PointNet++, with around 30% parameters and 50% computation saving. Finally, we conduct experiments to reveal the robustness of RPNet with regard to rigid transformation and noises.

While Multimodal Large Language Models (MLLMs) excel in semantic tasks, they frequently lack the "spatial sense" essential for sophisticated geometric reasoning. Current models typically suffer from exorbitant modality-alignment costs and deficiency in fine-grained structural modeling precision.We introduce SSR, a framework designed for Structured Scene Reasoning that seamlessly integrates 2D and 3D representations via a lightweight alignment mechanism. To minimize training overhead, our framework anchors 3D geometric features to the large language model's pre-aligned 2D visual semantics through cross-modal addition and token interleaving, effectively obviating the necessity for large-scale alignment pre-training. To underpin complex spatial reasoning, we propose a novel scene graph generation pipeline that represents global layouts as a chain of independent local triplets defined by relative coordinates. This is complemented by an incremental generation algorithm, enabling the model to construct "language-model-friendly" structural scaffolds for complex environments. Furthermore, we extend these capabilities to global-scale 3D global grounding task, achieving absolute metric precision across heterogeneous data sources. At a 7B parameter scale, SSR achieves state-of-the-art performance on multiple spatial intelligence benchmarks, notably scoring 73.9 on VSI-Bench. Our approach significantly outperforms much larger models, demonstrating that efficient feature alignment and structured scene reasoning are the cornerstones of authentic spatial intelligence.

The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to images and audio. Despite this progress, a critical gap remains in empowering LLMs to proficiently understand and reason on graph data. Recent studies underscore LLMs' underwhelming performance on fundamental graph reasoning tasks. In this paper, we endeavor to unearth the obstacles that impede LLMs in graph reasoning, pinpointing the common practice of converting graphs into natural language descriptions (Graph2Text) as a fundamental bottleneck. To overcome this impediment, we introduce GraphLLM, a pioneering end-to-end approach that synergistically integrates graph learning models with LLMs. This synergy equips LLMs with the ability to proficiently interpret and reason on graph data, harnessing the superior expressive power of graph learning models. Our empirical evaluations across four fundamental graph reasoning tasks validate the effectiveness of GraphLLM. The results exhibit a substantial average accuracy enhancement of 54.44%, alongside a noteworthy context reduction of 96.45% across various graph reasoning tasks.

We propose STRuCT-LLM, a unified framework for training large language models (LLMs) to perform structured reasoning over both relational and graph-structured data. Our approach jointly optimizes Text-to-SQL and Text-to-Cypher tasks using reinforcement learning (RL) combined with Chain-of-Thought (CoT) supervision. To support fine-grained optimization in graph-based parsing, we introduce a topology-aware reward function based on graph edit distance. Unlike prior work that treats relational and graph formalisms in isolation, STRuCT-LLM leverages shared abstractions between SQL and Cypher to induce cross-formalism transfer, enabling SQL training to improve Cypher performance and vice versa - even without shared schemas. Our largest model (QwQ-32B) achieves substantial relative improvements across tasks: on semantic parsing, Spider improves by 13.5\% and Text2Cypher by 73.1\%. The model also demonstrates strong zero-shot generalization, improving performance on downstream tabular QA (TableBench: 8.5\%) and knowledge graph QA (CR-LT-KGQA: 1.7\%) without any QA-specific supervision. These results demonstrate both the effectiveness of executable queries as scaffolds for structured reasoning and the synergistic benefits of jointly training on SQL and Cypher (code available at https://github.com/bouv/STRuCT-LLM).

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

Although Large Language Models (LLMs) have demonstrated remarkable progress, their proficiency in graph-related tasks remains notably limited, hindering the development of truly general-purpose models. Previous attempts, including pretraining graph foundation models or employing supervised fine-tuning, often face challenges such as the scarcity of large-scale, universally represented graph data. We introduce G1, a simple yet effective approach demonstrating that Reinforcement Learning (RL) on synthetic graph-theoretic tasks can significantly scale LLMs' graph reasoning abilities. To enable RL training, we curate Erd\~os, the largest graph reasoning dataset to date comprising 50 diverse graph-theoretic tasks of varying difficulty levels, 100k training data and 5k test data, all drived from real-world graphs. With RL on Erd\~os, G1 obtains substantial improvements in graph reasoning, where our finetuned 3B model even outperforms Qwen2.5-72B-Instruct (24x size). RL-trained models also show strong zero-shot generalization to unseen tasks, domains, and graph encoding schemes, including other graph-theoretic benchmarks as well as real-world node classification and link prediction tasks, without compromising general reasoning abilities. Our findings offer an efficient, scalable path for building strong graph reasoners by finetuning LLMs with RL on graph-theoretic tasks, which combines the strengths of pretrained LLM capabilities with abundant, automatically generated synthetic data, suggesting that LLMs possess graph understanding abilities that RL can elicit successfully.

Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.

Graph Neural Networks (GNNs) have achieved remarkable performance on graph-based tasks. The key idea for GNNs is to obtain informative representation through aggregating information from local neighborhoods. However, it remains an open question whether the neighborhood information is adequately aggregated for learning representations of nodes with few neighbors. To address this, we propose a simple and efficient data augmentation strategy, local augmentation, to learn the distribution of the node features of the neighbors conditioned on the central node's feature and enhance GNN's expressive power with generated features. Local augmentation is a general framework that can be applied to any GNN model in a plug-and-play manner. It samples feature vectors associated with each node from the learned conditional distribution as additional input for the backbone model at each training iteration. Extensive experiments and analyses show that local augmentation consistently yields performance improvement when applied to various GNN architectures across a diverse set of benchmarks. For example, experiments show that plugging in local augmentation to GCN and GAT improves by an average of 3.4\% and 1.6\% in terms of test accuracy on Cora, Citeseer, and Pubmed. Besides, our experimental results on large graphs (OGB) show that our model consistently improves performance over backbones. Code is available at https://github.com/SongtaoLiu0823/LAGNN.

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

Recent advances in question answering have led to substantial progress in tasks such as multi-hop reasoning. However, global sensemaking-answering questions by synthesizing information from an entire corpus remains a significant challenge. A prior graph-based approach to global sensemaking lacks retrieval mechanisms, topic specificity, and incurs high inference costs. To address these limitations, we propose ReTAG, a Retrieval-Enhanced, Topic-Augmented Graph framework that constructs topic-specific subgraphs and retrieves the relevant summaries for response generation. Experiments show that ReTAG improves response quality while significantly reducing inference time compared to the baseline. Our code is available at https://github.com/bykimby/retag.

Large language models (LLMs) have demonstrated impressive reasoning abilities, but they still struggle with faithful reasoning due to knowledge gaps and hallucinations. To address these issues, knowledge graphs (KGs) have been utilized to enhance LLM reasoning through their structured knowledge. However, existing KG-enhanced methods, either retrieval-based or agent-based, encounter difficulties in accurately retrieving knowledge and efficiently traversing KGs at scale. In this work, we introduce graph-constrained reasoning (GCR), a novel framework that bridges structured knowledge in KGs with unstructured reasoning in LLMs. To eliminate hallucinations, GCR ensures faithful KG-grounded reasoning by integrating KG structure into the LLM decoding process through KG-Trie, a trie-based index that encodes KG reasoning paths. KG-Trie constrains the decoding process, allowing LLMs to directly reason on graphs and generate faithful reasoning paths grounded in KGs. Additionally, GCR leverages a lightweight KG-specialized LLM for graph-constrained reasoning alongside a powerful general LLM for inductive reasoning over multiple reasoning paths, resulting in accurate reasoning with zero reasoning hallucination. Extensive experiments on several KGQA benchmarks demonstrate that GCR achieves state-of-the-art performance and exhibits strong zero-shot generalizability to unseen KGs without additional training.

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

Reasoning over commonsense knowledge bases (CSKB) whose elements are in the form of free-text is an important yet hard task in NLP. While CSKB completion only fills the missing links within the domain of the CSKB, CSKB population is alternatively proposed with the goal of reasoning unseen assertions from external resources. In this task, CSKBs are grounded to a large-scale eventuality (activity, state, and event) graph to discriminate whether novel triples from the eventuality graph are plausible or not. However, existing evaluations on the population task are either not accurate (automatic evaluation with randomly sampled negative examples) or of small scale (human annotation). In this paper, we benchmark the CSKB population task with a new large-scale dataset by first aligning four popular CSKBs, and then presenting a high-quality human-annotated evaluation set to probe neural models' commonsense reasoning ability. We also propose a novel inductive commonsense reasoning model that reasons over graphs. Experimental results show that generalizing commonsense reasoning on unseen assertions is inherently a hard task. Models achieving high accuracy during training perform poorly on the evaluation set, with a large gap between human performance. We will make the data publicly available for future contributions. Codes and data are available at https://github.com/HKUST-KnowComp/CSKB-Population.

Reasoning over visual relationships-spatial, functional, interactional, social, etc.-is considered to be a fundamental component of human cognition. Yet, despite the major advances in visual comprehension in multimodal language models (MLMs), precise reasoning over relationships and their generations remains a challenge. We introduce ROBIN: an MLM instruction-tuned with densely annotated relationships capable of constructing high-quality dense scene graphs at scale. To train ROBIN, we curate SVG, a synthetic scene graph dataset by completing the missing relations of selected objects in existing scene graphs using a teacher MLM and a carefully designed filtering process to ensure high-quality. To generate more accurate and rich scene graphs at scale for any image, we introduce SG-EDIT: a self-distillation framework where GPT-4o further refines ROBIN's predicted scene graphs by removing unlikely relations and/or suggesting relevant ones. In total, our dataset contains 146K images and 5.6M relationships for 2.6M objects. Results show that our ROBIN-3B model, despite being trained on less than 3 million instances, outperforms similar-size models trained on over 300 million instances on relationship understanding benchmarks, and even surpasses larger models up to 13B parameters. Notably, it achieves state-of-the-art performance in referring expression comprehension with a score of 88.9, surpassing the previous best of 87.4. Our results suggest that training on the refined scene graph data is crucial to maintaining high performance across diverse visual reasoning task.

Rule learning is critical to improving knowledge graph (KG) reasoning due to their ability to provide logical and interpretable explanations. Recently, Graph Neural Networks (GNNs) with tail entity scoring achieve the state-of-the-art performance on KG reasoning. However, the theoretical understandings for these GNNs are either lacking or focusing on single-relational graphs, leaving what the kind of rules these GNNs can learn an open problem. We propose to fill the above gap in this paper. Specifically, GNNs with tail entity scoring are unified into a common framework. Then, we analyze their expressivity by formally describing the rule structures they can learn and theoretically demonstrating their superiority. These results further inspire us to propose a novel labeling strategy to learn more rules in KG reasoning. Experimental results are consistent with our theoretical findings and verify the effectiveness of our proposed method. The code is publicly available at https://github.com/LARS-research/Rule-learning-expressivity.

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.

Current Scene Graph Generation (SGG) methods explore contextual information to predict relationships among entity pairs. However, due to the diverse visual appearance of numerous possible subject-object combinations, there is a large intra-class variation within each predicate category, e.g., "man-eating-pizza, giraffe-eating-leaf", and the severe inter-class similarity between different classes, e.g., "man-holding-plate, man-eating-pizza", in model's latent space. The above challenges prevent current SGG methods from acquiring robust features for reliable relation prediction. In this paper, we claim that the predicate's category-inherent semantics can serve as class-wise prototypes in the semantic space for relieving the challenges. To the end, we propose the Prototype-based Embedding Network (PE-Net), which models entities/predicates with prototype-aligned compact and distinctive representations and thereby establishes matching between entity pairs and predicates in a common embedding space for relation recognition. Moreover, Prototype-guided Learning (PL) is introduced to help PE-Net efficiently learn such entitypredicate matching, and Prototype Regularization (PR) is devised to relieve the ambiguous entity-predicate matching caused by the predicate's semantic overlap. Extensive experiments demonstrate that our method gains superior relation recognition capability on SGG, achieving new state-of-the-art performances on both Visual Genome and Open Images datasets.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating external knowledge. Current hybrid RAG system retrieves evidence from both knowledge graphs (KGs) and text documents to support LLM reasoning. However, it faces challenges like handling multi-hop reasoning, multi-entity questions, multi-source verification, and effective graph utilization. To address these limitations, we present Hydra, a training-free framework that unifies graph topology, document semantics, and source reliability to support deep, faithful reasoning in LLMs. Hydra handles multi-hop and multi-entity problems through agent-driven exploration that combines structured and unstructured retrieval, increasing both diversity and precision of evidence. To tackle multi-source verification, Hydra uses a tri-factor cross-source verification (source trustworthiness assessment, cross-source corroboration, and entity-path alignment), to balance topic relevance with cross-modal agreement. By leveraging graph structure, Hydra fuses heterogeneous sources, guides efficient exploration, and prunes noise early. Comprehensive experiments on seven benchmark datasets show that Hydra achieves overall state-of-the-art results on all benchmarks with GPT-3.5, outperforming the strong hybrid baseline ToG-2 by an average of 20.3% and up to 30.1%. Furthermore, Hydra enables smaller models (e.g., Llama-3.1-8B) to achieve reasoning performance comparable to that of GPT-4-Turbo.

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data is both challenging and time consuming. The core problem is that no machine learning method is capable of learning on multiple tables interconnected by primary-foreign key relations. Current methods can only learn from a single table, so the data must first be manually joined and aggregated into a single training table, the process known as feature engineering. Feature engineering is slow, error prone and leads to suboptimal models. Here we introduce an end-to-end deep representation learning approach to directly learn on data laid out across multiple tables. We name our approach Relational Deep Learning (RDL). The core idea is to view relational databases as a temporal, heterogeneous graph, with a node for each row in each table, and edges specified by primary-foreign key links. Message Passing Graph Neural Networks can then automatically learn across the graph to extract representations that leverage all input data, without any manual feature engineering. Relational Deep Learning leads to more accurate models that can be built much faster. To facilitate research in this area, we develop RelBench, a set of benchmark datasets and an implementation of Relational Deep Learning. The data covers a wide spectrum, from discussions on Stack Exchange to book reviews on the Amazon Product Catalog. Overall, we define a new research area that generalizes graph machine learning and broadens its applicability to a wide set of AI use cases.

Graph Retrieval-Augmented Generation (GraphRAG) is dominated by a retrieve-then-reason paradigm, where context is retrieved using heuristics and then reasoned over. Such methods struggle to adapt to the query-specific logic required for complex multi-hop tasks, often accumulating irrelevant context or missing correct relational paths. We propose DotRAG, a training-free GraphRAG framework that reformulates retrieval as a reasoning process over paths. Our approach generates query-conditioned constraints that guide graph exploration, prune irrelevant regions, and iteratively discover relational paths without relying on explicit step-by-step reasoning chains. We introduce Division of Thought (DOT), an abstraction that decomposes retrieval into localized search spaces and adapts the search strategy to each query. DotRAG achieves SOTA performance on MetaQA and UltraDomain, with consistent gains on multi-hop tasks, demonstrating the effectiveness of reasoning-guided retrieval.

Text-rich graphs, which integrate complex structural dependencies with abundant textual information, are ubiquitous yet remain challenging for existing learning paradigms. Conventional methods and even LLM-hybrids compress rich text into static embeddings or summaries before structural reasoning, creating an information bottleneck and detaching updates from the raw content. We argue that in text-rich graphs, the text is not merely a node attribute but the primary medium through which structural relationships are manifested. We introduce RAMP, a Raw-text Anchored Message Passing approach that moves beyond using LLMs as mere feature extractors and instead recasts the LLM itself as a graph-native aggregation operator. RAMP exploits the text-rich nature of the graph via a novel dual-representation scheme: it anchors inference on each node's raw text during each iteration while propagating dynamically optimized messages from neighbors. It further handles both discriminative and generative tasks under a single unified generative formulation. Extensive experiments show that RAMP effectively bridges the gap between graph propagation and deep text reasoning, achieving competitive performance and offering new insights into the role of LLMs as graph kernels for general-purpose graph learning.

Reasoning about time and temporal relations is an integral aspect of human cognition, essential for perceiving the world and navigating our experiences. Though large language models (LLMs) have demonstrated impressive performance in many reasoning tasks, temporal reasoning remains challenging due to its intrinsic complexity. In this work, we first study an essential task of temporal reasoning -- temporal graph generation, to unveil LLMs' inherent, global reasoning capabilities. We show that this task presents great challenges even for the most powerful LLMs, such as GPT-3.5/4. We also notice a significant performance gap by small models (<10B) that lag behind LLMs by 50%. Next, we study how to close this gap with a budget constraint, e.g., not using model finetuning. We propose a new prompting technique tailored for temporal reasoning, Narrative-of-Thought (NoT), that first converts the events set to a Python class, then prompts a small model to generate a temporally grounded narrative, guiding the final generation of a temporal graph. Extensive experiments showcase the efficacy of NoT in improving various metrics. Notably, NoT attains the highest F1 on the Schema-11 evaluation set, while securing an overall F1 on par with GPT-3.5. NoT also achieves the best structural similarity across the board, even compared with GPT-3.5/4. Our code is available at https://github.com/launchnlp/NoT.

Transformers flexibly operate over sets of real-valued vectors representing task-specific entities and their attributes, where each vector might encode one word-piece token and its position in a sequence, or some piece of information that carries no position at all. But as set processors, transformers are at a disadvantage in reasoning over more general graph-structured data where nodes represent entities and edges represent relations between entities. To address this shortcoming, we generalize transformer attention to consider and update edge vectors in each transformer layer. We evaluate this relational transformer on a diverse array of graph-structured tasks, including the large and challenging CLRS Algorithmic Reasoning Benchmark. There, it dramatically outperforms state-of-the-art graph neural networks expressly designed to reason over graph-structured data. Our analysis demonstrates that these gains are attributable to relational attention's inherent ability to leverage the greater expressivity of graphs over sets.

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.

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

Knowledge graph (KG) reasoning is an important problem for knowledge graphs. In this paper, we propose a novel and principled framework called RulE (stands for {Rul}e {E}mbedding) to effectively leverage logical rules to enhance KG reasoning. Unlike knowledge graph embedding (KGE) methods, RulE learns rule embeddings from existing triplets and first-order {rules} by jointly representing entities, relations and logical rules in a unified embedding space. Based on the learned rule embeddings, a confidence score can be calculated for each rule, reflecting its consistency with the observed triplets. This allows us to perform logical rule inference in a soft way, thus alleviating the brittleness of logic. On the other hand, RulE injects prior logical rule information into the embedding space, enriching and regularizing the entity/relation embeddings. This makes KGE alone perform better too. RulE is conceptually simple and empirically effective. We conduct extensive experiments to verify each component of RulE. Results on multiple benchmarks reveal that our model outperforms the majority of existing embedding-based and rule-based approaches.

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

Complex logical query answering (CLQA) is a recently emerged task of graph machine learning that goes beyond simple one-hop link prediction and solves a far more complex task of multi-hop logical reasoning over massive, potentially incomplete graphs in a latent space. The task received a significant traction in the community; numerous works expanded the field along theoretical and practical axes to tackle different types of complex queries and graph modalities with efficient systems. In this paper, we provide a holistic survey of CLQA with a detailed taxonomy studying the field from multiple angles, including graph types (modality, reasoning domain, background semantics), modeling aspects (encoder, processor, decoder), supported queries (operators, patterns, projected variables), datasets, evaluation metrics, and applications. Refining the CLQA task, we introduce the concept of Neural Graph Databases (NGDBs). Extending the idea of graph databases (graph DBs), NGDB consists of a Neural Graph Storage and a Neural Graph Engine. Inside Neural Graph Storage, we design a graph store, a feature store, and further embed information in a latent embedding store using an encoder. Given a query, Neural Query Engine learns how to perform query planning and execution in order to efficiently retrieve the correct results by interacting with the Neural Graph Storage. Compared with traditional graph DBs, NGDBs allow for a flexible and unified modeling of features in diverse modalities using the embedding store. Moreover, when the graph is incomplete, they can provide robust retrieval of answers which a normal graph DB cannot recover. Finally, we point out promising directions, unsolved problems and applications of NGDB for future research.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Modeling spatial-temporal relations is imperative for recognizing human actions, especially when a human is interacting with objects, while multiple objects appear around the human differently over time. Most existing action recognition models focus on learning overall visual cues of a scene but disregard informative fine-grained features, which can be captured by learning human-object relationships and interactions. In this paper, we learn human-object relationships by exploiting the interaction of their local and global contexts. We hence propose the Global-Local Interaction Distillation Network (GLIDN), learning human and object interactions through space and time via knowledge distillation for fine-grained scene understanding. GLIDN encodes humans and objects into graph nodes and learns local and global relations via graph attention network. The local context graphs learn the relation between humans and objects at a frame level by capturing their co-occurrence at a specific time step. The global relation graph is constructed based on the video-level of human and object interactions, identifying their long-term relations throughout a video sequence. More importantly, we investigate how knowledge from these graphs can be distilled to their counterparts for improving human-object interaction (HOI) recognition. We evaluate our model by conducting comprehensive experiments on two datasets including Charades and CAD-120 datasets. We have achieved better results than the baselines and counterpart approaches.

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.

Aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. To better comprehend long complicated sentences and obtain accurate aspect-specific information, linguistic and commonsense knowledge are generally required in this task. However, most current methods employ complicated and inefficient approaches to incorporate external knowledge, e.g., directly searching the graph nodes. Additionally, the complementarity between external knowledge and linguistic information has not been thoroughly studied. To this end, we propose a knowledge graph augmented network KGAN, which aims to effectively incorporate external knowledge with explicitly syntactic and contextual information. In particular, KGAN captures the sentiment feature representations from multiple different perspectives, i.e., context-, syntax- and knowledge-based. First, KGAN learns the contextual and syntactic representations in parallel to fully extract the semantic features. Then, KGAN integrates the knowledge graphs into the embedding space, based on which the aspect-specific knowledge representations are further obtained via an attention mechanism. Last, we propose a hierarchical fusion module to complement these multi-view representations in a local-to-global manner. Extensive experiments on five popular ABSA benchmarks demonstrate the effectiveness and robustness of our KGAN. Notably, with the help of the pretrained model of RoBERTa, KGAN achieves a new record of state-of-the-art performance among all datasets.

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.

Large Language Models (LLMs) demonstrate remarkable potential in dynamic graph reasoning, but suffer from a scaling bottleneck: current models can only handle graphs with tens of nodes, constrained by exponential reasoning overhead and finite context windows. While multi-agent systems (MAS) offer collective reasoning and topology-aware orchestration, capabilities naturally suited for graph-structured tasks, their application to dynamic graphs remains unexplored. This paper presents Scaling LLM Reasoning on Dynamic Graphs via Adaptive Spatio-Temporal Multi-Agent Collaboration (AdaSTORM), a framework that reformulates large-scale dynamic graph reasoning into two stages: (i) Adaptive Partitioning, partitioning large-scale dynamic graphs into subregions that match the model's reasoning capacity while minimizing inference cost; and (ii) Collaborative Reasoning, aligning graph partition topologies with a spatio-temporal decoupled multi-agent architecture. AdaSTORM is the first multi-agent framework tailored for dynamic graph reasoning. Extensive experiments show that AdaSTORM successfully breaks through the scaling bottleneck, scaling reasoning to thousand-node graphs with over 90% accuracy across several large-scale dynamic graph settings without external tools, significantly outperforms seven competitive baselines. Furthermore, it achieves state-of-the-art accuracy on existing benchmarks and generalizes robustly to real-world datasets. The source code is available at: https://github.com/irisorchid107/AdaSTORM/.

Multi-hop question answering over knowledge graphs remains computationally challenging due to the combinatorial explosion of possible reasoning paths. Recent approaches rely on expensive Large Language Model (LLM) inference for both entity linking and path ranking, limiting their practical deployment. Additionally, LLM-generated answers often lack verifiable grounding in structured knowledge. We present two complementary hybrid algorithms that address both efficiency and verifiability: (1) LLM-Guided Planning that uses a single LLM call to predict relation sequences executed via breadth-first search, achieving near-perfect accuracy (micro-F1 > 0.90) while ensuring all answers are grounded in the knowledge graph, and (2) Embedding-Guided Neural Search that eliminates LLM calls entirely by fusing text and graph embeddings through a lightweight 6.7M-parameter edge scorer, achieving over 100 times speedup with competitive accuracy. Through knowledge distillation, we compress planning capability into a 4B-parameter model that matches large-model performance at zero API cost. Evaluation on MetaQA demonstrates that grounded reasoning consistently outperforms ungrounded generation, with structured planning proving more transferable than direct answer generation. Our results show that verifiable multi-hop reasoning does not require massive models at inference time, but rather the right architectural inductive biases combining symbolic structure with learned representations.

Knowledge Graph Question Answering (KGQA) aims to answer user-questions from a knowledge graph (KG) by identifying the reasoning relations between topic entity and answer. As a complex branch task of KGQA, multi-hop KGQA requires reasoning over the multi-hop relational chain preserved in KG to arrive at the right answer. Despite recent successes, the existing works on answering multi-hop complex questions still face the following challenges: i) The absence of an explicit relational chain order reflected in user-question stems from a misunderstanding of a user's intentions. ii) Incorrectly capturing relational types on weak supervision of which dataset lacks intermediate reasoning chain annotations due to expensive labeling cost. iii) Failing to consider implicit relations between the topic entity and the answer implied in structured KG because of limited neighborhoods size constraint in subgraph retrieval-based algorithms.To address these issues in multi-hop KGQA, we propose a novel model herein, namely Relational Chain based Embedded KGQA (Rce-KGQA), which simultaneously utilizes the explicit relational chain revealed in natural language question and the implicit relational chain stored in structured KG. Our extensive empirical study on three open-domain benchmarks proves that our method significantly outperforms the state-of-the-art counterparts like GraftNet, PullNet and EmbedKGQA. Comprehensive ablation experiments also verify the effectiveness of our method on the multi-hop KGQA task. We have made our model's source code available at github: https://github.com/albert-jin/Rce-KGQA.

Graph neural networks (GNNs) have gained significant attention in recent years for their ability to process data that may be represented as graphs. This has prompted several studies to explore their representational capability based on the graph isomorphism task. Notably, these works inherently assume a countable node feature representation, potentially limiting their applicability. Interestingly, only a few study GNNs with uncountable node feature representation. In the paper, a new perspective on the representational capability of GNNs is investigated across all levelsx2014node-level, neighborhood-level, and graph-levelx2014when the space of node feature representation is uncountable. Specifically, the injective and metric requirements of previous works are softly relaxed by employing a pseudometric distance on the space of input to create a soft-injective function such that distinct inputs may produce similar outputs if and only if the pseudometric deems the inputs to be sufficiently similar on some representation. As a consequence, a simple and computationally efficient soft-isomorphic relational graph convolution network (SIR-GCN) that emphasizes the contextualized transformation of neighborhood feature representations via anisotropic and dynamic message functions is proposed. Furthermore, a mathematical discussion on the relationship between SIR-GCN and key GNNs in literature is laid out to put the contribution into context, establishing SIR-GCN as a generalization of classical GNN methodologies. To close, experiments on synthetic and benchmark datasets demonstrate the relative superiority of SIR-GCN, outperforming comparable models in node and graph property prediction tasks.

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.

Large language models (LLMs), while exhibiting exceptional performance, suffer from hallucinations, especially on knowledge-intensive tasks. Existing works propose to augment LLMs with individual text units retrieved from external knowledge corpora to alleviate the issue. However, in many domains, texts are interconnected (e.g., academic papers in a bibliographic graph are linked by citations and co-authorships) which form a (text-attributed) graph. The knowledge in such graphs is encoded not only in single texts/nodes but also in their associated connections. To facilitate the research of augmenting LLMs with graphs, we manually construct a Graph Reasoning Benchmark dataset called GRBench, containing 1,740 questions that can be answered with the knowledge from 10 domain graphs. Then, we propose a simple and effective framework called Graph Chain-of-thought (Graph-CoT) to augment LLMs with graphs by encouraging LLMs to reason on the graph iteratively. Each Graph-CoT iteration consists of three sub-steps: LLM reasoning, LLM-graph interaction, and graph execution. We conduct systematic experiments with three LLM backbones on GRBench, where Graph-CoT outperforms the baselines consistently. The code is available at https://github.com/PeterGriffinJin/Graph-CoT.

Graph embedding methods such as Graph Neural Networks (GNNs) and Graph Transformers have contributed to the development of graph reasoning algorithms for various tasks on knowledge graphs. However, the lack of interpretability and explainability of graph embedding methods has limited their applicability in scenarios requiring explicit reasoning. In this paper, we introduce the Graph Agent (GA), an intelligent agent methodology of leveraging large language models (LLMs), inductive-deductive reasoning modules, and long-term memory for knowledge graph reasoning tasks. GA integrates aspects of symbolic reasoning and existing graph embedding methods to provide an innovative approach for complex graph reasoning tasks. By converting graph structures into textual data, GA enables LLMs to process, reason, and provide predictions alongside human-interpretable explanations. The effectiveness of the GA was evaluated on node classification and link prediction tasks. Results showed that GA reached state-of-the-art performance, demonstrating accuracy of 90.65%, 95.48%, and 89.32% on Cora, PubMed, and PrimeKG datasets, respectively. Compared to existing GNN and transformer models, GA offered advantages of explicit reasoning ability, free-of-training, easy adaption to various graph reasoning tasks

Graph retrieval-augmented generation (GraphRAG) has emerged as a powerful paradigm for enhancing large language models (LLMs) with external knowledge. It leverages graphs to model the hierarchical structure between specific concepts, enabling more coherent and effective knowledge retrieval for accurate reasoning.Despite its conceptual promise, recent studies report that GraphRAG frequently underperforms vanilla RAG on many real-world tasks. This raises a critical question: Is GraphRAG really effective, and in which scenarios do graph structures provide measurable benefits for RAG systems? To address this, we propose GraphRAG-Bench, a comprehensive benchmark designed to evaluate GraphRAG models onboth hierarchical knowledge retrieval and deep contextual reasoning. GraphRAG-Bench features a comprehensive dataset with tasks of increasing difficulty, coveringfact retrieval, complex reasoning, contextual summarization, and creative generation, and a systematic evaluation across the entire pipeline, from graph constructionand knowledge retrieval to final generation. Leveraging this novel benchmark, we systematically investigate the conditions when GraphRAG surpasses traditional RAG and the underlying reasons for its success, offering guidelines for its practical application. All related resources and analyses are collected for the community at https://github.com/GraphRAG-Bench/GraphRAG-Benchmark.

This paper introduces Grounded Image Text Matching with Mismatched Relation (GITM-MR), a novel visual-linguistic joint task that evaluates the relation understanding capabilities of transformer-based pre-trained models. GITM-MR requires a model to first determine if an expression describes an image, then localize referred objects or ground the mismatched parts of the text. We provide a benchmark for evaluating pre-trained models on this task, with a focus on the challenging settings of limited data and out-of-distribution sentence lengths. Our evaluation demonstrates that pre-trained models lack data efficiency and length generalization ability. To address this, we propose the Relation-sensitive Correspondence Reasoning Network (RCRN), which incorporates relation-aware reasoning via bi-directional message propagation guided by language structure. RCRN can be interpreted as a modular program and delivers strong performance in both length generalization and data efficiency.

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.

Chain-of-thought (CoT) traces have been shown to improve performance of large language models on a plethora of reasoning tasks, yet there is no consensus on the mechanism by which this boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGraphs), which are directed acyclic graphs automatically extracted from reasoning traces that model fine-grained causal dependencies in language-model outputs. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K, and AIME, together with their associated CCGraphs, has been compiled into our dataset -- KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCGraphs are causal contributors to the final answer, which we argue is constitutive of reasoning; and (ii) LLMs emphasize the reasoning paths captured by the CCGraphs, indicating that the models internally realize structures similar to our graphs. KisMATH enables controlled, graph-aligned interventions and opens avenues for further investigation into the role of CoT in LLM reasoning.

A variety of knowledge graph embedding approaches have been developed. Most of them obtain embeddings by learning the structure of the knowledge graph within a link prediction setting. As a result, the embeddings reflect only the semantics of a single knowledge graph, and embeddings for different knowledge graphs are not aligned, e.g., they cannot be used to find similar entities across knowledge graphs via nearest neighbor search. However, knowledge graph embedding applications such as entity disambiguation require a more global representation, i.e., a representation that is valid across multiple sources. We propose to learn universal knowledge graph embeddings from large-scale interlinked knowledge sources. To this end, we fuse large knowledge graphs based on the owl:sameAs relation such that every entity is represented by a unique identity. We instantiate our idea by computing universal embeddings based on DBpedia and Wikidata yielding embeddings for about 180 million entities, 15 thousand relations, and 1.2 billion triples. Moreover, we develop a convenient API to provide embeddings as a service. Experiments on link prediction show that universal knowledge graph embeddings encode better semantics compared to embeddings computed on a single knowledge graph. For reproducibility purposes, we provide our source code and datasets open access at https://github.com/dice-group/Universal_Embeddings

Multi-relational graphs (MRGs) are an expressive data structure for modeling diverse interactions/relations among real objects (i.e., nodes), which pervade extensive applications and scenarios. Given an MRG G with N nodes, partitioning the node set therein into K disjoint clusters (MRGC) is a fundamental task in analyzing MRGs, which has garnered considerable attention. However, the majority of existing solutions towards MRGC either yield severely compromised result quality by ineffective fusion of heterogeneous graph structures and attributes, or struggle to cope with sizable MRGs with millions of nodes and billions of edges due to the adoption of sophisticated and costly deep learning models. In this paper, we present DEMM and DEMM+, two effective MRGC approaches to address the limitations above. Specifically, our algorithms are built on novel two-stage optimization objectives, where the former seeks to derive high-caliber node feature vectors by optimizing the multi-relational Dirichlet energy specialized for MRGs, while the latter minimizes the Dirichlet energy of clustering results over the node affinity graph. In particular, DEMM+ achieves significantly higher scalability and efficiency over our based method DEMM through a suite of well-thought-out optimizations. Key technical contributions include (i) a highly efficient approximation solver for constructing node feature vectors, and (ii) a theoretically-grounded problem transformation with carefully-crafted techniques that enable linear-time clustering without explicitly materializing the NxN dense affinity matrix. Further, we extend DEMM+ to handle attribute-less MRGs through non-trivial adaptations. Extensive experiments, comparing DEMM+ against 20 baselines over 11 real MRGs, exhibit that DEMM+ is consistently superior in terms of clustering quality measured against ground-truth labels, while often being remarkably faster.

Image-text matching plays a critical role in bridging the vision and language, and great progress has been made by exploiting the global alignment between image and sentence, or local alignments between regions and words. However, how to make the most of these alignments to infer more accurate matching scores is still underexplored. In this paper, we propose a novel Similarity Graph Reasoning and Attention Filtration (SGRAF) network for image-text matching. Specifically, the vector-based similarity representations are firstly learned to characterize the local and global alignments in a more comprehensive manner, and then the Similarity Graph Reasoning (SGR) module relying on one graph convolutional neural network is introduced to infer relation-aware similarities with both the local and global alignments. The Similarity Attention Filtration (SAF) module is further developed to integrate these alignments effectively by selectively attending on the significant and representative alignments and meanwhile casting aside the interferences of non-meaningful alignments. We demonstrate the superiority of the proposed method with achieving state-of-the-art performances on the Flickr30K and MSCOCO datasets, and the good interpretability of SGR and SAF modules with extensive qualitative experiments and analyses.