Daily Papers

Accurately recognizing a revisited place is crucial for embodied agents to localize and navigate. This requires visual representations to be distinct, despite strong variations in camera viewpoint and scene appearance. Existing visual place recognition pipelines encode the "whole" image and search for matches. This poses a fundamental challenge in matching two images of the same place captured from different camera viewpoints: "the similarity of what overlaps can be dominated by the dissimilarity of what does not overlap". We address this by encoding and searching for "image segments" instead of the whole images. We propose to use open-set image segmentation to decompose an image into `meaningful' entities (i.e., things and stuff). This enables us to create a novel image representation as a collection of multiple overlapping subgraphs connecting a segment with its neighboring segments, dubbed SuperSegment. Furthermore, to efficiently encode these SuperSegments into compact vector representations, we propose a novel factorized representation of feature aggregation. We show that retrieving these partial representations leads to significantly higher recognition recall than the typical whole image based retrieval. Our segments-based approach, dubbed SegVLAD, sets a new state-of-the-art in place recognition on a diverse selection of benchmark datasets, while being applicable to both generic and task-specialized image encoders. Finally, we demonstrate the potential of our method to ``revisit anything'' by evaluating our method on an object instance retrieval task, which bridges the two disparate areas of research: visual place recognition and object-goal navigation, through their common aim of recognizing goal objects specific to a place. Source code: https://github.com/AnyLoc/Revisit-Anything.

Subgraphs of a larger global graph may be distributed across multiple devices, and only locally accessible due to privacy restrictions, although there may be links between subgraphs. Recently proposed subgraph Federated Learning (FL) methods deal with those missing links across local subgraphs while distributively training Graph Neural Networks (GNNs) on them. However, they have overlooked the inevitable heterogeneity between subgraphs comprising different communities of a global graph, consequently collapsing the incompatible knowledge from local GNN models. To this end, we introduce a new subgraph FL problem, personalized subgraph FL, which focuses on the joint improvement of the interrelated local GNNs rather than learning a single global model, and propose a novel framework, FEDerated Personalized sUBgraph learning (FED-PUB), to tackle it. Since the server cannot access the subgraph in each client, FED-PUB utilizes functional embeddings of the local GNNs using random graphs as inputs to compute similarities between them, and use the similarities to perform weighted averaging for server-side aggregation. Further, it learns a personalized sparse mask at each client to select and update only the subgraph-relevant subset of the aggregated parameters. We validate our FED-PUB for its subgraph FL performance on six datasets, considering both non-overlapping and overlapping subgraphs, on which it significantly outperforms relevant baselines. Our code is available at https://github.com/JinheonBaek/FED-PUB.

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

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.

The problems of detecting and recovering planted structures/subgraphs in Erdős-Rényi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an arbitrary planted subgraph Γ= Γ_n in an Erdős-Rényi random graph G(n, q_n), where the edge probability within Γ is p_n. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities p_n and q_n are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting Γ, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on Γ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of p_n and q_n as functions of n. Accordingly, we also analyze the sparse regime where q_n = Θ(n^{-α}) and p_n-q_n =Θ(q_n), with αin[0,2], as well as the critical regime where p_n=1-o(1) and q_n = Θ(n^{-α}), both of which have been widely studied, for specific choices of Γ. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus farand many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of q_n.

Information retrieval based knowledge base question answering (KBQA) first retrieves a subgraph to reduce search space, then reasons on the subgraph to select answer entities. Existing approaches have three issues that impede the retrieval of such subgraphs. Firstly, there is no off-the-shelf toolkit for semantic-relevant subgraph retrieval. Secondly, existing methods are knowledge-graph-dependent, resulting in outdated knowledge graphs used even in recent studies. Thirdly, previous solutions fail to incorporate the best available techniques for entity linking or path expansion. In this paper, we present SRTK, a user-friendly toolkit for semantic-relevant subgraph retrieval from large-scale knowledge graphs. SRTK is the first toolkit that streamlines the entire lifecycle of subgraph retrieval across multiple knowledge graphs. Additionally, it comes with state-of-the-art subgraph retrieval algorithms, guaranteeing an up-to-date solution set out of the box.

Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive subgraphs. Notably, the relative fair clique emerges as a robust model, ensuring not only comprehensive attribute coverage but also greater flexibility in distributing attribute vertices. Motivated by the strength of this model, we for the first time pioneer an investigation into the identification of the maximum relative fair clique in large-scale graphs. We introduce a novel concept of colorful support, which serves as the foundation for two innovative graph reduction techniques. These techniques effectively narrow the graph's size by iteratively removing edges that do not belong to relative fair cliques. Furthermore, a series of upper bounds of the maximum relative fair clique size is proposed by incorporating consideration of vertex attributes and colors. The pruning techniques derived from these upper bounds can significantly trim unnecessary search space during the branch-and-bound procedure. Adding to this, we present a heuristic algorithm with a linear time complexity, employing both a degree-based greedy strategy and a colored degree-based greedy strategy to identify a larger relative fair clique. This heuristic algorithm can serve a dual purpose by aiding in branch pruning, thereby enhancing overall search efficiency. Extensive experiments conducted on six real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.

Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods. However, they suffer from exponential computational costs or searching the matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we first prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. We can then yield an implementation of linear time complexity by the built-in tree-structured aggregation mechanism on graph neural networks. Moreover, circle structures and node attributes can be easily incorporated in D2Match to boost the matching performance. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed exploits the subtrees and differs from existing GNNs-based subgraph matching methods that depend on memorizing the data distribution divergence

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

To deduce new facts on a knowledge graph (KG), a link predictor learns from the graph structure and collects local evidence to find the answer to a given query. However, existing methods suffer from a severe scalability problem due to the utilization of the whole KG for prediction, which hinders their promise on large scale KGs and cannot be directly addressed by vanilla sampling methods. In this work, we propose the one-shot-subgraph link prediction to achieve efficient and adaptive prediction. The design principle is that, instead of directly acting on the whole KG, the prediction procedure is decoupled into two steps, i.e., (i) extracting only one subgraph according to the query and (ii) predicting on this single, query dependent subgraph. We reveal that the non-parametric and computation-efficient heuristics Personalized PageRank (PPR) can effectively identify the potential answers and supporting evidence. With efficient subgraph-based prediction, we further introduce the automated searching of the optimal configurations in both data and model spaces. Empirically, we achieve promoted efficiency and leading performances on five large-scale benchmarks. The code is publicly available at: https://github.com/tmlr-group/one-shot-subgraph.

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

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

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

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

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

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

Graph retrieval based on subgraph isomorphism has several real-world applications such as scene graph retrieval, molecular fingerprint detection and circuit design. Roy et al. [35] proposed IsoNet, a late interaction model for subgraph matching, which first computes the node and edge embeddings of each graph independently of paired graph and then computes a trainable alignment map. Here, we present IsoNet++, an early interaction graph neural network (GNN), based on several technical innovations. First, we compute embeddings of all nodes by passing messages within and across the two input graphs, guided by an injective alignment between their nodes. Second, we update this alignment in a lazy fashion over multiple rounds. Within each round, we run a layerwise GNN from scratch, based on the current state of the alignment. After the completion of one round of GNN, we use the last-layer embeddings to update the alignments, and proceed to the next round. Third, IsoNet++ incorporates a novel notion of node-pair partner interaction. Traditional early interaction computes attention between a node and its potential partners in the other graph, the attention then controlling messages passed across graphs. In contrast, we consider node pairs (not single nodes) as potential partners. Existence of an edge between the nodes in one graph and non-existence in the other provide vital signals for refining the alignment. Our experiments on several datasets show that the alignments get progressively refined with successive rounds, resulting in significantly better retrieval performance than existing methods. We demonstrate that all three innovations contribute to the enhanced accuracy. Our code and datasets are publicly available at https://github.com/structlearning/isonetpp.

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the graph cumulants of the distribution (without any increase in computational complexity). We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants. In summary, when analyzing data using subgraph/motif densities, we suggest using the corresponding graph cumulants instead.

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

This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Python library for computations with Cayley and Schreier graphs. Compared with systems such as GAP and Sage, CayleyPy handles much larger graphs and performs several orders of magnitude faster. Using CayleyPy we obtained about 200 new conjectures on Cayley and Schreier graphs, focused on diameters and growth. For many Cayley graphs of symmetric groups Sn we observe quasi polynomial diameter formulas: a small set of quadratic or linear polynomials indexed by n mod s. We conjecture that this is a general phenomenon, giving efficient diameter computation despite the problem being NP hard. We propose a refinement of the Babai type conjecture on diameters of Sn: n^2/2 + 4n upper bounds in the undirected case, compared to previous O(n^2) bounds. We also provide explicit generator families, related to involutions in a square with whiskers pattern, conjectured to maximize the diameter; search confirms this for all n up to 15. We further conjecture an answer to a question posed by V M Glushkov in 1968 on directed Cayley graphs generated by a cyclic shift and a transposition. For nilpotent groups we conjecture an improvement of J S Ellenberg's results on upper unitriangular matrices over Z/pZ, showing linear dependence of diameter on p. Moreover. Some conjectures are LLM friendly, naturally stated as sorting problems verifiable by algorithms or Python code. To benchmark path finding we created more than 10 Kaggle datasets. CayleyPy works with arbitrary permutation or matrix groups and includes over 100 predefined generators. Our growth computation code outperforms GAP and Sage up to 1000 times in speed and size.

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

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

This paper generalizes Kocay's lemma, with particular applications to graph reconstruction, as well as discussing and proving aspects around the power of these generalizations and Kocay's original lemma, with a result on the reconstruction of the multiplicity of a tree T as a subgraph of G.

Recent advancements in large language models (LLMs) have shown impressive versatility across various tasks. To eliminate its hallucinations, retrieval-augmented generation (RAG) has emerged as a powerful approach, leveraging external knowledge sources like knowledge graphs (KGs). In this paper, we study the task of KG-driven RAG and propose a novel Similar Graph Enhanced Retrieval-Augmented Generation (SimGRAG) method. It effectively addresses the challenge of aligning query texts and KG structures through a two-stage process: (1) query-to-pattern, which uses an LLM to transform queries into a desired graph pattern, and (2) pattern-to-subgraph, which quantifies the alignment between the pattern and candidate subgraphs using a graph semantic distance (GSD) metric. We also develop an optimized retrieval algorithm that efficiently identifies the top-k subgraphs within 1-second latency on a 10-million-scale KG. Extensive experiments show that SimGRAG outperforms state-of-the-art KG-driven RAG methods in both question answering and fact verification, offering superior plug-and-play usability and scalability.

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.

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

Text-rich Graph Knowledge Bases (TG-KBs) have become increasingly crucial for answering queries by providing textual and structural knowledge. However, current retrieval methods often retrieve these two types of knowledge in isolation without considering their mutual reinforcement and some hybrid methods even bypass structural retrieval entirely after neighboring aggregation. To fill in this gap, we propose a Mixture of Structural-and-Textual Retrieval (MoR) to retrieve these two types of knowledge via a Planning-Reasoning-Organizing framework. In the Planning stage, MoR generates textual planning graphs delineating the logic for answering queries. Following planning graphs, in the Reasoning stage, MoR interweaves structural traversal and textual matching to obtain candidates from TG-KBs. In the Organizing stage, MoR further reranks fetched candidates based on their structural trajectory. Extensive experiments demonstrate the superiority of MoR in harmonizing structural and textual retrieval with insights, including uneven retrieving performance across different query logics and the benefits of integrating structural trajectories for candidate reranking. Our code is available at https://github.com/Yoega/MoR.

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

Entity resolution is a widely studied problem with several proposals to match records across relations. Matching textual content is a widespread task in many applications, such as question answering and search. While recent methods achieve promising results for these two tasks, there is no clear solution for the more general problem of matching textual content and structured data. We introduce a framework that supports this new task in an unsupervised setting for any pair of corpora, being relational tables or text documents. Our method builds a fine-grained graph over the content of the corpora and derives word embeddings to represent the objects to match in a low dimensional space. The learned representation enables effective and efficient matching at different granularity, from relational tuples to text sentences and paragraphs. Our flexible framework can exploit pre-trained resources, but it does not depends on their existence and achieves better quality performance in matching content when the vocabulary is domain specific. We also introduce optimizations in the graph creation process with an "expand and compress" approach that first identifies new valid relationships across elements, to improve matching, and then prunes nodes and edges, to reduce the graph size. Experiments on real use cases and public datasets show that our framework produces embeddings that outperform word embeddings and fine-tuned language models both in results' quality and in execution times.

Since long, corporations are looking for knowledge sources which can provide structured description of data and can focus on meaning and shared understanding. Structures which can facilitate open world assumptions and can be flexible enough to incorporate and recognize more than one name for an entity. A source whose major purpose is to facilitate human communication and interoperability. Clearly, databases fail to provide these features and ontologies have emerged as an alternative choice, but corporations working on same domain tend to make different ontologies. The problem occurs when they want to share their data/knowledge. Thus we need tools to merge ontologies into one. This task is termed as ontology matching. This is an emerging area and still we have to go a long way in having an ideal matcher which can produce good results. In this paper we have shown a framework to matching ontologies using graphs.

The need to analyze graphs is ubiquitous across various fields, from social networks to biological research and recommendation systems. Therefore, enabling the ability of large language models (LLMs) to process graphs is an important step toward more advanced general intelligence. However, current LLM benchmarks on graph analysis require models to directly reason over the prompts describing graph topology, and are thus limited to small graphs with only a few dozens of nodes. In contrast, human experts typically write programs based on popular libraries for task solving, and can thus handle graphs with different scales. To this end, a question naturally arises: can LLMs analyze graphs like professionals? In this paper, we introduce ProGraph, a manually crafted benchmark containing 3 categories of graph tasks. The benchmark expects solutions based on programming instead of directly reasoning over raw inputs. Our findings reveal that the performance of current LLMs is unsatisfactory, with the best model achieving only 36% accuracy. To bridge this gap, we propose LLM4Graph datasets, which include crawled documents and auto-generated codes based on 6 widely used graph libraries. By augmenting closed-source LLMs with document retrieval and fine-tuning open-source ones on the codes, we show 11-32% absolute improvements in their accuracies. Our results underscore that the capabilities of LLMs in handling structured data are still under-explored, and show the effectiveness of LLM4Graph in enhancing LLMs' proficiency of graph analysis. The benchmark, datasets and enhanced open-source models are available at https://github.com/BUPT-GAMMA/ProGraph.

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

Despite steady progress in layout-to-image generation, current methods still struggle with layouts containing significant overlap between bounding boxes. We identify two primary challenges: (1) large overlapping regions and (2) overlapping instances with minimal semantic distinction. Through both qualitative examples and quantitative analysis, we demonstrate how these factors degrade generation quality. To systematically assess this issue, we introduce OverLayScore, a novel metric that quantifies the complexity of overlapping bounding boxes. Our analysis reveals that existing benchmarks are biased toward simpler cases with low OverLayScore values, limiting their effectiveness in evaluating model performance under more challenging conditions. To bridge this gap, we present OverLayBench, a new benchmark featuring high-quality annotations and a balanced distribution across different levels of OverLayScore. As an initial step toward improving performance on complex overlaps, we also propose CreatiLayout-AM, a model fine-tuned on a curated amodal mask dataset. Together, our contributions lay the groundwork for more robust layout-to-image generation under realistic and challenging scenarios. Project link: https://mlpc-ucsd.github.io/OverLayBench.

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

Graph-based retrieval-augmented generation (Graph-based RAG) has demonstrated significant potential in enhancing Large Language Models (LLMs) with structured knowledge. However, existing methods face three critical challenges: Inaccurate Graph Construction, caused by LLM hallucination; Poor Reasoning Ability, caused by failing to generate explicit reasons telling LLM why certain chunks were selected; and Inadequate Answering, which only partially answers the query due to the inadequate LLM reasoning, making their performance lag behind NaiveRAG on certain tasks. To address these issues, we propose AGRAG, an advanced graph-based retrieval-augmented generation framework. When constructing the graph, AGRAG substitutes the widely used LLM entity extraction method with a statistics-based method, avoiding hallucination and error propagation. When retrieval, AGRAG formulates the graph reasoning procedure as the Minimum Cost Maximum Influence (MCMI) subgraph generation problem, where we try to include more nodes with high influence score, but with less involving edge cost, to make the generated reasoning paths more comprehensive. We prove this problem to be NP-hard, and propose a greedy algorithm to solve it. The MCMI subgraph generated can serve as explicit reasoning paths to tell LLM why certain chunks were retrieved, thereby making the LLM better focus on the query-related part contents of the chunks, reducing the impact of noise, and improving AGRAG's reasoning ability. Furthermore, compared with the simple tree-structured reasoning paths, our MCMI subgraph can allow more complex graph structures, such as cycles, and improve the comprehensiveness of the generated reasoning paths.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

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

This systematic review explores the application of Large Language Models (LLMs) in Combinatorial Optimization (CO). We report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We conduct a literature search via Scopus and Google Scholar, examining over 2,000 publications. We assess publications against four inclusion and four exclusion criteria related to their language, research focus, publication year, and type. Eventually, we select 103 studies. We classify these studies into semantic categories and topics to provide a comprehensive overview of the field, including the tasks performed by LLMs, the architectures of LLMs, the existing datasets specifically designed for evaluating LLMs in CO, and the field of application. Finally, we identify future directions for leveraging LLMs in this field.

While fine-tuned language models perform well on many tasks, they were also shown to rely on superficial surface features such as lexical overlap. Excessive utilization of such heuristics can lead to failure on challenging inputs. We analyze the use of lexical overlap heuristics in natural language inference, paraphrase detection, and reading comprehension (using a novel contrastive dataset), and find that larger models are much less susceptible to adopting lexical overlap heuristics. We also find that longer training leads models to abandon lexical overlap heuristics. Finally, we provide evidence that the disparity between models size has its source in the pre-trained model

The Machine Learning for Combinatorial Optimization (ML4CO) NeurIPS 2021 competition aims to improve state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning models. On the dual task, we design models to make branching decisions to promote the dual bound increase faster. We propose a knowledge inheritance method to generalize knowledge of different models from the dataset aggregation process, named KIDA. Our improvement overcomes some defects of the baseline graph-neural-networks-based methods. Further, we won the 1st Place on the dual task. We hope this report can provide useful experience for developers and researchers. The code is available at https://github.com/megvii-research/NeurIPS2021-ML4CO-KIDA.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

A legal knowledge graph constructed from court cases, judgments, laws and other legal documents can enable a number of applications like question answering, document similarity, and search. While the use of knowledge graphs for distant supervision in NLP tasks is well researched, using knowledge graphs for downstream graph tasks like node similarity presents challenges in selecting node types and their features. In this demo, we describe our solution for predicting similar nodes in a case graph derived from our legal knowledge graph.

Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

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

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

Large language models with retrieval-augmented generation encounter a pivotal challenge in intricate retrieval tasks, e.g., multi-hop question answering, which requires the model to navigate across multiple documents and generate comprehensive responses based on fragmented information. To tackle this challenge, we introduce a novel Knowledge Graph-based RAG framework with a hierarchical knowledge retriever, termed KG-Retriever. The retrieval indexing in KG-Retriever is constructed on a hierarchical index graph that consists of a knowledge graph layer and a collaborative document layer. The associative nature of graph structures is fully utilized to strengthen intra-document and inter-document connectivity, thereby fundamentally alleviating the information fragmentation problem and meanwhile improving the retrieval efficiency in cross-document retrieval of LLMs. With the coarse-grained collaborative information from neighboring documents and concise information from the knowledge graph, KG-Retriever achieves marked improvements on five public QA datasets, showing the effectiveness and efficiency of our proposed RAG framework.

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.

Finding relevant literature underpins the practice of evidence-based medicine. From 2014 to 2016, TREC conducted a clinical decision support track, wherein participants were tasked with finding articles relevant to clinical questions posed by physicians. In total, 87 teams have participated over the past three years, generating 395 runs. During this period, each team has trialled a variety of methods. While there was significant overlap in the methods employed by different teams, the results were varied. Due to the diversity of the platforms used, the results arising from the different techniques are not directly comparable, reducing the ability to build on previous work. By using a stable platform, we have been able to compare different document and query processing techniques, allowing us to experiment with different search parameters. We have used our system to reproduce leading teams runs, and compare the results obtained. By benchmarking our indexing and search techniques, we can statistically test a variety of hypotheses, paving the way for further research.

In this study, we propose a novel graph neural network called propagate-selector (PS), which propagates information over sentences to understand information that cannot be inferred when considering sentences in isolation. First, we design a graph structure in which each node represents an individual sentence, and some pairs of nodes are selectively connected based on the text structure. Then, we develop an iterative attentive aggregation and a skip-combine method in which a node interacts with its neighborhood nodes to accumulate the necessary information. To evaluate the performance of the proposed approaches, we conduct experiments with the standard HotpotQA dataset. The empirical results demonstrate the superiority of our proposed approach, which obtains the best performances, compared to the widely used answer-selection models that do not consider the intersentential relationship.

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

Multi-hop query answering over a Knowledge Graph (KG) involves traversing one or more hops from the start node to answer a query. Path-based and logic-based methods are state-of-the-art for multi-hop question answering. The former is used in link prediction tasks. The latter is for answering complex logical queries. The logical multi-hop querying technique embeds the KG and queries in the same embedding space. The existing work incorporates First Order Logic (FOL) operators, such as conjunction (wedge), disjunction (vee), and negation (neg), in queries. Though current models have most of the building blocks to execute the FOL queries, they cannot use the dense information of multi-modal entities in the case of Multi-Modal Knowledge Graphs (MMKGs). We propose RConE, an embedding method to capture the multi-modal information needed to answer a query. The model first shortlists candidate (multi-modal) entities containing the answer. It then finds the solution (sub-entities) within those entities. Several existing works tackle path-based question-answering in MMKGs. However, to our knowledge, we are the first to introduce logical constructs in querying MMKGs and to answer queries that involve sub-entities of multi-modal entities as the answer. Extensive evaluation of four publicly available MMKGs indicates that RConE outperforms the current state-of-the-art.

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.

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

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

With the web getting bigger and assimilating knowledge about different concepts and domains, it is becoming very difficult for simple database driven applications to capture the data for a domain. Thus developers have come out with ontology based systems which can store large amount of information and can apply reasoning and produce timely information. Thus facilitating effective knowledge management. Though this approach has made our lives easier, but at the same time has given rise to another problem. Two different ontologies assimilating same knowledge tend to use different terms for the same concepts. This creates confusion among knowledge engineers and workers, as they do not know which is a better term then the other. Thus we need to merge ontologies working on same domain so that the engineers can develop a better application over it. This paper shows the development of one such matcher which merges the concepts available in two ontologies at two levels; 1) at string level and 2) at semantic level; thus producing better merged ontologies. We have used a graph matching technique which works at the core of the system. We have also evaluated the system and have tested its performance with its predecessor which works only on string matching. Thus current approach produces better results.

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

We investigate the problem of producing structured graph representations of visual scenes. Our work analyzes the role of motifs: regularly appearing substructures in scene graphs. We present new quantitative insights on such repeated structures in the Visual Genome dataset. Our analysis shows that object labels are highly predictive of relation labels but not vice-versa. We also find that there are recurring patterns even in larger subgraphs: more than 50% of graphs contain motifs involving at least two relations. Our analysis motivates a new baseline: given object detections, predict the most frequent relation between object pairs with the given labels, as seen in the training set. This baseline improves on the previous state-of-the-art by an average of 3.6% relative improvement across evaluation settings. We then introduce Stacked Motif Networks, a new architecture designed to capture higher order motifs in scene graphs that further improves over our strong baseline by an average 7.1% relative gain. Our code is available at github.com/rowanz/neural-motifs.

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

The Honeymoon Oberwolfach Problem HOP(2m_1,2m_2,ldots,2m_t) asks the following question. Given n=m_1+m_2+ldots +m_t newlywed couples at a conference and t round tables of sizes 2m_1,2m_2,ldots,2m_t, is it possible to arrange the 2n participants at these tables for 2n-2 meals so that each participant sits next to their spouse at every meal, and sits next to every other participant exactly once? A solution to HOP(2m_1,2m_2,ldots,2m_t) is a decomposition of K_{2n}+(2n-3)I, the complete graph K_{2n} with 2n-3 additional copies of a fixed 1-factor I, into 2-factors, each consisting of disjoint I-alternating cycles of lengths 2m_1,2m_2,ldots,2m_t. The Honeymoon Oberwolfach Problem was introduced in a 2019 paper by Lepine and Sajna. The authors conjectured that HOP(2m_1,2m_2,ldots, 2m_t) has a solution whenever the obvious necessary conditions are satisfied, and proved the conjecture for several large cases, including the uniform cycle length case m_1=ldots=m_t, and the small cases with n le 9. In the present paper, we extend the latter result to all cases with n le 20 using a computer search.

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

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper explores both traditional and more recent approaches to graph clustering. Firstly, key concepts and definitions in graph theory are introduced. The background section covers essential topics, including graph Laplacians and the integration of Deep Learning in graph analysis. The paper then delves into traditional clustering methods, including Spectral Clustering and the Leiden algorithm. Following this, state-of-the-art clustering techniques that leverage deep learning are examined. A comprehensive comparison of these methods is made through experiments. The paper concludes with a discussion of the practical applications of graph clustering and potential future research directions.

Network embedding has been widely used in social recommendation and network analysis, such as recommendation systems and anomaly detection with graphs. However, most of previous approaches cannot handle large graphs efficiently, due to that (i) computation on graphs is often costly and (ii) the size of graph or the intermediate results of vectors could be prohibitively large, rendering it difficult to be processed on a single machine. In this paper, we propose an efficient and effective distributed algorithm for network embedding on large graphs using Apache Spark, which recursively partitions a graph into several small-sized subgraphs to capture the internal and external structural information of nodes, and then computes the network embedding for each subgraph in parallel. Finally, by aggregating the outputs on all subgraphs, we obtain the embeddings of nodes in a linear cost. After that, we demonstrate in various experiments that our proposed approach is able to handle graphs with billions of edges within a few hours and is at least 4 times faster than the state-of-the-art approaches. Besides, it achieves up to 4.25% and 4.27% improvements on link prediction and node classification tasks respectively. In the end, we deploy the proposed algorithms in two online games of Tencent with the applications of friend recommendation and item recommendation, which improve the competitors by up to 91.11% in running time and up to 12.80% in the corresponding evaluation metrics.

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.

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

Retrieving graphs from a large corpus, that contain a subgraph isomorphic to a given query graph, is a core operation in many real-world applications. While recent multi-vector graph representations and scores based on set alignment and containment can provide accurate subgraph isomorphism tests, their use in retrieval remains limited by their need to score corpus graphs exhaustively. We introduce CORGII (Contextual Representation of Graphs for Inverted Indexing), a graph indexing framework in which, starting with a contextual dense graph representation, a differentiable discretization module computes sparse binary codes over a learned latent vocabulary. This text document-like representation allows us to leverage classic, highly optimized inverted indices, while supporting soft (vector) set containment scores. Pushing this paradigm further, we replace the classical, fixed impact weight of a `token' on a graph (such as TFIDF or BM25) with a data-driven, trainable impact weight. Finally, we explore token expansion to support multi-probing the index for smoother accuracy-efficiency tradeoffs. To our knowledge, CORGII is the first indexer of dense graph representations using discrete tokens mapping to efficient inverted lists. Extensive experiments show that CORGII provides better trade-offs between accuracy and efficiency, compared to several baselines.

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

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

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

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

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

The {K_{1,1}, K_{1,2},C_m: mgeq3}-factor of a graph is a spanning subgraph whose each component is an element of {K_{1,1}, K_{1,2},C_m: mgeq3}. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a {K_2}-factor. We get a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

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

Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal similarity, assuming tighter coupling between graph and text representations improves transfer performance. However, our empirical analysis reveals that both natural gap expansion and forced gap reduction result in performance degradation by disrupting pre-trained knowledge structures and impairing generalization. This arises from the geometric incompatibility between encoders, where graph encoders capture topological patterns, while text encoders capture semantic structures. Over-alignment compresses these distinct spaces into shared subspaces, causing structure collapse that diminishes both topological reasoning and semantic understanding. We propose LLM4GTA, a gap-aware alignment framework that preserves representation gaps as geometric necessities for maintaining modality-specific knowledge and improving transfer performance. LLM4GTA includes an adaptive gap preservation module to prevent over-alignment by monitoring similarity evolution and an intra-modal compensation mechanism that boosts discriminative power using auxiliary classifiers in graph space. Extensive experiments show significant improvements over existing methods in zero-shot and few-shot scenarios.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

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

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.

Traditional similarity-based schema matching methods are incapable of resolving semantic ambiguities and conflicts in domain-specific complex mapping scenarios due to missing commonsense and domain-specific knowledge. The hallucination problem of large language models (LLMs) also makes it challenging for LLM-based schema matching to address the above issues. Therefore, we propose a Knowledge Graph-based Retrieval-Augmented Generation model for Schema Matching, referred to as the KG-RAG4SM. In particular, KG-RAG4SM introduces novel vector-based, graph traversal-based, and query-based graph retrievals, as well as a hybrid approach and ranking schemes that identify the most relevant subgraphs from external large knowledge graphs (KGs). We showcase that KG-based retrieval-augmented LLMs are capable of generating more accurate results for complex matching cases without any re-training. Our experimental results show that KG-RAG4SM outperforms the LLM-based state-of-the-art (SOTA) methods (e.g., Jellyfish-8B) by 35.89% and 30.50% in terms of precision and F1 score on the MIMIC dataset, respectively; KG-RAG4SM with GPT-4o-mini outperforms the pre-trained language model (PLM)-based SOTA methods (e.g., SMAT) by 69.20% and 21.97% in terms of precision and F1 score on the Synthea dataset, respectively. The results also demonstrate that our approach is more efficient in end-to-end schema matching, and scales to retrieve from large KGs. Our case studies on the dataset from the real-world schema matching scenario exhibit that the hallucination problem of LLMs for schema matching is well mitigated by our solution.

Co-occurrence networks are an important method in the field of natural language processing and text mining for discovering semantic relationships within texts. However, the traditional traversal algorithm for constructing co-occurrence networks has high time complexity and space complexity when dealing with large-scale text data. In this paper, we propose an optimized algorithm based on inverted indexing and breadth-first search to improve the efficiency of co-occurrence network construction and reduce memory consumption. Firstly, the traditional traversal algorithm is analyzed, and its performance issues in constructing co-occurrence networks are identified. Then, the detailed implementation process of the optimized algorithm is presented. Subsequently, the CSL large-scale Chinese scientific literature dataset is used for experimental validation, comparing the performance of the traditional traversal algorithm and the optimized algorithm in terms of running time and memory usage. Finally, using non-parametric test methods, the optimized algorithm is proven to have significantly better performance than the traditional traversal algorithm. The research in this paper provides an effective method for the rapid construction of co-occurrence networks, contributing to the further development of the Information Organization fields.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

As part of its scholarly data efforts, the Internet Archive (IA) releases a first version of a citation graph dataset, named refcat, derived from scholarly publications and additional data sources. It is composed of data gathered by the fatcat cataloging project (the catalog that underpins IA Scholar), related web-scale crawls targeting primary and secondary scholarly outputs, as well as metadata from the Open Library project and Wikipedia. This first version of the graph consists of over 1.3B citations. We release this dataset under a CC0 Public Domain Dedication, accessible through Internet Archive. The source code used for the derivation process, including exact and fuzzy citation matching, is released under an MIT license. The goal of this report is to describe briefly the current contents and the derivation of the dataset.

Generalized Tur\'an problems ask for the maximum number of copies of a graph H in an n-vertex, F-free graph, denoted by ex(n,H,F). We show how to extend the new, localized approach of Bradac, Malec, and Tompkins to generalized Tur\'{a}n problems. We weight the copies of H (typically taking H=K_t), instead of the edges, based on the size of the largest clique, path, or star containing the vertices of the copy of H, and in each case prove a tight upper bound on the sum of the weights. A consequence of our new localized theorems is an asymptotic determination of ex(n,H,K_{1,r}) for every H having at least one dominating vertex and mex(m,H,K_{1,r}) for every H having at least two dominating vertices.

Assessing the degree of similarity of code fragments is crucial for ensuring software quality, but it remains challenging due to the need to capture the deeper semantic aspects of code. Traditional syntactic methods often fail to identify these connections. Recent advancements have addressed this challenge, though they frequently sacrifice interpretability. To improve this, we present an approach aiming to improve the transparency of the similarity assessment by using GraphCodeBERT, which enables the identification of semantic relationships between code fragments. This approach identifies similar code fragments and clarifies the reasons behind that identification, helping developers better understand and trust the results. The source code for our implementation is available at https://www.github.com/jorge-martinez-gil/graphcodebert-interpretability.

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

Knowledge graphs are useful tools to organize, recommend and sort data. Hierarchies in knowledge graphs provide significant benefit in improving understanding and compartmentalization of the data within a knowledge graph. This work leverages large language models to generate and augment hierarchies in an existing knowledge graph. For small (<100,000 node) domain-specific KGs, we find that a combination of few-shot prompting with one-shot generation works well, while larger KG may require cyclical generation. We present techniques for augmenting hierarchies, which led to coverage increase by 98% for intents and 99% for colors in our knowledge graph.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

We present POTATO, a task- and languageindependent framework for human-in-the-loop (HITL) learning of rule-based text classifiers using graph-based features. POTATO handles any type of directed graph and supports parsing text into Abstract Meaning Representations (AMR), Universal Dependencies (UD), and 4lang semantic graphs. A streamlit-based user interface allows users to build rule systems from graph patterns, provides real-time evaluation based on ground truth data, and suggests rules by ranking graph features using interpretable machine learning models. Users can also provide patterns over graphs using regular expressions, and POTATO can recommend refinements of such rules. POTATO is applied in projects across domains and languages, including classification tasks on German legal text and English social media data. All components of our system are written in Python, can be installed via pip, and are released under an MIT License on GitHub.

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.

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%.

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

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

Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large graphs can be fast and easy if they are compressed sufficiently to fit in main memory or even cache. Graph summarization, which yields a coarse-grained summary graph with merged nodes, stands out with several advantages among graph compression techniques. Thus, a number of algorithms have been developed for obtaining a concise summary graph with little information loss or equivalently small reconstruction error. However, the existing methods focus solely on reducing the number of nodes, and they often yield dense summary graphs, failing to achieve better compression rates. Moreover, due to their limited scalability, they can be applied only to moderate-size graphs. In this work, we propose SSumM, a scalable and effective graph-summarization algorithm that yields a sparse summary graph. SSumM not only merges nodes together but also sparsifies the summary graph, and the two strategies are carefully balanced based on the minimum description length principle. Compared with state-of-the-art competitors, SSumM is (a) Concise: yields up to 11.2X smaller summary graphs with similar reconstruction error, (b) Accurate: achieves up to 4.2X smaller reconstruction error with similarly concise outputs, and (c) Scalable: summarizes 26X larger graphs while exhibiting linear scalability. We validate these advantages through extensive experiments on 10 real-world graphs.

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

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

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

Various human-designed prompt engineering techniques have been proposed to improve problem solvers based on Large Language Models (LLMs), yielding many disparate code bases. We unify these approaches by describing LLM-based agents as computational graphs. The nodes implement functions to process multimodal data or query LLMs, and the edges describe the information flow between operations. Graphs can be recursively combined into larger composite graphs representing hierarchies of inter-agent collaboration (where edges connect operations of different agents). Our novel automatic graph optimizers (1) refine node-level LLM prompts (node optimization) and (2) improve agent orchestration by changing graph connectivity (edge optimization). Experiments demonstrate that our framework can be used to efficiently develop, integrate, and automatically improve various LLM agents. The code can be found at https://github.com/metauto-ai/gptswarm.

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), such as ChatGPT and LLaMA, are creating significant advancements in natural language processing, due to their strong text encoding/decoding ability and newly found emergent capability (e.g., reasoning). While LLMs are mainly designed to process pure texts, there are many real-world scenarios where text data are associated with rich structure information in the form of graphs (e.g., academic networks, and e-commerce networks) or scenarios where graph data are paired with rich textual information (e.g., molecules with descriptions). Besides, although LLMs have shown their pure text-based reasoning ability, it is underexplored whether such ability can be generalized to graph scenarios (i.e., graph-based reasoning). In this paper, we provide a systematic review of scenarios and techniques related to large language models on graphs. We first summarize potential scenarios of adopting LLMs on graphs into three categories, namely pure graphs, text-rich graphs, and text-paired graphs. We then discuss detailed techniques for utilizing LLMs on graphs, including LLM as Predictor, LLM as Encoder, and LLM as Aligner, and compare the advantages and disadvantages of different schools of models. Furthermore, we mention the real-world applications of such methods and summarize open-source codes and benchmark datasets. Finally, we conclude with potential future research directions in this fast-growing field. The related source can be found at https://github.com/PeterGriffinJin/Awesome-Language-Model-on-Graphs.

Artificial General Intelligence (AGI) has revolutionized numerous fields, yet its integration with graph data, a cornerstone in our interconnected world, remains nascent. This paper presents a pioneering survey on the emerging domain of graph prompts in AGI, addressing key challenges and opportunities in harnessing graph data for AGI applications. Despite substantial advancements in AGI across natural language processing and computer vision, the application to graph data is relatively underexplored. This survey critically evaluates the current landscape of AGI in handling graph data, highlighting the distinct challenges in cross-modality, cross-domain, and cross-task applications specific to graphs. Our work is the first to propose a unified framework for understanding graph prompt learning, offering clarity on prompt tokens, token structures, and insertion patterns in the graph domain. We delve into the intrinsic properties of graph prompts, exploring their flexibility, expressiveness, and interplay with existing graph models. A comprehensive taxonomy categorizes over 100 works in this field, aligning them with pre-training tasks across node-level, edge-level, and graph-level objectives. Additionally, we present, ProG, a Python library, and an accompanying website, to support and advance research in graph prompting. The survey culminates in a discussion of current challenges and future directions, offering a roadmap for research in graph prompting within AGI. Through this comprehensive analysis, we aim to catalyze further exploration and practical applications of AGI in graph data, underlining its potential to reshape AGI fields and beyond. ProG and the website can be accessed by https://github.com/WxxShirley/Awesome-Graph-Prompt, and https://github.com/sheldonresearch/ProG, respectively.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Drug discovery is a complex and time-intensive process that requires identifying and validating new therapeutic candidates. Computational approaches using large-scale biomedical knowledge graphs (KGs) offer a promising solution to accelerate this process. However, extracting meaningful insights from large-scale KGs remains challenging due to the complexity of graph traversal. Existing subgraph-based methods are tailored to graph neural networks (GNNs), making them incompatible with other models, such as large language models (LLMs). We introduce K-Paths, a retrieval framework that extracts structured, diverse, and biologically meaningful paths from KGs. Integrating these paths enables LLMs and GNNs to effectively predict unobserved drug-drug and drug-disease interactions. Unlike traditional path-ranking approaches, K-Paths retrieves and transforms paths into a structured format that LLMs can directly process, facilitating explainable reasoning. K-Paths employs a diversity-aware adaptation of Yen's algorithm to retrieve the K shortest loopless paths between entities in an interaction query, prioritizing biologically relevant and diverse relationships. Our experiments on benchmark datasets show that K-Paths improves the zero-shot performance of Llama 8.1B's F1-score by 12.45 points on drug repurposing and 13.42 points on interaction severity prediction. We also show that Llama 70B achieves F1-score gains of 6.18 and 8.46 points, respectively. K-Paths also improves the supervised training efficiency of EmerGNN, a state-of-the-art GNN, by reducing KG size by 90% while maintaining strong predictive performance. Beyond its scalability and efficiency, K-Paths uniquely bridges the gap between KGs and LLMs, providing explainable rationales for predicted interactions. These capabilities show that K-Paths is a valuable tool for efficient data-driven drug discovery.

Assume n, m are positive integers and G is a graph. Let P_{n,m} be the graph obtained from the path with vertices {-m, -(m-1), ldots, 0, ldots, n} by adding a loop at vertex 0. The double cone Delta_{n,m}(G) over a graph G is obtained from the direct product G times P_{n,m} by identifying V(G) times {n} into a single vertex (star, n), identifying V(G) times {-m} into a single vertex (star, -m), and adding an edge connecting (star, -m) and (star, n). This paper determines the fractional chromatic number of Delta_{n,m}(G). In particular, if n < m or n=m is even, then chi_f(Delta_{n,m}(G)) = chi_f(Delta_n(G)), where Delta_n(G) is the nth cone over G. If n=m is odd, then chi_f(Delta_{n,m}(G)) > chi_f(Delta_n(G)). The chromatic number of Delta_{n,m}(G) is also discussed.

Retrieval-Augmented Generation (RAG) systems often struggle with imperfect retrieval, as traditional retrievers focus on lexical or semantic similarity rather than logical relevance. To address this, we propose HopRAG, a novel RAG framework that augments retrieval with logical reasoning through graph-structured knowledge exploration. During indexing, HopRAG constructs a passage graph, with text chunks as vertices and logical connections established via LLM-generated pseudo-queries as edges. During retrieval, it employs a retrieve-reason-prune mechanism: starting with lexically or semantically similar passages, the system explores multi-hop neighbors guided by pseudo-queries and LLM reasoning to identify truly relevant ones. Experiments on multiple multi-hop benchmarks demonstrate that HopRAG's retrieve-reason-prune mechanism can expand the retrieval scope based on logical connections and improve final answer quality.

The web is full of guidance on a wide variety of tasks, from changing the oil in your car to baking an apple pie. However, as content is created independently, a single task could have thousands of corresponding procedural texts. This makes it difficult for users to view the bigger picture and understand the multiple ways the task could be accomplished. In this work we propose an unsupervised learning approach for summarizing multiple procedural texts into an intuitive graph representation, allowing users to easily explore commonalities and differences. We demonstrate our approach on recipes, a prominent example of procedural texts. User studies show that our representation is intuitive and coherent and that it has the potential to help users with several sensemaking tasks, including adapting recipes for a novice cook and finding creative ways to spice up a dish.

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.

Let G be a graph with adjacency matrix A(G). We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where n^+(G) and n^-(G) denote the number of positive and negative eigenvalues of A(G), respectively. This conjecture generalizes to all graphs the well-known absolute bound for strongly regular graphs. The conjecture also relates to a question posed by Torgasev. We prove the conjecture for special graph families, including line graphs and planar graphs, and provide examples where the conjecture is exact. We also conjecture that for any connected graph G, its line graph L(G) satisfies n^+(L(G)) le n^-(L(G)) + 1 and obtain partial results.

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

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.

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

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

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

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

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

Understanding the origins of militarized conflict is a complex, yet important undertaking. Existing research seeks to build this understanding by considering bi-lateral relationships between entity pairs (dyadic causes) and multi-lateral relationships among multiple entities (systemic causes). The aim of this work is to compare these two causes in terms of how they correlate with conflict between two entities. We do this by devising a set of textual and graph-based features which represent each of the causes. The features are extracted from Wikipedia and modeled as a large graph. Nodes in this graph represent entities connected by labeled edges representing ally or enemy-relationships. This allows casting the problem as an edge classification task, which we term dyad classification. We propose and evaluate classifiers to determine if a particular pair of entities are allies or enemies. Our results suggest that our systemic features might be slightly better correlates of conflict. Further, we find that Wikipedia articles of allies are semantically more similar than enemies.

Extracting entities and relations from unstructured text has attracted increasing attention in recent years but remains challenging, due to the intrinsic difficulty in identifying overlapping relations with shared entities. Prior works show that joint learning can result in a noticeable performance gain. However, they usually involve sequential interrelated steps and suffer from the problem of exposure bias. At training time, they predict with the ground truth conditions while at inference it has to make extraction from scratch. This discrepancy leads to error accumulation. To mitigate the issue, we propose in this paper a one-stage joint extraction model, namely, TPLinker, which is capable of discovering overlapping relations sharing one or both entities while immune from the exposure bias. TPLinker formulates joint extraction as a token pair linking problem and introduces a novel handshaking tagging scheme that aligns the boundary tokens of entity pairs under each relation type. Experiment results show that TPLinker performs significantly better on overlapping and multiple relation extraction, and achieves state-of-the-art performance on two public datasets.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

Fine-tuning pre-trained language models (PLMs) has recently shown a potential to improve knowledge graph completion (KGC). However, most PLM-based methods focus solely on encoding textual information, neglecting the long-tailed nature of knowledge graphs and their various topological structures, e.g., subgraphs, shortest paths, and degrees. We claim that this is a major obstacle to achieving higher accuracy of PLMs for KGC. To this end, we propose a Subgraph-Aware Training framework for KGC (SATKGC) with two ideas: (i) subgraph-aware mini-batching to encourage hard negative sampling and to mitigate an imbalance in the frequency of entity occurrences during training, and (ii) new contrastive learning to focus more on harder in-batch negative triples and harder positive triples in terms of the structural properties of the knowledge graph. To the best of our knowledge, this is the first study to comprehensively incorporate the structural inductive bias of the knowledge graph into fine-tuning PLMs. Extensive experiments on three KGC benchmarks demonstrate the superiority of SATKGC. Our code is available.

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

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.