Daily Papers

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

We address the challenging problem of semi-supervised learning in the context of multiple visual interpretations of the world by finding consensus in a graph of neural networks. Each graph node is a scene interpretation layer, while each edge is a deep net that transforms one layer at one node into another from a different node. During the supervised phase edge networks are trained independently. During the next unsupervised stage edge nets are trained on the pseudo-ground truth provided by consensus among multiple paths that reach the nets' start and end nodes. These paths act as ensemble teachers for any given edge and strong consensus is used for high-confidence supervisory signal. The unsupervised learning process is repeated over several generations, in which each edge becomes a "student" and also part of different ensemble "teachers" for training other students. By optimizing such consensus between different paths, the graph reaches consistency and robustness over multiple interpretations and generations, in the face of unknown labels. We give theoretical justifications of the proposed idea and validate it on a large dataset. We show how prediction of different representations such as depth, semantic segmentation, surface normals and pose from RGB input could be effectively learned through self-supervised consensus in our graph. We also compare to state-of-the-art methods for multi-task and semi-supervised learning and show superior performance.

Open-vocabulary 3D instance segmentation is cutting-edge for its ability to segment 3D instances without predefined categories. However, progress in 3D lags behind its 2D counterpart due to limited annotated 3D data. To address this, recent works first generate 2D open-vocabulary masks through 2D models and then merge them into 3D instances based on metrics calculated between two neighboring frames. In contrast to these local metrics, we propose a novel metric, view consensus rate, to enhance the utilization of multi-view observations. The key insight is that two 2D masks should be deemed part of the same 3D instance if a significant number of other 2D masks from different views contain both these two masks. Using this metric as edge weight, we construct a global mask graph where each mask is a node. Through iterative clustering of masks showing high view consensus, we generate a series of clusters, each representing a distinct 3D instance. Notably, our model is training-free. Through extensive experiments on publicly available datasets, including ScanNet++, ScanNet200 and MatterPort3D, we demonstrate that our method achieves state-of-the-art performance in open-vocabulary 3D instance segmentation. Our project page is at https://pku-epic.github.io/MaskClustering.

The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperative consensus. To resolve unobservable deadlocks, we restrict interaction topologies to chordal graphs and apply matrix decomposition with Gram-Schmidt orthogonalization, proving that rank-one spectral edge perturbations deterministically break expertise symmetry by shifting eigenvalues into the stable left-half plane. Core contributions include consensus theorems, polynomial-time Perfect Elimination Ordering verification algorithms, and large-scale empirical validation on clustered ensembles of LLaMA-3, Mistral, and Gemma agents.

Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC.

Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse communication graphs. To track opinion evolution, we map each message to an opinion score via sentiment analysis. We find that agents typically reach consensus and the disagreement between the agents decays exponentially. However, the limiting opinion departs from DeGroot's network-centrality-weighted forecast. The consensus between LLM agents turns out to be largely insensitive to initial conditions and instead depends strongly on the discussion subject and inherent biases. Nevertheless, transient dynamics align with classical graph theory and the convergence rate of opinions is closely related to the second-largest eigenvalue of the graph's combination matrix. Together, these findings can be useful for LLM-driven social-network simulations and the design of resource-efficient multi-agent LLM applications.

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.

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accelerated communication rates for a certain class of time-varying graphs using a specific consensus algorithm.

Knowledge Graphs (KGs) store structured factual knowledge by linking entities through relationships, crucial for many applications. These applications depend on the KG's factual accuracy, so verifying facts is essential, yet challenging. Expert manual verification is ideal but impractical on a large scale. Automated methods show promise but are not ready for real-world KGs. Large Language Models (LLMs) offer potential with their semantic understanding and knowledge access, yet their suitability and effectiveness for KG fact validation remain largely unexplored. In this paper, we introduce FactCheck, a benchmark designed to evaluate LLMs for KG fact validation across three key dimensions: (1) LLMs internal knowledge; (2) external evidence via Retrieval-Augmented Generation (RAG); and (3) aggregated knowledge employing a multi-model consensus strategy. We evaluated open-source and commercial LLMs on three diverse real-world KGs. FactCheck also includes a RAG dataset with 2+ million documents tailored for KG fact validation. Additionally, we offer an interactive exploration platform for analyzing verification decisions. The experimental analyses demonstrate that while LLMs yield promising results, they are still not sufficiently stable and reliable to be used in real-world KG validation scenarios. Integrating external evidence through RAG methods yields fluctuating performance, providing inconsistent improvements over more streamlined approaches -- at higher computational costs. Similarly, strategies based on multi-model consensus do not consistently outperform individual models, underscoring the lack of a one-fits-all solution. These findings further emphasize the need for a benchmark like FactCheck to systematically evaluate and drive progress on this difficult yet crucial task.

The subject of green AI has been gaining attention within the deep learning community given the recent trend of ever larger and more complex neural network models. Existing solutions for reducing the computational load of training at inference time usually involve pruning the network parameters. Pruning schemes often create extra overhead either by iterative training and fine-tuning for static pruning or repeated computation of a dynamic pruning graph. We propose a new parameter pruning strategy for learning a lighter-weight sub-network that minimizes the energy cost while maintaining comparable performance to the fully parameterised network on given downstream tasks. Our proposed pruning scheme is green-oriented, as it only requires a one-off training to discover the optimal static sub-networks by dynamic pruning methods. The pruning scheme consists of a binary gating module and a novel loss function to uncover sub-networks with user-defined sparsity. Our method enables pruning and training simultaneously, which saves energy in both the training and inference phases and avoids extra computational overhead from gating modules at inference time. Our results on CIFAR-10 and CIFAR-100 suggest that our scheme can remove 50% of connections in deep networks with less than 1% reduction in classification accuracy. Compared to other related pruning methods, our method demonstrates a lower drop in accuracy for equivalent reductions in computational cost.

The task of describing video content in natural language is commonly referred to as video captioning. Unlike conventional video captions, which are typically brief and widely available, long-form paragraph descriptions in natural language are scarce. This limitation of current datasets is due to the expensive human manual annotation required and to the highly challenging task of explaining the language formation process from the perspective of the underlying story, as a complex system of interconnected events in space and time. Through a thorough analysis of recently published methods and available datasets, we identify a general lack of published resources dedicated to the problem of describing videos in complex language, beyond the level of descriptions in the form of enumerations of simple captions. Furthermore, while state-of-the-art methods produce impressive results on the task of generating shorter captions from videos by direct end-to-end learning between the videos and text, the problem of explaining the relationship between vision and language is still beyond our reach. In this work, we propose a shared representation between vision and language, based on graphs of events in space and time, which can be obtained in an explainable and analytical way, to integrate and connect multiple vision tasks to produce the final natural language description. Moreover, we also demonstrate how our automated and explainable video description generation process can function as a fully automatic teacher to effectively train direct, end-to-end neural student pathways, within a self-supervised neuro-analytical system. We validate that our explainable neuro-analytical approach generates coherent, rich and relevant textual descriptions on videos collected from multiple varied datasets, using both standard evaluation metrics, human annotations and consensus from ensembles of state-of-the-art VLMs.

As a fundamental problem in computer vision, 3D point cloud registration (PCR) aims to seek the optimal pose to align a point cloud pair. In this paper, we present a 3D registration method with maximal cliques (MAC). The key insight is to loosen the previous maximum clique constraint, and mine more local consensus information in a graph for accurate pose hypotheses generation: 1) A compatibility graph is constructed to render the affinity relationship between initial correspondences. 2) We search for maximal cliques in the graph, each of which represents a consensus set. We perform node-guided clique selection then, where each node corresponds to the maximal clique with the greatest graph weight. 3) Transformation hypotheses are computed for the selected cliques by the SVD algorithm and the best hypothesis is used to perform registration. Extensive experiments on U3M, 3DMatch, 3DLoMatch and KITTI demonstrate that MAC effectively increases registration accuracy, outperforms various state-of-the-art methods and boosts the performance of deep-learned methods. MAC combined with deep-learned methods achieves state-of-the-art registration recall of 95.7% / 78.9% on 3DMatch / 3DLoMatch.

3D object detection is fundamental for spatial understanding. Real-world environments demand models capable of recognizing diverse, previously unseen objects, which remains a major limitation of closed-set methods. Existing open-vocabulary 3D detectors relax annotation requirements but still depend on training scenes, either as point clouds or images. We take this a step further by introducing Zoo3D, the first training-free 3D object detection framework. Our method constructs 3D bounding boxes via graph clustering of 2D instance masks, then assigns semantic labels using a novel open-vocabulary module with best-view selection and view-consensus mask generation. Zoo3D operates in two modes: the zero-shot Zoo3D_0, which requires no training at all, and the self-supervised Zoo3D_1, which refines 3D box prediction by training a class-agnostic detector on Zoo3D_0-generated pseudo labels. Furthermore, we extend Zoo3D beyond point clouds to work directly with posed and even unposed images. Across ScanNet200 and ARKitScenes benchmarks, both Zoo3D_0 and Zoo3D_1 achieve state-of-the-art results in open-vocabulary 3D object detection. Remarkably, our zero-shot Zoo3D_0 outperforms all existing self-supervised methods, hence demonstrating the power and adaptability of training-free, off-the-shelf approaches for real-world 3D understanding. Code is available at https://github.com/col14m/zoo3d .

We have entered an era where the importance of decentralized solutions has become more obvious. Blockchain technology and its derivatives are distributed ledger technologies that keep the registry of data between peers of a network. This ledger is secured within a successive over looping cryptographic chain. The accomplishment of the Bitcoin cryptocurrency proved that blockchain technology and its derivatives could be used to eliminate intermediaries and provide security for cyberspace. However, there are some challenges in the implementation of blockchain technology. This chapter first explains the concept of blockchain technology and the data that we can store therein. The main advantage of blockchain is the security services that it provides. This section continues by describing these services.. The challenges of blockchain; blockchain anomalies, energy consumption, speed, scalability, interoperability, privacy and cryptology in the age of quantum computing are described. Selected solutions for these challenges are given. Remarkable derivatives of blockchain, which use different solutions (directed acyclic graph, distributed hash table, gossip consensus protocol) to solve some of these challenges are described. Then the data storage in blockchain and evolving data solutions are explained. The comparison of decentralized solutions with the lcentralized database systems is given. A multi-platform interoperable scalable architecture (MPISA) is proposed. In the conclusion we include the evolution assumptions of data storage in a decentralized world.

This paper introduces the concept of {mutual consensus} as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the {OWA-MCC} model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.

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.

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.

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

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.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Reader reviews of literary fiction on social media, especially those in persistent, dedicated forums, create and are in turn driven by underlying narrative frameworks. In their comments about a novel, readers generally include only a subset of characters and their relationships, thus offering a limited perspective on that work. Yet in aggregate, these reviews capture an underlying narrative framework comprised of different actants (people, places, things), their roles, and interactions that we label the "consensus narrative framework". We represent this framework in the form of an actant-relationship story graph. Extracting this graph is a challenging computational problem, which we pose as a latent graphical model estimation problem. Posts and reviews are viewed as samples of sub graphs/networks of the hidden narrative framework. Inspired by the qualitative narrative theory of Greimas, we formulate a graphical generative Machine Learning (ML) model where nodes represent actants, and multi-edges and self-loops among nodes capture context-specific relationships. We develop a pipeline of interlocking automated methods to extract key actants and their relationships, and apply it to thousands of reviews and comments posted on Goodreads.com. We manually derive the ground truth narrative framework from SparkNotes, and then use word embedding tools to compare relationships in ground truth networks with our extracted networks. We find that our automated methodology generates highly accurate consensus narrative frameworks: for our four target novels, with approximately 2900 reviews per novel, we report average coverage/recall of important relationships of > 80% and an average edge detection rate of >89\%. These extracted narrative frameworks can generate insight into how people (or classes of people) read and how they recount what they have read to others.

We introduce EvoGit, a decentralized multi-agent framework for collaborative software development driven by autonomous code evolution. EvoGit deploys a population of independent coding agents, each proposing edits to a shared codebase without centralized coordination, explicit message passing, or shared memory. Instead, all coordination emerges through a Git-based phylogenetic graph that tracks the full version lineage and enables agents to asynchronously read from and write to the evolving code repository. This graph-based structure supports fine-grained branching, implicit concurrency, and scalable agent interaction while preserving a consistent historical record. Human involvement is minimal but strategic: users define high-level goals, periodically review the graph, and provide lightweight feedback to promote promising directions or prune unproductive ones. Experiments demonstrate EvoGit's ability to autonomously produce functional and modular software artifacts across two real-world tasks: (1) building a web application from scratch using modern frameworks, and (2) constructing a meta-level system that evolves its own language-model-guided solver for the bin-packing optimization problem. Our results underscore EvoGit's potential to establish a new paradigm for decentralized, automated, and continual software development. EvoGit is open-sourced at https://github.com/BillHuang2001/evogit.

We introduce a distributed algorithm, termed noise-robust distributed maximum consensus (RD-MC), for estimating the maximum value within a multi-agent network in the presence of noisy communication links. Our approach entails redefining the maximum consensus problem as a distributed optimization problem, allowing a solution using the alternating direction method of multipliers. Unlike existing algorithms that rely on multiple sets of noise-corrupted estimates, RD-MC employs a single set, enhancing both robustness and efficiency. To further mitigate the effects of link noise and improve robustness, we apply moving averaging to the local estimates. Through extensive simulations, we demonstrate that RD-MC is significantly more robust to communication link noise compared to existing maximum-consensus algorithms.

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges, and they appear frequently as components in the study of distributed algorithms. In particular, we give a O(log^* n)-round algorithm to (Δ+1)-color cluster graphs of at least polylogarithmic degree. The previous best bound known was poly(log n) [Flin et al., SODA'24]. This properly generalizes results in the CONGEST model and shows that distributed graph problems can be solved quickly even when the node itself is decentralized.

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

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

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

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

In this paper we present the initial design of Minerva consensus protocol for Truechain and other technical details. Currently, it is widely believed in the blockchain community that a public chain cannot simultaneously achieve high performance, decentralization and security. This is true in the case of a Nakamoto chain (low performance) or a delegated proof of stake chain (partially centralized), which are the most popular block chain solutions at time of writing. Our consensus design enjoys the same consistency, liveness, transaction finality and security guarantee, a de-facto with the Hybrid Consensus. We go on to propose the idea of a new virtual machine on top of Ethereum which adds permissioned-chain based transaction processing capabilities in a permissionless setting. We also use the idea of data sharding and speculative transactions, and evaluation of smart contracts in a sharding friendly virtual machine. Finally, we will briefly discuss our fundamentally ASIC resistant mining algorithm, Truehash.

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

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.

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.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

A key challenge in social network analysis is understanding the position, or stance, of people in the graph on a large set of topics. While past work has modeled (dis)agreement in social networks using signed graphs, these approaches have not modeled agreement patterns across a range of correlated topics. For instance, disagreement on one topic may make disagreement(or agreement) more likely for related topics. We propose the Stance Embeddings Model(SEM), which jointly learns embeddings for each user and topic in signed social graphs with distinct edge types for each topic. By jointly learning user and topic embeddings, SEM is able to perform cold-start topic stance detection, predicting the stance of a user on topics for which we have not observed their engagement. We demonstrate the effectiveness of SEM using two large-scale Twitter signed graph datasets we open-source. One dataset, TwitterSG, labels (dis)agreements using engagements between users via tweets to derive topic-informed, signed edges. The other, BirdwatchSG, leverages community reports on misinformation and misleading content. On TwitterSG and BirdwatchSG, SEM shows a 39% and 26% error reduction respectively against strong baselines.

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.

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

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.

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

A k-clique is a dense graph, consisting of k fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint k-cliques in a given large real-world graph with a user-defined fixed number k, which can contribute to a good performance of teaming collaborative events in online games. However, this problem is NP-hard when k geq 3, making it difficult to solve. To address that, we propose an efficient lightweight method that avoids significant overheads and achieves a k-approximation to the optimal, which is equipped with several optimization techniques, including the ordering method, degree estimation in the clique graph, and a lightweight implementation. Besides, to handle dynamic graphs that are widely seen in real-world social networks, we devise an efficient indexing method with careful swapping operations, leading to the efficient maintenance of a near-optimal result with frequent updates in the graph. In various experiments on several large graphs, our proposed approaches significantly outperform the competitors by up to 2 orders of magnitude in running time and 13.3\% in the number of computed disjoint k-cliques, which demonstrates the superiority of the proposed approaches in terms of efficiency and effectiveness.

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.

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

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

Language models have been effective in a wide range of applications, yet the most sophisticated models are often proprietary. For example, GPT-4 by OpenAI and various models by Anthropic are expensive and consume substantial energy. In contrast, the open-source community has produced competitive models, like Llama3. Furthermore, niche-specific smaller language models, such as those tailored for legal, medical or financial tasks, have outperformed their proprietary counterparts. This paper introduces a novel approach that employs functional tokens to integrate multiple open-source models, each optimized for particular tasks. Our newly developed Octopus v4 model leverages functional tokens to intelligently direct user queries to the most appropriate vertical model and reformat the query to achieve the best performance. Octopus v4, an evolution of the Octopus v1, v2, and v3 models, excels in selection and parameter understanding and reformatting. Additionally, we explore the use of graph as a versatile data structure that effectively coordinates multiple open-source models by harnessing the capabilities of the Octopus model and functional tokens. Use our open-sourced GitHub (https://www.nexa4ai.com/) to try Octopus v4 models (https://huggingface.co/NexaAIDev/Octopus-v4), and contrite to a larger graph of language models. By activating models less than 10B parameters, we achieved SOTA MMLU score of 74.8 among the same level models.

Graph Contrastive Learning (GCL) is an effective way to learn generalized graph representations in a self-supervised manner, and has grown rapidly in recent years. However, the underlying community semantics has not been well explored by most previous GCL methods. Research that attempts to leverage communities in GCL regards them as having the same influence on the graph, leading to extra representation errors. To tackle this issue, we define ''community strength'' to measure the difference of influence among communities. Under this premise, we propose a Community-Strength-enhanced Graph Contrastive Learning (CSGCL) framework to preserve community strength throughout the learning process. Firstly, we present two novel graph augmentation methods, Communal Attribute Voting (CAV) and Communal Edge Dropping (CED), where the perturbations of node attributes and edges are guided by community strength. Secondly, we propose a dynamic ''Team-up'' contrastive learning scheme, where community strength is used to progressively fine-tune the contrastive objective. We report extensive experiment results on three downstream tasks: node classification, node clustering, and link prediction. CSGCL achieves state-of-the-art performance compared with other GCL methods, validating that community strength brings effectiveness and generality to graph representations. Our code is available at https://github.com/HanChen-HUST/CSGCL.

Recent advances in large language model-powered multi-agent systems have demonstrated remarkable collective intelligence through effective communication. However, existing approaches face two primary challenges: (i) Ineffective group collaboration modeling, as they rely on pairwise edge representations in graph structures, limiting their ability to capture relationships among multiple agents; and (ii) Limited task-adaptiveness in communication topology design, leading to excessive communication cost for simple tasks and insufficient coordination for complex scenarios. These issues restrict the scalability and practical deployment of adaptive collaboration frameworks. To address these challenges, we propose HyperAgent, a hypergraph-based framework that optimizes communication topologies and effectively captures group collaboration patterns using direct hyperedge representations. Unlike edge-based approaches, HyperAgent uses hyperedges to link multiple agents within the same subtask and employs hypergraph convolutional layers to achieve one-step information aggregation in collaboration groups. Additionally, it incorporates a variational autoencoder framework with sparsity regularization to dynamically adjust hypergraph topologies based on task complexity. Experiments highlight the superiority of HyperAgent in both performance and efficiency. For instance, on GSM8K, HyperAgent achieves 95.07\% accuracy while reducing token consumption by 25.33\%, demonstrating the potential of hypergraph-based optimization for multi-agent communication.

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.

Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by k-means), limiting trade-off control, interpretability, and scalability. We introduce DFNMF, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter lambda tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.

The growing importance of understanding and addressing algorithmic bias in artificial intelligence (AI) has led to a surge in research on AI fairness, which often assumes that the underlying data is independent and identically distributed (IID). However, real-world data frequently exists in non-IID graph structures that capture connections among individual units. To effectively mitigate bias in AI systems, it is essential to bridge the gap between traditional fairness literature, designed for IID data, and the prevalence of non-IID graph data. This survey reviews recent advancements in fairness amidst non-IID graph data, including the newly introduced fair graph generation and the commonly studied fair graph classification. In addition, available datasets and evaluation metrics for future research are identified, the limitations of existing work are highlighted, and promising future directions are proposed.

Autoregressive decoding in Large Language Models (LLMs) is inherently sequential, creating a latency bottleneck that scales linearly with output length. While ``Decomposition-and-Fill'' methods like Skeleton-of-Thought attempt to parallelize generation via external orchestration, they suffer from coherence drift due to the lack of cross-stream communication. In this work, we introduce the Parallel Decoder Transformer (PDT), a parameter-efficient architecture that embeds coordination primitives directly into the inference process of a frozen pre-trained model. Instead of retraining the base model, PDT injects lightweight Speculative Note Conditioning (SNC) adapters that allow parallel decoding streams to synchronize via a shared, dynamic latent space. We formulate coordination as a speculative consensus problem, where sibling streams broadcast semantic ``notes'' to a global bus, gated by a learned verification head. We validate our approach on a 50,000-step curriculum using a frozen 20B-parameter backbone. Our results demonstrate that PDT achieves effective self-correction, reaching 77.8\% precision in coverage prediction and recovering approximate serial semantics without modifying the trunk weights. This establishes PDT as a scalable, efficient alternative to full model fine-tuning for structured parallel generation.

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

Multi-agent systems (MAS) based on Large Language Models (LLMs) have the potential to solve tasks that are beyond the reach of any single LLM. However, this potential can only be realized when the collaboration mechanism between agents is optimized. Specifically, optimizing the communication structure between agents is critical for fruitful collaboration. Most existing approaches rely on fixed topologies, pretrained graph generators, optimization over edges, or employ external LLM judges, thereby adding to the complexity. In this work, we introduce a response-conditioned framework that adapts communication on-the-fly. Agents independently generate responses to the user query and assess peer contributions using an approximation of the Shapley value. A directed acyclic graph (DAG) is then constructed to regulate the propagation of the responses among agents, which ensures stable and efficient message transmission from high-contributing agents to others. This graph is dynamically updated based on the agent responses from the previous collaboration round. Since the proposed framework enables the self-organization of agents without additional supervision or training, we refer to it as SelfOrg. The SelfOrg framework goes beyond task- and query-level optimization and takes into account the stochastic nature of agent responses. Experiments with both strong and weak LLM backends demonstrate robust performance, with significant gains in the weak regime where prior methods collapse. We also theoretically show that multiple agents increase the chance of correctness and that the correct responses naturally dominate the information flow.

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.

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.

We performed a billion locality sensitive hash comparisons between artificially generated data samples to answer the critical question - can we verify the "correctness" of generative AI output in a non-deterministic, trustless, decentralized network? We generate millions of data samples from a variety of open source diffusion and large language models and describe the procedures and trade-offs between generating more verses less deterministic output in a heterogenous, stochastic network. Further, we analyze the outputs to provide empirical evidence of different parameterizations of tolerance and error bounds for verification. Finally, given that we have the generated an enormous amount of simulated data, we also release a new training dataset called ImageNet-Gen for use in augmenting existing training pipelines. For our results, we show that with a majority vote between three independent verifiers, we can detect image generated perceptual collisions in generated AI with over 99.89% probability and less than 0.0267% chance of intra-class collision. For large language models (LLMs), we are able to gain 100% consensus using greedy methods or n-way beam searches to generate consensus demonstrated on different LLMs. In the context of generative AI training, we pinpoint and minimize the major sources of stochasticity and present gossip and synchronization training techniques for verifiability. Thus, this work provides a practical, solid foundation for AI verification and consensus for the minimization of trust in a decentralized network.

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.

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

As centralized AI hits compute ceilings and diminishing returns from ever-larger training runs, meeting demand requires an inference layer that scales horizontally in both capacity and capability. We present Fortytwo, a novel protocol that leverages swarm intelligence principles and distributed pairwise ranking consensus to achieve superior performance in AI inference. Our approach reimagines collaboration among AI nodes using swarm inference: a peer-ranked, reputation-weighted consensus across heterogeneous models that surfaces the highest-quality responses. Using pairwise ranking with a custom Bradley-Terry-style aggregation model, we demonstrate that swarm inference substantially outperforms majority voting, achieving 85.90% on GPQA Diamond versus 68.69% for majority voting with the same model set - an improvement of +17.21 percentage points (approximately +25.1% relative). The protocol incorporates on-chain reputation so node influence adapts to demonstrated accuracy over time, yielding a meritocratic consensus that filters low-quality or malicious participants. To resist Sybil attacks, Fortytwo employs proof-of-capability in its consensus: nodes must successfully complete calibration/test requests and stake reputation to enter ranking rounds, making multi-identity attacks economically unattractive while preserving openness. Across six challenging benchmarks, including GPQA Diamond, LiveCodeBench, and AIME, our evaluation indicates higher accuracy and strong resilience to adversarial and noisy free-form prompting (e.g., prompt-injection degradation of only 0.12% versus 6.20% for a monolithic single-model baseline), while retaining practical deployability. Together, these results establish a foundation for decentralized AI systems - democratizing access to high-quality inference through collective intelligence without sacrificing reliability or security.

The Weighted-Mean Subsequence Reduced (W-MSR) algorithm, the state-of-the-art method for Byzantine-resilient design of decentralized multi-robot systems, is based on discarding outliers received over Linear Consensus Protocol (LCP). Although W-MSR provides well-understood theoretical guarantees relating robust network connectivity to the convergence of the underlying consensus, the method comes with several limitations preventing its use at scale: (1) the number of Byzantine robots, F, to tolerate should be known a priori, (2) the requirement that each robot maintains 2F+1 neighbors is impractical for large F, (3) information propagation is hindered by the requirement that F+1 robots independently make local measurements of the consensus property in order for the swarm's decision to change, and (4) W-MSR is specific to LCP and does not generalize to applications not implemented over LCP. In this work, we propose a Decentralized Blocklist Protocol (DBP) based on inter-robot accusations. Accusations are made on the basis of locally-made observations of misbehavior, and once shared by cooperative robots across the network are used as input to a graph matching algorithm that computes a blocklist. DBP generalizes to applications not implemented via LCP, is adaptive to the number of Byzantine robots, and allows for fast information propagation through the multi-robot system while simultaneously reducing the required network connectivity relative to W-MSR. On LCP-type applications, DBP reduces the worst-case connectivity requirement of W-MSR from (2F+1)-connected to (F+1)-connected and the number of cooperative observers required to propagate new information from F+1 to just 1 observer. We demonstrate empirically that our approach to Byzantine resilience scales to hundreds of robots on cooperative target tracking, time synchronization, and localization case studies.

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

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

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Co-Salient Object Detection (CoSOD) aims at detecting common salient objects within a group of relevant source images. Most of the latest works employ the attention mechanism for finding common objects. To achieve accurate CoSOD results with high-quality maps and high efficiency, we propose a novel Memory-aided Contrastive Consensus Learning (MCCL) framework, which is capable of effectively detecting co-salient objects in real time (~150 fps). To learn better group consensus, we propose the Group Consensus Aggregation Module (GCAM) to abstract the common features of each image group; meanwhile, to make the consensus representation more discriminative, we introduce the Memory-based Contrastive Module (MCM), which saves and updates the consensus of images from different groups in a queue of memories. Finally, to improve the quality and integrity of the predicted maps, we develop an Adversarial Integrity Learning (AIL) strategy to make the segmented regions more likely composed of complete objects with less surrounding noise. Extensive experiments on all the latest CoSOD benchmarks demonstrate that our lite MCCL outperforms 13 cutting-edge models, achieving the new state of the art (~5.9% and ~6.2% improvement in S-measure on CoSOD3k and CoSal2015, respectively). Our source codes, saliency maps, and online demos are publicly available at https://github.com/ZhengPeng7/MCCL.

Graph-based collaborative filtering methods have prevailing performance for recommender systems since they can capture high-order information between users and items, in which the graphs are constructed from the observed user-item interactions that might miss links or contain spurious positive interactions in industrial scenarios. The Bayesian Graph Neural Network framework approaches this issue with generative models for the interaction graphs. The critical problem is to devise a proper family of graph generative models tailored to recommender systems. We propose an efficient generative model that jointly considers the preferences of users, the concurrence of items and some important graph structure information. Experiments on four popular benchmark datasets demonstrate the effectiveness of our proposed graph generative methods for recommender systems.

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.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

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

Large Generative Models (LGMs) such as GPT, Stable Diffusion, Sora, and Suno are trained on a huge amount of language corpus, images, videos, and audio that are extremely diverse from numerous domains. This training paradigm over diverse well-curated data lies at the heart of generating creative and sensible content. However, all previous graph generative models (e.g., GraphRNN, MDVAE, MoFlow, GDSS, and DiGress) have been trained only on one dataset each time, which cannot replicate the revolutionary success achieved by LGMs in other fields. To remedy this crucial gap, we propose a new class of graph generative model called Large Graph Generative Model (LGGM) that is trained on a large corpus of graphs (over 5000 graphs) from 13 different domains. We empirically demonstrate that the pre-trained LGGM has superior zero-shot generative capability to existing graph generative models. Furthermore, our pre-trained LGGM can be easily fine-tuned with graphs from target domains and demonstrate even better performance than those directly trained from scratch, behaving as a solid starting point for real-world customization. Inspired by Stable Diffusion, we further equip LGGM with the capability to generate graphs given text prompts (Text-to-Graph), such as the description of the network name and domain (i.e., "The power-1138-bus graph represents a network of buses in a power distribution system."), and network statistics (i.e., "The graph has a low average degree, suitable for modeling social media interactions."). This Text-to-Graph capability integrates the extensive world knowledge in the underlying language model, offering users fine-grained control of the generated graphs. We release the code, the model checkpoint, and the datasets at https://lggm-lg.github.io/.

Real-world networks, with their evolving relations, are best captured as temporal graphs. However, existing software libraries are largely designed for static graphs where the dynamic nature of temporal graphs is ignored. Bridging this gap, we introduce TGX, a Python package specially designed for analysis of temporal networks that encompasses an automated pipeline for data loading, data processing, and analysis of evolving graphs. TGX provides access to eleven built-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as well as any novel datasets in the .csv format. Beyond data loading, TGX facilitates data processing functionalities such as discretization of temporal graphs and node subsampling to accelerate working with larger datasets. For comprehensive investigation, TGX offers network analysis by providing a diverse set of measures, including average node degree and the evolving number of nodes and edges per timestamp. Additionally, the package consolidates meaningful visualization plots indicating the evolution of temporal patterns, such as Temporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX package is a robust tool for examining the features of temporal graphs and can be used in various areas like studying social networks, citation networks, and tracking user interactions. We plan to continuously support and update TGX based on community feedback. TGX is publicly available on: https://github.com/ComplexData-MILA/TGX.

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Knowledge Graphs (KGs) have emerged as invaluable resources for enriching recommendation systems by providing a wealth of factual information and capturing semantic relationships among items. Leveraging KGs can significantly enhance recommendation performance. However, not all relations within a KG are equally relevant or beneficial for the target recommendation task. In fact, certain item-entity connections may introduce noise or lack informative value, thus potentially misleading our understanding of user preferences. To bridge this research gap, we propose a novel knowledge graph diffusion model for recommendation, referred to as DiffKG. Our framework integrates a generative diffusion model with a data augmentation paradigm, enabling robust knowledge graph representation learning. This integration facilitates a better alignment between knowledge-aware item semantics and collaborative relation modeling. Moreover, we introduce a collaborative knowledge graph convolution mechanism that incorporates collaborative signals reflecting user-item interaction patterns, guiding the knowledge graph diffusion process. We conduct extensive experiments on three publicly available datasets, consistently demonstrating the superiority of our DiffKG compared to various competitive baselines. We provide the source code repository of our proposed DiffKG model at the following link: https://github.com/HKUDS/DiffKG.

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.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

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.

Fully decentralized learning enables the distribution of learning resources and decision-making capabilities across multiple user devices or nodes, and is rapidly gaining popularity due to its privacy-preserving and decentralized nature. Importantly, this crowdsourcing of the learning process allows the system to continue functioning even if some nodes are affected or disconnected. In a disaster scenario, communication infrastructure and centralized systems may be disrupted or completely unavailable, hindering the possibility of carrying out standard centralized learning tasks in these settings. Thus, fully decentralized learning can help in this case. However, transitioning from centralized to peer-to-peer communications introduces a dependency between the learning process and the topology of the communication graph among nodes. In a disaster scenario, even peer-to-peer communications are susceptible to abrupt changes, such as devices running out of battery or getting disconnected from others due to their position. In this study, we investigate the effects of various disruptions to peer-to-peer communications on decentralized learning in a disaster setting. We examine the resilience of a decentralized learning process when a subset of devices drop from the process abruptly. To this end, we analyze the difference between losing devices holding data, i.e., potential knowledge, vs. devices contributing only to the graph connectivity, i.e., with no data. Our findings on a Barabasi-Albert graph topology, where training data is distributed across nodes in an IID fashion, indicate that the accuracy of the learning process is more affected by a loss of connectivity than by a loss of data. Nevertheless, the network remains relatively robust, and the learning process can achieve a good level of accuracy.

In federated learning (FL), data heterogeneity is one key bottleneck that causes model divergence and limits performance. Addressing this, existing methods often regard data heterogeneity as an inherent property and propose to mitigate its adverse effects by correcting models. In this paper, we seek to break this inherent property by generating data to complement the original dataset to fundamentally mitigate heterogeneity level. As a novel attempt from the perspective of data, we propose federated learning with consensus-oriented generation (FedCOG). FedCOG consists of two key components at the client side: complementary data generation, which generates data extracted from the shared global model to complement the original dataset, and knowledge-distillation-based model training, which distills knowledge from global model to local model based on the generated data to mitigate over-fitting the original heterogeneous dataset. FedCOG has two critical advantages: 1) it can be a plug-and-play module to further improve the performance of most existing FL methods, and 2) it is naturally compatible with standard FL protocols such as Secure Aggregation since it makes no modification in communication process. Extensive experiments on classical and real-world FL datasets show that FedCOG consistently outperforms state-of-the-art methods.

This work studies self-supervised graph learning for text-attributed graphs (TAGs) where nodes are represented by textual attributes. Unlike traditional graph contrastive methods that perturb the numerical feature space and alter the graph's topological structure, we aim to improve view generation through language supervision. This is driven by the prevalence of textual attributes in real applications, which complement graph structures with rich semantic information. However, this presents challenges because of two major reasons. First, text attributes often vary in length and quality, making it difficulty to perturb raw text descriptions without altering their original semantic meanings. Second, although text attributes complement graph structures, they are not inherently well-aligned. To bridge the gap, we introduce GAugLLM, a novel framework for augmenting TAGs. It leverages advanced large language models like Mistral to enhance self-supervised graph learning. Specifically, we introduce a mixture-of-prompt-expert technique to generate augmented node features. This approach adaptively maps multiple prompt experts, each of which modifies raw text attributes using prompt engineering, into numerical feature space. Additionally, we devise a collaborative edge modifier to leverage structural and textual commonalities, enhancing edge augmentation by examining or building connections between nodes. Empirical results across five benchmark datasets spanning various domains underscore our framework's ability to enhance the performance of leading contrastive methods as a plug-in tool. Notably, we observe that the augmented features and graph structure can also enhance the performance of standard generative methods, as well as popular graph neural networks. The open-sourced implementation of our GAugLLM is available at Github.

Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

Attributed Graph Clustering (AGC) is a fundamental unsupervised task that integrates structural topology and node attributes to uncover latent patterns in graph-structured data. Despite its significance in industrial applications such as fraud detection and user segmentation, a significant chasm persists between academic research and real-world deployment. Current evaluation protocols suffer from the small-scale, high-homophily citation datasets, non-scalable full-batch training paradigms, and a reliance on supervised metrics that fail to reflect performance in label-scarce environments. To bridge these gaps, we present PyAGC, a comprehensive, production-ready benchmark and library designed to stress-test AGC methods across diverse scales and structural properties. We unify existing methodologies into a modular Encode-Cluster-Optimize framework and, for the first time, provide memory-efficient, mini-batch implementations for a wide array of state-of-the-art AGC algorithms. Our benchmark curates 12 diverse datasets, ranging from 2.7K to 111M nodes, specifically incorporating industrial graphs with complex tabular features and low homophily. Furthermore, we advocate for a holistic evaluation protocol that mandates unsupervised structural metrics and efficiency profiling alongside traditional supervised metrics. Battle-tested in high-stakes industrial workflows at Ant Group, this benchmark offers the community a robust, reproducible, and scalable platform to advance AGC research towards realistic deployment. The code and resources are publicly available via GitHub (https://github.com/Cloudy1225/PyAGC), PyPI (https://pypi.org/project/pyagc), and Documentation (https://pyagc.readthedocs.io).

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.

GossipSub is a new peer-to-peer communication protocol designed to counter attacks from misbehaving peers by controlling what information is sent and to whom, via a score function computed by each peer that captures positive and negative behaviors of its neighbors. The score function depends on several parameters (weights, caps, thresholds) that can be configured by applications using GossipSub. The specification for GossipSub is written in English and its resilience to attacks from misbehaving peers is supported empirically by emulation testing using an implementation in Golang. In this work we take a foundational approach to understanding the resilience of GossipSub to attacks from misbehaving peers. We build the first formal model of GossipSub, using the ACL2s theorem prover. Our model is officially endorsed by the GossipSub developers. It can simulate GossipSub networks of arbitrary size and topology, with arbitrarily configured peers, and can be used to prove and disprove theorems about the protocol. We formalize fundamental security properties stating that the score function is fair, penalizes bad behavior, and rewards good behavior. We prove that the score function is always fair, but can be configured in ways that either penalize good behavior or ignore bad behavior. Using our model, we run GossipSub with the specific configurations for two popular real-world applications: the FileCoin and Eth2.0 blockchains. We show that all properties hold for FileCoin. However, given any Eth2.0 network (of any topology and size) with any number of potentially misbehaving peers, we can synthesize attacks where these peers are able to continuously misbehave by never forwarding topic messages, while maintaining positive scores so that they are never pruned from the network by GossipSub.

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.

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.

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

Personalized PageRank (PPR) has enormous applications, such as link prediction and recommendation systems for social networks, which often require the fully PPR to be known. Besides, most of real-life graphs are edge-weighted, e.g., the interaction between users on the Facebook network. However, it is computationally difficult to compute the fully PPR, especially on large graphs, not to mention that most existing approaches do not consider the weights of edges. In particular, the existing approach cannot handle graphs with billion edges on a moderate-size cluster. To address this problem, this paper presents a novel study on the computation of fully edge-weighted PPR on large graphs using the distributed computing framework. Specifically, we employ the Monte Carlo approximation that performs a large number of random walks from each node of the graph, and exploits the parallel pipeline framework to reduce the overall running time of the fully PPR. Based on that, we develop several optimization techniques which (i) alleviate the issue of large nodes that could explode the memory space, (ii) pre-compute short walks for small nodes that largely speedup the computation of random walks, and (iii) optimize the amount of random walks to compute in each pipeline that significantly reduces the overhead. With extensive experiments on a variety of real-life graph datasets, we demonstrate that our solution is several orders of magnitude faster than the state-of-the-arts, and meanwhile, largely outperforms the baseline algorithms in terms of accuracy.

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

A Harris Graph is a tough, Eulerian, non-Hamiltonian graph. Several approaches to creating new Harris graphs from existing ones are explored, including creating families of Harris graphs and combining Harris graphs. Pictures of all Harris Graphs through order 9 and the number of Harris graphs through order 12 are included. We also prove a result about barnacle-free Harris 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.

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

We introduce a self-supervised approach for learning node and graph level representations by contrasting structural views of graphs. We show that unlike visual representation learning, increasing the number of views to more than two or contrasting multi-scale encodings do not improve performance, and the best performance is achieved by contrasting encodings from first-order neighbors and a graph diffusion. We achieve new state-of-the-art results in self-supervised learning on 8 out of 8 node and graph classification benchmarks under the linear evaluation protocol. For example, on Cora (node) and Reddit-Binary (graph) classification benchmarks, we achieve 86.8% and 84.5% accuracy, which are 5.5% and 2.4% relative improvements over previous state-of-the-art. When compared to supervised baselines, our approach outperforms them in 4 out of 8 benchmarks. Source code is released at: https://github.com/kavehhassani/mvgrl

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

Since its 2009 genesis block, the Bitcoin network has processed >1.08 billion (B) transactions representing >8.72B BTC, offering rich potential for machine learning (ML); yet, its pseudonymity and obscured flow of funds inherent in its \utxo-based design, have rendered this data largely inaccessible for ML research. Addressing this gap, we present an ML-compatible graph modeling the Bitcoin's economic topology by reconstructing the flow of funds. This temporal, heterogeneous graph encompasses complete transaction history up to block \cutoffHeight, consisting of >2.4B nodes and >39.72B edges. Additionally, we provide custom sampling methods yielding node and edge feature vectors of sampled communities, tools to load and analyze the Bitcoin graph data within specialized graph databases, and ready-to-use database snapshots. This comprehensive dataset and toolkit empower the ML community to tackle Bitcoin's intricate ecosystem at scale, driving progress in applications such as anomaly detection, address classification, market analysis, and large-scale graph ML benchmarking. Dataset and code available at https://github.com/B1AAB/EBA{github.com/b1aab/eba}

In this study, we propose a novel graph-based approach to model, analyze and comprehend user interactions within a social media platform based on post-comment relationship. We construct a user interaction graph from social media data and analyze it to gain insights into community dynamics, user behavior, and content preferences. Our investigation reveals that while 56.05% of the active users are strongly connected within the community, only 0.8% of them significantly contribute to its dynamics. Moreover, we observe temporal variations in community activity, with certain periods experiencing heightened engagement. Additionally, our findings highlight a correlation between user activity and popularity showing that more active users are generally more popular. Alongside these, a preference for positive and informative content is also observed where 82.41% users preferred positive and informative content. Overall, our study provides a comprehensive framework for understanding and managing online communities, leveraging graph-based techniques to gain valuable insights into user behavior and community dynamics.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

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

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

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

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

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking and node embedding. While prior work on local graph clustering mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with node attributes that provide valuable additional information. We present a simple local graph clustering algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while accounting for both structural and attribute proximities. Using high-dimensional concentration results, we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster with a single seed node. We give conditions under which a target cluster generated from a fairly general contextual random graph model, which includes both the stochastic block model and the planted cluster model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.

Large Language Models (LLMs) have shown remarkable reasoning capabilities in mathematical and scientific tasks. To enhance complex reasoning, multi-agent systems have been proposed to harness the collective intelligence of LLM agents. However, existing collaboration structures are either predefined or rely on majority voting or round-table debates, which can suppress correct but less dominant agent contributions. Recent approaches model multi-agent systems as graph networks but optimize purely for agent performance, neglecting the quality of interactions. We hypothesize that effective agent communication is crucial for multi-agent reasoning and that debating quality plays a significant role. To address this, we propose ours, a multi-agent verbal reinforcement learning algorithm that dynamically constructs and refines multi-agent collaboration structures. Our method defines action spaces and a feedback mechanism that evaluates communication robustness and coherence throughout the debate. The final decision is achieved through a majority vote over all the agents. We assess ours on various reasoning tasks, including mathematical reasoning, creative writing, scientific reasoning, and numerical sorting. Results demonstrate that our approach significantly outperforms single-agent prompting methods and state-of-the-art multi-agent frameworks on diverse tasks.

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

In numerous artificial intelligence applications, the collaborative efforts of multiple intelligent agents are imperative for the successful attainment of target objectives. To enhance coordination among these agents, a distributed communication framework is often employed. However, indiscriminate information sharing among all agents can be resource-intensive, and the adoption of manually pre-defined communication architectures imposes constraints on inter-agent communication, thus limiting the potential for effective collaboration. Moreover, the communication framework often remains static during inference, which may result in sustained high resource consumption, as in most cases, only key decisions necessitate information sharing among agents. In this study, we introduce a novel approach wherein we conceptualize the communication architecture among agents as a learnable graph. We formulate this problem as the task of determining the communication graph while enabling the architecture parameters to update normally, thus necessitating a bi-level optimization process. Utilizing continuous relaxation of the graph representation and incorporating attention units, our proposed approach, CommFormer, efficiently optimizes the communication graph and concurrently refines architectural parameters through gradient descent in an end-to-end manner. Additionally, we introduce a temporal gating mechanism for each agent, enabling dynamic decisions on whether to receive shared information at a given time, based on current observations, thus improving decision-making efficiency. Extensive experiments on a variety of cooperative tasks substantiate the robustness of our model across diverse cooperative scenarios, where agents are able to develop more coordinated and sophisticated strategies regardless of changes in the number of agents.

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

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.

We study how to train personalized models for different tasks on decentralized devices with limited local data. We propose "Structured Cooperative Learning (SCooL)", in which a cooperation graph across devices is generated by a graphical model prior to automatically coordinate mutual learning between devices. By choosing graphical models enforcing different structures, we can derive a rich class of existing and novel decentralized learning algorithms via variational inference. In particular, we show three instantiations of SCooL that adopt Dirac distribution, stochastic block model (SBM), and attention as the prior generating cooperation graphs. These EM-type algorithms alternate between updating the cooperation graph and cooperative learning of local models. They can automatically capture the cross-task correlations among devices by only monitoring their model updating in order to optimize the cooperation graph. We evaluate SCooL and compare it with existing decentralized learning methods on an extensive set of benchmarks, on which SCooL always achieves the highest accuracy of personalized models and significantly outperforms other baselines on communication efficiency. Our code is available at https://github.com/ShuangtongLi/SCooL.

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

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Attributed bipartite graphs (ABGs) are an expressive data model for describing the interactions between two sets of heterogeneous nodes that are associated with rich attributes, such as customer-product purchase networks and author-paper authorship graphs. Partitioning the target node set in such graphs into k disjoint clusters (referred to as k-ABGC) finds widespread use in various domains, including social network analysis, recommendation systems, information retrieval, and bioinformatics. However, the majority of existing solutions towards k-ABGC either overlook attribute information or fail to capture bipartite graph structures accurately, engendering severely compromised result quality. The severity of these issues is accentuated in real ABGs, which often encompass millions of nodes and a sheer volume of attribute data, rendering effective k-ABGC over such graphs highly challenging. In this paper, we propose TPO, an effective and efficient approach to k-ABGC that achieves superb clustering performance on multiple real datasets. TPO obtains high clustering quality through two major contributions: (i) a novel formulation and transformation of the k-ABGC problem based on multi-scale attribute affinity specialized for capturing attribute affinities between nodes with the consideration of their multi-hop connections in ABGs, and (ii) a highly efficient solver that includes a suite of carefully-crafted optimizations for sidestepping explicit affinity matrix construction and facilitating faster convergence. Extensive experiments, comparing TPO against 19 baselines over 5 real ABGs, showcase the superior clustering quality of TPO measured against ground-truth labels. Moreover, compared to the state of the arts, TPO is often more than 40x faster over both small and large ABGs.

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

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

Proof-of-Work (PoW) consensus mechanism is popular among current blockchain systems, which leads to an increasing concern about the tremendous waste of energy due to massive meaningless computation. To address this issue, we propose a novel and energy-efficient blockchain system, CrowdMine, which exploits useful crowdsourcing computation to achieve decentralized consensus. CrowdMine solves user-proposed computing tasks and utilizes the computation committed to the task solving process to secure decentralized on-chain storage. With our designed ``Proof of Crowdsourcing Work'' (PoCW) protocol, our system provides an efficient paradigm for computation and storage in a trustless and decentralized environment. We further show that the system can defend against potential attacks on blockchain, including the short-term 51\% attack, the problem-constructing attack, and the solution-stealing attack. We also implement the system with 40 distributed nodes to demonstrate its performance and robustness. To the best of our knowledge, this is the first system that enables decentralized Proof of Useful Work (PoUW) with general user-proposed tasks posted in a permissionless and trustless network.

Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs, in terms of the minimum-cost edit sequence that transforms one graph to the other. However, the exact computation of GED is NP-Hard, which has recently motivated the design of neural methods for GED estimation. However, they do not explicitly account for edit operations with different costs. In response, we propose GRAPHEDX, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion and node addition. We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs. Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence require aligning nodes and edges of the two graphs. We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node-pairs. Experiments on several datasets, under a variety of edit cost settings, show that GRAPHEDX consistently outperforms state-of-the-art methods and heuristics in terms of prediction error.

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient (epsilon,delta)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with k nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) epsilon-DP algorithm would result in substantial error.

Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions, they often overlook the inherent locality and efficiency of Message Passing Neural Networks (MPNNs). We propose a new concept called fractal nodes, inspired by the fractal structure observed in real-world networks. Our approach is based on the intuition that graph partitioning naturally induces fractal structure, where subgraphs often reflect the connectivity patterns of the full graph. Fractal nodes are designed to coexist with the original nodes and adaptively aggregate subgraph-level feature representations, thereby enforcing feature similarity within each subgraph. We show that fractal nodes alleviate the over-squashing problem by providing direct shortcut connections that enable long-range propagation of subgraph-level representations. Experiment results show that our method improves the expressive power of MPNNs and achieves comparable or better performance to graph Transformers while maintaining the computational efficiency of MPNN by improving the long-range dependencies of MPNN.

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

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.

While machine learning on graphs has demonstrated promise in drug design and molecular property prediction, significant benchmarking challenges hinder its further progress and relevance. Current benchmarking practices often lack focus on transformative, real-world applications, favoring narrow domains like two-dimensional molecular graphs over broader, impactful areas such as combinatorial optimization, relational databases, or chip design. Additionally, many benchmark datasets poorly represent the underlying data, leading to inadequate abstractions and misaligned use cases. Fragmented evaluations and an excessive focus on accuracy further exacerbate these issues, incentivizing overfitting rather than fostering generalizable insights. These limitations have prevented the development of truly useful graph foundation models. This position paper calls for a paradigm shift toward more meaningful benchmarks, rigorous evaluation protocols, and stronger collaboration with domain experts to drive impactful and reliable advances in graph learning research, unlocking the potential of graph learning.

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

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.