Daily Papers

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

Large Language Models (LLMs) are increasingly asked to reason over structured data such as graphs, yet how reliably they can carry out multi-step graph algorithms in language remains unclear. Existing evaluations tend to use simple tasks on small graphs, to score code generation rather than reasoning over the graph itself, or to fix a single input format. We introduce Graph Theory Bench (GT Bench), a benchmark covering 24 classical graph problems in 44 task-structure settings, with over 100,000 examples across four representations: natural language, structured language, adjacency list, and adjacency matrix. Evaluating eight LLMs on GT Bench shows that accuracy is strongly tied to the input representation, that the best representation shifts with graph density, size, and topology as well as with the model, and that this sensitivity persists, attenuated, in the strongest reasoning models. Building on these observations, we propose the Graph Theory Agent (GTA), which pairs a preference-trained representation selector with plan-and-decompose scaffolding around a frozen executor LLM. GTA lifts Phi-4 from 53.5% to 69.1% on the benchmark's easy split and from 33.0% to 41.5% on its hard split, outperforming eight prompting and agent baselines, and transfers without retraining to GraCoRe and NLGraph. Code for benchmark generation and evaluation: https://github.com/xzx34/GTA. The project homepage is available at https://xzx34.github.io/gta/.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is previous work on Graph Neural Networks (Scarselli et al., 2009), which we modify to use gated recurrent units and modern optimization techniques and then extend to output sequences. The result is a flexible and broadly useful class of neural network models that has favorable inductive biases relative to purely sequence-based models (e.g., LSTMs) when the problem is graph-structured. We demonstrate the capabilities on some simple AI (bAbI) and graph algorithm learning tasks. We then show it achieves state-of-the-art performance on a problem from program verification, in which subgraphs need to be matched to abstract data structures.

Transformers often fail to learn generalizable algorithms, instead relying on brittle heuristics. Using graph connectivity as a testbed, we explain this phenomenon both theoretically and empirically. We consider a simplified Transformer architecture, the disentangled Transformer, and prove that an L-layer model has capacity to solve for graphs with diameters up to exactly 3^L, implementing an algorithm equivalent to computing powers of the adjacency matrix. We analyze the training-dynamics, and show that the learned strategy hinges on whether most training instances are within this model capacity. Within-capacity graphs (diameter leq 3^L) drive the learning of a correct algorithmic solution while beyond-capacity graphs drive the learning of a simple heuristic based on node degrees. Finally, we empirically demonstrate that restricting training data within a model's capacity leads to both standard and disentangled transformers learning the exact algorithm rather than the degree-based heuristic.

Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture's neural algorithmic reasoning capability to simulate hypergraph algorithms, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. We establish theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.

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

Retrieval-augmented generation (RAG) empowers large language models to access external and private corpus, enabling factually consistent responses in specific domains. By exploiting the inherent structure of the corpus, graph-based RAG methods further enrich this process by building a knowledge graph index and leveraging the structural nature of graphs. However, current graph-based RAG approaches seldom prioritize the design of graph structures. Inadequately designed graph not only impede the seamless integration of diverse graph algorithms but also result in workflow inconsistencies and degraded performance. To further unleash the potential of graph for RAG, we propose NodeRAG, a graph-centric framework introducing heterogeneous graph structures that enable the seamless and holistic integration of graph-based methodologies into the RAG workflow. By aligning closely with the capabilities of LLMs, this framework ensures a fully cohesive and efficient end-to-end process. Through extensive experiments, we demonstrate that NodeRAG exhibits performance advantages over previous methods, including GraphRAG and LightRAG, not only in indexing time, query time, and storage efficiency but also in delivering superior question-answering performance on multi-hop benchmarks and open-ended head-to-head evaluations with minimal retrieval tokens. Our GitHub repository could be seen at https://github.com/Terry-Xu-666/NodeRAG.

Approximate nearest neighbor search (ANNS) is a fundamental building block in information retrieval with graph-based indices being the current state-of-the-art and widely used in the industry. Recent advances in graph-based indices have made it possible to index and search billion-point datasets with high recall and millisecond-level latency on a single commodity machine with an SSD. However, existing graph algorithms for ANNS support only static indices that cannot reflect real-time changes to the corpus required by many key real-world scenarios (e.g. index of sentences in documents, email, or a news index). To overcome this drawback, the current industry practice for manifesting updates into such indices is to periodically re-build these indices, which can be prohibitively expensive. In this paper, we present the first graph-based ANNS index that reflects corpus updates into the index in real-time without compromising on search performance. Using update rules for this index, we design FreshDiskANN, a system that can index over a billion points on a workstation with an SSD and limited memory, and support thousands of concurrent real-time inserts, deletes and searches per second each, while retaining >95% 5-recall@5. This represents a 5-10x reduction in the cost of maintaining freshness in indices when compared to existing methods.

Localizing the root cause of network faults is crucial to network operation and maintenance. However, due to the complicated network architectures and wireless environments, as well as limited labeled data, accurately localizing the true root cause is challenging. In this paper, we propose a novel algorithm named NetRCA to deal with this problem. Firstly, we extract effective derived features from the original raw data by considering temporal, directional, attribution, and interaction characteristics. Secondly, we adopt multivariate time series similarity and label propagation to generate new training data from both labeled and unlabeled data to overcome the lack of labeled samples. Thirdly, we design an ensemble model which combines XGBoost, rule set learning, attribution model, and graph algorithm, to fully utilize all data information and enhance performance. Finally, experiments and analysis are conducted on the real-world dataset from ICASSP 2022 AIOps Challenge to demonstrate the superiority and effectiveness of our approach.

The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such unfairness. However, there is little work on enhancing fairness in graph algorithms. Here, we develop a simple, effective and general method, CrossWalk, that enhances fairness of various graph algorithms, including influence maximization, link prediction and node classification, applied to node embeddings. CrossWalk is applicable to any random walk based node representation learning algorithm, such as DeepWalk and Node2Vec. The key idea is to bias random walks to cross group boundaries, by upweighting edges which (1) are closer to the groups' peripheries or (2) connect different groups in the network. CrossWalk pulls nodes that are near groups' peripheries towards their neighbors from other groups in the embedding space, while preserving the necessary structural properties of the graph. Extensive experiments show the effectiveness of our algorithm to enhance fairness in various graph algorithms, including influence maximization, link prediction and node classification in synthetic and real networks, with only a very small decrease in performance.

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes in the ternary field (Z_T), where coefficients are restricted to {-1, 0, 1} to minimize naive additive complexity. The core of the method is a GPU-accelerated meta flip graph algorithm that maintains ternary safety through specialized arithmetic operations and sign symmetry breaking. Key results include new best ranks for the formats 4 times 5 times 12, 5 times 6 times 10, and 6 times 7 times 9, the independent discovery of 32 schemes in Z_T that match known optimal ranks (including 8 previously known only with rational coefficients), and 30 rank improvements in the binary field. The analysis of 164 known schemes shows that 92 can be implemented in Z_T, while 72 could not be found in the ternary field with current methods, defining the current boundaries of this approach. All software, results, and discovered schemes are provided as open-source.

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

Web3Recommend is a decentralized Social Recommender System implementation that enables Web3 Platforms on Android to generate recommendations that balance trust and relevance. Generating recommendations in decentralized networks is a non-trivial problem because these networks lack a global perspective due to the absence of a central authority. Further, decentralized networks are prone to Sybil Attacks in which a single malicious user can generate multiple fake or Sybil identities. Web3Recommend relies on a novel graph-based content recommendation design inspired by GraphJet, a recommendation system used in Twitter enhanced with MeritRank, a decentralized reputation scheme that provides Sybil-resistance to the system. By adding MeritRank's decay parameters to the vanilla Social Recommender Systems' personalized SALSA graph algorithm, we can provide theoretical guarantees against Sybil Attacks in the generated recommendations. Similar to GraphJet, we focus on generating real-time recommendations by only acting on recent interactions in the social network, allowing us to cater temporally contextual recommendations while keeping a tight bound on the memory usage in resource-constrained devices, allowing for a seamless user experience. As a proof-of-concept, we integrate our system with MusicDAO, an open-source Web3 music-sharing platform, to generate personalized, real-time recommendations. Thus, we provide the first Sybil-resistant Social Recommender System, allowing real-time recommendations beyond classic user-based collaborative filtering. The system is also rigorously tested with extensive unit and integration tests. Further, our experiments demonstrate the trust-relevance balance of recommendations against multiple adversarial strategies in a test network generated using data from real music platforms.

Reactive programming frameworks such as React allow developers to build interactive applications by declaratively specifying how outputs depend on changing inputs. Although this model makes it easy to reason about what an application computes, the temporal behavior of reactive programs remains difficult to understand and verify. Applications implicitly rely on timing assumptions buried in framework runtimes, leading to subtle bugs such as stale reads, transient inconsistencies, order-dependent behavior, and unintended feedback cycles. To address these challenges, this paper presents Willow, a core calculus for reactive programming inspired by React. Willow gives a time-aware operational semantics that models computation in terms of renders, the fundamental evaluation step in which components produce user interface descriptions, and pairs it with a novel type-and-effect system that statically tracks timing behavior as effects. A "next" modality expresses delays measured not only in renders but in any unit the host environment exposes--renders, network requests, or milliseconds. A family of modalities tracks the lifecycle of event handlers: when they are registered, when they fire, when pending events are canceled and when handlers are removed. A key insight is that the resulting effects form a temporal dependency graph, letting standard graph algorithms statically detect render cascades and inter-render loops that cause non-termination or performance degradation. We formalize Willow and prove preservation of the effect system with respect to the time-aware semantics. We also implement a prototype checker with automatic effect inference and evaluate it on representative reactive patterns such as debouncing, form inputs, and API-driven updates. Our results demonstrate that time-aware typing provides a practical foundation for reasoning about the temporal correctness of reactive programs.

Large language models (LLMs) achieve strong performance across diverse tasks, largely driven by high-quality web data used in pre-training. However, recent studies indicate this data source is rapidly depleting. Synthetic data emerges as a promising alternative, but it remains unclear whether synthetic datasets exhibit predictable scalability comparable to raw pre-training data. In this work, we systematically investigate the scaling laws of synthetic data by introducing SynthLLM, a scalable framework that transforms pre-training corpora into diverse, high-quality synthetic datasets. Our approach achieves this by automatically extracting and recombining high-level concepts across multiple documents using a graph algorithm. Key findings from our extensive mathematical experiments on SynthLLM include: (1) SynthLLM generates synthetic data that reliably adheres to the rectified scaling law across various model sizes; (2) Performance improvements plateau near 300B tokens; and (3) Larger models approach optimal performance with fewer training tokens. For instance, an 8B model peaks at 1T tokens, while a 3B model requires 4T. Moreover, comparisons with existing synthetic data generation and augmentation methods demonstrate that SynthLLM achieves superior performance and scalability. Our findings highlight synthetic data as a scalable and reliable alternative to organic pre-training corpora, offering a viable path toward continued improvement in model performance.

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.

We develop graph-based methods for semi-supervised learning based on label propagation on a data similarity graph. When data is abundant or arrive in a stream, the problems of computation and data storage arise for any graph-based method. We propose a fast approximate online algorithm that solves for the harmonic solution on an approximate graph. We show, both empirically and theoretically, that good behavior can be achieved by collapsing nearby points into a set of local representative points that minimize distortion. Moreover, we regularize the harmonic solution to achieve better stability properties. We also present graph-based methods for detecting conditional anomalies and apply them to the identification of unusual clinical actions in hospitals. Our hypothesis is that patient-management actions that are unusual with respect to the past patients may be due to errors and that it is worthwhile to raise an alert if such a condition is encountered. Conditional anomaly detection extends standard unconditional anomaly framework but also faces new problems known as fringe and isolated points. We devise novel nonparametric graph-based methods to tackle these problems. Our methods rely on graph connectivity analysis and soft harmonic solution. Finally, we conduct an extensive human evaluation study of our conditional anomaly methods by 15 experts in critical care.

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.

We derive a new proof to show that the incremental resparsification algorithm proposed by Kelner and Levin (2013) produces a spectral sparsifier in high probability. We rigorously take into account the dependencies across subsequent resparsifications using martingale inequalities, fixing a flaw in the original analysis.

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at https://github.com/google-research/google-research/tree/master/cluster_gcn.

Knowledge graphs are powerful tools for representing and organising complex biomedical data. Several knowledge graph embedding algorithms have been proposed to learn from and complete knowledge graphs. However, a recent study demonstrates the limited efficacy of these embedding algorithms when applied to biomedical knowledge graphs, raising the question of whether knowledge graph embeddings have limitations in biomedical settings. This study aims to apply state-of-the-art knowledge graph embedding models in the context of a recent biomedical knowledge graph, BioKG, and evaluate their performance and potential downstream uses. We achieve a three-fold improvement in terms of performance based on the HITS@10 score over previous work on the same biomedical knowledge graph. Additionally, we provide interpretable predictions through a rule-based method. We demonstrate that knowledge graph embedding models are applicable in practice by evaluating the best-performing model on four tasks that represent real-life polypharmacy situations. Results suggest that knowledge learnt from large biomedical knowledge graphs can be transferred to such downstream use cases. Our code is available at https://github.com/aryopg/biokge.

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more. While LLMs have advanced the state-of-the-art on these tasks with structure implications, whether LLMs could explicitly process textual descriptions of graphs and structures, map them to grounded conceptual spaces, and perform structured operations remains underexplored. To this end, we propose NLGraph (Natural Language Graph), a comprehensive benchmark of graph-based problem solving designed in natural language. NLGraph contains 29,370 problems, covering eight graph reasoning tasks with varying complexity from simple tasks such as connectivity and shortest path up to complex problems such as maximum flow and simulating graph neural networks. We evaluate LLMs (GPT-3/4) with various prompting approaches on the NLGraph benchmark and find that 1) language models do demonstrate preliminary graph reasoning abilities, 2) the benefit of advanced prompting and in-context learning diminishes on more complex graph problems, while 3) LLMs are also (un)surprisingly brittle in the face of spurious correlations in graph and problem settings. We then propose Build-a-Graph Prompting and Algorithmic Prompting, two instruction-based approaches to enhance LLMs in solving natural language graph problems. Build-a-Graph and Algorithmic prompting improve the performance of LLMs on NLGraph by 3.07% to 16.85% across multiple tasks and settings, while how to solve the most complicated graph reasoning tasks in our setup with language models remains an open research question. The NLGraph benchmark and evaluation code are available at https://github.com/Arthur-Heng/NLGraph.

Vision Transformers (ViTs) have revolutionized the field of computer vision, yet their deployments on resource-constrained devices remain challenging due to high computational demands. To expedite pre-trained ViTs, token pruning and token merging approaches have been developed, which aim at reducing the number of tokens involved in the computation. However, these methods still have some limitations, such as image information loss from pruned tokens and inefficiency in the token-matching process. In this paper, we introduce a novel Graph-based Token Propagation (GTP) method to resolve the challenge of balancing model efficiency and information preservation for efficient ViTs. Inspired by graph summarization algorithms, GTP meticulously propagates less significant tokens' information to spatially and semantically connected tokens that are of greater importance. Consequently, the remaining few tokens serve as a summarization of the entire token graph, allowing the method to reduce computational complexity while preserving essential information of eliminated tokens. Combined with an innovative token selection strategy, GTP can efficiently identify image tokens to be propagated. Extensive experiments have validated GTP's effectiveness, demonstrating both efficiency and performance improvements. Specifically, GTP decreases the computational complexity of both DeiT-S and DeiT-B by up to 26% with only a minimal 0.3% accuracy drop on ImageNet-1K without finetuning, and remarkably surpasses the state-of-the-art token merging method on various backbones at an even faster inference speed. The source code is available at https://github.com/Ackesnal/GTP-ViT.

Market valuations for professional athletes is a difficult problem, given the amount of variability in performance and location from year to year. In the National Basketball Association (NBA), a straightforward way to address this problem is to build a tabular data set and use supervised machine learning to predict a player's salary based on the player's performance in the previous year. For younger players, whose contracts are mostly built on draft position, this approach works well, however it can fail for veterans or those whose salaries are on the high tail of the distribution. In this paper, we show that building a knowledge graph with on and off court data, embedding that graph in a vector space, and including that vector in the tabular data allows the supervised learning to better understand the landscape of factors that affect salary. We compare several graph embedding algorithms and show that such a process is vital to NBA salary prediction.

Graph convolutional networks (GCN) is widely used to handle irregular data since it updates node features by using the structure information of graph. With the help of iterated GCN, high-order information can be obtained to further enhance the representation of nodes. However, how to apply GCN to structured data (such as pictures) has not been deeply studied. In this paper, we explore the application of graph attention networks (GAT) in image feature extraction. First of all, we propose a novel graph generation algorithm to convert images into graphs through matrix transformation. It is one magnitude faster than the algorithm based on K Nearest Neighbors (KNN). Then, GAT is used on the generated graph to update the node features. Thus, a more robust representation is obtained. These two steps are combined into a module called pixel-wise graph attention module (PGA). Since the graph obtained by our graph generation algorithm can still be transformed into a picture after processing, PGA can be well combined with CNN. Based on these two modules, we consulted the ResNet and design a pixel-wise graph attention network (PGANet). The PGANet is applied to the task of person re-identification in the datasets Market1501, DukeMTMC-reID and Occluded-DukeMTMC (outperforms state-of-the-art by 0.8\%, 1.1\% and 11\% respectively, in mAP scores). Experiment results show that it achieves the state-of-the-art performance. https://github.com/wenyu1009/PGANet{The code is available here}.

Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks. Previous work (Kim et al., 2022) shows that with proper position embedding, GT can approximate MPNN arbitrarily well, implying that GT is at least as powerful as MPNN. In this paper, we study the inverse connection and show that MPNN with virtual node (VN), a commonly used heuristic with little theoretical understanding, is powerful enough to arbitrarily approximate the self-attention layer of GT. In particular, we first show that if we consider one type of linear transformer, the so-called Performer/Linear Transformer (Choromanski et al., 2020; Katharopoulos et al., 2020), then MPNN + VN with only O(1) depth and O(1) width can approximate a self-attention layer in Performer/Linear Transformer. Next, via a connection between MPNN + VN and DeepSets, we prove the MPNN + VN with O(n^d) width and O(1) depth can approximate the self-attention layer arbitrarily well, where d is the input feature dimension. Lastly, under some assumptions, we provide an explicit construction of MPNN + VN with O(1) width and O(n) depth approximating the self-attention layer in GT arbitrarily well. On the empirical side, we demonstrate that 1) MPNN + VN is a surprisingly strong baseline, outperforming GT on the recently proposed Long Range Graph Benchmark (LRGB) dataset, 2) our MPNN + VN improves over early implementation on a wide range of OGB datasets and 3) MPNN + VN outperforms Linear Transformer and MPNN on the climate modeling task.

We introduce PersonalAI 2.0 (PAI-2), a novel framework, designed to enhance large language model (LLM) based systems through integration of external knowledge graphs (KG). The proposed approach addresses key limitations of existing Graph Retrieval-Augmented Generation (GraphRAG) methods by incorporating a dynamic, multistage query processing pipeline. The central point of PAI-2 design is its ability to perform adaptive, iterative information search, guided by extracted entities, matched graph vertices and generated clue-queries. Conducted evaluation over six benchmarks (Natural Questions, TriviaQA, HotpotQA, 2WikiMultihopQA, MuSiQue and DiaASQ) demonstrates improvement in factual correctness of generating answers compared to analogues methods (LightRAG, RAPTOR, and HippoRAG 2). PAI-2 achieves 4% average gain by LLM-as-a-Judge across four benchmarks, reflecting its effectiveness in reducing hallucination rates and increasing precision. We show that use of graph traversal algorithms (e.g. BeamSearch, WaterCircles) gain superior results compared to standard flatten retriever on average 6%, while enabled search plan enhancement mechanism gain 18% boost compared to disabled one by LLM-as-a-Judge across six datasets. In addition, ablation study reveals that PAI-2 achieves the SOTA result on MINE-1 benchmark, achieving 89% information-retention score, using LLMs from 7-14B tiers. Collectively, these findings underscore the potential of PAI-2 to serve as a foundational model for next-generation personalized AI applications, requiring scalable, context-aware knowledge representation and reasoning capabilities.

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

Grounding language queries in videos aims at identifying the time interval (or moment) semantically relevant to a language query. The solution to this challenging task demands understanding videos' and queries' semantic content and the fine-grained reasoning about their multi-modal interactions. Our key idea is to recast this challenge into an algorithmic graph matching problem. Fueled by recent advances in Graph Neural Networks, we propose to leverage Graph Convolutional Networks to model video and textual information as well as their semantic alignment. To enable the mutual exchange of information across the modalities, we design a novel Video-Language Graph Matching Network (VLG-Net) to match video and query graphs. Core ingredients include representation graphs built atop video snippets and query tokens separately and used to model intra-modality relationships. A Graph Matching layer is adopted for cross-modal context modeling and multi-modal fusion. Finally, moment candidates are created using masked moment attention pooling by fusing the moment's enriched snippet features. We demonstrate superior performance over state-of-the-art grounding methods on three widely used datasets for temporal localization of moments in videos with language queries: ActivityNet-Captions, TACoS, and DiDeMo.

Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in few-shot learning settings. However, it remains unclear how LLMs genuinely understand the abstract meaning of each reasoning step and the overall algorithm from only a limited number of demonstrations. This work aims to localize the attention heads responsible for individual reasoning steps and characterize the types of information transferred among them. We first align constituent reasoning steps with their corresponding token logits under a symbolic-aided Chain-of-Thought (CoT) prompting framework. Our analysis shows that token positions that steer the reasoning process are associated with low confidence scores caused by constraints on satisfying reasoning behavior patterns in demonstrations. We then adopt causal mediation analysis techniques to identify the attention heads responsible for these patterns. In addition, our findings indicate that LLMs retrieve factual and rule-based information for individual sub-reasoning tasks through specialized attention heads (approximately 3% total heads), whereas higher layers predominantly facilitate information integration and the emergence of global reasoning strategies (e.g., graph traversal algorithms) that coordinate multiple intermediate reasoning steps to solve the overall task.

GNNs, like other deep learning models, are data and computation hungry. There is a pressing need to scale training of GNNs on large datasets to enable their usage on low-resource environments. Graph distillation is an effort in that direction with the aim to construct a smaller synthetic training set from the original training data without significantly compromising model performance. While initial efforts are promising, this work is motivated by two key observations: (1) Existing graph distillation algorithms themselves rely on training with the full dataset, which undermines the very premise of graph distillation. (2) The distillation process is specific to the target GNN architecture and hyper-parameters and thus not robust to changes in the modeling pipeline. We circumvent these limitations by designing a distillation algorithm called Mirage for graph classification. Mirage is built on the insight that a message-passing GNN decomposes the input graph into a multiset of computation trees. Furthermore, the frequency distribution of computation trees is often skewed in nature, enabling us to condense this data into a concise distilled summary. By compressing the computation data itself, as opposed to emulating gradient flows on the original training set-a prevalent approach to date-Mirage transforms into an unsupervised and architecture-agnostic distillation algorithm. Extensive benchmarking on real-world datasets underscores Mirage's superiority, showcasing enhanced generalization accuracy, data compression, and distillation efficiency when compared to state-of-the-art baselines.

We apply a complex network approach to analyse the time series of five solar parameters, and propose an strategy to predict the number of sunspots for the next solar maximum, and when will this maximum will occur. The approach is based on the Visibility Graph (VG) algorithm, and a slightly modified version of it, the Horizontal Visibility Graph (HVG), which map a time series into a complex network. Various network metrics exhibit either an exponential or a scale-free behavior, and we find that the evolution of the characteristic decay exponents is consistent with variations of the sunspots number along solar cycles. During solar minimum, the sunspots number and the solar index time series have characteristic decay exponents that correlate well with the next maximum sunspots number, suggesting that they may be good precursors of the intensity of the next solar maximum. Based on this observation, we find that, based on current data, the algorithm predicts a number of 179 sunspots for cycle 25. Combining this with the Hathaway function, adjusted to yield such maximum sunspots number, we find that the maximum for solar cycle 25 will occur in December 2024/January 2025.

Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them infeasible to represent heterogeneous structures. In this paper, we present the Heterogeneous Graph Transformer (HGT) architecture for modeling Web-scale heterogeneous graphs. To model heterogeneity, we design node- and edge-type dependent parameters to characterize the heterogeneous attention over each edge, empowering HGT to maintain dedicated representations for different types of nodes and edges. To handle dynamic heterogeneous graphs, we introduce the relative temporal encoding technique into HGT, which is able to capture the dynamic structural dependency with arbitrary durations. To handle Web-scale graph data, we design the heterogeneous mini-batch graph sampling algorithm---HGSampling---for efficient and scalable training. Extensive experiments on the Open Academic Graph of 179 million nodes and 2 billion edges show that the proposed HGT model consistently outperforms all the state-of-the-art GNN baselines by 9%--21% on various downstream tasks.

Associating unstructured data with structured information is crucial for real-world tasks that require relevance search. However, existing graph learning benchmarks often overlook the rich semantic information associate with each node. To bridge such gap, we introduce the Multimodal Graph Benchmark (MM-GRAPH), the first comprehensive multi-modal graph benchmark that incorporates both textual and visual information. MM-GRAPH surpasses previous efforts, which have primarily focused on text-attributed graphs with various connectivity patterns. MM-GRAPH consists of five graph learning datasets of various scales that are appropriate for different learning tasks. Their multimodal node features, enabling a more comprehensive evaluation of graph learning algorithms in real-world scenarios. To facilitate research on multimodal graph learning, we further provide an extensive study on the performance of various graph neural networks in the presence of features from various modalities. MM-GRAPH aims to foster research on multimodal graph learning and drive the development of more advanced and robust graph learning algorithms. By providing a diverse set of datasets and benchmarks, MM-GRAPH enables researchers to evaluate and compare their models in realistic settings, ultimately leading to improved performance on real-world applications that rely on multimodal graph data.

To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to a connected component. The breadth-first search is the usual choice when constructing efficient algorithms for finding connected components of a graph. Methods of simple iteration for solving systems of linear equations with modified graph adjacency matrices and with the properly specified right-hand side can be considered as graph traversal algorithms. These traversal algorithms, generally speaking, turn out to be non-equivalent neither to the depth-first search nor the breadth-first search. The example of such a traversal algorithm is the one associated with the Gauss-Seidel method. For an arbitrary connected graph, to visit all its vertices, the algorithm requires not more iterations than that is required for BFS. For a large number of instances of the problem, fewer iterations will be required.

3D point cloud (PC) -- a collection of discrete geometric samples of a physical object's surface -- is typically large in size, which entails expensive subsequent operations like viewpoint image rendering and object recognition. Leveraging on recent advances in graph sampling, we propose a fast PC sub-sampling algorithm that reduces its size while preserving the overall object shape. Specifically, to articulate a sampling objective, we first assume a super-resolution (SR) method based on feature graph Laplacian regularization (FGLR) that reconstructs the original high-resolution PC, given 3D points chosen by a sampling matrix H. We prove that minimizing a worst-case SR reconstruction error is equivalent to maximizing the smallest eigenvalue λ_{min} of a matrix H^{top} H + μcL, where cL is a symmetric, positive semi-definite matrix computed from the neighborhood graph connecting the 3D points. Instead, for fast computation we maximize a lower bound λ^-_{min}(H^{top} H + μcL) via selection of H in three steps. Interpreting cL as a generalized graph Laplacian matrix corresponding to an unbalanced signed graph cG, we first approximate cG with a balanced graph cG_B with the corresponding generalized graph Laplacian matrix cL_B. Second, leveraging on a recent theorem called Gershgorin disc perfect alignment (GDPA), we perform a similarity transform cL_p = §cL_B §^{-1} so that Gershgorin disc left-ends of cL_p are all aligned at the same value λ_{min}(cL_B). Finally, we perform PC sub-sampling on cG_B using a graph sampling algorithm to maximize λ^-_{min}(H^{top} H + μcL_p) in roughly linear time. Experimental results show that 3D points chosen by our algorithm outperformed competing schemes both numerically and visually in SR reconstruction quality.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Deep graph learning has gained grand popularity over the past years due to its versatility and success in representing graph data across a wide range of domains. However, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose a significant barrier to comprehending advancements in this field. To bridge this gap, we introduce IGL-Bench, a foundational comprehensive benchmark for imbalanced graph learning, embarking on 16 diverse graph datasets and 24 distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, IGL-Bench systematically investigates state-of-the-art IGL algorithms in terms of effectiveness, robustness, and efficiency on node-level and graph-level tasks, with the scope of class-imbalance and topology-imbalance. Extensive experiments demonstrate the potential benefits of IGL algorithms on various imbalanced conditions, offering insights and opportunities in the IGL field. Further, we have developed an open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, which is available at https://github.com/RingBDStack/IGL-Bench.

The widespread application of graph data inevitably brings significant privacy risks, as its unprotected use can lead to the leakage of sensitive information. These risks are particularly acute in the setting with an untrusted curator, where the data remains decentralized and each user only holds the connections to their neighbors. To mitigate such privacy risks, we adopt local differential privacy (LDP) to collect users' private information and generate a synthetic graph. However, existing methods suffer from either excessive noise injection by perturbing the local adjacency lists or significant structural information loss due to the simplistic graph encoding process. To address these issues, we propose LDPGraph, an effective graph synthesis algorithm that takes one step further by exploiting neighborhood structures under LDP. To obtain neighborhood statistics beyond degrees, LDPGraph aggregates a noisy global view from perturbed adjacency lists and combines it with projected local connections to estimate node-level triangle counts. To correct the structural inconsistency caused by separately perturbing degree and triangle count, LDPGraph jointly refines them into feasible degree-triangle targets. To reconstruct a global graph from these estimated targets, LDPGraph adopts a triangle-first strategy that first preserves local clustering structures and then fulfills remaining degree requirements. Extensive experiments on four real-world datasets and multiple commonly used graph metrics validate the superiority of LDPGraph. Source code is available at https://github.com/ZJU-TrustAID/LDPGraph.

Biological neural networks define the brain function and intelligence of humans and other mammals, and form ultra-large, spatial, structured graphs. Their neuronal organization is closely interconnected with the spatial organization of the brain's microvasculature, which supplies oxygen to the neurons and builds a complementary spatial graph. This vasculature (or the vessel structure) plays an important role in neuroscience; for example, the organization of (and changes to) vessel structure can represent early signs of various pathologies, e.g. Alzheimer's disease or stroke. Recently, advances in tissue clearing have enabled whole brain imaging and segmentation of the entirety of the mouse brain's vasculature. Building on these advances in imaging, we are presenting an extendable dataset of whole-brain vessel graphs based on specific imaging protocols. Specifically, we extract vascular graphs using a refined graph extraction scheme leveraging the volume rendering engine Voreen and provide them in an accessible and adaptable form through the OGB and PyTorch Geometric dataloaders. Moreover, we benchmark numerous state-of-the-art graph learning algorithms on the biologically relevant tasks of vessel prediction and vessel classification using the introduced vessel graph dataset. Our work paves a path towards advancing graph learning research into the field of neuroscience. Complementarily, the presented dataset raises challenging graph learning research questions for the machine learning community, in terms of incorporating biological priors into learning algorithms, or in scaling these algorithms to handle sparse,spatial graphs with millions of nodes and edges. All datasets and code are available for download at https://github.com/jocpae/VesselGraph .

The rise of the Internet and the exponential increase in data have made manual data summarization and analysis a challenging task. Instagram social network is a prominent social network widely utilized in Iran for information sharing and communication across various age groups. The inherent structure of Instagram, characterized by its text-rich content and graph-like data representation, enables the utilization of text and graph processing techniques for data analysis purposes. The degree distributions of these networks exhibit scale-free characteristics, indicating non-random growth patterns. Recently, word co-occurrence has gained attention from researchers across multiple disciplines due to its simplicity and practicality. Keyword extraction is a crucial task in natural language processing. In this study, we demonstrated that high-precision extraction of keywords from Instagram posts in the Persian language can be achieved using unsupervised word co-occurrence methods without resorting to conventional techniques such as clustering or pre-trained models. After graph visualization and community detection, it was observed that the top topics covered by news agencies are represented by these graphs. This approach is generalizable to new and diverse datasets and can provide acceptable outputs for new data. To the author's knowledge, this method has not been employed in the Persian language before on Instagram social network. The new crawled data has been publicly released on GitHub for exploration by other researchers. By employing this method, it is possible to use other graph-based algorithms, such as community detections. The results help us to identify the key role of different news agencies in information diffusion among the public, identify hidden communities, and discover latent patterns among a massive amount of data.

In recent years, the use of multi-modal pre-trained Transformers has led to significant advancements in visually-rich document understanding. However, existing models have mainly focused on features such as text and vision while neglecting the importance of layout relationship between text nodes. In this paper, we propose GraphLayoutLM, a novel document understanding model that leverages the modeling of layout structure graph to inject document layout knowledge into the model. GraphLayoutLM utilizes a graph reordering algorithm to adjust the text sequence based on the graph structure. Additionally, our model uses a layout-aware multi-head self-attention layer to learn document layout knowledge. The proposed model enables the understanding of the spatial arrangement of text elements, improving document comprehension. We evaluate our model on various benchmarks, including FUNSD, XFUND and CORD, and achieve state-of-the-art results among these datasets. Our experimental results demonstrate that our proposed method provides a significant improvement over existing approaches and showcases the importance of incorporating layout information into document understanding models. We also conduct an ablation study to investigate the contribution of each component of our model. The results show that both the graph reordering algorithm and the layout-aware multi-head self-attention layer play a crucial role in achieving the best performance.

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.

Automatic patent summarization approaches that help in the patent analysis and comprehension procedure are in high demand due to the colossal growth of innovations. The development of natural language processing (NLP), text mining, and deep learning has notably amplified the efficacy of text summarization models for abundant types of documents. Summarizing patent text remains a pertinent challenge due to the labyrinthine writing style of these documents, which includes technical and legal intricacies. Additionally, these patent document contents are considerably lengthier than archetypal documents, which complicates the process of extracting pertinent information for summarization. Embodying extractive and abstractive text summarization methodologies into a hybrid framework, this study proposes a system for efficiently creating abstractive summaries of patent records. The procedure involves leveraging the LexRank graph-based algorithm to retrieve the important sentences from input parent texts, then utilizing a Bidirectional Auto-Regressive Transformer (BART) model that has been fine-tuned using Low-Ranking Adaptation (LoRA) for producing text summaries. This is accompanied by methodical testing and evaluation strategies. Furthermore, the author employed certain meta-learning techniques to achieve Domain Generalization (DG) of the abstractive component across multiple patent fields.

Most graph neural network models learn embeddings of nodes in static attributed graphs for predictive analysis. Recent attempts have been made to learn temporal proximity of the nodes. We find that real dynamic attributed graphs exhibit complex co-evolution of node attributes and graph structure. Learning node embeddings for forecasting change of node attributes and birth and death of links over time remains an open problem. In this work, we present a novel framework called CoEvoGNN for modeling dynamic attributed graph sequence. It preserves the impact of earlier graphs on the current graph by embedding generation through the sequence. It has a temporal self-attention mechanism to model long-range dependencies in the evolution. Moreover, CoEvoGNN optimizes model parameters jointly on two dynamic tasks, attribute inference and link prediction over time. So the model can capture the co-evolutionary patterns of attribute change and link formation. This framework can adapt to any graph neural algorithms so we implemented and investigated three methods based on it: CoEvoGCN, CoEvoGAT, and CoEvoSAGE. Experiments demonstrate the framework (and its methods) outperform strong baselines on predicting an entire unseen graph snapshot of personal attributes and interpersonal links in dynamic social graphs and financial graphs.

Fact-centric information needs are rarely one-shot; users typically ask follow-up questions to explore a topic. In such a conversational setting, the user's inputs are often incomplete, with entities or predicates left out, and ungrammatical phrases. This poses a huge challenge to question answering (QA) systems that typically rely on cues in full-fledged interrogative sentences. As a solution, we develop CONVEX: an unsupervised method that can answer incomplete questions over a knowledge graph (KG) by maintaining conversation context using entities and predicates seen so far and automatically inferring missing or ambiguous pieces for follow-up questions. The core of our method is a graph exploration algorithm that judiciously expands a frontier to find candidate answers for the current question. To evaluate CONVEX, we release ConvQuestions, a crowdsourced benchmark with 11,200 distinct conversations from five different domains. We show that CONVEX: (i) adds conversational support to any stand-alone QA system, and (ii) outperforms state-of-the-art baselines and question completion strategies.

Turkish Wikipedia Named-Entity Recognition and Text Categorization (TWNERTC) dataset is a collection of automatically categorized and annotated sentences obtained from Wikipedia. We constructed large-scale gazetteers by using a graph crawler algorithm to extract relevant entity and domain information from a semantic knowledge base, Freebase. The constructed gazetteers contains approximately 300K entities with thousands of fine-grained entity types under 77 different domains. Since automated processes are prone to ambiguity, we also introduce two new content specific noise reduction methodologies. Moreover, we map fine-grained entity types to the equivalent four coarse-grained types: person, loc, org, misc. Eventually, we construct six different dataset versions and evaluate the quality of annotations by comparing ground truths from human annotators. We make these datasets publicly available to support studies on Turkish named-entity recognition (NER) and text categorization (TC).

Graph Neural Networks (GNNs) are widely used today in recommendation systems, fraud detection, and node/link classification tasks. Real world GNNs continue to scale in size and require a large memory footprint for storing graphs and embeddings that often exceed the memory capacities of the target GPUs used for training. To address limited memory capacities, traditional GNN training approaches use graph partitioning and sharding techniques to scale up across multiple GPUs within a node and/or scale out across multiple nodes. However, this approach suffers from the high computational costs of graph partitioning algorithms and inefficient communication across GPUs. To address these overheads, we propose Large-scale Storage-based Multi-GPU GNN framework (LSM-GNN), a storagebased approach to train GNN models that utilizes a novel communication layer enabling GPU software caches to function as a system-wide shared cache with low overheads.LSM-GNN incorporates a hybrid eviction policy that intelligently manages cache space by using both static and dynamic node information to significantly enhance cache performance. Furthermore, we introduce the Preemptive Victim-buffer Prefetcher (PVP), a mechanism for prefetching node feature data from a Victim Buffer located in CPU pinned-memory to further reduce the pressure on the storage devices. Experimental results show that despite the lower compute capabilities and memory capacities, LSM-GNN in a single node with two GPUs offers superior performance over two-node-four-GPU Dist-DGL baseline and provides up to 3.75x speed up on end-to-end epoch time while running large-scale GNN training

This paper aims at developing an integrated system of clothing co-parsing, in order to jointly parse a set of clothing images (unsegmented but annotated with tags) into semantic configurations. We propose a data-driven framework consisting of two phases of inference. The first phase, referred as "image co-segmentation", iterates to extract consistent regions on images and jointly refines the regions over all images by employing the exemplar-SVM (E-SVM) technique [23]. In the second phase (i.e. "region co-labeling"), we construct a multi-image graphical model by taking the segmented regions as vertices, and incorporate several contexts of clothing configuration (e.g., item location and mutual interactions). The joint label assignment can be solved using the efficient Graph Cuts algorithm. In addition to evaluate our framework on the Fashionista dataset [30], we construct a dataset called CCP consisting of 2098 high-resolution street fashion photos to demonstrate the performance of our system. We achieve 90.29% / 88.23% segmentation accuracy and 65.52% / 63.89% recognition rate on the Fashionista and the CCP datasets, respectively, which are superior compared with state-of-the-art methods.

RNA design aims to find a sequence that folds with highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA folding model. Understanding the specific local structures (i.e., "motifs") that contribute to undesignability is crucial for refining RNA folding models and determining the limits of RNA designability. Despite its importance, this problem has received very little attention, and previous efforts are neither scalable nor interpretable. We develop a new theoretical framework for motif (un-)designability, and design scalable and interpretable algorithms to identify minimal undesignable motifs within a given RNA secondary structure. Our approach establishes motif undesignability by searching for rival motifs, rather than exhaustively enumerating all (partial) sequences that could potentially fold into the motif. Furthermore, we exploit rotational invariance in RNA structures to detect, group, and reuse equivalent motifs and to construct a database of unique minimal undesignable motifs. To achieve that, we propose a loop-pair graph representation for motifs and a recursive graph isomorphism algorithm for motif equivalence. Our algorithms successfully identify 24 unique minimal undesignable motifs among 18 undesignable puzzles from the Eterna100 benchmark. Surprisingly, we also find over 350 unique minimal undesignable motifs and 663 undesignable native structures in the ArchiveII dataset, drawn from a diverse set of RNA families. Our source code is available at https://github.com/shanry/RNA-Undesign and our web server is available at http://linearfold.org/motifs.

Large language models (LMs) are currently trained to predict tokens given document prefixes, enabling them to directly perform long-form generation and prompting-style tasks which can be reduced to document completion. Existing pretraining pipelines train LMs by concatenating random sets of short documents to create input contexts but the prior documents provide no signal for predicting the next document. We instead present In-Context Pretraining, a new approach where language models are pretrained on a sequence of related documents, thereby explicitly encouraging them to read and reason across document boundaries. We can do In-Context Pretraining by simply changing the document ordering so that each context contains related documents, and directly applying existing pretraining pipelines. However, this document sorting problem is challenging. There are billions of documents and we would like the sort to maximize contextual similarity for every document without repeating any data. To do this, we introduce approximate algorithms for finding related documents with efficient nearest neighbor search and constructing coherent input contexts with a graph traversal algorithm. Our experiments show In-Context Pretraining offers a simple and scalable approach to significantly enhance LMs'performance: we see notable improvements in tasks that require more complex contextual reasoning, including in-context learning (+8%), reading comprehension (+15%), faithfulness to previous contexts (+16%), long-context reasoning (+5%), and retrieval augmentation (+9%).

Sharing knowledge between information extraction tasks has always been a challenge due to the diverse data formats and task variations. Meanwhile, this divergence leads to information waste and increases difficulties in building complex applications in real scenarios. Recent studies often formulate IE tasks as a triplet extraction problem. However, such a paradigm does not support multi-span and n-ary extraction, leading to weak versatility. To this end, we reorganize IE problems into unified multi-slot tuples and propose a universal framework for various IE tasks, namely Mirror. Specifically, we recast existing IE tasks as a multi-span cyclic graph extraction problem and devise a non-autoregressive graph decoding algorithm to extract all spans in a single step. It is worth noting that this graph structure is incredibly versatile, and it supports not only complex IE tasks, but also machine reading comprehension and classification tasks. We manually construct a corpus containing 57 datasets for model pretraining, and conduct experiments on 30 datasets across 8 downstream tasks. The experimental results demonstrate that our model has decent compatibility and outperforms or reaches competitive performance with SOTA systems under few-shot and zero-shot settings. The code, model weights, and pretraining corpus are available at https://github.com/Spico197/Mirror .

Given a small set of labeled data and a large set of unlabeled data, semi-supervised learning (SSL) attempts to leverage the location of the unlabeled datapoints in order to create a better classifier than could be obtained from supervised methods applied to the labeled training set alone. Effective SSL imposes structural assumptions on the data, e.g. that neighbors are more likely to share a classification or that the decision boundary lies in an area of low density. For complex and high-dimensional data, neural networks can learn feature embeddings to which traditional SSL methods can then be applied in what we call hybrid methods. Previously-developed hybrid methods iterate between refining a latent representation and performing graph-based SSL on this representation. In this paper, we introduce a novel hybrid method that instead applies low-density separation to the embedded features. We describe it in detail and discuss why low-density separation may be better suited for SSL on neural network-based embeddings than graph-based algorithms. We validate our method using in-house customer survey data and compare it to other state-of-the-art learning methods. Our approach effectively classifies thousands of unlabeled users from a relatively small number of hand-classified examples.

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.

Person search aims at jointly solving Person Detection and Person Re-identification (re-ID). Existing works have designed end-to-end networks based on Faster R-CNN. However, due to the parallel structure of Faster R-CNN, the extracted features come from the low-quality proposals generated by the Region Proposal Network, rather than the detected high-quality bounding boxes. Person search is a fine-grained task and such inferior features will significantly reduce re-ID performance. To address this issue, we propose a Sequential End-to-end Network (SeqNet) to extract superior features. In SeqNet, detection and re-ID are considered as a progressive process and tackled with two sub-networks sequentially. In addition, we design a robust Context Bipartite Graph Matching (CBGM) algorithm to effectively employ context information as an important complementary cue for person matching. Extensive experiments on two widely used person search benchmarks, CUHK-SYSU and PRW, have shown that our method achieves state-of-the-art results. Also, our model runs at 11.5 fps on a single GPU and can be integrated into the existing end-to-end framework easily.

The release of nuPlan marks a new era in vehicle motion planning research, offering the first large-scale real-world dataset and evaluation schemes requiring both precise short-term planning and long-horizon ego-forecasting. Existing systems struggle to simultaneously meet both requirements. Indeed, we find that these tasks are fundamentally misaligned and should be addressed independently. We further assess the current state of closed-loop planning in the field, revealing the limitations of learning-based methods in complex real-world scenarios and the value of simple rule-based priors such as centerline selection through lane graph search algorithms. More surprisingly, for the open-loop sub-task, we observe that the best results are achieved when using only this centerline as scene context (\ie, ignoring all information regarding the map and other agents). Combining these insights, we propose an extremely simple and efficient planner which outperforms an extensive set of competitors, winning the nuPlan planning challenge 2023.

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

We propose SC-Captioner, a reinforcement learning framework that enables the self-correcting capability of image caption models. Our crucial technique lies in the design of the reward function to incentivize accurate caption corrections. Specifically, the predicted and reference captions are decomposed into object, attribute, and relation sets using scene-graph parsing algorithms. We calculate the set difference between sets of initial and self-corrected captions to identify added and removed elements. These elements are matched against the reference sets to calculate correctness bonuses for accurate refinements and mistake punishments for wrong additions and removals, thereby forming the final reward. For image caption quality assessment, we propose a set of metrics refined from CAPTURE that alleviate its incomplete precision evaluation and inefficient relation matching problems. Furthermore, we collect a fine-grained annotated image caption dataset, RefinedCaps, consisting of 6.5K diverse images from COCO dataset. Experiments show that applying SC-Captioner on large visual-language models can generate better image captions across various scenarios, significantly outperforming the direct preference optimization training strategy.

Generating molecules that satisfy precise numeric constraints over multiple physicochemical properties is critical and challenging. Although large language models (LLMs) are expressive, they struggle with precise multi-objective control and numeric reasoning without external structure and feedback. We introduce M olGen, a fragment-level, retrieval-augmented, two-stage framework for molecule generation under multi-property constraints. Stage I : Prototype generation: a multi-agent reasoner performs retrieval-anchored, fragment-level edits to produce a candidate near the feasible region. Stage II : RL-based fine-grained optimization: a fragment-level optimizer trained with Group Relative Policy Optimization (GRPO) applies one- or multi-hop refinements to explicitly minimize the property errors toward our target while regulating edit complexity and deviation from the prototype. A large, automatically curated dataset with reasoning chains of fragment edits and measured property deltas underpins both stages, enabling deterministic, reproducible supervision and controllable multi-hop reasoning. Unlike prior work, our framework better reasons about molecules by leveraging fragments and supports controllable refinement toward numeric targets. Experiments on generation under two sets of property constraints (QED, LogP, Molecular Weight and HOMO, LUMO) show consistent gains in validity and precise satisfaction of multi-property targets, outperforming strong LLMs and graph-based algorithms.

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We motivate the approach, compare it to existing work, and prove a bound on its generalization error. The quality of our solutions is evaluated on a synthetic problem and three UCI ML repository datasets. In most cases, we outperform manifold regularization of support vector machines, which is a state-of-the-art approach to semi-supervised max-margin learning.

In this paper, the causal bandit problem is investigated, in which the objective is to select an optimal sequence of interventions on nodes in a causal graph. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. By exploiting the causal relationships between the nodes whose signals contribute to the reward, interventions are optimized. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed, which strongly reduces sample complexity relative to the prior art by learning sub-graphs. Under the assumption of Gaussian exogenous inputs and minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound based intervention selection to optimize the reward. To cope with non-stationary bandits, a sub-graph change detection mechanism is proposed, with high sample efficiency. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in both stationary and non-stationary settings. Compared to existing approaches, the proposed scheme takes 67% fewer samples to learn the causal structure and achieves an average reward gain of 85%.

This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of clustering. The average indegree reflects the density near a sample, and the average outdegree characterizes the local geometry around a sample. Based on such insights, we define the affinity measure of clusters via the product of average indegree and average outdegree. The product-based affinity makes our algorithm robust to noise. The algorithm has three main advantages: good performance, easy implementation, and high computational efficiency. We test the algorithm on two fundamental computer vision problems: image clustering and object matching. Extensive experiments demonstrate that it outperforms the state-of-the-arts in both applications.

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.

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.

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

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

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

Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including recommender systems and social networks. However, this performance is based on static graph structures assumption which limits the Graph Neural Networks performance when the data varies with time. Spatiotemporal Graph Neural Networks are extension of Graph Neural Networks that takes the time factor into account. Recently, various Spatiotemporal Graph Neural Network algorithms were proposed and achieved superior performance compared to other deep learning algorithms in several time dependent applications. This survey discusses interesting topics related to Spatiotemporal Graph Neural Networks, including algorithms, applications, and open challenges.

Recent years have witnessed tremendous interest in deep learning on graph-structured data. Due to the high cost of collecting labeled graph-structured data, domain adaptation is important to supervised graph learning tasks with limited samples. However, current graph domain adaptation methods are generally adopted from traditional domain adaptation tasks, and the properties of graph-structured data are not well utilized. For example, the observed social networks on different platforms are controlled not only by the different crowd or communities but also by the domain-specific policies and the background noise. Based on these properties in graph-structured data, we first assume that the graph-structured data generation process is controlled by three independent types of latent variables, i.e., the semantic latent variables, the domain latent variables, and the random latent variables. Based on this assumption, we propose a disentanglement-based unsupervised domain adaptation method for the graph-structured data, which applies variational graph auto-encoders to recover these latent variables and disentangles them via three supervised learning modules. Extensive experimental results on two real-world datasets in the graph classification task reveal that our method not only significantly outperforms the traditional domain adaptation methods and the disentangled-based domain adaptation methods but also outperforms the state-of-the-art graph domain adaptation algorithms.

Graph Convolutional Networks(GCNs) play a crucial role in graph learning tasks, however, learning graph embedding with few supervised signals is still a difficult problem. In this paper, we propose a novel training algorithm for Graph Convolutional Network, called Multi-Stage Self-Supervised(M3S) Training Algorithm, combined with self-supervised learning approach, focusing on improving the generalization performance of GCNs on graphs with few labeled nodes. Firstly, a Multi-Stage Training Framework is provided as the basis of M3S training method. Then we leverage DeepCluster technique, a popular form of self-supervised learning, and design corresponding aligning mechanism on the embedding space to refine the Multi-Stage Training Framework, resulting in M3S Training Algorithm. Finally, extensive experimental results verify the superior performance of our algorithm on graphs with few labeled nodes under different label rates compared with other state-of-the-art approaches.

Equivariant Graph Neural Networks (EGNNs) have emerged as a promising approach in Multi-Agent Reinforcement Learning (MARL), leveraging symmetry guarantees to greatly improve sample efficiency and generalization. However, real-world environments often exhibit inherent asymmetries arising from factors such as external forces, measurement inaccuracies, or intrinsic system biases. This paper introduces Partially Equivariant Graph NeUral Networks (PEnGUiN), a novel architecture specifically designed to address these challenges. We formally identify and categorize various types of partial equivariance relevant to MARL, including subgroup equivariance, feature-wise equivariance, regional equivariance, and approximate equivariance. We theoretically demonstrate that PEnGUiN is capable of learning both fully equivariant (EGNN) and non-equivariant (GNN) representations within a unified framework. Through extensive experiments on a range of MARL problems incorporating various asymmetries, we empirically validate the efficacy of PEnGUiN. Our results consistently demonstrate that PEnGUiN outperforms both EGNNs and standard GNNs in asymmetric environments, highlighting their potential to improve the robustness and applicability of graph-based MARL algorithms in real-world scenarios.

Obtaining large pre-trained models that can be fine-tuned to new tasks with limited annotated samples has remained an open challenge for medical imaging data. While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images. To bridge this gap, we introduce LVM-Med, the first family of deep networks trained on large-scale medical datasets. We have collected approximately 1.3 million medical images from 55 publicly available datasets, covering a large number of organs and modalities such as CT, MRI, X-ray, and Ultrasound. We benchmark several state-of-the-art self-supervised algorithms on this dataset and propose a novel self-supervised contrastive learning algorithm using a graph-matching formulation. The proposed approach makes three contributions: (i) it integrates prior pair-wise image similarity metrics based on local and global information; (ii) it captures the structural constraints of feature embeddings through a loss function constructed via a combinatorial graph-matching objective; and (iii) it can be trained efficiently end-to-end using modern gradient-estimation techniques for black-box solvers. We thoroughly evaluate the proposed LVM-Med on 15 downstream medical tasks ranging from segmentation and classification to object detection, and both for the in and out-of-distribution settings. LVM-Med empirically outperforms a number of state-of-the-art supervised, self-supervised, and foundation models. For challenging tasks such as Brain Tumor Classification or Diabetic Retinopathy Grading, LVM-Med improves previous vision-language models trained on 1 billion masks by 6-7% while using only a ResNet-50.

Generating 3D scenes from natural language holds great promise for applications in gaming, film, and design. However, existing methods struggle with automation, 3D consistency, and fine-grained control. We present DreamScene, an end-to-end framework for high-quality and editable 3D scene generation from text or dialogue. DreamScene begins with a scene planning module, where a GPT-4 agent infers object semantics and spatial constraints to construct a hybrid graph. A graph-based placement algorithm then produces a structured, collision-free layout. Based on this layout, Formation Pattern Sampling (FPS) generates object geometry using multi-timestep sampling and reconstructive optimization, enabling fast and realistic synthesis. To ensure global consistent, DreamScene employs a progressive camera sampling strategy tailored to both indoor and outdoor settings. Finally, the system supports fine-grained scene editing, including object movement, appearance changes, and 4D dynamic motion. Experiments demonstrate that DreamScene surpasses prior methods in quality, consistency, and flexibility, offering a practical solution for open-domain 3D content creation. Code and demos are available at https://jahnsonblack.github.io/DreamScene-Full/.

This paper proposes an algorithm for real-time learning without explicit feedback. The algorithm combines the ideas of semi-supervised learning on graphs and online learning. In particular, it iteratively builds a graphical representation of its world and updates it with observed examples. Labeled examples constitute the initial bias of the algorithm and are provided offline, and a stream of unlabeled examples is collected online to update this bias. We motivate the algorithm, discuss how to implement it efficiently, prove a regret bound on the quality of its solutions, and apply it to the problem of real-time face recognition. Our recognizer runs in real time, and achieves superior precision and recall on 3 challenging video datasets.

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

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Models with fewer parameters are necessary for the neural control of memory-limited, performant robots. Finding these smaller neural network architectures can be time-consuming. We propose HyperPPO, an on-policy reinforcement learning algorithm that utilizes graph hypernetworks to estimate the weights of multiple neural architectures simultaneously. Our method estimates weights for networks that are much smaller than those in common-use networks yet encode highly performant policies. We obtain multiple trained policies at the same time while maintaining sample efficiency and provide the user the choice of picking a network architecture that satisfies their computational constraints. We show that our method scales well - more training resources produce faster convergence to higher-performing architectures. We demonstrate that the neural policies estimated by HyperPPO are capable of decentralized control of a Crazyflie2.1 quadrotor. Website: https://sites.google.com/usc.edu/hyperppo

DeepRobust is a PyTorch adversarial learning library which aims to build a comprehensive and easy-to-use platform to foster this research field. It currently contains more than 10 attack algorithms and 8 defense algorithms in image domain and 9 attack algorithms and 4 defense algorithms in graph domain, under a variety of deep learning architectures. In this manual, we introduce the main contents of DeepRobust with detailed instructions. The library is kept updated and can be found at https://github.com/DSE-MSU/DeepRobust.

Training large AI models on numerous GPUs consumes a massive amount of energy. We observe that not all energy consumed during training directly contributes to end-to-end training throughput, and a significant portion can be removed without slowing down training, which we call energy bloat. In this work, we identify two independent sources of energy bloat in large model training, intrinsic and extrinsic, and propose Perseus, a unified optimization framework that mitigates both. Perseus obtains the "iteration time-energy" Pareto frontier of any large model training job using an efficient iterative graph cut-based algorithm and schedules energy consumption of its forward and backward computations across time to remove intrinsic and extrinsic energy bloat. Evaluation on large models like GPT-3 and Bloom shows that Perseus reduces energy consumption of large model training by up to 30%, enabling savings otherwise unobtainable before.

In liberalised railway systems, operators must set prices dynamically in an environment with partial observability, as they retain private information about their objectives and performance, where regulatory constraints prohibit communication or direct information exchange between competitors to prevent explicit collusion. Consequently, agents must learn to infer strategic interactions only from observable market data which presents a significant challenge for multi-agent reinforcement learning, where standard approaches typically treat observations as unstructured vectors, ignoring the underlying market topology that governs strategic interactions. To address this, an entity graph modelling approach is proposed, which represents the environment as a graph of operational units, rather than decision-making agents or static infrastructure, encoding competition, coordination, and connectivity relations between entities. Then, an extension of the multi-agent twin delayed deep deterministic policy gradient algorithm with graph-based representation learning processes the features of the entities through a multi-layer relational graph convolutional network and aggregates them via a learnt attention mechanism. Experimental results in a rail pricing reinforcement learning environment show that this novel framework achieves higher revenue and stability in two different settings of increasing market complexity compared to a representative selection of relational and non-relational baselines. The code is publicly available at: https://github.com/Kinrre/RelationalRailPricing-RL

Detecting which nodes in graphs are outliers is a relatively new machine learning task with numerous applications. Despite the proliferation of algorithms developed in recent years for this task, there has been no standard comprehensive setting for performance evaluation. Consequently, it has been difficult to understand which methods work well and when under a broad range of settings. To bridge this gap, we present--to the best of our knowledge--the first comprehensive benchmark for unsupervised outlier node detection on static attributed graphs called BOND, with the following highlights. (1) We benchmark the outlier detection performance of 14 methods ranging from classical matrix factorization to the latest graph neural networks. (2) Using nine real datasets, our benchmark assesses how the different detection methods respond to two major types of synthetic outliers and separately to "organic" (real non-synthetic) outliers. (3) Using an existing random graph generation technique, we produce a family of synthetically generated datasets of different graph sizes that enable us to compare the running time and memory usage of the different outlier detection algorithms. Based on our experimental results, we discuss the pros and cons of existing graph outlier detection algorithms, and we highlight opportunities for future research. Importantly, our code is freely available and meant to be easily extendable: https://github.com/pygod-team/pygod/tree/main/benchmark

Foundation models have emerged as powerful tools across various domains including language, vision, and multimodal tasks. While prior works have addressed unsupervised image segmentation, they significantly lag behind supervised models. In this paper, we use a diffusion UNet encoder as a foundation vision encoder and introduce DiffCut, an unsupervised zero-shot segmentation method that solely harnesses the output features from the final self-attention block. Through extensive experimentation, we demonstrate that the utilization of these diffusion features in a graph based segmentation algorithm, significantly outperforms previous state-of-the-art methods on zero-shot segmentation. Specifically, we leverage a recursive Normalized Cut algorithm that softly regulates the granularity of detected objects and produces well-defined segmentation maps that precisely capture intricate image details. Our work highlights the remarkably accurate semantic knowledge embedded within diffusion UNet encoders that could then serve as foundation vision encoders for downstream tasks. Project page at https://diffcut-segmentation.github.io

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

Scaling laws for Large Language Models (LLMs) establish that model quality improves with computational scale, yet edge deployment imposes strict constraints on compute, memory, and power. Since General Matrix Multiplication (GEMM) accounts for up to 90% of inference time, efficient GEMM acceleration is critical for edge AI. The Adaptive Intelligent Engines available in the AMD Versal adaptive SoCs are well suited for this task, but existing state-of-the-art (SOTA) frameworks maximize performance through spatial scaling, distributing workloads across hundreds of cores -- an approach that fails on resource-limited edge SoCs due to physical implementation failures, bandwidth saturation, and excessive resource consumption. We propose Tempus, a Resource-Invariant Temporal GEMM framework for the AMD Versal AI Edge SoC. Rather than expanding hardware resources with matrix size, Tempus employs a fixed compute block of 16 AIE-ML cores, achieving scalability through iterative graph execution and algorithmic data tiling and replication in the Programmable Logic. High-speed cascade streaming ensures low-latency partial sum reduction at Initiation Interval (II) of 1, while a deadlock-free DATAFLOW protocol maximizes transfer-compute overlap and PLIO reuse. Evaluated on GEMM workloads, Tempus achieves 607 GOPS at 10.677 W total on-chip power. By characterizing system-level efficiency through the Platform-Aware Utility (PAU) metric, we prove that Tempus achieves a 211.2x higher prominence factor than the leading spatial SOTA (ARIES). Furthermore, the framework maintains a 0.00% utilization of URAM/DSP, yielding 22.0x core frugality, 7.1x power frugality, and a 6.3x reduction in I/O demand, establishing a sustainable, scalable foundation for edge LLM inference.

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.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).

We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph G with n vertices and m edges, determines the orientable genus of G in O(n(4^m/n)^{n/t}) steps where t is the girth of G. This algorithm avoids difficulties that many other genus algorithms have with handling bridge placements which is a well-known issue. The algorithm has a number of useful properties for practical use: it is simple to implement, it outputs the faces of an optimal embedding, and it iteratively narrows both upper and lower bounds. We illustrate the algorithm by determining the genus of the (3,12) cage (which is 17); other graphs are also considered.

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from scalability issues since they require extracting subgraphs for each training or test query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over six homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10times speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement.

Biomedical knowledge graphs (BioMedKGs) are essential infrastructures for biomedical and healthcare big data and artificial intelligence (AI), facilitating natural language processing, model development, and data exchange. For decades, these knowledge graphs have been developed via expert curation; however, this method can no longer keep up with today's AI development, and a transition to algorithmically generated BioMedKGs is necessary. In this work, we introduce the Biomedical Informatics Ontology System (BIOS), the first large-scale publicly available BioMedKG generated completely by machine learning algorithms. BIOS currently contains 4.1 million concepts, 7.4 million terms in two languages, and 7.3 million relation triplets. We present the methodology for developing BIOS, including the curation of raw biomedical terms, computational identification of synonymous terms and aggregation of these terms to create concept nodes, semantic type classification of the concepts, relation identification, and biomedical machine translation. We provide statistics on the current BIOS content and perform preliminary assessments of term quality, synonym grouping, and relation extraction. The results suggest that machine learning-based BioMedKG development is a viable alternative to traditional expert curation.

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Neural Architecture Search (NAS) aims to find efficient models for multiple tasks. Beyond seeking solutions for a single task, there are surging interests in transferring network design knowledge across multiple tasks. In this line of research, effectively modeling task correlations is vital yet highly neglected. Therefore, we propose Arch-Graph, a transferable NAS method that predicts task-specific optimal architectures with respect to given task embeddings. It leverages correlations across multiple tasks by using their embeddings as a part of the predictor's input for fast adaptation. We also formulate NAS as an architecture relation graph prediction problem, with the relational graph constructed by treating candidate architectures as nodes and their pairwise relations as edges. To enforce some basic properties such as acyclicity in the relational graph, we add additional constraints to the optimization process, converting NAS into the problem of finding a Maximal Weighted Acyclic Subgraph (MWAS). Our algorithm then strives to eliminate cycles and only establish edges in the graph if the rank results can be trusted. Through MWAS, Arch-Graph can effectively rank candidate models for each task with only a small budget to finetune the predictor. With extensive experiments on TransNAS-Bench-101, we show Arch-Graph's transferability and high sample efficiency across numerous tasks, beating many NAS methods designed for both single-task and multi-task search. It is able to find top 0.16\% and 0.29\% architectures on average on two search spaces under the budget of only 50 models.

Effectively managing Air Traffic Control Officer (ATCO) workload is crucial in maintaining operational safety. Group supervisors use tools that estimate upcoming traffic load to aid decision-making. However, industry-standard models can fail to capture the nuances of upcoming air traffic complexity. This study presents a probabilistic approach to forecast the complexity of an airspace sector using the number of relevant aircraft pairs, i.e., those that require monitoring or deconfliction by a controller, as a proxy measure for ATCO workload. We adapted an existing filter algorithm to make it suitable for use in London Middle Sector (LMS), a complex airspace sector with multiple flows of traffic above some of the busiest airports in Europe. Through iterative feedback with ATCOs, the algorithm was refined and extended to handle specific geometric and operational considerations. The updated algorithm outperformed the original, with an F1-score of 0.84 compared to 0.69 on a labelled set of 50 traffic scenarios. To produce forecasts of future numbers of relevant aircraft pairs in the sector, a graph representation of the LMS route network was constructed, standardising the spatial fidelity of route legs. The forecasting method accounts for uncertainty in aircraft arrival times by modelling the probability of each aircraft occupying route segments at future query times. When combined with historic distributions of relevant interactions and a live operational data stream, predictions of upcoming ATCO workload could be made up to 45 minutes in advance. The proposed method to forecast upcoming workload showed a significantly stronger correlation with actual relevant interactions (Spearman's ρ= 0.68) than a standard traffic volume prediction (ρ= 0.55). The resulting data-driven tool shows promise for use by group supervisors to inform sector configuration and ATCO rostering decisions.

We present a detailed theoretical and computational analysis of the Watset meta-algorithm for fuzzy graph clustering, which has been found to be widely applicable in a variety of domains. This algorithm creates an intermediate representation of the input graph that reflects the "ambiguity" of its nodes. Then, it uses hard clustering to discover clusters in this "disambiguated" intermediate graph. After outlining the approach and analyzing its computational complexity, we demonstrate that Watset shows competitive results in three applications: unsupervised synset induction from a synonymy graph, unsupervised semantic frame induction from dependency triples, and unsupervised semantic class induction from a distributional thesaurus. Our algorithm is generic and can be also applied to other networks of linguistic data.

Graph Neural Networks (GNNs) are a popular technique for modelling graph-structured data and computing node-level representations via aggregation of information from the neighborhood of each node. However, this aggregation implies an increased risk of revealing sensitive information, as a node can participate in the inference for multiple nodes. This implies that standard privacy-preserving machine learning techniques, such as differentially private stochastic gradient descent (DP-SGD) - which are designed for situations where each data point participates in the inference for one point only - either do not apply, or lead to inaccurate models. In this work, we formally define the problem of learning GNN parameters with node-level privacy, and provide an algorithmic solution with a strong differential privacy guarantee. We employ a careful sensitivity analysis and provide a non-trivial extension of the privacy-by-amplification technique to the GNN setting. An empirical evaluation on standard benchmark datasets demonstrates that our method is indeed able to learn accurate privacy-preserving GNNs which outperform both private and non-private methods that completely ignore graph information.

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

This study introduces a novel framework, G3Reg, for fast and robust global registration of LiDAR point clouds. In contrast to conventional complex keypoints and descriptors, we extract fundamental geometric primitives, including planes, clusters, and lines (PCL) from the raw point cloud to obtain low-level semantic segments. Each segment is represented as a unified Gaussian Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth centers are encompassed with a certain degree of probability. Utilizing these GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility Graph for Global Registration (PAGOR). Specifically, we establish an upper bound, which can be traversed based on the confidence level for compatibility testing to construct the pyramid graph. Then, we solve multiple maximum cliques (MAC) for each level of the pyramid graph, thus generating the corresponding transformation candidates. In the verification phase, we adopt a precise and efficient metric for point cloud alignment quality, founded on geometric primitives, to identify the optimal candidate. The algorithm's performance is validated on three publicly available datasets and a self-collected multi-session dataset. Parameter settings remained unchanged during the experiment evaluations. The results exhibit superior robustness and real-time performance of the G3Reg framework compared to state-of-the-art methods. Furthermore, we demonstrate the potential for integrating individual GEM and PAGOR components into other registration frameworks to enhance their efficacy. Code: https://github.com/HKUST-Aerial-Robotics/G3Reg

Existing offline hierarchical reinforcement learning methods rely on high-level policy learning to generate subgoal sequences. However, their efficiency degrades as task horizons increase, and they lack effective strategies for stitching useful state transitions across different trajectories. We propose Graph-Assisted Stitching (GAS), a novel framework that formulates subgoal selection as a graph search problem rather than learning an explicit high-level policy. By embedding states into a Temporal Distance Representation (TDR) space, GAS clusters semantically similar states from different trajectories into unified graph nodes, enabling efficient transition stitching. A shortest-path algorithm is then applied to select subgoal sequences within the graph, while a low-level policy learns to reach the subgoals. To improve graph quality, we introduce the Temporal Efficiency (TE) metric, which filters out noisy or inefficient transition states, significantly enhancing task performance. GAS outperforms prior offline HRL methods across locomotion, navigation, and manipulation tasks. Notably, in the most stitching-critical task, it achieves a score of 88.3, dramatically surpassing the previous state-of-the-art score of 1.0. Our source code is available at: https://github.com/qortmdgh4141/GAS.

The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Network (GNN)-based dynamics models with structure-exploiting Model Predictive Control to enable real-time control of high-dimensional systems. By representing the system as a graph with localized interactions, the GNN preserves sparsity, while a tailored condensing algorithm eliminates state variables from the control problem, ensuring efficient computation. The complexity of our condensing algorithm scales linearly with the number of system nodes, and leverages Graphics Processing Unit (GPU) parallelization to achieve real-time performance. The proposed approach is validated in simulation and experimentally on a physical soft robotic trunk. Results show that our method scales to systems with up to 1,000 nodes at 100 Hz in closed-loop, and demonstrates real-time reference tracking on hardware with sub-centimeter accuracy, outperforming baselines by 63.6%. Finally, we show the capability of our method to achieve effective full-body obstacle avoidance.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

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

In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly improve upon those of standard multi-armed bandit (MAB) algorithms under mild conditions. Lastly, we prove our mild conditions are necessary: without them one cannot do better than standard MAB algorithms.

Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

Knowledge graph (KG) embedding is a fundamental task in natural language processing, and various methods have been proposed to explore semantic patterns in distinctive ways. In this paper, we propose to learn an ensemble by leveraging existing methods in a relation-aware manner. However, exploring these semantics using relation-aware ensemble leads to a much larger search space than general ensemble methods. To address this issue, we propose a divide-search-combine algorithm RelEns-DSC that searches the relation-wise ensemble weights independently. This algorithm has the same computation cost as general ensemble methods but with much better performance. Experimental results on benchmark datasets demonstrate the effectiveness of the proposed method in efficiently searching relation-aware ensemble weights and achieving state-of-the-art embedding performance. The code is public at https://github.com/LARS-research/RelEns.

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

Intrusion detection system (IDS) is an important part of enterprise security system architecture. In particular, anomaly-based IDS has been widely applied to detect abnormal process behaviors that deviate from the majority. However, such abnormal behavior usually consists of a series of low-level heterogeneous events. The gap between the low-level events and the high-level abnormal behaviors makes it hard to infer which single events are related to the real abnormal activities, especially considering that there are massive "noisy" low-level events happening in between. Hence, the existing work that focus on detecting single entities/events can hardly achieve high detection accuracy. Different from previous work, we design and implement GID, an efficient graph-based intrusion detection technique that can identify abnormal event sequences from a massive heterogeneous process traces with high accuracy. GID first builds a compact graph structure to capture the interactions between different system entities. The suspiciousness or anomaly score of process paths is then measured by leveraging random walk technique to the constructed acyclic directed graph. To eliminate the score bias from the path length, the Box-Cox power transformation based approach is introduced to normalize the anomaly scores so that the scores of paths of different lengths have the same distribution. The efficiency of suspicious path discovery is further improved by the proposed optimization scheme. We fully implement our GID algorithm and deploy it into a real enterprise security system, and it greatly helps detect the advanced threats, and optimize the incident response. Executing GID on system monitoring datasets showing that GID is efficient (about 2 million records per minute) and accurate (higher than 80% in terms of detection rate).

In this paper, we introduce a novel graph-based method to classify the regions with similar climate in a local area. We refer our proposed method as Graph Partition Based Method (GPBM). Our proposed method attempts to overcome the shortcomings of the current state-of-the-art methods in the literature. It has no limit on the number of variables that can be used and also preserves the nature of climate data. To illustrate the capability of our proposed algorithm, we benchmark its performance with other state-of-the-art climate classification techniques. The climate data is collected from 24 synoptic stations in Fars province in southern Iran. The data includes seven climate variables stored as time series from 1951 to 2017. Our results exhibit that our proposed method performs a more realistic climate classification with less computational time. It can save more information during the climate classification process and is therefore efficient in further data analysis. Furthermore, using our method, we can introduce seasonal graphs to better investigate seasonal climate changes. To the best of our knowledge, our proposed method is the first graph-based climate classification system.

Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used by spectral clustering module to assign labels to clusters. However, such approach ignores complementary information that exist in other layers of the encoder (including the input data themselves). Herein, we apply selected linear subspace clustering algorithm to learn representation matrices from representations learned by all layers of encoder network including the input data. Afterward, we learn a multilayer graph that in a multi-view like manner integrates information from graph Laplacians of all used layers. That improves further performance of selected DSC network. Furthermore, we also provide formulation of our approach to cluster out-of-sample/test data points. We validate proposed approach on four well-known datasets with two DSC networks as baseline models. In almost all the cases, proposed approach achieved statistically significant improvement in three performance metrics. MATLAB code of proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.

Effective communication is key to successful, decentralized, multi-robot path planning. Yet, it is far from obvious what information is crucial to the task at hand, and how and when it must be shared among robots. To side-step these issues and move beyond hand-crafted heuristics, we propose a combined model that automatically synthesizes local communication and decision-making policies for robots navigating in constrained workspaces. Our architecture is composed of a convolutional neural network (CNN) that extracts adequate features from local observations, and a graph neural network (GNN) that communicates these features among robots. We train the model to imitate an expert algorithm, and use the resulting model online in decentralized planning involving only local communication and local observations. We evaluate our method in simulations {by navigating teams of robots to their destinations in 2D} cluttered workspaces. We measure the success rates and sum of costs over the planned paths. The results show a performance close to that of our expert algorithm, demonstrating the validity of our approach. In particular, we show our model's capability to generalize to previously unseen cases (involving larger environments and larger robot teams).

Recent advancements in deep neural networks for graph-structured data have led to state-of-the-art performance on recommender system benchmarks. However, making these methods practical and scalable to web-scale recommendation tasks with billions of items and hundreds of millions of users remains a challenge. Here we describe a large-scale deep recommendation engine that we developed and deployed at Pinterest. We develop a data-efficient Graph Convolutional Network (GCN) algorithm PinSage, which combines efficient random walks and graph convolutions to generate embeddings of nodes (i.e., items) that incorporate both graph structure as well as node feature information. Compared to prior GCN approaches, we develop a novel method based on highly efficient random walks to structure the convolutions and design a novel training strategy that relies on harder-and-harder training examples to improve robustness and convergence of the model. We also develop an efficient MapReduce model inference algorithm to generate embeddings using a trained model. We deploy PinSage at Pinterest and train it on 7.5 billion examples on a graph with 3 billion nodes representing pins and boards, and 18 billion edges. According to offline metrics, user studies and A/B tests, PinSage generates higher-quality recommendations than comparable deep learning and graph-based alternatives. To our knowledge, this is the largest application of deep graph embeddings to date and paves the way for a new generation of web-scale recommender systems based on graph convolutional architectures.

Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable.We propose GVEX, a novel paradigm that generates Graph Views for EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is Σ^2_P-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4 approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX.

Neural Module Network (NMN) is a machine learning model for solving the visual question answering tasks. NMN uses programs to encode modules' structures, and its modularized architecture enables it to solve logical problems more reasonably. However, because of the non-differentiable procedure of module selection, NMN is hard to be trained end-to-end. To overcome this problem, existing work either included ground-truth program into training data or applied reinforcement learning to explore the program. However, both of these methods still have weaknesses. In consideration of this, we proposed a new learning framework for NMN. Graph-based Heuristic Search is the algorithm we proposed to discover the optimal program through a heuristic search on the data structure named Program Graph. Our experiments on FigureQA and CLEVR dataset show that our methods can realize the training of NMN without ground-truth programs and achieve superior efficiency over existing reinforcement learning methods in program exploration.

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size (k). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the long-standing inference bottleneck of kNN, establishing a new structural paradigm for graph-based nonparametric learning.

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many studies on structure learning with various types of data, the structure learning on the dynamic graph has not been explored yet, and thus we study the learning problem of node feature generation mechanism on such ubiquitous dynamic graph data. In a dynamic graph, we propose to simultaneously estimate contemporaneous relationships and time-lagged interaction relationships between the node features. These two kinds of relationships form a DAG, which could effectively characterize the feature generation process in a concise way. To learn such a DAG, we cast the learning problem as a continuous score-based optimization problem, which consists of a differentiable score function to measure the validity of the learned DAGs and a smooth acyclicity constraint to ensure the acyclicity of the learned DAGs. These two components are translated into an unconstraint augmented Lagrangian objective which could be minimized by mature continuous optimization techniques. The resulting algorithm, named GraphNOTEARS, outperforms baselines on simulated data across a wide range of settings that may encounter in real-world applications. We also apply the proposed approach on two dynamic graphs constructed from the real-world Yelp dataset, demonstrating our method could learn the connections between node features, which conforms with the domain knowledge.

Multimodal learning combines multiple data modalities, broadening the types and complexity of data our models can utilize: for example, from plain text to image-caption pairs. Most multimodal learning algorithms focus on modeling simple one-to-one pairs of data from two modalities, such as image-caption pairs, or audio-text pairs. However, in most real-world settings, entities of different modalities interact with each other in more complex and multifaceted ways, going beyond one-to-one mappings. We propose to represent these complex relationships as graphs, allowing us to capture data with any number of modalities, and with complex relationships between modalities that can flexibly vary from one sample to another. Toward this goal, we propose Multimodal Graph Learning (MMGL), a general and systematic framework for capturing information from multiple multimodal neighbors with relational structures among them. In particular, we focus on MMGL for generative tasks, building upon pretrained Language Models (LMs), aiming to augment their text generation with multimodal neighbor contexts. We study three research questions raised by MMGL: (1) how can we infuse multiple neighbor information into the pretrained LMs, while avoiding scalability issues? (2) how can we infuse the graph structure information among multimodal neighbors into the LMs? and (3) how can we finetune the pretrained LMs to learn from the neighbor context in a parameter-efficient manner? We conduct extensive experiments to answer these three questions on MMGL and analyze the empirical results to pave the way for future MMGL research.