Graph Representations

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by treating layers independently or aggregating them. To address this, we propose T-GINEE (Tensor-Based Generalized Multilayer-graph Estimating Equation), a statistical regularization framework combining tensor-based generalized estimating equations with task-specific loss to model cross-network correlations explicitly. Key innovations include: (1) CP tensor decomposition capturing structural dependencies via shared latent factors; (2) a generalized estimating equation framework modeling inter-layer correlations through working covariance matrices; and (3) a flexible link function accommodating characteristics like sparsity. Our theoretical analysis establishes consistency and asymptotic normality under mild conditions. Extensive experiments on synthetic and real-world datasets validate T-GINEE's effectiveness for multilayer network analysis.

Flowcharts are widely used in industrial requirements, but usually remain embedded as static images. Vision Language Models (VLMs) show promise in the conversion of these flowcharts into machine-readable models for RE activities, yet, when directly applied to flowchart conversion, they often fail on topology-critical visual details. To address this, we propose EdgeFlow that augments a VLM's original input with a deterministically extracted Canny edge map-acting as a structural prior-to improve flowchart-to-Mermaid conversion, without requiring annotated training data or domain-specific model fine-tuning. We evaluate EdgeFlow on IndusReqFlow, a dataset sourced from real-world requirements. Compared with off-the-shelf VLMs, EdgeFlow improves node-level F1 by 17.39 percentage points and edge-level F1 by 16.94 percentage points. At the path level, EdgeFlow improves path F1 by 11.06 percentage points, enabling better support for model-based testing. These results demonstrate that EdgeFlow provides a practical, training-free means to improve topology-preserving flowchart-to-Mermaid conversion for industrial RE. Cross-dataset evaluation results on a public synthetic benchmark show no significant improvement; this highlights the need for diverse benchmarks incorporating industrial data for the comprehensive evaluation of future VLM-based RE tools.

Scientific paper evaluation often involves not only assessing a manuscript itself, but also relating it to contemporaneous research and prior literature. However, existing LLM-based methods typically model these signals separately and lack a unified mechanism for propagating review evidence across papers. We propose $\textbf{GraphReview}$, a graph-based LLM framework that formulates paper evaluation as review-signal message passing over a semantic paper graph. The graph jointly captures intrinsic quality, synchronic links among contemporaneous papers, and diachronic links to prior work. LLMs are used to estimate node-level quality priors and generate edge-level comparative evidence through pairwise paper comparisons, while Personalized PageRank integrates review signals for quality ranking, decision prediction, and review generation. To produce higher-quality graph evidence, we propose reward-induced maximum likelihood objectives for training the LLM backbones. Experiments show that GraphReview consistently outperforms the strongest baseline, achieving average improvements of 29.7% on decision and ranking metrics, including gains of 23.7% in Accuracy and 57.6% in Spearman's $ρ$. It also produces higher-quality review texts and generalizes effectively across time periods and conference venues. The code is available at https://github.com/ECNU-Text-Computing/GraphReview.

In computational pathology, Whole Slide Images (WSIs) survival analysis is crucial for patient prognosis assessment, but it faces multiple technical challenges. Although the Transformer captures long-range dependencies through its self-attention mechanism, its $O(N^2)$ time complexity causes a severe computational bottleneck in large-scale WSIs graph structures. The Mamba model breaks through the Transformer's computational bottleneck with linear complexity. But, owing to Mamba's high sensitivity to the order of input data, traditional node sorting methods in Graph Mamba, such as those based on node degree or subgraph size, fail to adequately account for the topological connectivity of graph data. This inadequacy consequently restricts the performance of Mamba's sequential modeling. Moreover, its unidirectional architecture cannot leverage the bidirectional spatial structure of images. To address these challenges, this paper proposes a novel Graph Mamba survival analysis framework based on topology-aware ordering (TopoMamSurv) to adapt to the sequential sensitivity of Mamba. Our visualization experiments further confirmed that the nodes extracted through the topology-aware ordering (TAO) strategy indeed exhibit higher similarity. Furthermore, we designed a bidirectional Mamba module and integrated a Graph Convolutional Network (GCN) to achieve bidirectional spatial context modeling of images, forming a hierarchical feature learning architecture for "local aggregation - global capture." This framework effectively reconciles the contradiction between long-range dependency modeling, computational efficiency, and spatial structure utilization in WSIs analysis through its systematic design of TAO, bidirectional semantic modeling, and hierarchical feature fusion. This framework has been validated for its comprehensive performance advantage on five TCGA datasets.

Estimating individual treatment effect (ITE) from observational graph data is crucial for decision-making in the fields such as commerce and medicine. This task is challenging due to interference, where individual outcomes can be influenced by the treatments and covariates of their neighbors. Existing methods attempt to model such interference for accurate ITE estimation. However, a critical issue is often overlooked: differentiated networked effect (DNE), an effect caused by local networks consisting of neighbors with varying importance and scales. Capturing DNE is vital; otherwise, we will end up with imprecise ITE estimation due to an erroneous characterization of interference, which can result in misguided decisions. To address this challenge, we propose a novel interference modeling mechanism that incorporates two partial attention mechanisms and a message amplifier. The partial attention mechanisms automatically estimate the importance of different neighbors in contributing to interference, while the message amplifier adjusts the results of the interference modeling mechanism based on the scale of neighbors, all of which enables the model to capture DNE. Experiments on three real-world graphs demonstrate that our methods outperform existing approaches for ITE estimation from graph data, which corroborates the importance of explicitly capturing DNE.

Defending Graph Neural Networks (GNNs) against adversarial attacks requires balancing accuracy and robustness, a trade-off often mishandled by traditional methods like adversarial training that intertwine these conflicting objectives within a single classifier. To overcome this limitation, we propose a self-supervised adversarial purification framework. We separate robustness from the classifier by introducing a dedicated purifier, which cleanses the input data before classification. In contrast to prior adversarial purification methods, we propose GPR-GAE, a novel graph auto-encoder (GAE), as a specialized purifier trained with a self-supervised strategy, adapting to diverse graph structures in a data-driven manner. Utilizing multiple Generalized PageRank (GPR) filters, GPR-GAE captures diverse structural representations for robust and effective purification. Our multi-step purification process further facilitates GPR-GAE to achieve precise graph recovery and robust defense against structural perturbations. Experiments across diverse datasets and attack scenarios demonstrate the state-of-the-art robustness of GPR-GAE, showcasing it as an independent plug-and-play purifier for GNN classifiers.

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision. We investigate standard deep ensembles specifically for message-passing graph neural networks. Benchmarking across seven datasets representing varied tasks and complexities, we reveal that ensembles provide surprisingly little improvement over a single model. Instead, the observed marginal gains stem primarily from stabilizing optimization noise in point predictions rather than yielding meaningfully better uncertainty estimates. Through an aleatoric-epistemic decomposition, we identify epistemic collapse: independently trained networks consistently converge to overly similar predictions. Because disagreement is the fundamental mechanism through which ensembles capture epistemic uncertainty, this lack of diversity neutralizes their key advantage. Analyzing this phenomenon further, we suggest this collapse is driven by functional rather than weight-space convexity, where distinct parameter solutions induce almost identical behavior. Our results suggest that deep ensemble success does not seamlessly transfer to graph machine learning.

Large Language Model (LLM)-based agents demonstrate strong reasoning and execution capabilities on complex tasks when guided by structured instructions, commonly referred to as workflows. However, existing workflow-assisted agent serving systems typically rely on predefined templates and shallow matching mechanisms, which limit their ability to capture deep semantic relationships and generalize to previously unseen tasks. To address these limitations, we propose a new workflow management paradigm that represents workflows using a unified graph, termed wGraph, where each node corresponds to an atomic operation. wGraph serves as a shared substrate from which task-specific workflows are dynamically instantiated. Building on wGraph primitives, we introduce GraphFlow, a system that efficiently integrates workflows into agent serving through two key designs. First, adaptive workflow generation dynamically constructs workflows from wGraph based on task semantics and constraint requirements. Second, workflow state management exploits wGraph structure to efficiently manage Key-Value (KV) caches, reducing redundant computation during agent serving. Extensive experiments across five benchmark datasets show that GraphFlow consistently outperforms state-of-the-art methods, yielding an average performance improvement of approximately 4.95 percentage points, while achieving an approximately 4$\times$ reduction in memory footprint.

Aspect-based sentiment analysis (ABSA) requires models to bind sentiment evidence to the correct aspect, making it a natural testbed for fine-grained structural reasoning. We introduce GHI, a Graphormer-over-Conditioned-Hypergraph-Incidence framework that is designed as an incidence-based structural reasoning layer built on a bipartite topology. GHI represents diverse linguistic and semantic evidence as token--hyperedge incidence relations, allowing different structural signals to be incorporated through a unified interface. Extensive experiments on six standard ABSA benchmarks show that GHI outperforms all baselines on the SemEval domains, and multi-seed evaluations show stable improvements over strong DeBERTa. Further experiments show that with only 247M parameters, GHI approaches the performance of 11B Flan-T5 based methods on the ISE benchmark. Moreover, it demonstrates strong robustness on the challenging ARTS datasets, maintaining highly competitive performance where traditional models degrade. These results demonstrate that compact structural reasoning remains a valuable alternative to scale-driven approaches for fine-grained tasks.

Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as an arbitrary graph, forming the actual graph of thoughts. Originally, the graph of operations is defined manually, which requires in-depth knowledge about the solution of the problem to solve. Such a static graph of operations is rigid and therefore lacks adaptability. We propose Reinforced Graph of Thoughts (RGoT), an automated approach to the GoT prompting paradigm that leverages reinforcement learning (RL) to adaptively generate a graph of operations from a human-defined set. Results indicate that, under certain constraints, it is possible to construct graphs of operations adaptively to the task's complexity in an automated way.

Most agent frameworks are built around the language model: a conversation loop comes first, then tools, then rules, and finally a logging layer bolted on for observability, with state persisted as retrievable "memory." We describe ActiveGraph, a runtime that inverts this arrangement. The append-only event log is the source of truth; the working graph is a deterministic projection of that log; and behaviors--ordinary functions, classes, LLM-backed routines, or logic attached to typed edges--react to changes in the graph and emit new events. No component instructs another; coordination happens entirely through the shared graph. This single design decision yields three properties that retrieval-and-summarization memory systems do not provide: deterministic replay of any run from its log, cheap forking that branches a run at any event without re-executing the shared prefix, and end-to-end lineage from a high-level goal down to the individual model call that produced each artifact. We present the architecture, a determinism contract that makes replay sound, and a worked diligence example whose full causal structure is reconstructable from the log alone. We discuss--without claiming to demonstrate--why this substrate is unusually well suited to self-improving agents, and how it extends the BabyAGI lineage and prior graph-memory research.

Graph combinatorial optimization (GCO) has attracted growing interest, as many NP-hard problems naturally admit graph formulations, yet their combinatorial explosion renders exact methods computationally intractable. Recent advances in Reinforcement Learning (RL) combined with Graph Neural Networks (GNNs) have significantly improved learning-based GCO solvers. However, existing approaches face limitations in both generalization across diverse graph instances and computational scalability as action spaces grow. To address both challenges, we introduce projection agents, a novel RL-GCO approach that operates directly in a continuous GNN-based action embedding space, predicting a desired latent action in a single forward pass and subsequently decoding it into a valid discrete action. Additionally, we enable fair comparison across RL methods through a shared embedding space for both observations and actions. Across diverse benchmarks, our approach achieves up to 16.2x faster inference and up to 40% better generalization than existing solutions using only simple nearest-neighbor decoding, while opening the door to strong RL performance in super-linear decision spaces with multiple interdependent variables. Finally, we release LaGCO-RL, a Python library that automates latent action-space construction and supports existing RL-GCO solutions, promoting reproducibility and adaptation to new GCO benchmarks.

Sparse goal-conditioned planning with few cost-to-go labels can be viewed as a graph-PDE Dirichlet extension problem: extend sparse labels on a goal-dependent boundary to unlabelled graph vertices so that greedy rollouts reach the goal. We study which graph value extensions are planner-admissible under the operational argmin-Q planner. Our main result is a local action-gap certificate: if the surrogate value error along the rollout stays below half the true action gap, then the greedy rollout reaches the goal. Absolutely Minimal Lipschitz Extension (AMLE), the p=infinity endpoint of the graph p-Laplacian family, instantiates this certificate through a comparison-principle fill-distance bound. Harmonic extension, by contrast, can mis-rank local actions because its values reflect boundary hitting probabilities rather than shortest-path greedy order. On 120 AntMaze layout-derived graph configurations, harmonic extension achieves 0.584 aggregate rollout success, while AMLE reaches 0.970. Finite high-p methods also enter a high-success regime, with success 0.903 for p=4, 0.973 for p=8, and 0.982 for a fixed-budget p=16 solver, though the p=16 row is not used as a converged endpoint ranking due to incomplete solver certification. Mechanism audits show that many rollout decisions occur in AMLE-compatible but harmonic-incompatible local geometry, and that AMLE corrects most harmonic inversions on the rollout-weighted decision scope.

Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore, Graph Signal Processing (GSP) has been developed to analyze signals on graph nodes, such as temperature measurements (node signals) across different regions of a country represented as a graph. Topological Signal Processing (TSP) is an emerging field that generalizes GSP, enabling the analysis of signals defined not only on nodes but also on edges, triangles, and higher-dimensional network elements, modeled as simplicial complexes and related topological structures. This makes TSP naturally well-suited for studying higher-order interactions in complex systems by extending classical signal processing concepts, such as filtering and Fourier transforms, to the topological level. Despite its versatility, TSP remains challenging for many practitioners. Therefore, we present an accessible overview of TSP foundations while drawing connections with application-oriented settings. We focus on processing techniques based on the combinatorial Hodge Laplacian, which generalizes the graph Laplacian to simplicial complexes. In particular, we review key TSP concepts, relate them to real-world examples, and discuss how higher-order structures and signals can be derived from datasets. For instance, we introduce an edge-level signal capturing lagged interactions between nodal signals, and demonstrate its use in a case study on TSP-based analysis of brain imaging data, revealing nontrivial interactions between sets of brain regions. Overall, we aim to promote a broader adoption of TSP by bridging methodological developments with applications, fostering its use among a wide community of theoretical and applied researchers.

We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function $h$ is represented by its graph measure $γ_h$, with finite tokens $\{(x_j,h(x_j))\}_{j=1}^N$ being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers, a graph-preserving subclass of measure-theoretic transformers that maps graph measures to graph measures, which is to say that outputs remain single-valued functions. Crucially, this additional structure does not reduce generality: we prove that the resulting graph-preserving maps can be approximated by finite compositions of standard softmax self-attention layers and pointwise MLPs, yielding universal approximation results for broad classes of nonlinear operators. Unlike existing theoretical approaches to operator learning with transformers, the measure-theoretic framework also accommodates regularized negative-order Sobolev inputs for which discretization invariance is particularly challenging, as well as query points on different output domains. Overall, function graph transformers provide a continuum viewpoint and mathematical toolkit for transformer-based operator learning, clarifying the roles of positional encodings, graph structure, regularization, and ensuring consistency across discretizations.

Conventional approaches to learning on graphs involve message passing along existing (i.e., positive) edges to update node features. However, these approaches often disregard the potentially valuable information contained in the absence (i.e., negative) of edges. Here, we theoretically analyze the value of negative edges in graph representations and prove that in settings of low label rates, high homophily, and high edge density, access to negative edges provides significant information gain over using only positive edges. Motivated by this insight, we introduce Contrastive Message Passing (CMP), a general message passing architecture that enable graph neural network layers to reason over positive and negative edges. By imposing soft positive semidefinite constraints on the learnable weights, our approach differentially applies similarity-preserving transformations to positively connected nodes and dissimilarity-inducing transformations to negatively connected nodes. Over simulated and real datasets in varying data regimes, CMP consistently outperforms baselines in low-label settings when negative edges are informative.

Property prediction and inverse structural design of catalytic materials are typically modeled as two independent tasks: the former predicts target properties from given structures, whereas the latter generates candidate structures according to desired properties. Although the decoupled paradigm facilitates the implementation of a generation--evaluation--screening'' workflow, the inconsistency between the generative model and the property prediction model in terms of representation spaces and training objectives can readily introduce data distribution shifts and evaluator bias, thereby limiting the stability of closed-loop optimization. In this work, we propose CatalyticMLLM, a unified graph--text multimodal large language model for catalytic materials, which integrates property prediction and \textbf{inverse design} within the same model and shared representation space. Under this unified framework, CatalyticMLLM can not only perform reliable property prediction by leveraging three-dimensional structures and textual information, but also generate and screen physically feasible CIF candidates conditioned on target properties, thereby forming a closed-loop optimization workflow of inverse design--prediction--screening--redesign.'' Experimental results demonstrate that this unified paradigm outperforms decoupled baselines on both catalytic relaxed-energy prediction and inverse design tasks, validating the effectiveness of jointly modeling property prediction and structure generation within a single multimodal model.

Multimodal magnetic resonance imaging (MRI) is crucial for brain tumor segmentation, with many methods leveraging its four key modalities to capture complementary information for effective sub-region analysis. However, the absence of several modalities is very common in practice, leading to severe performance degradation in existing full-modality segmentation methods. Limited by the structured data model, recent works often adopt a multi-stage training strategy for full-modality and missing-modality scenarios, which increases training costs and inadequately addresses the interference of miss. In this work, we propose a graph-based one-stage framework for robust brain tumor segmentation with missing modalities. Specifically, we introduce modality-specific virtual nodes that serve as supplementary information sources to compensate for missing modalities. To enhance model robustness against arbitrary modality combinations, we leverage the inherent flexibility of graph networks to devise a dynamic connection strategy. This mechanism dynamically adjusts the adjacency matrix based on modality availability, preserving beneficial information flow while mitigating interference effects caused by missing modalities. Furthermore, we enhance the graph network through heterogeneous weight matrices, enhancing its adaptability to multimodal scenarios. Extensive experiments on the BRATS-2018 and BRATS-2020 datasets demonstrate that our method outperforms the state-of-the-art methods on almost all subsets of incomplete modalities.

Security knowledge graphs can provide computable external memory for security agents, but constructing them from long-form cyber threat intelligence (CTI) remains difficult: LLMs often lack grounded security-domain knowledge, and end-to-end document-to-graph training is hard to supervise with cheap, stable rewards. We present GRID (Graph Representation of Intelligence Data), an end-to-end framework for security text knowledge graph construction. GRID first builds security-domain supervision from CTI articles by creating traceable article-graph alignments through graph extraction and knowledge-graph-conditioned text revision. It then turns document-to-graph learning into a scripted task bank combining four-option multi-select questions with triple-level regex matching targets, yielding more stable task-specific rewards than repeatedly scoring full graph outputs with an LLM judge. Using this supervision pipeline, we train two Qwen3-4B-Instruct-2507-based 4B extractors: a primary Task-bank Reward model and a secondary End2End Reward model with LLM-as-judge precision/recall rewards. On 249 CTI articles from GRID, CASIE, CTINexus, MalKG, and SecureNLP, the Task-bank Reward model with the ontology-guided GRID extraction pipeline reaches 84.62% source-averaged precision, 64.91% source-averaged recall, and 68.53% Avg F1, achieving the best source-averaged recall and near-top Avg F1 with lower token usage and deployment cost. The End2End Reward model reaches 76.91% precision, 53.85% recall, and 58.06% Avg F1. Further analyses show that task-bank rewards can be built once offline and reused across later post-training runs, outperforming online End2End LLM-as-judge reward and weaker alternatives such as Choice-only Reward and End2End SFT without RL.

Graph Neural Networks (GNNs) have become the dominant framework for inductive graph-level learning. Yet most benchmarks focus on the regime $n \gg p$, where the number of graphs $n$ greatly exceeds the number of nodes per graph $p$. This overlooks biological domains such as omics, which operate in the opposite $n \ll p$ regime, characterized by large graphs of genes, transcripts, or proteins across few patient samples. This raises the question: \textit{how do GNNs perform in this low-sample, high-node omics setting?} We introduce \texttt{OgBench} (Omics-Graph Bench), the first benchmarking platform for graph-level prediction in the $n \ll p$ regime characteristic of omics data. We provide a standardized, end-to-end modular infrastructure from raw omics data to families of featured graphs with varied structural properties. We benchmark classical GNNs, as well as GNNs designed for large graphs and omics applications, alongside MLPs and machine learning baselines to establish reference performances. Our results show that widely used GNNs often do not outperform simple MLPs and classical baselines. These findings challenge the prevailing assumption that graph structure inherently adds value in this domain, fostering a critical reassessment of current learning paradigms. Ultimately, by exposing these limitations, OgBench provides the open-source ecosystem necessary for the community to develop and validate novel architectures explicitly tailored for biological graphs. The code is available at https://github.com/geometric-intelligence/ogbench.

We introduce an empowered transposed Fully Connected Weighted (t-FCW) graph representation to embed point clouds into a metric space. While original t-FCW has shown promising results for point cloud classification, the reasons behind its effectiveness and its broader applicability remained unclear. In this work, we analyze the properties that make the empowered and original t-FCW effective and design a network that uses the empowered t-FCW exclusively as feature extractors. From an interpretability perspective, we build memory banks for classification, part segmentation, and semantic segmentation using the empowered t-FCW. Our analysis reveals that the empowered t-FCW inherits robustness from surface descriptors, provides interpretability through dimension-wise relations. These properties enable a highly efficient and interpretable network, which processes the ModelNet40 classification problem in approximately 7 seconds on an NVIDIA RTX A5000 GPU. Importantly, empowered t-FCW can function both as a lightweight standalone baseline and as a complementary plug-in to existing deep models.

GraphFlow is a visual workflow system designed to improve the reliability of agentic AI automation in multi-step, mission-critical processes. In these workflows, small errors compound rapidly: under an idealized model of independent steps, a ten-step process with 90% per-step reliability completes successfully only 35% of the time. Existing workflow platforms provide durable execution and observability but offer few semantic correctness guarantees, while agentic systems plan at inference time, making behavior sensitive to prompt variation and difficult to audit. GraphFlow is designed to address this gap by treating workflow diagrams as the executable specification, a single artifact defining data scope, execution semantics, and monitoring. At compile time, a restricted class of diagrams is specified to produce reusable automations whose contracts (preconditions, postconditions, and composition obligations) are intended to be proof-checked before admission to a shared library. At runtime, a durable engine records outcomes in an append-only event log and can enforce contracts at system boundaries, supporting replay, retries, and audit. Swimlanes make trust boundaries explicit, separating verified logic from external systems, human judgment, and AI decisions. A year-long pilot across three clinical sites executed 8,728 cohort-enrolled workflow runs with a 97.08% completion rate under an early prototype without the verified-core subsystem; observed failures were localized primarily to external integrations. The formal semantics and proof-checked admission model described here are specified and under active development. Evaluation of the verified core is reserved for future work.

Graph Neural Networks (GNNs) have advanced significantly in handling graph-structured data, but a comprehensive framework for evaluating explainability remains lacking. Existing evaluation frameworks primarily involve post-hoc explanations, and operate in the setting where multiple methods generate a suite of explanations for a single model. This makes comparison of explanations across models difficult. Evaluation of inherently interpretable models often targets a specific aspect of interpretability relevant to the model, but remains underdeveloped in terms of generating insight across a suite of measures. We introduce AIM, a comprehensive framework that addresses these limitations by measuring Accuracy, Instance-level explanations, and Model-level explanations. AIM is formulated with minimal constraints to enhance flexibility and facilitate broad applicability. Here, we use AIM in a pipeline, extracting explanations from inherently interpretable GNNs such as graph kernel networks (GKNs) and prototype networks (PNs), evaluating these explanations with AIM, identifying their limitations and obtaining insights to their characteristics. Taking GKNs as a case study, we show how the insights obtained from AIM can be used to develop an updated model, xGKN, that maintains high accuracy while demonstrating improved explainability. Our approach aims to advance the field of Explainable AI (XAI) for GNNs, providing more robust and practical solutions for understanding and improving complex models.

Retrieval-Augmented Generation (RAG) has become a powerful and widely used approach for improving large language models by grounding generation in retrieved evidence. However, RAG systems still produce incorrect answers in many cases. Why RAG fails despite having access to external information remains poorly understood. We present a model-internal study of retrieval-augmented generation that examines how retrieved evidence influences answer generation. Using circuit tracing, we construct attribution graphs that model the flow of information through transformer layers during decoding. These graphs represent interactions among retrieved context, intermediate model activations, and generated tokens, providing a graph, circuit-level view of how external evidence is integrated into the model's reasoning process across multiple question answering benchmarks, we observe consistent structural differences: correct predictions exhibit deeper reasoning paths, more distributed evidence flow, and a more structured pattern of local connectivity, while failed predictions show shallower, fragmented, and overly concentrated evidence flow. Building on these findings, we develop a graph-based error detection framework that uses attribution-graph topology features. Furthermore, we show that attribution graphs enable targeted interventions. By reinforcing question-constrained evidence grounding, we reshape internal routing so that answer generation remains guided by the question, leading to more effective integration of retrieved information and fewer errors.

Reference-based graph compression encodes each vertex's neighbor list as differences from a nearby encoded list. WebGraph's BVGraph fixes a single encoding pipeline and relies on a separately chosen vertex ordering -- typically URL-lexicographic or Layered Label Propagation (LLP). Their interaction is rarely measured. We propose a two-stage Leiden+LLP ordering: global LLP seeds labels, Leiden detects communities, and a final LLP pass reorders each community internally. We study how it interacts with reference-based compression, using BVGraph and three encoders we contribute -- BG, CS, and CG -- each picking, per vertex, the cheapest of up to 28 candidate decompositions. On graphs with poor initial vertex order, reordering with Leiden+LLP improves compression for every encoder measured, saving 0.9 to 4.6 bits per edge (bpe) over the original order on SNAP-style graphs delivered in vertex-ID order. The gain barely depends on the encoder: on four of five weakly ordered datasets, the four encoders agree on the Leiden+LLP-vs-plain-LLP gain within about +/- 0.04 bpe. On URL-ordered web crawls, where the ordering already encodes locality, BG and CS still benefit, while residual-sensitive configurations (BVGraph default, BV-HC, and CG relying on community contiguity) regress. The transfer holds across two encoder generations (Fibonacci-coded and fully context-adaptive range-coded) and three ordering seeds. With every structural bit entropy-coded, the best of our three encoders beats the strongest published baseline in each regime (Zuckerli, and the stronger of BV-HC / BVGraph default) on all seven datasets in every whole-graph and random-access comparison -- 28/28 cells, +0.3 to +35% over Zuckerli -- with the encoder-level gain consistently smaller than the ordering-level gain. All algorithms, the ordering pipeline, and generators are released as the Adjacently Julia library.

The Industry Foundation Classes (IFC) standard is central to building data exchange across the lifecycle, from design and construction to facility management and Digital Twin integration. In operational settings, stakeholders increasingly require access to building information without specialist knowledge of IFC's complex, deeply nested schema, motivating natural language interfaces. Existing LLM-based querying approaches typically rely on a single data representation, which is not equally suited to attribute retrieval and spatial reasoning. We present IfcLLM, a framework that combines complementary relational and graph representations, routing each query type to the more suitable backend. An LLM agent integrates both through iterative retry-and-refine reasoning, recovering from failures without user input. Evaluated across three IFC models on 30 query scenarios, our implementation achieves first-attempt accuracy between 93.3% and 100%, with all failed queries resolved via a fallback LLM. Built on an open-weight LLM, it supports local deployment in data-sensitive AEC settings.

Graph neural networks (GNNs) deployed as cloud services can be stolen through model-extraction attacks, which train a surrogate from query responses to reproduce the target's behavior, and a growing line of ownership defenses tries to prevent or trace such theft. This paper asks two questions: how hard is it to steal a GNN, and can we stop it? Prior work cannot answer either, because experiments use inconsistent datasets, threat models, and metrics. We introduce GraphIP-Bench, a unified benchmark that evaluates both sides under a single black-box protocol. GraphIP-Bench integrates twelve extraction attacks, twelve defenses spanning watermarking, output perturbation, and query-pattern detection, ten public graphs covering homophilic, heterophilic, and large-scale regimes, three GNN backbones, and three graph-learning tasks. It reports fidelity, task utility, ownership verification, and computational cost on shared splits, queries, and budgets. We further add a joint attack-and-defense track that runs every attack on every defended target and measures watermark verification on the resulting surrogate, exposing how much protection a defense retains after extraction. The empirical picture is clear: stealing a GNN is easy at medium query budgets and most defenses do not change this; several watermarks verify reliably on the protected model but lose most of their verification signal on the extracted surrogate, exposing a gap that single-model evaluations miss; and heterophilic graphs are systematically harder to steal, while a cross-architecture mismatch between target and surrogate reduces but does not prevent extraction. We release GraphIP-Bench with reproducible scripts and configurations, and integrate the attacks and defenses into the PyGIP library. Code: https://github.com/LabRAI/GraphIP-Bench. Library: https://labrai.github.io/PyGIP/index.html.

Long-term memory is becoming a central bottleneck for language agents. Exsting RAG and GraphRAG systems largely treat memory graphs as static retrieval middleware, which limits their ability to recover complete evidence chains from partial cues, exploit reusable graph-structrual roles, and improve the memory itself through downstream feedback. We introduce SAGE, a Self-evolving Agentic Graph-memory Engine that models graph memory as a dynamic long-term memory substrate. SAGE couples two roles: a memory writer that incrementally constucts structured graph memory from interaction histories, and a Graph Foundation Model-based memory reader to perform retrieval and provide feedback to the memory writer. We provide rigorooous theoretical annalyses supporting the framework. Across multi-hop QA, open-domain retireval, domain-specific review QA, and long-term agent-memory benchmarks, SAGE improves evidence recovery, answer grounding, and retrieval efficiency: after two self-evolution rounds, it achieves the best average rank on multi-hop QA; in zero-shot open-domain transfer, it reaches 82.5/91.6 Recall@2/5 on NQ. Further results on LongMemEval and HaluMem show that traning and reader-writer feedback improve multiple long-term memory and hallucination-diagnostic metrics, suggesting that self-evolving, structure-aware graph memory is a promising foundation for robust long-horizon language agents.

Graph Neural Networks (GNNs) have emerged as a powerful paradigm in Knowledge Graphs (KGs) due to their intrinsic ability to model graph-structured data. However, there remains a lack of a systematic review about GNN-based methodologies across the entire knowledge graph technologies pipeline. To address this gap, we first propose a novel two-level taxonomy framework for GNN-based knowledge graph technologies: the KG technologies pipeline and GNN-based perspective. Specifically, the knowledge graph technologies pipeline covers knowledge graph construction, knowledge graph embedding, knowledge reasoning and knowledge graph applications. Meanwhile, the GNN-based perspective provides a new categorization of knowledge graph technologies with GNN models, such as GCN, GAT, and HGNN. Then, we analyze the advantages of GNN technology based on the characteristics of different tasks in the knowledge graph lifecycle. Furthermore, we detailed review various GNN-based models for knowledge graph following the proposed taxonomy, and summarize strengths and limitations. Finally, we discuss unresolved challenges and outline promising directions for future research.

The counting power of Message Passing Neural Networks (MPNN) has been the subject of many recent papers, showing that they can express logic that involves counting up to a threshold or more generally satisfy a linear arithmetic constraint. In this paper, we study the counting capabilities of MPNN beyond linear arithmetic, primarily utilising local and global mean aggregations. In particular, our goal is to tease out conditions required to express extensions of graded modal logic with polynomial counting constraints. We show that global polynomial counting constraints in node-labelled graphs can be checked using mean MPNN under mild assumptions. Checking local constraints is also possible, if we consider formulas with no nested modalities and additionally either (i) permit sum/max aggregations, or (ii) only restrict to regular graphs. We also show how formulas with nested modalities can be captured by mean MPNN over graphs with tree-like structures and similar assumptions.

Graph foundation models (GFMs), pretrained on massive graph data, have transformed graph machine learning by supporting general-purpose reasoning across diverse graph tasks and domains. Existing GFMs pretrained with fixed-hop subgraph sampling impose a fixed receptive field, causing scale mismatch on diverse tasks, which often require heterogeneous and unknown structural contexts beyond a fixed sampling scale. We propose R-GFM, a Riemannian Graph-of-Graphs (GoG) based foundation model, that treats structural scale as a first-class citizen in modeling. R-GFM constructs a multi-scale GoG over-sampled subgraphs at different hop distances and learns geometry-adaptive representations from Riemannian manifolds. Theoretical analysis shows that R-GFM reduces structural domain generalization error compared to fixed-scale GFMs. Experiments on various datasets demonstrate that R-GFM achieves state-of-the-art performance, with up to a 49% relative improvement on downstream tasks. Our code is available at https://github.com/USTC-DataDarknessLab/R-GFM.

Scene graphs (SGs) represent objects and their relationships as structured graphs, enabling applications in image generation, robotics, and 3D understanding. Recent work suggests that conditioning image generation on scene graphs improves compositional fidelity compared to text-only prompting. However, since users typically provide text rather than structured graphs, a key challenge is to generate scene graphs from natural language. Prior work on discrete diffusion has demonstrated success in generating generic graphs such as molecules and circuits, but fails to account for the hierarchical structure and strong dependencies between objects, edges, and relations in scene graphs. We address this limitation by introducing a dependency-aware, hierarchically constrained discrete diffusion model for scene graph generation. Our approach decouples structure and semantics across the forward and reverse processes, enabling the model to capture conditional dependencies. At inference time, we perform training-free conditioning to sample text-aligned scene graphs. We evaluate our method on standard SG benchmarks and demonstrate improvements over both continuous and discrete graph generation baselines across graph and layout metrics. When fed to downstream image generation, our approach yields improved compositional alignment compared to text-to-image models, particularly in multi-object scenarios.

Graph-based agent memory is increasingly used in LLM agents to support structured long-term recall and multi-hop reasoning, but it also creates a new poisoning surface: an attacker can inject a crafted relation into graph memory so that it is later retrieved and influences agent behavior. Existing agent-memory poisoning attacks mainly target flat textual records and are ineffective in graph-based memory because malicious relations often fail to be extracted, merged into the target anchor neighborhood, or retrieved for the victim query. We present SHADOWMERGE, a poisoning attack against graph-based agent memory that exploits relation-channel conflicts. Its key insight is that a poisoned relation can share the same query-activated anchor and canonicalized relation channel as benign evidence while carrying a conflicting value. To realize this, we design AIR, a pipeline that converts the conflict into an ordinary interaction that can be extracted, merged, and retrieved by the graph-memory system. We evaluate SHADOWMERGE on Mem0 and three public real-world datasets: PubMedQA, WebShop, and ToolEmu. SHADOWMERGE achieves 93.8% average attack success rate, improving the best baseline by 50.3 absolute points, while having negligible impact on unrelated benign tasks. Mechanism studies show that SHADOWMERGE overcomes the three key limitations of existing agent-memory poisoning attacks, and defense analysis shows that representative input-side defenses are insufficient to mitigate it. We have responsibly disclosed our findings to affected graph-memory vendors and open sourced SHADOWMERGE.

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.

EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra of the target task. Concretely: static timing analysis is a max-plus/min-plus recurrence on a topologically ordered DAG, structurally aligned with asynchronous DAG-GNNs; placement is governed by hypergraph wirelength and density penalties and is exploited by differentiable placers rather than by message-passing GNNs alone; routing congestion is a sparse demand-supply field over a layout grid; switching-activity propagation is a probabilistic recurrence on a directed netlist; IR drop is a linear system on the power-delivery network; and analog symmetry extraction is a discrete constraint-prediction problem on schematic graphs. Through these task-by-task alignments we (i) review the GNN architectural toolkit relevant to circuits, (ii) formalize how circuit graphs differ from generic graphs (directed, heterogeneous, multi-scale, with sequential and clock structure), (iii) characterize where current methods succeed and where the algebra-architecture mismatch limits them, and (iv) identify failure modes--stage leakage, proxy-to-signoff gap, calibration, and design-distribution shift--that we believe are likely to dominate the next phase of work. We position the paper as a GNN-for-EDA, task-aligned analysis rather than a comprehensive AI-for-chip-design survey. Continuous SE(3)-equivariant geometric GNNs are usually mismatched to Manhattan digital layout, and LLM-for-RTL, HLS, and RL/diffusion-based topology generation are outside our scope.

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

Graph Anomaly Detection (GAD) is a critical task in graph machine learning with vital applications in financial fraud detection and social platform governance. However, existing GAD benchmarks are often restricted to small-scale, curated graphs with relatively balanced anomaly ratios, leaving a substantial gap between academic evaluation and real-world deployment. To bridge this gap, we present a multi-dimensional benchmark that systematically evaluates GAD models under three deployment-relevant challenges: million-scale graphs, extreme anomaly scarcity, and missing node attributes. We derive a family of controlled benchmark variants from five diverse graphs, including two native industrial-scale datasets with over 3.7 million nodes. Our extensive evaluation of nine representative GAD models reveals three major limitations: (1) most GNN-based methods fail to scale to million-node graphs due to prohibitive memory requirements; (2) detection performance drops sharply under realistic anomaly ratios (e.g., 0.1%), often resulting in zero recall; and (3) reconstruction-based models are highly sensitive to attribute imputation strategies. Our findings suggest that strong performance in laboratory settings does not guarantee robustness in production environments. We release this benchmark and empirical evaluation as a diagnostic testbed to promote the development of robust and scalable GAD systems for large-scale, imperfect graphs encountered in practice. Code is available at https://anonymous.4open.science/r/Benchmark_GAD-E7A3.

Knowledge graphs automatically constructed from text are increasingly used in real-world applications. However, their inherent noise, fragmentation, and semantic inconsistencies significantly affect the performance of Graph Neural Networks (GNNs) on downstream tasks. Assessing their performance and robustness remains difficult, as it is often unclear whether observed results stem from the learning model or from the quality of the constructed graph itself. In this work, we introduce a dual-purpose benchmark designed to jointly evaluate (i) the performance of GNNs on noisy, text-derived graphs and (ii) the effectiveness of graph construction methods on a downstream task. The benchmark is built in the biomedical domain from a single textual corpus and includes two automatically constructed graphs generated using different extraction methods, alongside a high-quality reference graph curated by experts that serves as an upper performance bound. This design enables controlled comparison of construction methods and systematic evaluation of GNN robustness through semi-supervised node classification. We further provide a standardized, reproducible, and extensible evaluation framework, facilitating the integration of new graph extraction methods and learning models.

System Neural Diversity (SND) measures behavioral heterogeneity in multi-agent reinforcement learning by averaging pairwise distances over all $\binom{n}{2}$ agent pairs, making each call quadratic in team size. We introduce Graph-SND, which replaces this complete-graph average with a weighted average over the edges of an arbitrary graph $G$. Three regimes follow: $G=K_n$ recovers SND exactly; a fixed sparse $G$ defines a localized diversity measure at $O(|E|)$ cost; and random edge samples yield an unbiased Horvitz-Thompson estimator and a normalized sample mean with $O(1/\sqrt{m})$ concentration in the sampled edge count $m$. For fixed sparse graphs we prove forwarding-index distortion bounds for expanders and a spectral refinement under low-rank distance structure; for random $d$-regular graphs we prove an unconditional probabilistic $\widetilde{\mathcal{O}}(D_{\max}/\sqrt{n})$ bound. On VMAS we verify recovery, unbiasedness, concentration, and wall-clock scaling, with a PettingZoo TVD panel checking non-Gaussian transfer. In a 500-iteration $n=100$ PPO run, Bernoulli-$0.1$ Graph-SND tracks full SND while reducing per-call metric time by about $10\times$, and frozen-policy GPU timing up to $n=500$ follows the predicted $\binom{n}{2}/|E|$ speedup. Random $d$-regular expanders empirically achieve $\mathrm{SND}_{G}^{\mathrm{u}}/\mathrm{SND} \in [0.9987, 1.0013]$ at $Θ(n \log n)$ edges. In DiCo diversity control at $n=50$, Bernoulli-$0.1$ Graph-SND preserves set-point tracking with paired reward differences indistinguishable from zero across nine matched cells while cutting per-call metric cost by ${\sim}9.5\times$. Together, these results show that the SND aggregation bottleneck can be removed without changing the metric's semantics, yielding a drop-in sparse alternative that scales beyond complete-graph SND and supports both passive measurement and closed-loop diversity control.

LLM-empowered multi-agent systems offer new potential to accelerate scientific discovery by generating novel research ideas. However, existing methods typically coordinate agents through temporary texts, such as drafts or chat logs; it is difficult to pinpoint the weaknesses in the generated ideas and how the agents refine them. To this end, we introduce \textbf{Evolving Idea Graphs} (EIG), a graph-based multi-agent scientific ideation framework that can generate high-performance research ideas across various benchmark-native metrics, such as novelty, feasibility, and clarity. Instead of coordinating solely through texts, EIG represents a partially formed proposal as an evolving idea graph, where nodes capture scientific claims and edges encode relations (e.g., support and conflict), enabling unresolved weaknesses to remain identifiable throughout the idea evolving process. Specifically, a learned two-head controller operates over the evolving graph to guide the ideation: one head selects graph edits for agents to execute, while the other decides when the graph is ready for commit as final proposal synthesis. On AI Idea Bench 2025 and LiveIdeaBench, EIG outperforms all compared systems on both automatic benchmark scores and blind expert ratings. Ablations further show that explicit graph state provides the main performance gains, and learned edit-and-commit control adds consistent improvements.

Humans can acquire a highly structured intuitive understanding of musical patterns, yet these patterns often require multiple iterations of reflection and re-listening to internalize fully. To capture such an internalization process, we present a computational model for the learning of jazz harmonic patterns based on library learning. Given a corpus of harmonic progressions, our model searches over a space of programs composed of primitive harmonic relations in order to discover concise generative explanations of the corpus. The model first enumerates possible programs for each piece, and then jointly learns a library of harmonic patterns and refactored programs. To efficiently navigate the vast joint space of programs and libraries, we integrate deductive parsing with library learning on e-graphs. We explore how well our model captures aspects of human musical pattern learning by evaluating the intuitiveness of both programs and libraries, as well as similarities to human-written harmonic derivations.

We describe a dynamical system in which a symbolic field is coupled to a geometric field via a bipartite Hilbert-Schmidt kernel. The system is fully described by a retarded functional differential equation (RFDE) on the history space, subject to Lipschitz and small gain conditions. We show that the RFDE is well-posed under constant input and that it admits a compact global attractor. The principal subsystem $(H_L, X_R, P)$, which is comprised of the two primary fields as well as an executive field, is shown to be globally stable independent of delay, provided that the interfield coupling satisfies $C_{\mathcal{K}}^2<μ_Lμ_R$. In addition, we describe design specifications that fulfill the hypotheses of the main Theorem.

Graph federated learning (GFL) facilitates decentralized training on distributed graph data while keeping sensitive user information local, aligning with policies such as GDPR and CCPA that grant users the right to freely join or withdraw from learning systems. However, even decentralized, user information can persist after quitting, potentially propagating to central servers and then redistributing to malicious clients. This privacy leakage during user withdrawal, despite its importance, has received seldom attention in GFL. To fill the gap, we explore the potential of machine unlearning (MU) to thoroughly remove user information. However, classical MU methods are known to degrade overall performance, a problem that is exacerbated in GFL due to local message passing and global model collaboration. To this end, we make two adjustments to mitigate this challenge for GFL. First, we ensure unlearning updates that minimally affect overall performance, steering them in directions orthogonal to the gradients from learning other data. Second, we introduce virtual clients, maintained by the central server, to preserve graph topology and global embeddings without recovering information of removed entities. We conduct comprehensive experiments under a representative user-withdrawal scenario and propose a novel membership inference framework to rigorously evaluate and validate the reliability of our privacy preservation. The experimental results demonstrate the effectiveness of our approach, which also surpasses the performance of seven state-of-the-art baseline methods.

We give new examples of graphs and trees with dominating set sequences that are not log-concave. These examples were generated by PatternBoost, a transformer-based reinforcement learning software developed by Charton-Ellenberg-Wagner-Williamson. We also show: for any positive integer $m$, there exists a tree whose dominating set sequence is not log-concave for at least $m$ indices by modifying a similar construction of Bautista-Ramos for the independent set sequence. We show that a large class of caterpillar graphs has log-concave dominating set sequences. A continuous analogue of the sequence is also log-concave for all graphs.

Stabilized regression aims to identify a set of predictors whose conditional relationship with a response variable remains invariant across different environments. Existing graphical characterizations of the stable blanket are mainly developed for structural causal models (SCMs) without hidden variables or causal cycles. However, latent variables and feedback relationships naturally arise in many applications, and they can change both the Markov blanket and the set of predictors that remain stable under interventions. This paper studies stable blankets in graphical causal models with hidden variables, causal cycles, and both features simultaneously. For models with hidden variables, we use acyclic directed mixed graphs (ADMGs) and $m$-separation to characterize the Markov blanket and to construct intervention-stable predictor sets. We introduce the notion of an intervened sub-district and use it to describe how interventions may affect districts connected to the response. For models with cycles, we work with directed graphs (DGs) and directed mixed graphs (DMGs) together with $σ$-separation, treating strongly connected components (SCCs) as the basic graphical units. We then combine these ideas to analyze models with both hidden variables and cycles. The main results give graphical characterizations of Markov blankets, stable frontiers, and stable blankets in these generalized settings. In particular, we identify conditions under which the response is conditionally independent of intervention variables given a suitable predictor set, and we describe when such sets are minimal or unique. These results extend the graphical interpretation of stabilized regression beyond acyclic fully observed models.

LLM routing is increasingly important for selecting suitable models under diverse user needs and deployment constraints, but its practical effectiveness depends on continual adaptation to emerging queries and newly released models. New-LLM integration is particularly challenging, as newly released models lack the query-response-reward interactions required for router training and cannot be profiled as directly as new queries via semantic embeddings. Existing profiles are limited: LLM-generated descriptions are often coarse, while interaction-based embeddings are costly to construct. To address this problem, we propose RouteProfile, a graph-based profiling framework that constructs LLM profiles from public signals in technical reports or model cards, including model family, model description, reported benchmark scores, and benchmark domains. RouteProfile organizes these heterogeneous signals into a graph and studies profile construction along four dimensions: organizational form, representation type, aggregation depth, and learning configuration. We evaluate RouteProfile in training-free cold-start routing and new-LLM integration settings. Experiments show that: (1) structured profiles outperform flat baselines in training-free cold-start routing; (2) model family metadata is more reliable than benchmark domain information; and (3) effective new-LLM integration requires profile-router co-design. Overall, our findings highlight the importance of profile design for enabling routing systems to adapt to the evolving model ecosystem.

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.

Every document format in existence was designed for a human reader moving linearly through text. Autonomous LLM agents do not read - they retrieve. This fundamental mismatch forces agents to inject entire documents into their context window, wasting tokens on irrelevant content, compounding state across multi-turn loops, and broadcasting information indiscriminately across agent roles. We argue this is not a prompt engineering problem, not a retrieval problem, and not a compression problem: it is a format problem. We introduce OBJECTGRAPH (.og), a file format that reconceives the document as a typed, directed knowledge graph to be traversed rather than a string to be injected. OBJECTGRAPH is a strict superset of Markdown - every .md file is a valid .og file - requires no infrastructure beyond a two-primitive query protocol, and is readable by both humans and agents without tooling. We formalize the Document Consumption Problem, characterise six structural properties no existing format satisfies simultaneously, and prove OBJECTGRAPH satisfies all six. We further introduce the Progressive Disclosure Model, the Role-Scoped Access Protocol, and Executable Assertion Nodes as native format primitives. Empirical evaluation across five document classes and eight agent task types demonstrates up to 95.3 percent token reduction with no statistically significant degradation in task accuracy (p > 0.05). Transpiler fidelity reaches 98.7 percent content preservation on a held-out document benchmark.

Entity search, i.e., finding the most similar entities to a query entity, faces unique challenges in e-commerce, where product similarity varies across categories and contexts. Traditional embedding-based approaches often struggle to capture nuanced context-specific attribute relevance. In this paper, we present a two-stage approach combining Large Language Model (LLM)-driven attribute graph construction with graph-aware LLM ranking. In the offline stage, we extract structured product attributes from unstructured text, and construct a reusable attribute graph with category-aware schemas. In the online stage, we rank retrieved candidates by reasoning over this structured representation rather than raw text, reducing per-product token usage by 57% while improving ranking precision. Experiments show that our approach outperforms multiple baselines under zero-shot scenarios, achieving a over 5% improvement in average precision without requiring training data, generalizes robustly across diverse product categories, and shows immense potential for real-world deployment.

Heterogeneous graphs with heterophily have emerged as a powerful abstraction for modeling complex real-world systems, where nodes of different types and labels interact in diverse and often non-homophilous ways. Despite recent advances, robust representation learning for such graphs remains largely unexplored, particularly in the presence of noisy or misleading connectivity. In this work, we investigate this problem and identify structural noise as a critical challenge that significantly degrades model performance. To address this issue, we propose a unified framework, Heterogeneous Graph Unified Learning (HGUL), which jointly handles heterophily and noisy graph structures. The framework consists of three complementary modules: a kNN-based graph construction module that recovers reliable local neighborhoods, a graph structure learning module that adaptively refines the adjacency by filtering noisy edges, and a heterogeneous affinity learning module that captures class-level relationships via an extended affinity matrix derived from a polynomial graph kernel. Extensive experiments on multiple datasets demonstrate that HGUL consistently outperforms existing methods on clean graphs and maintains strong robustness under varying levels of structural noise. The results further underscore the importance of jointly modeling heterophily and noise in heterogeneous graph learning.

Biomedical knowledge graphs (KGs) are widely used in the life sciences, yet many are derived from unstructured documents and therefore lack schema-level constraints, whereas graphs assembled from structured resources are difficult to harmonize into a unified representation. We present OptimusKG, a multimodal biomedical labeled property graph (LPG) built from structured and semi-structured resources to preserve factual, type-specific metadata across molecular, anatomical, clinical, and environmental domains. OptimusKG contains 190,939 nodes across 10 entity types, 21,818,752 edges across 27 edge types, and 67,070,490 property instances encoding 109,665,797 values across 145 distinct property keys, derived from 18 ontologies and controlled vocabularies. The graph enforces a top-level schema for nodes and edges and retains granular, type-specific properties, cross-references, and provenance. We assessed the validity of OptimusKG by evaluating whether graph relationships are supported by evidence from the scientific literature using a multimodal agent, PaperQA3. PaperQA3 identified supporting evidence for 70.0% of sampled edges, whereas 83.4% of sampled false edges received no supporting evidence. Edges without literature support were concentrated in associations derived from experimental and functional genomics resources, suggesting that OptimusKG captures biomedical knowledge that may precede synthesis in the scientific literature. OptimusKG is distributed as Apache Parquet files, providing a standardized resource for graph-based machine learning, knowledge-grounded retrieval with large language models, and biomedical discovery use cases such as hypothesis generation.

Reusing verification artefacts requires identifying structural and semantic similarities across programs and their specifications. In this paper, we focus on graph construction as a foundational step toward this goal. We present a pipeline that converts imperative programs and their annotations into typed, attributed graphs. Our experiments cover datasets including C with ACSL, Java with JML, and Dafny programs. The pipeline integrates abstract syntax tree parsing with semantic embeddings derived from models such as SentenceTransformer and CodeBERT. This enables the generation of graph representations that capture both structural relationships and semantic context. Our results show that consistent graph representations can be constructed across different languages and annotation styles. This work provides a practical basis for future steps in semantic enrichment and approximate graph matching for scalable verification artefact reuse.

Current research on distributed multi-modal learning typically assumes that clients can access complete information across all modalities, which may not hold in practice. In this paper, we explore patchwork learning, in which the modalities available to different clients vary, and the objective is to impute the missing modalities for each client in an unsupervised manner. Existing methods are shown not to fully utilize the modality information as they tend to rely on only a subset of the observed modalities. To address this issue, we propose GraphPL, which combines graph neural networks with patchwork learning to flexibly integrate all observed modalities and remains robust with noisy inputs. Experimental results show that GraphPL achieves SOTA performance on benchmark datasets. Our results on real-world distributed electronic health record dataset show GraphPL learns strong downstream features and enables tasks like disease prediction via superior modality imputation.

Graph Neural Networks (GNNs) have demonstrated impressive performance in learning representations from graph-structured data. However, their message-passing mechanism inherently relies on the assumption of label consistency among connected nodes, limiting their applicability to low-homophily settings. Moreover, since message passing operates as a hierarchical diffusion process, GNNs face challenges in capturing long-range dependencies. As network depth increases, the structural noise along heterophilic edges tends to be amplified, resulting in over-smoothing. This issue becomes especially prominent in highly heterophilic graphs, where the propagation of inconsistent semantics across the topology continually exacerbates misaggregation. To address this issue, we propose a novel framework named Layer Embedding Deep Fusion Graph Neural Network (LEDF-GNN). Specifically, we design a Layer Embedding Deep Fusion (LEDF) operator that nonlinearly fuses multi-layer embeddings to capture inter-layer dependencies and effectively alleviate deep propagation degradation. Meanwhile, to mitigate structural heterophily, LEDF-GNN employs a Dual-Topology Parallel Strategy (DTPS) that simultaneously leverages the original and reconstructed topologies, allowing for adaptive structure-semantics co-optimization under diverse homophily conditions. Extensive semi-supervised classification experiments on the citation and image benchmarks demonstrate that, under both homophilic and heterophilic settings, LEDF-GNN consistently outperforms state-of-the-art baselines, validating its effectiveness and generalization capability across diverse graph types.

This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision-making systems, graph neural networks, knowledge graphs, and cognitive maps. By organizing diverse uncertainty-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems.

Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent dependency relationships across the two groups only, remain largely unexplored. We formalize the CriticalSet problem: given an arbitrary bipartite graph modeling dependencies of items on contributors, identify the set of k contributors whose removal isolates the largest number of items. We prove that this problem is NP-hard and requires maximizing a supermodular set function, for which standard forward greedy algorithms provide no approximation guarantees. Consequently, we model CriticalSet as a coalitional game, deriving a closed-form centrality, ShapleyCov, based on the Shapley value. This measure can be interpreted as the expected number of items isolated by a contributor's departure. Leveraging these insights, we propose MinCov, a linear-time iterative peeling algorithm that explicitly accounts for connection redundancy, prioritizing contributors who uniquely support many items. Extensive experiments on synthetic and large-scale real datasets, including a Wikipedia graph with over 250 million edges, reveal that MinCov and ShapleyCov significantly outperform traditional baselines. Notably, MinCov achieves near-optimal performance, within 0.02 AUC of a Stochastic Hill Climbing metaheuristic, while remaining several orders of magnitude faster.

Vision Graph Neural Networks (ViGs) represent an image as a graph of patch tokens, enabling adaptive, feature-driven neighborhoods. Unlike CNNs with fixed grid biases or Vision Transformers with global token interactions, ViGs rely on dynamic graph convolution: at each layer, a feature-dependent graph is built via k-nearest-neighbor (kNN) search on current patch features, followed by message passing. This per-layer graph construction is the main bottleneck, consuming 50--95% of graph convolution time on CPUs and GPUs, scaling as $O(N^2)$ with the number of patches $N$, and creating a sequential dependency between graph construction and feature updates. We introduce GraphLeap, a simple reformulation that removes this dependency by decoupling graph construction from feature update across layers. GraphLeap performs the feature update at layer $\ell$ using a graph built from the previous layer's features, while simultaneously using the current layer's features to construct the graph for layer $\ell+1$. This one-layer-lookahead graph construction enables concurrent graph construction and message passing. Although using prior-layer features can introduce minor accuracy degradation, lightweight fine-tuning for a few epochs is sufficient to recover the original accuracy. Building on GraphLeap, we present the first end-to-end FPGA accelerator for Vision GNNs. Our streaming, layer-pipelined design overlaps a kNN graph construction engine with a feature update engine, exploits node- and channel-level parallelism, and enables efficient on-chip dataflow without explicit edge-feature materialization. Evaluated on isotropic and pyramidal ViG models on an Alveo U280 FPGA, GraphLeap achieves up to $95.7\times$ speedup over CPU and $8.5\times$ speedup over GPU baselines, demonstrating the feasibility of real-time Vision GNN inference.

While LLMs demonstrate remarkable fluency in narrative generation, existing methods struggle to maintain global narrative coherence, contextual logical consistency, and smooth character development, often producing monotonous scripts with structural fractures. To this end, we introduce PLOTTER, a framework that performs narrative planning on structural graph representations instead of the direct sequential text representations used in existing work. Specifically, PLOTTER executes the Evaluate-Plan-Revise cycle on the event graph and character graph. By diagnosing and repairing issues of the graph topology under rigorous logical constraints, the model optimizes the causality and narrative skeleton before complete context generation. Experiments demonstrate that PLOTTER significantly outperforms representative baselines across diverse narrative scenarios. These findings verify that planning narratives on structural graph representations-rather than directly on text-is crucial to enhance the long context reasoning of LLMs in complex narrative generation.

Graph Neural Networks (GNNs) excel on relational data, but standard benchmarks unrealistically assume the graph is centrally available. In practice, settings such as Federated Graph Learning, distributed systems, and privacy-sensitive applications involve graph data that are localized, fragmented, noisy, and privacy-leaking. We present a unified framework for this setting. We introduce LoGraB (Local Graph Benchmark), which decomposes standard datasets into fragmented benchmarks using three strategies and four controls: neighborhood radius $d$, spectral quality $k$, noise level $σ$, and coverage ratio $p$. LoGraB supports graph reconstruction, localized node classification, and inter-fragment link prediction, with Island Cohesion. We propose AFR (Adaptive Fidelity-driven Reconstruction), a method for noisy spectral fragments. AFR scores patch quality via a fidelity measure combining a gap-to-truncation stability ratio and structural entropy, then assembles fragments using RANSAC-Procrustes alignment, adaptive stitching, and Bundle Adjustment. Rather than forcing a single global graph, AFR recovers large faithful islands. We prove heat-kernel edge recovery under a separation condition, Davis--Kahan perturbation stability, and bounded alignment error. We establish a Spectral Leakage Proposition: under a spectral-gap assumption, polynomial-time Bayesian recovery is feasible once enough eigenvectors are shared, complementing AFR's deterministic guarantees. Experiments on nine benchmarks show that LoGraB reveals model strengths and weaknesses under fragmentation, AFR achieves the best F1 on 7/9 datasets, and under per-embedding $(ε,δ)$-Gaussian differential privacy, AFR retains 75% of its undefended F1 at $ε=2$. Our anonymous code is available at https://anonymous.4open.science/r/JMLR_submission

Designing and optimizing multi-agent systems (MAS) is a complex, labor-intensive process of "Agent Engineering." Existing automatic optimization methods, primarily focused on flat prompt tuning, lack the structural awareness to debug the intricate web of interactions in MAS. More critically, these optimizers are static; they do not learn from experience to improve their own optimization strategies. To address these gaps, we introduce Textual Parameter Graph Optimization (TPGO), a framework that enables a multi-agent system to learn to evolve. TPGO first models the MAS as a Textual Parameter Graph (TPG), where agents, tools, and workflows are modular, optimizable nodes. To guide evolution, we derive "textual gradients," structured natural language feedback from execution traces, to pinpoint failures and suggest granular modifications. The core of our framework is Group Relative Agent Optimization (GRAO), a novel meta-learning strategy that learns from historical optimization experiences. By analyzing past successes and failures, GRAO becomes progressively better at proposing effective updates, allowing the system to learn how to optimize itself. Extensive experiments on complex benchmarks like GAIA and MCP-Universe show that TPGO significantly enhances the performance of state-of-the-art agent frameworks, achieving higher success rates through automated, self-improving optimization.