Graph Neural Networks

Learning a sparse graph from scarce data is practically important but challenging. Motivated by the desirable combination of local sparsity and strong global connectivity exhibited by expander-like graphs, we propose spectral connectivity-regularized graph learning (SCoGL), a framework that incorporates a family of Laplacian spectral priors to explicitly promote global connectivity. Specifically, SCoGL augments a combinatorial-Laplacian-constrained graphical lasso (GLASSO) objective over a target adjacency matrix $\mathbf{W}$ with a general connectivity prior computed from Laplacian eigenvalues. We derive gradients for several representative connectivity priors and develop a projected gradient descent (PGD) algorithm with Armijo backtracking to efficiently optimize $\mathbf{W}$. Experiments show that the proposed SCoGL variants improve graph recovery and enhance downstream tasks such as graph signal denoising when signal observations are scarce.

Many node-classification GNNs apply a linear classifier to a nonnegative mixture of local messages. An error can reflect either poor mixture weights or a reachable logit set poorly positioned for the classifier. We separate these causes with an exact-mass linear program and two learned post-hoc repairs. Every reweighted prediction has an equivalent centered logit translation, but only translations in a message-induced displacement set are realizable by reweighting. Across eight datasets, eight GNN backbones, and ten splits, mean accuracy rises from 62.6% for the frozen models to 63.8% with reweighting and 65.3% with set-conditioned translation. A parameter-matched node-only translator reaches 64.6%, showing that translation explains most of the gain while the message set supplies a smaller additional benefit. Although oracle reweighting can correct many errors, label-free reweighting captures little of this potential: local evidence is often present but hard to select, and relaxing the evidence constraint is more effective than learning within it.

Graph neural networks dominate recent work on microservice root-cause analysis, yet recent results question whether the graph contributes. Those results compare whole pipelines, so when a flat model wins one cannot tell whether structure is useless or redundant. We run the comparison they imply on RCAEval: three learned arms with identical features, optimiser, validation split, early-stopping rule and scoring head, in which a single term separates the graph arms. Across two RCAEval benchmarks, two topology sources and four regimes we find no reliable graph-specific effect: in-distribution the graph model leads the conventional flat model by 0.003 Avg@5 (p = 0.844, n = 6 disjoint folds). Auditing the pipeline surfaced two benchmark properties that condition any result on it. RCAEval injects faults into only five services per system while exposing 12 to 70 in telemetry, and the headline metric is Avg@5: a ranker reading no telemetry at all places the true culprit in the top five on 99.7 percent of held-out incidents, scoring Avg@5 0.488. That prior, not the uniform-random 0.137, is the honest in-distribution floor, and it collapses to 0.192 across systems. The second property is a non-uniform column schema that silently zeroes telemetry for most RE1 cases. We reproduce a published baseline, BARO, RCAEval's own reference implementation; on the one system with a clean schema it reaches similar aggregate accuracy to our heuristic, within 0.004, under a different scoring rule. The audit motivated a new model. PSC-GRCA separates a candidate score into a system prior, telemetry evidence and a centred graph residual, and reaches mean Avg@5 0.915 against 0.864 for the flat baseline, while its ablations locate most of the gain in the prior term rather than the graph. We close with a twelve-item checklist for graph-versus-flat ablation studies, distilled from sixty-two recorded defects.

Relational Deep Learning (RDL) models multi-table databases as heterogeneous temporal graphs, and graph transformers currently achieve state-of-the-art performance on benchmarks like RelBench. However, the current leading model, RelGT, suffers from two key limitations: its random local sampler yields loosely connected subgraphs that hinder message passing, and its global attention module relies on a single, seed-feature-based memory that ignores broader macro-level dynamics. To overcome these limitations, we introduce QUARTET, an expressive graph transformer architecture that applies full self-attention on local subgraphs while enriching global context through cross-attention branches. Specifically, QUARTET employs a Causal Random Walk (CRW) sampler based on recency-truncated Personalized PageRank (PPR) to extract compact, hub-robust, and densely connected local subgraphs without temporal leakage. Concurrently, a quad-branch cross-attention module integrates global context from four complementary perspectives: seed feature, seed topology, temporal dynamics, and collaborative dynamics. Across the RelBench v1 classification tasks, QUARTET consistently matches or outperforms the current state-of-the-art graph transformer baselines (HGT and RelGT). Ablation studies confirm that the CRW sampler significantly enriches local neighborhood quality, while the global branches provide essential, task-specific predictive gains.

Graph neural networks have achieved strong performance in node classification by aggregating information from graph neighborhoods. However, a single aggregation mechanism may be insufficient to capture diverse structural patterns across graph datasets. Moreover, independently training multiple structural branches can introduce substantial overhead without necessarily producing stable node representations. To address these issues, this paper proposes PreGS, a parameter-transfer-based multi-expert graph neural network framework. PreGS first pretrains a multi-head graph attention network (GAT) and transfers the linear transformation weights of its first-layer attention heads to multiple GraphSAGE experts. The transferred experts are frozen and used as complementary structural branches. The fused raw node features, GAT head representations, and GraphSAGE expert representations are fed into a multilayer perceptron (MLP), whose output is further fused with the pretrained GAT logits. Based on PreGS, we further develop PreGSv2, which introduces source-level weighting and a structural gating mechanism for adaptive multi-source feature integration. Experiments on eight public graph datasets show that PreGS and PreGSv2 achieve competitive performance against representative graph neural network baselines. Ablation, parameter-transfer, sensitivity, aggregator, visualization, and training-time analyses further validate the effectiveness and stability of the proposed framework. The code and datasets are available at https://github.com/LH-Czc/PreGS.

Signed graphs arise in trust--distrust networks, financial correlation systems, biological interaction graphs, and many other domains in which edges can be positive or negative and may also be directed. While signed graph neural networks have improved task-specific learning, graph transfer learning on signed graphs remains underdeveloped. In this paper, we introduce TopoSIGN, a pioneer topology-guided graph pre-training and prompt learning framework for signed graphs. TopoSIGN combines a structural encoder built on the magnetic signed Laplacian with a novel persistent-homology branch that summarizes signed topology through Dowker-complex persistence images. The fused embeddings are then transferred to a prompt learning function. Experimental results on synthetic and real-world datasets demonstrate the efficacy of TopoSIGN in extracting useful structural information in signed graphs, as well as the adaptability and flexibility of the proposed general framework.

Soccer tactics are interactive: an attacking action changes the opponent's defensive problem, and the observed response depends on the multi-agent match state. We introduce SambaGraph, an action--reaction spatio-temporal graph dataset and benchmark for soccer tactical response modeling. From tracking and event data for all 64 matches of the 2022 FIFA World Cup, we curate 4,070 action-centered episodes represented as temporally aligned 23-node player--ball graph sequences with attack/defense views, response labels, and 26,270 split-safe attack--defense pairs. We study three questions: whether observed responses can be classified from graph episodes, whether successful defenses can be retrieved for a query attack, and whether graph-derived summaries support grounded LLM reasoning. A compact signature MLP obtains $0.796\pm0.007$ macro-F1 for response classification, while a fused graph--signature dual encoder reaches $0.471\pm0.029$ Hit@5 and $0.655\pm0.051$ Hit@10 for full-bank defensive retrieval. Hard negatives maximize pair discrimination but not retrieval quality. Local LLMs underperform supervised encoders for direct classification and do not improve over a strong original order in eight-candidate reranking, but they provide grounded tactical rationales. These results position SambaGraph as a reproducible benchmark for graph-based soccer strategy-response research. Code and dataset are available at: https://github.com/areyesan/SambaGraph.

Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constrained graph estimation for Gaussian Markov random fields, focusing on the underdetermined regime in which the number of samples is smaller than the number of graph nodes. Existing approaches often formulate the problem as a sparsity-regularized maximum-likelihood estimation problem. While effective, such methods typically require iterative optimization and are often computationally demanding, particularly under Laplacian constraints. Instead, we propose a non-iterative estimator of graph Laplacians that uses effective resistance for regularization, and evaluate the method using a simple sparsification procedure. Experiments show that with some trade-off in edge and weight recovery on the considered dataset, computational cost for moderately sized graphs can be substantially reduced.

Modeling articulated objects from sparse monocular views is challenging because each observation reveals only partial geometry and motion evidence. Most feed-forward methods infer articulation from a single observation and therefore rely heavily on learned category-level shape priors. We present FAMOS, a feed-forward model that predicts movable-part segmentation and joint parameters from a sparse, unordered set of partial point clouds. Our model jointly reasons over multiple observations and naturally supports a variable number of inputs, including a single view. To aggregate articulation cues across observations, we introduce a Multi-state Articulation Transformer with alternating state-wise and global attention. We further propose an observed articulation span objective that supervises the motion range each part exhibits across the input observations, encouraging the model to leverage the full observation set. To overcome the limited scale and diversity of existing datasets, we introduce a procedural data generator that synthesizes self-annotated assets during training. Experiments on PartNet-Mobility, ACD, and ArtiCraft-10K demonstrate consistent improvements over both feed-forward and optimization-based baselines. Project page: https://kevinqu7.github.io/famos

Effective troubleshooting agents in enterprise customer support depend on retrieving actionable guidance from similar historical cases, yet existing retrieval-augmented generation (RAG) systems treat support cases as static documents and overlook their multi-stage, stateful nature. We introduce RAFT (Retrieval-Augmented Framework for Troubleshooting Agents), a stateful RAG framework that abstracts each closed historical case into a directed chain of timeline entries and retrieves at the entry level, surfacing cases whose intermediate states match the active case and returning the parent-case trajectory anchored at the matched state; an optional case-level graph links cases through a configurable similarity representation. We evaluate this retrieval layer directly, which, unlike evaluating a full agent system, requires no production deployment. Because public multi-stage troubleshooting data is extremely rare, we pair a synthetic benchmark built from Microsoft Learn Windows Server documentation with real Apache Jira issues carrying human-created duplicate labels. RAFT improves Case Hit over vanilla RAG and GraphRAG baselines at every stage of case progress, with statistically significant gains over the strongest baseline; the Jira results provide directional evidence that the advantage transfers to real case histories. We release our benchmark, implementation, and the Apache Jira evaluation set.

Graph foundation models (GFMs) aim to learn transferable representations across severely heterogeneous graph domains. However, severe domain shifts in topology, graph scale, and feature semantics impede the construction of a unified, domain-agnostic representation space. To address this, we propose SCGFM-ART, a structure-centric GFM framework that aligns arbitrary graphs onto a shared relational atlas via Amortized Relational Transport (ART). The relational atlas serves as a universal coordinate system defined by a finite set of relational landmarks (bases), while ART directly predicts reusable, end-to-end graph-to-base transport plans, bypassing costly runtime Gromov-Wasserstein optimizations. Under this formulation, SCGFM-ART decomposes a graph into a unified representation: globally via its relational response coordinates relative to the atlas, and locally via its node-to-role structural correspondences. These correspondences project disparate node attributes into a canonical role space, resolving structural and semantic heterogeneity within a singular alignment interface. Rigorously modeling graphs and atlas bases as finite measured relational spaces, we establish coordinate fidelity bounds, prove stability under predicted transport plans, and derive an amortized coverage bound that guarantees our learning objective tightly surrogates ideal relational coverage. Benchmarked across 14 cross-domain graph- and node-level classification tasks, SCGFM-ART achieves state-of-the-art transferability, securing superior average ranks of 2.29 and 1.14, respectively. Topological perturbation analyses demonstrate that node-role transport retains fine-grained structural nuances beyond global coordinates. On real-world benchmarks, the amortized formulation yields 44.2 to 85.1 times faster frozen target-domain inference by avoiding iterative alignment at test time.

The Antibandwidth and Cyclic Antibandwidth problems are NP-hard graph labeling problems that aim to maximize the minimum (cyclic) distance between labels assigned to adjacent vertices. Extensive research on these problems has resulted in a variety of mathematical formulations and computational approaches. However, their minimum span perspective, in which a prescribed minimum (cyclic) distance is fixed and the objective is to minimize the label span, has received comparatively little attention. In this paper, we consider this complementary perspective by introducing the Minimum Span Antibandwidth/Cyclic Antibandwidth Labeling (MSABL/MSCABL) problems and developing a unified Boolean Satisfiability (SAT)-based framework for solving them. The SAT-based framework formulates MSABL/MSCABL as a sequence of decision problems and exploits their monotonicity to accelerate the search process. We also consider two SAT solving strategies, parallel and incremental SAT solving: the former examines multiple candidate spans concurrently, while the latter reuses a single SAT instance while progressively restricting the label domain. The proposed approaches are evaluated on benchmark instances from the Harwell-Boeing Sparse Matrix Collection and compared with CPLEXCP, CPLEXMIP, and Gurobi. The results show that SAT-based approaches are highly competitive in solution quality, with the parallel approach performing best overall for MSCABL and the incremental approach for MSABL. With the no-hole constraint, they remain competitive with CPLEXCP and significantly outperform CPLEXMIP and Gurobi, particularly for MSCABL. These results demonstrate the effectiveness of SAT solving as an exact approach for MSABL and MSCABL.

Effective manipulation across diverse objects is critical for applications ranging from agricultural harvesting to laboratory and domestic automation. While the inherent compliance of soft robotics is well suited to this challenge, designing grippers that generalize across tasks remains difficult due to the vast design space of continuum mechanics and the risk of overfitting to specific scenarios. We propose a graph-based design space for representing soft structures and mechanisms, coupled with a multi-objective, diversity-driven genetic optimization framework that explicitly promotes solution variety throughout the design process. Using multiple grasping scenarios during optimization, we study how task diversity influences the emergence of generalization to unseen objects and contact conditions. Our results show that optimization over a sufficiently diverse set of grasping cases leads to designs with emergent generalization, exhibiting improved robustness compared to task-specific solutions on novel scenarios. These findings suggest that diversity-driven optimization offers a principled pathway toward general-purpose soft grippers, aligned with the adaptable nature of soft robotics.

Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.

Modern networks must support changing topologies, configurations, and performance objectives, motivating fast and reliable performance estimation. Network digital twins (NDTs) enable what-if analysis for performance estimation in such network scenarios, however, existing machine learning-based NDT approaches often rely on entire topology representations, which are inherently monolithic and lack reusability under topological or traffic changes in the network. This paper introduces a composable NDT approach that decomposes networks into subgraphs represented by reusable unit twins that capture subgraph structure, configuration and traffic behaviours. A lightweight composer aggregates unit twin combinations to create NDTs that predict per-route end-to-end latency through an overall topology. Evaluation across controlled synthetic topologies and diverse traffic scenarios, real-world Topology Zoo topologies, and a public NDT challenge dataset demonstrates that the composable NDTs achieve high in-distribution accuracy while remaining stable under out-of-distribution scenarios. Comparison with monolithic full topology NDTs demonstrates that our composable approach achieves reusability, while achieving comparable or superior accuracy.

Logic resynthesis preserves circuit functionality while changing gate vocabulary, topology, and structural statistics, creating domain shift for circuit graph neural networks (GNNs) without changing task labels. To study this setting, we introduce ReDIL-GNN, a resynthesis domain-incremental learning framework that adapts a fixed prediction or representation head as new synthesis styles arrive and evaluates retention on all previously observed domains. Because not every shift should be adapted blindly, ReDIL-GNN further introduces the Resynthesis Adaptability Index (RAI), a pre-adaptation score that combines adaptation need, source-equivalence recoverability, structural coverage, and update compatibility. We evaluate supervised hardware-security tasks and representation-learning models using task-native metrics for classifiers and source-equivalence retrieval metrics for embedding models, comparing naive fine-tuning with LwF, Online EWC, MAS, ER, A-GEM, DER++, ER+LwF, and equivalence-guided replay. Across the studied pipelines, RAI separates unsupported shifts from promising updates, ranging from 0.001 for a structurally uncovered GNN-RE ABC-rewrite shift to 0.824 for the best original-only GNN-RE adaptation case. In practice, ReDIL-GNN turns resynthesis-aware circuit learning into a deployment control loop: RAI screens each new synthesis flow before update, guiding whether to reuse the current model, apply retention-aware adaptation, or defer adaptation until the shift is better supported.

Graph neural networks are widely used for transductive node classification, with accuracy typically measured on randomly drawn train/validation/test splits. Reported accuracy has been shown to shift substantially across different random splits of the same dataset, making published comparisons between architectures unreliable. The classical remedy in non-graph settings is stratified $k$-fold cross-validation, which ensures each test fold reflects the full class distribution of the dataset. We argue that class stratification alone is insufficient for graphs: nodes are not isolated but connected, and folds that differ in their distribution of local neighbourhood homophily expose the model to systematically different relational conditions that directly affect message-passing behaviour. The resulting cross-fold variation reflects the homophily composition of each split, inflating reported variance beyond what model behaviour alone would produce. To address this, we propose \hp{}, a topology-aware stratification procedure that treats node homophily as the primary stratification axis, aligning folds with respect to local relational consistency alongside the class marginal that standard stratification already controls. Stratifying on homophily alone does not guarantee class balance, so \hp{} incorporates class label as a secondary axis, preserving class representativeness as a natural consequence of the procedure. We evaluate \hp{} on a broad benchmark suite comprising 15 node-classification datasets spanning the full homophily spectrum and 7 GNN architectures. \hp{} achieves a mean stability rank of 1.49 compared to 2.31 for random $k$-fold, achieving the lowest mean stability rank on 13 of 15 datasets while preserving class balance close to class-stratified splits and substantially better than random. We argue that homophily-aware split construction merits broader adoption for GNN evaluation.

Personalized agents are required to reason over long-term history interactions to infer both explicit preferences and implicit behavioral evidence. While early flat retrieval methods score memory fragments independently and neglect the distributed information, current structured memory frameworks rely on query-agnostic static graphs that fail to capture the context-dependent relations. Crucially, raw textual memories are inherently entangled and noisy, making fine-grained personalization and cross-session reasoning computationally prohibitive. To this end, we present LGM, a novel neuro-symbolic framework that shifts long-term memory disentanglement into a continuous latent space. Specifically, (i) instead of persisting fixed graphs, we design a tailored latent graph construction with a sparse autoencoder. Subject to each query, it maps historical interactions into latent memory nodes and disentangles the memory traces into sparse concept activations, dynamically synthesizing query-aware relational edge weights. (ii) A graph encoder then treats the query embedding as a conditioning preference to direct non-linear message passing across the task-specific latent subgraph. This yields a highly expressive memory representation for effective activations. Extensive experiments on long-term personalization benchmarks demonstrate that LGM significantly outperforms state-of-the-art baselines in capturing both explicit and implicit preferences while enabling personalized responses.

Real-world agents fundamentally require persistent non-parametric knowledge for dynamic reasoning, i.e., long-term memory and retrieval-augmented generation. While graphs have shown reliable advantages in providing structured evidence, the sparse graph representations naturally restrict machine readability and semantic density required for complex agentic workflows. Driven by this limitation, the entire industry is witnessing a paradigm shift from traditional sparse graphs to LLM Wiki, an agent-native knowledge representation that couples dense document contexts with markdown files containing multi-layered topological linkages. However, parameterizing such rich semantics is challenging to encode dense textual contexts using traditional sparse graph embeddings. Moreover, learning LLM Wiki with existing graph encoders could overwhelm distributed system overheads that hinder deployment in large-scale commercial scenarios. To this end, we propose a novel paradigm Wiki Foundation Model, i.e., WFM, tailored for scalable, agent-native representation and retrieval. Specifically, (i) we formalize a Wiki Graph schema that seamlessly bridges fine-grained structures with dense contexts, maintaining explicit topologies alongside continuous semantics; (ii) A query-conditioned attentive aggregation is tailored for rich wiki message passing and explicit attention variance regularization; (iii) We engineer an infrastructural NCCL boundary exchange protocol that hoists static partition indices and leverages fixed-shape GPU-to-GPU collectives, bypassing CPU serialization and memory copy overheads. Extensive evaluations across five long-term agent memory and multi-hop reasoning benchmarks demonstrate the remarkable performance of WFM, while achieving a 10.5 times training acceleration on distributed clusters.

Graph anomaly detection aims to identify graph structures (e.g., nodes, edges, or subgraphs) that deviate significantly from expected patterns, which supports critical applications in fraud detection, spam identification, network intrusion, etc. Despite the growing methods in the field, existing approaches follow a one-model-per-dataset paradigm, limiting their transferability across diverse real-world scenarios due to task heterogeneity, label scarcity, and domain variability. In this work, we introduce FoundAna, a GNN-assisted Foundation Model for Graph Anomaly Detection - the first foundation model framework designated for generalizable, cross-graph anomaly detection by combining GNNs and transformers. FoundAna integrates an anomaly detection-specific GNN component with a standard transformer encoder augmented by four complementary positional encodings, which enable the model to capture both local and global structural information. Specifically, the positional encoding enriched node representations are passed through attribute and adjacency decoders, and the reconstruction errors serve as the anomaly score. Extensive experiments on nine benchmark datasets spanning financial, social, and citation network domains demonstrate that FoundAna consistently outperforms state-of-the-art baselines. The code implementation and Supplementary materials are here: https://github.com/FoundAna331/FoundAna.

Graph-based retrieval-augmented generation (RAG) can help answer questions that require information from many documents. However, building a graph often requires many language-model calls during ingestion. It is therefore important to ask whether its quality gains justify the additional cost. We present EffiRAG, a graph-based RAG system designed to reduce this cost. It uses the graph to locate relevant passages and generates answers from the original text. This design preserves source information while keeping graph construction and query processing lightweight. We evaluate EffiRAG on UltraDomain, which contains 120 open-ended questions from four domains. Compared with LightRAG-hybrid, EffiRAG produces the preferred answer on 93 questions. LightRAG is preferred on 7, and the remaining 20 are splits. EffiRAG also reduces total system cost by 57 percent, from USD 0.952 to USD 0.408. The cost includes language-model calls during ingestion and querying. The advantage remains as the corpus grows. At 10 and 20 documents per domain, EffiRAG uses a lightweight, non-LLM filter to skip low-salience chunks. It remains preferred over LightRAG-hybrid. It costs 4.2 times and 4.5 times less, respectively. The comparisons identify different quality-cost trade-offs. Graph-based RAG systems should therefore be evaluated by both answer quality and cost. The results favor graph structure that locates and preserves source evidence.

We study the maximum strong independent set problem in a finite hypergraph: find the largest vertex set that intersects every hyperedge in at most one vertex. This objective arises whenever each observed block is a local incompatibility constraint but transitive closure across overlapping blocks is not justified. A motivating example is multi-band LSH-MinHash deduplication, where each collision bucket gives local evidence, while connected-component contraction can impose spurious global equivalences. The paper develops an incidence-structural toolkit for this problem. We prove exact reductions for dominance, incidence twins, and weight-1 blocks; derive closed-form and low-weight upper bounds; introduce puncturing and covering certificates that sharpen those bounds; and analyze a layered greedy clustering algorithm driven by block weights and residual incidence. The algorithmic analysis includes feasibility, maximality, conditional optimality, a layered witness-matching upper bound, and incidence-local complexity bounds. The results give correctness, termination, fixed-point, and optimality certificates for broad incidence families, together with examples showing when different certificates separate or coincide.

Calculating disequilibrium chemistry in exoplanet atmospheres remains a significant computational bottleneck in atmospheric retrievals. The increasing observational precision from facilities such as JWST and the Ariel mission requires including disequilibrium chemistry in these analyses. Previous studies have demonstrated that neural networks can emulate kinetic chemistry, although their spatial inductive bias does not align with the topology of chemical reaction networks. This study introduces a graph neural network surrogate that represents chemical species as nodes and temperature-dependent reaction rates as edges, thereby enabling information propagation along physically meaningful chemical pathways. The model is trained on atmospheres generated using the Venot+2020 chemical scheme and Guillot temperature-pressure profiles. The GNN accurately reconstructs disequilibrium abundances across the sampled parameter space and reduces the mean abundance error by a factor of approximately 3 compared to the previous U-Net model. When applied to transmission spectra, most predictions fall within the observational precision expected for JWST and Ariel, with only about 7% of test atmospheres exceeding a 20 ppm mean spectral error. Performance variations are primarily observed in chemically transitional regimes near a carbon-to-oxygen ratio of one and at low temperatures. An evaluation of the boundary-case planet WASP-39b demonstrates effective performance under a moderate domain shift. Perturbation analysis indicates that disturbances propagate along chemical connectivity rather than spatial adjacency, confirming that the architecture captures the structure of reaction networks. These results suggest that GNN surrogates provide accurate, computationally efficient predictions of disequilibrium chemistry, facilitating integration into the atmospheric retrieval pipeline.

A large language model (LLM) agent can follow more graph paths without acquiring more independent evidence. GraphEcho tests whether agents mistake these repeated encounters for additional corroboration. The benchmark varies path counts and evidential origins while holding evidence content fixed, and evaluates both judgments and active exploration. Controlled synthetic experiments reveal model-dependent judgment shifts, but redundant supporting paths increase the share of repeated walks across all evaluated frozen agents. Provenance-aware post-training (PAPT) reduces revisits and improves synthetic accuracy, yet covers fewer distinct sources. On scientific claims, it continues to reduce repetition while accuracy declines. These findings expose a gap between efficient exploration and effective evidence use: an agent can learn to stop repeating itself while overlooking information it needs. GraphEcho provides a controlled way to evaluate both what graph agents conclude and whether their exploration reaches distinct evidential sources.

We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative power is upper-bounded by the Weisfeiler--Lehman (1-WL) graph isomorphism test. This prevents GNNs from distinguishing certain non-isomorphic graphs with identical local neighborhood structures, often leading to similar graph representations. Unified Topological Signatures (UTS) capture compact, multi-scale representation of global graph topology derived from persistent homology. We introduce two complementary UTS signatures: Graph_UTS- a static signature of the input graph topology, and Embedding_UTS- a dynamic signature of the evolving embedding topology. They encode structural information inaccessible to 1-WL-based message-passing GNNs, yet their capabilities are explored solely for post-hoc embedding-space analysis. We integrate UTS into GNN training across three architectural interventions: (i) UTS-Aug: augmenting with standard readout feature that encodes graph's true topology; (ii) UTS-Reg: topological regularizer that constrains representation collapse; (iii) UTS-Pool: topology-guided pooling that retains structurally critical nodes. We further leverage UTS as a layer-wise diagnostic to quantify oversmoothing during GNN training. Theoretically, we show that integrating UTS into GNN optimization strictly extends GNN expressivity beyond the 1-WL hierarchy. Experiments on three graph classification benchmarks show consistent benefits: Graph-UTS, Dual-UTS, and UTS-Pool improve accuracy across all three datasets, Embedding-UTS provides smaller but similarly consistent gains, and UTS-Reg's benefit varies across graph domains. Accuracy improves by up to 5.8% with Graph-UTS augmentation, by up to 1.9% with UTS-Reg, and achieves comparable performance to TOGL with UTS-Pool.

Federated learning lets multiple participants train a shared model without pooling raw data, by exchanging locally trained model updates instead. Federated averaging assumes that averaging local models is a reasonable way to solve one shared problem when participants' data are broadly similar. Work on non-IID federated learning has shown that this assumption can withstand differences in label and feature distributions. We ask whether it survives a different strain specific to graph neural networks, where client graphs differ not in label or feature distribution but in structure itself, requiring the same shared weights to operate over fundamentally different topologies. We call the resulting harm structural negative transfer. In a federation of real citation networks and synthetic structural proxies, a structurally atypical client lost more than half its achievable accuracy simply by joining. In an initial six-client federation, two label-free structural statistics computable before training were strongly associated with this harm. Expanding to twenty clients showed that degree divergence remained associated with harm, although more weakly, and survived removal of domain contrast. Spectral divergence did not replicate, which we trace to a confound caused by the composition of the reference pool used for leave-one-out statistics. A causal intervention isolating topology found no significant effect. A degree-normalization mechanism held across twenty-four seeds but did not explain the harm when corrected. The best of five candidate fixes beat a tuned baseline only until a matched, structurally blind control was applied, after which the gain disappeared. What survives is a modest, partially replicated, degree-specific signal that is not yet a validated predictor at scale.

The Graph Coloring Problem (GCP) is NP-hard and DSATUR stands as one of the fastest heuristics for it despite producing colorings that typically use more colors than state-of-the-art coloring algorithms. We propose SSLD (Semidefinite Spectral Learning with DSATUR), which improves DSATUR by preprocessing a first good color class before letting DSATUR complete coloring the rest of the given graph. We obtain this color class from a Semidefinite Programming (SDP), similar to an SDP used to compute the Lovász theta number. To the best of our knowledge, SSLD is the first approach to improve DSATUR by preprocessing through fixed color classes. We evaluate SSLD against DSATUR and against a naive 1-color-class preprocessing algorithm on DIMACS instances, random graphs (Erdős--Rényi, Watts-Strogatz, Barabási--Albert), Frequency Assignment and Job Shop Scheduling instances. SSLD matches or beats DSATUR in almost every case across over 1600 benchmark instances, and out performs the naive GISD baseline, allows us to confirm the value brought by the SDP-guided choice of the first color class. This quality comes at a runtime cost of roughly 195 times slower that DSATUR, but demonstrating that SDP-guided preprocessing of a first color class is a direction for future improvements.

Recent advances in angiographic imaging have enabled longitudinal visualization of the microvasculature. Image processing pipelines based on vessel graphs are able to resolve subtle temporal changes at the level of individual blood vessels. However, current strategies for graph extraction, refinement, and matching are highly sensitive, with even minuscule differences in the underlying segmentation map resulting in substantially different vessel graphs. These artifacts severely inhibit the ability to accurately match sequential vessel graphs of the same subject over time. To address this problem, we propose a strategy that matches graphs before jointly refining them. Specifically, we perform an early matching after basic graph extraction before removing spurious bulges and merging junctions in both graphs using joint information. In experiments with complex retinal vessel graphs, we demonstrate that this strategy results in a higher matched area without graph fragmentation compared to separate or no refinement, respectively.

While Large Language Model (LLM)-based Natural Language Inference (NLI) systems achieve high accuracy, their decision-making processes lack auditable structures. This paper explores whether NLI can be performed using only interpretable, graph-based representations of evidence. We introduce a fully graph-based pipeline where the classifier never directly processes the input text. Instead, sentences are decomposed into atomic propositions, converted into ConceptNet triples via constrained decoding, and represented as three graphs per pair: premise, hypothesis, and a retrieved ConceptNet subgraph. These graphs are then fed into a fine-tuned 0.8-billion-parameter language model. On the SNLI dataset, our pipeline achieves 89.7% accuracy, just 1.9 points below an identically trained text-based model. On ANLI, it matches the published performance of RoBERTa-large on rounds R2 and R3 (48.0% vs. 48.9% and 44.9% vs. 44.4%) but trails by 16 points on R1, resulting in an overall gap of 9 to 14 points compared to its text counterpart. We term this gap the price of interpretability and demonstrate that it stems from representational limitations rather than data constraints. Ablation studies further reveal that graphs and text are complementary: combining both modalities achieves 92.1% accuracy on SNLI.

Power Flow (PF), Optimal Power Flow (OPF), and State Estimation (SE) are fundamental problems in power system analysis, but solving them is computationally expensive. Graph Neural Networks (GNNs) have been proposed as fast surrogates, yet existing solvers are trained for a single problem at a time, producing narrow models that must be rebuilt for each new task. We propose a more general approach: a single Heterogeneous Residual Gated Graph Convolutional Network that solves all three problems with one shared backbone. Rather than learning one mapping, the model learns a reusable representation of how the network behaves, from which PF, OPF, and SE can each be estimated. Trained jointly on the three problems across diverse topologies and loading conditions, and evaluated on the IEEE 14-bus and 118-bus systems, the shared model matches the accuracy of task-specific GNN solvers and stays robust on unseen loading levels and topologies. These results show that a single model can capture the basic operation of a power network and serve several analysis tasks at once, a first step toward a foundation model for power systems.

Provenance-Based Intrusion Detection Systems (PIDSs) detect Advanced Persistent Threats (APTs) by analyzing system interactions. However, existing methods largely treat relations uniformly, overlooking statistical heterogeneity; in CADETS, relation frequencies differ by approximately $140{,}000\times$. This may cause PIDSs to focus more on frequent relations and overlook differences in normal error levels across relations, increasing the risk of false alarms and missed detections. We present RECAL, an unsupervised framework using relation-balanced masked graph learning to better capture rare interaction patterns. It further calibrates reconstruction errors against each relation's benign error distribution to produce comparable anomaly evidence, helping distinguish attacks from benign behavior and reduce false alarms. On three DARPA E3 datasets, RECAL achieves F1 scores of 99.99%, 99.93%, and 99.99%, outperforming the best baseline on each dataset by 0.88, 0.82, and 0.42 percentage points, respectively. Compared with the baseline reporting the lowest FPR, RECAL reduces mean FPR by approximately $105\times$, $4\times$, and $41\times$.

Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their line graphs. However, the relation between fixed-dimensional Weisfeiler--Leman (WL) expressivity on line graphs and on their roots remains unresolved. We study this relation through Implicit Line-Graph WL (ILG-$k$-WL), which is exactly $k$-WL on $L(G)$, executed over the edges of $G$ with line-graph relations derived from endpoint incidence and without explicitly constructing $L(G)$. On the Whitney-general class, the relation between root-domain and line-graph WL depends on $k$. For $k=1,2$, ILG-$k$-WL adds no distinguishing power beyond root-domain $1$-WL and misses some pairs that $1$-WL separates. For $k=3$, we prove the backward containment $L(G)\equiv_{3\text{-WL}}L(H)\Rightarrow G\equiv_{3\text{-WL}}H$. Strongly regular witness pairs, including the Shrikhande/rook pair, show that ILG-$3$-WL is strictly more expressive than $3$-WL. The backward containment also extends to disconnected graphs with no isolated vertices when every connected component is Whitney-general. Deterministic ILG-$3$-WL separates all three substructure-counting witness pairs, all $105$ pairs in SR25, and $359$ of $400$ BREC pairs. An untrained dense ILG-$3$-GNN gives the same pairwise verdicts on these evaluations.

The sharp increase in mass shootings underscores an urgent need for systems that guide victims to safety in real time. An effective evacuation system must minimize threat exposure while also accounting for adversarial uncertainty and crowding dynamics. Current methods in the literature are rigidly constrained to layout-specific policies and computationally intractable in large-scale layouts, while practical guidelines simply advise victims to "run", "hide", or "fight". We propose GPEvac: a GNN-based PPO framework that computes adaptive evacuation routes during shooting events. To capture both local and long-distance dependencies, we introduce an edge-first sequential message-passing scheme with a learnable virtual global node. The resulting graph embeddings are integrated into a permutation-invariant scoring mechanism that allows a single learned policy to operate across building layouts of diverse topologies and sizes. Through extensive simulation, we show that GPEvac outperforms intelligent baselines across distinct architectural layouts, significantly reducing total threat exposure. Crucially, the system computes global evacuation routes in just 14.73 ms on local CPU hardware, enabling seamless integration with live surveillance systems. In addition to saving lives during shooting events, the methodologies developed are transferable to other graph-structured decision-making domains, including critical infrastructure, intelligent transportation systems, and adaptive sensor networks.

Complete suffix prediction is challenging in sequential decision settings, where the same prefix can remain compatible with several plausible suffixes. We propose a graphbased metric-learning framework that reformulates complete suffix prediction as latent retrieval over process graphs. Prefixes and suffixes are represented as directed attributed graphs and encoded by edge-conditioned graph neural networks, allowing event-level activities and transition-level durations to be modelled jointly. Prefix representations are projected into the latent suffix space through a predictor trained with a joint reconstruction and contrastive objective strengthened using process-aware hard negatives. To stabilise the learned retrieval geometry, spectral normalisation, and retrieval robustness, spectral normalisation is applied to enforce a Lipschitz constraint on both encoders and predictor. Experiments on two real-life process datasets demonstrate that the proposed framework achieves the best overall results across nearly all evaluated criteria. It improves semantic suffix accuracy measured by normalized Damerau-Levenshtein distance, yields strong retrieval quality through Recall@1, Recall@5, and MRR@5, and maintains temporal plausibility according to Mean Absolute Error. These results show that graph-based latent retrieval is an effective alternative to sequential suffix prediction for recommendation-oriented process monitoring under structural and KPI-related constraints.

Molecular property prediction requires representations that generalize from limited labeled data to structurally novel compounds. Existing molecular pretraining methods often rely on a single view: graph-based approaches model atom-bond topology but provide limited fragment-level supervision, whereas fingerprint descriptors encode chemical patterns but are typically used as fixed auxiliary features. We propose HiFi-Mol, a multi-view framework that separately pretrains a hierarchical graph encoder and a contextualized fingerprint encoder before downstream integration. The graph branch uses fragment-aware masking with multi-resolution supervision to capture substructure-aware representations, while the fingerprint branch tokenizes active entries from seven fingerprint families and applies masked language modeling to learn contextualized embeddings. During fine-tuning, HiFi-Mol combines projected multi-resolution graph features with fingerprint embeddings for downstream prediction. Evaluated on MoleculeNet benchmarks under the scaffold split, HiFi-Mol achieves a 2.77% improvement in average ROC-AUC over the best baseline across eight classification tasks while maintaining competitive performance on three regression tasks. Further analyses reveal that fragment-aware masking improves graph representation quality, and classification results demonstrate dataset-dependent strengths of the individual graph and fingerprint variants, confirming that the two views provide complementary predictive signals.

Unsupervised multivariate time series anomaly detection methods typically identify anomalies through forecasting, reconstruction, or representation discrepancies. However, industrial faults may first alter inter-variable structural patterns while individual trajectories remain close to normal, resulting in weak anomaly signals. In this paper, we propose GSLAD, a prototype-regularized graph structure learning framework that uses structural deviations for anomaly scoring. GSLAD adopts a two-phase training strategy. First, a condition-aware graph learner and a graph-based forecaster are optimized with predictive supervision. The inferred normal graphs are then clustered into multiple structural prototypes representing different normal operating regimes, with edge-wise variability characterizing structural uncertainty. Deviations from these prototypes regularize the graph learner in the second phase, encouraging stable and regime-specific structural patterns. During inference, uncertainty-normalized structural deviation is combined with predictive deviation for anomaly scoring. Experiments on four industrial benchmarks demonstrate strong overall performance of GSLAD and confirm the effectiveness of structural deviation for anomaly detection and diagnosis.

A robot following language instructions needs its semantic memory to keep naming the same physical object while the SLAM pose graph underneath is optimized, loop-closed and compressed. Maps committing each detection to a world coordinate cannot: a closure moves the anchor it was measured from, or the solver marginalizes that anchor, and the query then selects a different object although both graphs represent the same posterior. P-POSEMEM stores each observation as an immutable event at its birth keyframe, retains the Bayes-tree elimination conditional of every marginalized keyframe, and integrates the semantic likelihood over the reconstructed joint posterior of poses, anchors and identities. Dproj, the total-variation defect between the language-goal distributions of inference-equivalent full and marginalized graphs, measures this directly. Over 40 HM3DSem scenes and 112,000 queries, P-POSEMEM reproduces the full-graph oracle (Dproj = 0) and reduces goal flips against every memory-reducing baseline. On an eight-run campaign whose 761 closures rewrote the map by up to 47 m, Dproj stays below 10^-13 with 0/288 goal flips when elimination follows the closures, where every ablation and a coordinate committed at insertion flip goals it does not; under a live bounded solver the same memory flips 23/288 against 53 for that frozen coordinate. A pre-registered negative control is detected by Dproj while leaving calibration error and navigation success unchanged, indicating that these measures capture distinct failure modes. Retrieval is held fixed by a shared frozen detector, isolating the gain to memory consistency. Code and data: https://anonymous.4open.science/r/posemem-2328/.

End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderings. Such losses typically involve a costly graph-matching problem. We first study three Optimal Transport relaxations of this problem and show, theoretically and empirically, that the Gromov-Wasserstein (GW) objective is the most suitable for SGP. Then, to avoid solving the resulting inner optimization for every training example, we propose to amortize the graph matching (node alignment) problem. For each training sample, the loss function leverages a transport plan provided by a parametric matcher based on the differentiable Sinkhorn algorithm applied on empirical node distributions. The graph prediction module and the matcher are jointly learned. We showcase the efficiency of this approach on toy and real world SGP problems of increasing complexity including a novel Mass-spectra to Scaffold task that we introduce.

Accurate cell detection and classification are crucial for pathological analysis, directly affecting diagnostic accuracy and treatment planning. To capture complex cellular interactions beyond visual appearance within the tumor microenvironment, several approaches have employed graph neural networks to model spatial and relational patterns among cell nuclei, yielding promising results. However, these methods typically adopt a two-stage paradigm of visual extraction followed by relational modeling, which necessitates separate tuning for each stage, thereby increasing pipeline complexity and hindering end-to-end joint optimization. In this paper, we propose an end-to-end framework for cell detection and classification that jointly models patch-level visual representations and instance-level interactions, which incorporates a dynamic graph construction module and an instance-aware graph network. Specifically, the graph construction module dynamically builds the graph structure using learnable queries derived from patch-level features as cell instance representations, with adjacency defined by integrating feature similarity and spatial distances. The instance-aware graph network performs adaptive instance filtering and feature reorganization, aggregating them over the cell graph into a topological latent state for a selective state-space transition driven by visual cues, fusing appearance and relational evidence. When evaluated on multiple datasets with different staining protocols for cell and nucleus detection, our method significantly outperforms existing approaches in both detection and classification performance. The code will be released at https://github.com/RuochenLiu23/IGM.

Dynamic-vision-sensor (DVS) cameras generate events on a per-pixel basis with a $μ$s-level temporal resolution, calling for new algorithm-hardware co-design approaches compared to standard frame-based vision. While event-driven graph neural networks (EV-GNNs) emerge as a promising algorithmic solution, they raise new HW challenges by mixing dense-regular compute operations and sparse-irregular memory accesses. We present ETHEREAL, the first EV-GNN accelerator that scales to 640$\times$480 resolutions, thanks to a neighbor-parallel spline convolution engine and a 2D/3D-split memory hierarchy with a novel region-of-interest spatiotemporal caching mechanism. Measurement results demonstrate end-to-end inference with 25.6$μ$s latency and 1.7$μ$J energy per event on state-of-the-art workloads

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/.

SNAP-KG is a framework for assigning newly arriving entities to semantic communities in a growing knowledge graph (KG) using only their raw features, with no graph access and no retraining at inference time. It was evaluated on five multi-view benchmarks and a 2.4M-node OGB-WikiKG2 KG. In each of these datasets, at least one graph view is homophilous, meaning that connected nodes usually belong to the same class, and SNAP-KG performs well on all of them. This paper asks what happens outside that setting. We extend the evaluation to three heterophilous graphs (Texas, Wisconsin, Chameleon) and measure the edge homophily of every view. When no homophilous view is available, clustering quality drops sharply for both SNAP-KG and the transductive baselines used in its original evaluation. What decides this is the homophily of the relation, not the number of relations. Multi-view fusion still helps, but only when at least one homophilous relation provides a reliable foundation. The homophily assumption is therefore shared by the whole method family, not specific to SNAP-KG. We argue that heterophilous multi-view clustering is a separate research problem, outside the scope of this work. As future work, we outline how a heterophily-aware teacher could be distilled into SNAP-KG's projector to serve both homophilous and heterophilous KGs.

Finite element stress fields often exhibit strong local non-smoothness, where stress concentrations near holes, notches, and loading regions induce sharp spatial gradients and high-frequency graph components. Although graph neural networks naturally operate on irregular finite element meshes, conventional message passing is inherently smoothing and progressively attenuates such high-frequency information. Unitary propagation alleviates this problem by preserving spectral magnitudes, but typically relies on matrix functions and high-order approximations with $O(Ked)$ propagation complexity. We propose LiftGCN, an efficient spectrally stable graph network based on Joukowski spectral lifting. LiftGCN maps the real spectrum of a normalized graph operator onto the unit circle through the Joukowski relation and realizes the resulting spectral transformation as a simple second-order recurrence, avoiding matrix exponentials, eigendecomposition, and high-order polynomial truncation. We show that the linear Joukowski backbone has unit-modulus characteristic roots and admits an energy-preserving structure under a positive-definite metric, preventing exponential attenuation of graph-frequency components with depth. Each layer requires only one sparse neighborhood aggregation, yielding $O(ed)$ propagation complexity, while lightweight local nonlinear residuals provide expressive feature transformations. Experiments on finite element stress prediction demonstrate that LiftGCN achieves competitive overall accuracy while improving reconstruction of stress concentrations and local high-gradient structures with substantially reduced computational cost. Our code is available at https://github.com/ChenZeng001/LiftGCN.

Online scheduling of dependency-aware tasks in heterogeneous cloud clusters is a fundamental yet challenging problem due to the complex interplay between DAG topologies and multi-dimensional resource constraints. While DRL has shown promise, existing GNN-based approaches often struggle to efficiently model high-order topological dependencies and suffer from loose coupling between task and resource states, leading to myopic scheduling decisions. To address these limitations, we propose HiGFRL, a Hierarchical Graph Fusion-Driven Reinforcement Learning framework. HiGFRL constructs a novel three-level state representation comprising a Static Hypergraph, a Dynamic Global Graph, and a Local Bipartite Graph to explicitly model the interplay between task dependencies and real-time cluster dynamics. Specifically, we design a fusion-driven dual-network architecture to optimize RL decision-making, where a Context Fusion Allocator integrates local bipartite matching features with fused global context to execute precise task-to-node allocation, and a Global State Evaluator leverages the global dynamic graph representation to accurately estimate expected long-term cumulative reward. Furthermore, we incorporate a topology-prior-guided hybrid reward mechanism that distills static topological priors into the learning process to accelerate convergence. Extensive experiments using real-world Alibaba cluster traces demonstrate that HiGFRL significantly outperforms heuristics and DRL baselines. Specifically, in challenging large-scale high-load scenarios, HiGFRL reduces the Makespan by up to 32.55%, and optimizes the average task flow time and average task wait time by 13.58% and 13.79%, respectively. Experimental results confirm that HiGFRL not only significantly improves cluster throughput but also ensures superior QoS by substantially reducing queuing delays. Code Release:https://github.com/igeng/HiGFRL.

Recently, researchers have proposed a graph pooling operation, akin to the pooling process in conventional convolutional neural networks (CNN), aimed at reducing the computation cost of Graph convolutional neural networks (GCNNs). While most GCNN-based methods treat graph pooling as a node clustering problem and propose learning a cluster assignment matrix, existing clustering-based pooling methods tend to focus solely on the rough topology information of graphs, neglecting the exploitation of higher-order mutual connections among neighbors. In terms of message passing on graph, the ease of information passing on edges reflects the closeness between neighboring nodes, which significantly relies on the interconnectivity among neighbors. In this study, we address this gap by considering such local connection information and introducing a novel graph pooling method named RicciPool. We introduce discrete graph curvature, particularly Ollivier-Ricci curvature, as a measure of higher-order connectivity around an edge. Subsequently, we construct an Ollivier-Ricci flow formula to reweigh edge weights, leveraging the crucial information provided by Ricci curvature, particularly vital for extracting clusters in graphs. Building upon this foundation, we utilize the spectral clustering technique to learn a new cluster assignment matrix. Experimental results on multiple bioinformatics protein datasets and social networks underscore the effectiveness of our proposed method.

We present EXYGEN (EXplore Your Graphs ENgine), a framework for knowledge graph (KG) understanding that enables conversational access to KGs at scale. We address two questions in sequence. First, how effectively can LLMs perform text-to-SPARQL generation given only automatically derived structured metadata and small graph samples, rather than task-specific fine-tuning? We integrate VoID descriptions and ShEx schemas into a retrieval-augmented generation (RAG) pipeline and ablate KG-derived context on the SciQA benchmark. Our best configuration -- combining ShEx schemas, retrieved triples, and example question-query pairs -- reaches an exact match of 0.419 on execution results without any LLM fine-tuning. We further find that lexical metrics such as F1 poorly predict query correctness, and that larger general-purpose LLMs can outperform smaller code-specialized ones once given sufficient context. Second, we ask how to generate the structured metadata that this method relies on from very large KGs, where KG metadata generation becomes computationally intractable. We introduce a predicate-coverage-aware parallel graph sampling strategy that preserves structural diversity while remaining computationally tractable. On OpenCitations Meta and GESIS, it retains high predicate coverage with minimal triple loss and reduces runtime by over 80x; on ORKG, sampling is not just faster but the only tractable path to obtain complete metadata. Together, these results show that structured schema context and lightweight prompting can substantially reduce reliance on fine-tuning for scalable conversational access to KGs, though closing the remaining gap to fully fine-tuned approaches will likely require reducing dependence on curated question-query exemplars -- whether through synthetic generation or an execution-feedback-driven approach -- and validating these findings beyond a single benchmark.

Heteroscedastic forecasting, where a network estimates a scale parameter alongside a location parameter, is normally motivated by uncertainty quantification. This paper shows it also improves the point estimate, in contrast to reported negative results for heteroscedastic estimation outside time series. Halo is a modification that reuses an existing deep forecaster's architecture, giving it a second output for the scale of its implied distribution and training it under the matching negative log likelihood. Adapting three state-of-the-art models --- a transformer, a graph network paired with a variational autoencoder, and a single-layer convolutional network --- under both Gaussian and Laplacian losses demonstrates the phenomenon. On the five electricity price markets of a standard forecasting benchmark, Halo improves MSE and MAE in 28 of 30 model-market-metric comparisons, cutting average MSE by 2.6% to 16.5% and average MAE by 1.7% to 11.0%. Two findings emerge: (1) whether the scale estimate comes from a second projection head or from a full parallel network matters far less than whether the network estimates scale, and (2) the improvement holds under the hyperparameters already tuned for the point-estimate baseline, so retuning is optional.

In disinformation datasets, narratives are often understood as recurring interpretive patterns that group texts under narrative labels. Recent work formalized narrative mining as inductively inferring narrative labels from corpora, but its evaluation stays tied to predefined taxonomies, a closed-world setting that cannot capture narratives absent from the reference labels. We introduce a three-tier evaluation framework for unsupervised narrative label generation: recovery (against a corpus's own taxonomy), mining (against external label sets), and discovery (without predefined labels). Applying it, we compare clustering-based and graph-community-based pipelines across seven disinformation datasets, with human validation of discovery on two. The two families are complementary under automated metrics, but in a corpus with two prominent topics, clustering can reduce one topic to 2% of generated labels while graph-based pipelines stay balanced. Discovery validation also reveals many singletons (narrative labels derived from single claims, 30-62% of graph outputs), which clustering cannot produce. Annotators confirm many as recognizable disinformation narratives, suggesting that in open-world discovery the repetition assumed by narrative mining may be recognized outside the corpus, not within it. We release human-validated narrative candidate labels for the Climate Obstruction and PolyNarrative datasets to support taxonomy development and dataset extension.

Despite its ubiquity, clustering lacks a universally accepted definition of what is a cluster. Kleinberg's Impossibility Theorem formalizes this difficulty by showing that no flat clustering method can simultaneously satisfy three natural axioms: scale invariance, richness, and consistency. In this paper, we ask whether this impossibility persists when the output is a hierarchy rather than a single partition. We show that, in contrast to the flat clustering setting, the hierarchical analog of these axioms are jointly satisfiable. In fact, there exist uncountably many hierarchical clustering methods satisfying these axioms, which we call admissible. We explicitly construct several admissible methods, including methods based on well-separated clusters and a non-binary version of single linkage. For certain pairs of admissible methods, the hierarchy produced by one always refines that produced by the other. This refinement relation defines a partial order on the class of admissible methods. This partially ordered set has no greatest element and contains uncountably many pairwise incompatible maximal elements, revealing substantial diversity among admissible methods. Nevertheless, this diversity is constrained: every admissible method contains a hierarchy of sufficiently well-separated clusters, and every finite collection of admissible methods shares such a nontrivial common backbone.

Graph condensation aims to produce a small surrogate graph that preserves the downstream node-classification performance of a much larger original graph. Existing methods rely on Weisfeiler-Lehman neighbourhood aggregation or gradient-based distribution matching, both of which assume that adjacent nodes share the same label, an assumption that breaks down under heterophily. We propose HERALD (High-fidelity Exemplar Retrieval with Adaptive Landmark Distillation), a gradient-free graph condensation framework that adapts the node scoring and feature selection in the condensation pipeline to the graph's measured heterophily. HERALD selects features via a joint Fisher-discriminability and activation-density criterion that down-weights aggregated representations on heterophilic graphs, and scores nodes by a weighted combination of prototype representativeness, decision-boundary proximity, and Local Intrinsic Dimensionality (LID), where the weights are driven by a smooth sigmoid function of the heterophily ratio. Nodes are then assembled into a condensed subgraph through score-ordered BFS expansion, Personalised PageRank pruning, and class rebalancing, all at an identical storage budget to BONSAI, enabling direct comparison. Experiments on eight benchmark datasets spanning homophilic and heterophilic settings show that HERALD matches or outperforms state-of-the-art condensers on heterophilic graphs and remains competitive on homophilic ones across four GNN architectures.

Graph captions should help readers understand graph structure, rather than simply translate adjacency matrices into long textual edge lists. A useful graph caption abstracts connectivity into recognizable motifs, such as hubs, paths, cycles, cliques, and bridges, because these motifs provide compact structural units that are easier to read, compare, and recover. In this paper, we study motif-oriented graph captioning as a bidirectional graph-text translation task, where captions must both preserve enough topology for graph recovery and express the graph through concise motif-level descriptions. We show that direct prompting of GPT-5.1 often produces graph-recoverable captions by enumerating node-to-node connections, but these captions are verbose and can contain inconsistent motif interpretations. To address this gap, we introduce Structurally Speaking, a lightweight structured prompting protocol that guides translation between explicit connectivity and motif-level abstraction. Experiments on a synthetic motif-based dataset show that structured prompting produces shorter and more motif-consistent captions while maintaining comparable graph recovery. These results suggest that explicit topology-to-motif reasoning guidance can make LLM-generated graph captions more interpretable without model fine-tuning.

Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs) operating on covariance matrices as graphs. Covariance matrices are ubiquitous across domains, and hence, the deployment of GNNs often leverages graphs of pairwise statistical dependencies. Existing theoretical contributions on GNNs consider abstract graph representations and cannot accommodate the data-driven nuances associated with covariance matrices. This tutorial brings into focus various novel theoretical insights via mathematical analyses of VNNs that have broad signal processing implications, including: (i) a conceptual equivalence between VNNs and principal component analysis (PCA)-based information processing; (ii) refined stability bounds on predictive outcomes in the presence of finite sample-induced covariance matrix perturbations; and (iii) refined characterization of transferability of VNNs across multiscale datasets. The theoretical insights discussed herein provide the underlying principles and justification towards adopting VNNs over workhorse PCA-based learning pipelines, in applications where covariance matrices are useful descriptors of data structure. We also convey how impact of these foundational advances permeates to \textit{principled} designs and applications of learning methods across broad domains where covariance matrices emerge. Notably, we elucidate the conceptual insights facilitated by VNNs to the specific task of characterizing brain age gap for neurodegenerative conditions using neuroimaging datasets, a timely problem in computational neuroscience. Broader impacts to other application domains are discussed as well.

The banking system now depends on a small set of shared artificial intelligence vendors for fraud screening, credit decisioning, anti-money-laundering triage, customer analytics, and internal decision support. This paper studies how a compromise inside one of those vendors can propagate along a chain of operational, informational, and financial linkages until it triggers losses that look, from the outside, like a classical banking crisis. We build a four-layer heterogeneous network that couples AI vendors, financial institutions, interbank exposures, and customer accounts, and we propose CFC-Prop, a stochastic epidemic-and-clearing model that runs on that network. On a synthetic dataset with 60 vendors, 220 banks, roughly 2,500 vendor-bank service edges, and 1,400 interbank exposures, CFC-Prop reproduces the heavy-tailed loss distributions and the sharp dependence on patch latency that are consistent with prior cyber-financial evidence. We also train an early-warning model, CFC-GNN, that uses vendor-side incident telemetry and graph structure to flag high-cascade-risk vendors before impact. Across four baselines the proposed model reaches AUROC 0.82 and AUPRC 0.60 while keeping calibration errors bounded. We release the full code, synthetic data, and reproducible scripts. The results argue that cyber concentration among AI vendors is a first-order financial-stability problem and give supervisors a concrete quantitative tool for reasoning about it.

This paper introduces an evolutionary computation approach for consensus in structural Bayesian Network (BN) fusion under the constraint of limited treewidth. The consensus BN aims to reconcile multiple input BNs into a single one that retains key structural features present in the original networks. Treewidth, a graph-based parameter associated with computationally tractable inference, is utilized to restrict the complexity of the resulting network. A genetic algorithm is proposed to look for a BN that codifies as much information about the unrestricted fusion as possible while ensuring the treewidth restriction. Experimental evaluation demonstrates the genetic algorithm's ability to obtain consensus BNs with limited treewidth, providing a valuable tool for aggregating information from diverse sources while returning a computationally actionable model.

A graph retrieval-augmented generation pipeline chooses which triples to put in the prompt, a syntax to write them in, an order to write them in, and a sentence telling the model what to do with them. We vary all four over six large language models and two knowledge-graph question answering benchmarks. Two of the four choices move the answer and the other two are flat. The first is whether the answer path, the triples needed to reach the answer, is in the prompt at all. Holding the number of triples fixed and replacing every triple that is not on the chain with material from an unrelated entity changes answer accuracy by +0.003 F1, while removing the chain costs most of what the graph was worth. Retrieval budget belongs on recall, and precision in the range we can test buys nothing. There is no retriever here: subgraphs come from gold SPARQL, so precision describes the context we build, not a system setting. The second is the grounding instruction. With no facts in the prompt, telling a model to answer using only the provided facts drops F1 from 0.299 to 0.035, a factor of 8.63. That figure describes an evaluation with an empty context arm rather than a working pipeline, and an experiment that applies the instruction to its context arm but not to its no-context baseline manufactures a spurious finding that graph context hurts at depth. We found one in our own results and retract it. Syntax, triple order and subgraph size produce no effect we can measure at multi-hop depth. The comparison that would price the grounding instruction against correct context is not measurable with a format-sensitive scorer, because the instruction determines the response format; we report it as an open contrast rather than a number.

High Performance Computing-Quantum Computing (HPCQC) platforms expose multiple Quantum Processing Units (QPUs) that may differ in size, topology, native gates, and noise characteristics. For current noisy devices, errors compound along the compiled circuits quickly, and minimizing them, that is, maximizing the circuits' execution fidelity, is essential for reliable results. Fidelity depends on the compilation to a specific target device: the same high-level circuit may produce different executables and, therefore, different expected fidelities across QPUs. We present a low-overhead fidelity-aware scheduling framework for multi-QPU systems based on a Graph Neural Network (GNN) that estimates, before compilation, the expected fidelity of each circuit on each available QPU. Then, a tunable scheduler uses these estimates to control the trade-off between execution fidelity and parallelism. Results show that this framework allows for approximating an exhaustive fidelity-based assignment, saving computational resources compared to a brute-force approach that compiles each circuit on every device.

Malocclusion skeletal grading is a fundamental task in orthodontics, critical for diagnosis and treatment planning. Traditionally, cone-beam computed tomography (CBCT) is used for visual measurement, and the reconstructed lateral cephalograms are handed over to expert dentists for diagnosis. However, manual review is time-consuming, labor-intensive, and subject to inter-operator variability. Therefore, an automatic CBCT-based system is needed for reliable malocclusion skeletal grading. In this case, we develop TeethGNN, a novel graph-based framework designed to combine CBCT image features with morphological information for accurate and efficient malocclusion grading. TeethGNN utilizes a decoupled learnable decoder to directly predict key morphological indicators from CBCT images, eliminating the need for manual measurements. These morphological features are then fused with image features using a graph neural network (GNN), which effectively models the relationships between the modalities. To further enhance robustness and calibration, we introduce a collaborative calibration strategy. This strategy combines multi-scale graph adversarial perturbation for explicit calibration and nonlinear topological graph calibration for implicit confidence adjustment. Extensive experiments and ablation studies on our collected clinical dataset demonstrate that our malocclusion measurement system achieves 77.08% in accuracy and 89.61% in AUC, outperforming the compared state-of-the-art methods. These results validate the effectiveness of graph-based multimodal fusion and collaborative calibration in improving malocclusion grading performance. Our system shows strong potential for advancing computer-aided orthodontic diagnosis, providing an accurate and reliable solution for vision-based clinical measurement and diagnosis.

6G wireless technology is poised to adopt higher and wider frequency bands, leveraging highly directional beamforming. However, the vast bandwidths amplify the impact of beam squinting. Traditional solutions, such as adding a true-time-delay filter to each antenna, are cost-prohibitive due to the required hardware scale. This paper proposes a signal processing alternative using Graph Neural Networks (GNNs) to optimize hybrid beamforming in multicarrier wideband systems. Using a bipartite graph to represent a shared analog beamformer among multiple subcarriers, we develop three GNN structures with distinct digital beamformer representations (i) at the subcarrier nodes, (ii) at the edges, or (iii) integrating traditional singular-value decomposition solutions. By designing an efficient message-passing mechanism, these structures offer insights into the impact of different GNN designs on communication system performance and computational complexity. Extensive analysis and ablation studies show that our proposed GNN structures outperform traditional optimization methods and existing ML-based solutions. Furthermore, the proposed GNNs exhibit strong resiliency to beam squinting and better robustness against imperfect CSI than even fully digital beamforming and all existing hybrid designs. These GNNs can also be extended to multi-user scenarios and demonstrate excellent generalization capabilities, allowing trained models to adapt to diverse multicarrier and multi-user settings without retraining.