Graph Neural Networks

Driven by the pressing demand for graph anomaly detection (GAD) in high-stakes domains, the generalist GAD paradigm, which trains a single detector transferable across new graphs, has recently gained growing attention. However, existing methods often rely on scarce and costly annotations for training and sometimes even require few-shot support at inference, which limits their robustness to diverse and unseen anomaly patterns. To address this limitation, we introduce ProMoS, the first unsupervised generalist GAD framework, which detects anomalies by modeling the abundant normality in unlabeled data. ProMoS adopts a knowledge-distillation paradigm to distill normality priors from a frozen self-supervised graph neural network (GNN) teacher to a mixture-of-students model with shared global and lightweight personalized branches, enabling efficient and expressive normality modeling without learning from scratch. We further propose prototype-guided soft-label distillation to align teacher and student in a shared prototype space, enhancing cross-graph generalizability. During inference, ProMoS performs zero-shot anomaly detection on unseen graphs via distillation bias and prototype geometric deviation. Extensive experiments show the effectiveness and efficiency of ProMoS, charting a practical path toward label-free, zero-shot generalist GAD.

The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between the sparsity and convergence quality of coarse-grid operators. Classical AMG heuristics struggle to balance these objectives, often sacrificing stability or performance for sparsity. We propose RAPNet, a graph neural network (GNN) framework that resolves this trade-off by learning to generate sparse, robust coarse operators directly from the sparse algebraic system. Key to our approach is a level-wise training strategy that enables learning from small subgraphs and generalization to million-node domains, bypassing the bottlenecks of prior neural AMG attempts. RAPNet executes exclusively during the solver setup phase, ensuring that the solve phase retains its favorable computational properties. We show that our method outperforms classical non-Galerkin baselines on diverse PDE discretizations and graph Laplacians, making it particularly effective for multi-query tasks such as eigenproblems, time-dependent simulations, and inverse or design problems.

The Maximal Covering Location-Interdiction Problem (MCLIP) is a classic bi-level optimization problem, which is fundamental to resilient infrastructure planning yet remains computationally intractable. Specifically, the upper level determines facility locations to maximize coverage, while the lower level executes worst-case interdiction to minimize the coverage. The strong coupling between the upper and lower levels, combined with their respective high combinatorial complexity, renders traditional methods ineffective. To bridge this gap, we propose a Dual-Agent Deep Reinforcement Learning (DADRL) framework based on adversarial learning, comprising a location agent corresponding to the upper level and an interdiction agent corresponding to the lower level. Our contributions are threefold: (1) The location agent is trained simultaneously against an evolving interdiction agent, making it effectively capture the dynamic competitive interplay between the upper and lower levels; (2) To fully exploit the learned capabilities of the interdiction agent, we propose a Surrogate-based Ensemble Inference Strategy that utilizes the trained interdiction agent as a high-fidelity surrogate to guide the decisions of location agent; (3) Extensive experiments on synthetic and real-world datasets demonstrate that our approach achieves superior computational efficiency while maintaining highly competitive solution quality compared to other baselines. Furthermore, our DADRL framework is model-agnostic to network structures, while its underlying adversarial learning paradigm demonstrates strong potential for solving other bi-level optimization problems.

Graph anomaly detection (GAD) commonly relies on message passing to jointly encode node attributes and neighborhood context. However, once the two are mixed, an abnormal post-encoding state may reflect either an intrinsic node deviation or incompatible contextual influence, making its source ambiguous. We propose Disagreement-Driven Graph Anomaly Detection (DDGAD), which treats persistent incompatibility between node-wise and contextual estimates as anomaly evidence. Inspired by Adapt-Then-Combine (ATC), DDGAD reverses its consensus objective: Adapt produces a node-wise estimate without new same-step neighbor aggregation, while Combine forms a neighborhood-dependent contextual estimate, and their pre-consensus disagreement is accumulated across ATC steps for detection. We further characterize this signal from graph-spectral and source-response perspectives and derive sufficient conditions for anomaly--normal separation under contextual mixing. Experiments on six benchmarks show the highest average AUROC among the evaluated methods, while controlled interventions and Adapt-operator controls further support persistent disagreement as an effective detection signal.

Temporal signed networks (TSNs) model the time evolution of cooperative and adversarial relationships that arise in applications such as social media analysis, trust and reputation systems, and financial transaction networks. While graph neural networks (GNNs) perform well for static or unsigned link prediction, effective learning in temporal signed graphs remains challenging due to the interaction of signed relations, evolving structure, and balance-theoretic constraints. To address this gap, we propose a \emph{modular} temporal enhancement framework for signed GNNs that integrates historical context into otherwise static architectures. The framework introduces a Historical Context Integration Module (HCIM) that combines learnable recency-aware temporal weighting, LSTM-based embedding trajectory modeling, and multi-head temporal attention to capture both short- and long-term signed interaction dynamics. Historical information is fused with current node representations using either global or node-adaptive weighting, allowing the architecture-agnostic framework to accommodate heterogeneous temporal behaviors. We instantiate the approach on the Self-Explainable Signed Graph Transformer (SE-SGformer), preserving interpretability while extending it with temporal awareness. Experiments on real-world and synthetic TSNs, including Bitcoin OTC, Bitcoin Alpha, Reddit, and small-world network models, demonstrate consistent and statistically significant improvements over the static baseline.

Graph neural networks (GNNs) achieve strong performance on relational data, but real-world graphs are often distributed across organizations that cannot share raw data due to privacy and policy constraints. Existing federated GNN methods either ignore cross-client links, leading to degraded accuracy, or require frequent embedding exchanges, incurring substantial communication and privacy costs. We propose CE-FedGNN, a communication-efficient and privacy-preserving federated GNN framework for learning over such coupled graphs. Our approach avoids sharing raw data or per-round embeddings by infrequently exchanging aggregated node representations. To handle cross-client dependency and staleness, we introduce a moving-average estimator that continuously tracks node representations and enables their stable reuse across rounds. To provide formal privacy guarantees for the released representations, we adopt the metric differential privacy (metric-DP) framework, which measures privacy with respect to distances in the learned embedding space rather than worst-case input perturbations. This yields meaningful guarantees at noise levels where standard differential privacy becomes overly conservative. We establish convergence to a stationary point at a rate of $O(1/\sqrt{T})$ with $O(T^{3/4})$ communication complexity. In addition, we derive $(\varepsilon,δ)$-metric-DP guarantees via Rényi differential privacy composition under a public-cohort threat model. Experiments on synthetic interbank anti-money laundering benchmarks and citation networks demonstrate that CE-FedGNN achieves strong performance while significantly reducing communication and maintaining robustness under privacy-preserving noise.

Graph fraud detection has long depended on Graph Neural Networks (GNNs) to propagate and aggregate information across relational data. A critical obstacle in practice, however, is that fraudsters frequently disguise themselves by forging numerous connections with benign users, causing fraud signals to be progressively diluted during neighborhood aggregation and undermining detection reliability. While recent efforts have used Large Language Models (LLMs) to provide rich semantic cues for fraud detection, the underlying intent behind suspicious connections remains insufficiently explored. Compounding this issue, the scarcity of annotated fraud samples makes it difficult to train detectors that remain robust under heavy camouflage. To address these gaps, we propose L2IR, an LLM-driven Latent Intent Revealing framework for graph fraud detection. By uncovering latent intent from both user behaviors and suspicious connections, L2IR extracts intent-aware representations from raw behavioral traces and reasons about the true purpose behind individual connections, effectively distinguishing supportive links from misleading ones. It further incorporates adaptive self-training to enhance robustness under limited supervision. Evaluations on two real-world datasets characterized by pervasive camouflage demonstrate that L2IR surpasses strong baselines and can function as a plug-in enhancement for a range of GNN-based detectors, improving AUPRC by up to 8.27%.

Multi-domain graph pre-training is a crucial step in constructing foundational graph models with cross-domain generalization capabilities. However, existing methods predominantly rely on jointly training all source domain graphs, resulting in high computational costs. Furthermore, it remains unclear whether all source domain graph data contribute equally to effective transfer. This paper empirically reveals significant data redundancy in multi-domain graph pre-training. Based on this finding, we propose the Multi-domain Graph Pre-training Framework, MDGMIX, which combines boundary-aware subgraph mixing with hierarchical discrimination. By selecting boundary nodes to construct challenging mixed-domain subgraphs, MDGMIX employs coarse-grained domain discrimination and fine-grained domain decomposition losses to decouple shared patterns from domain-specific patterns. During adaptation, MDGMIX employs a lightweight prompt weighting mechanism to transfer source domain knowledge. Extensive experiments demonstrate that MDGMIX consistently outperforms strong baselines in few-shot classification tasks while exhibiting superior time and memory efficiency. The code is available at: https://github.com/zhengziyu77/MDGMIX.

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.

The process of decision-making in football is characterized by a complex interplay between spatial positioning, opponent pressure, and player intent. This work introduces a Graph Neural Network (GNN) framework designed to predict Receiver Selection, the optimal passing target, by modeling on-field interactions as dynamic graphs. Each player is represented as a node with positional and contextual features, while potential passing lines form weighted edges characterized by distance, angle, and pressure metrics. A Message-Passing Neural Network (MPNN) has been developed and trained using a combination of tracking data and event data from professional matches, synchronized through a robust pipeline based on an optimized version of the Needleman-Wunsch Algorithm. The model achieves competitive accuracy in identifying the actual chosen receiver and state-of-the-art accuracy within its top three suggestions. Our model further offers quantification of each option's likelihood, threat, and creativity, enabling performance analysts to evaluate over 1,000 passes in seconds.

Graph neural networks for node classification are typically trained by gradient descent over hundreds or thousands of epochs. Recent work has shown that, when properly tuned, classic GCN/SAGE/GAT architectures can match graph transformers on many node-classification benchmarks. We ask a complementary question: how much of this performance can be recovered by deterministic closed-form solvers, and what guarantees does this enable? We introduce a routed closed-form framework selected by adjusted homophily. For assortative graphs, we use SGC-style propagation followed by Ridge regression; for heterophilous graphs, we introduce LCF-Net, a layer-wise closed-form graph feature-refinement network whose per-layer Ridge solves are capped by a Gaussian kernel-Ridge head. Across 14 benchmarks, including ogbn-arxiv and ogbn-proteins, our closed-form predictors match or beat the best vanilla 2-layer GCN/SAGE/GAT on 9 of 9 measured datasets, tie tuned deep recipes within one standard deviation on 9 of 12 small benchmarks, and exceed the OGB-leaderboard plain GCN on both large graphs. The remaining heterophilous gap closely tracks the gain from vanilla 2-layer to deep SAGE, suggesting that the residual difference is primarily architectural. Because our predictors are explicit solutions of deterministic linear systems, modified graph inputs can be re-solved to obtain retrain-equivalent parameters. We formalize exact graph-object unlearning for label, feature, edge, node, and subgraph modifications, prove K-hop locality for Ridge components, and verify exactness across 109 configurations. On ogbn-arxiv, localized updates give $21$--$45\times$ speedups over full re-solving and roughly $10^{6}\times$ speedups over gradient retraining. Structural-inversion experiments further quantify the privacy floor of exact retraining and the additional leakage of approximate graph-unlearning methods.

In biomedical and neurodegenerative disorders, accurate and early disease identification remains challenging due to the scarcity of labeled data and the complexity of imaging patterns. To address these challenges, we introduce ARMA-C3, a unified unsupervised and semi-supervised graph learning framework for node classification based on contrastive learning and graph-cut regularization to learn structurally meaningful and discriminative representations. By modeling samples or images as graph nodes and exploiting inter-sample relationships, the proposed framework captures subject-level dependencies that conventional machine learning methods typically overlook. We conduct extensive binary classification experiments across five clinically relevant datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI), the Neuroimaging in Frontotemporal Dementia (NIFD) dataset, and three medical imaging benchmarks (BreastMNIST, PneumoniaMNIST, and a liver ultrasound dataset). Experimental results demonstrate that ARMA-C3 achieves competitive and frequently superior performance compared to classical clustering techniques, state-of-the-art machine learning models, and existing graph-based deep learning approaches across multiple evaluation settings, particularly under limited supervision and severe class imbalance. The proposed framework further demonstrates robust representation learning and strong cross-modal generalization across diverse biomedical imaging modalities.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterward perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; effectively, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. At each snapshot, we maintain a recurrent hidden state per node that summarises its history, pairs it with the node's current feature vector, and treats the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. We compare against fourteen link-prediction baselines under both the fixed-split and live-update evaluation regimes, and eleven baselines on node classification. Across the public benchmarks, SiST-GNN improves on the strongest prior method in link prediction by 1-18% in the fixed-split setting, and is the leading learned method on five of six datasets in the live-update setting, improving on the strongest prior method by 1-158% there. We additionally derive three dynamic node-classification tasks by discretizing the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7-23% and matches continuous-time (CTDG) methods that consume the raw events directly.

Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited mathematical understanding of the performance of GNNs. We discuss the various perspectives used to study statistical generalisation in GNNs. We identify three broad frameworks. The first approach, rooted in learning theory, relies on uniform convergence bounds and the complexity of the hypothesis class of specific GNN architectures. This approach also builds on the expressivity of GNNs, typically studied through the lens of graph isomorphism tests. The second principle is to simplify the neural architecture by analysing GNNs under the asymptotics of infinitely many parameters or infinite graph size. This approach approximates GNNs using Gaussian processes, neural tangent kernels or graphon neural network operators, which allow studying the generalisation or stability of trained GNNs. The third framework studies GNNs under random graph models, often the contextual stochastic block model, and derives non-asymptotic error rates using tools from high-dimensional statistics. We highlight some key theoretical results and discuss a few limitations and open research questions for each perspective.

We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the manifold heat semigroup $Q_t = e^{tΔ}$ can be approximated directly by iterating the graph transition matrix $P$, under only low regularity assumptions on the test function $f$, including the case $f \in L^\infty$. We bound $\| P^n f - Q_t f \|$ in $\infty$-norm, with the operator application to $f$ properly defined, and we recover the classical graph-Laplacian pointwise rate $O(N^{-2/(d+6)})$ up to logarithmic factors, for diffusion times $t$ up to $O(1)$ and longer. The rate holds for in-sample error as well as out-of-sample generalization, where the estimator of $Q_t f$ at a new point is defined via kernel convolution. To handle non-uniform sampling densities on the manifold, we introduce a right-normalization of the graph transition matrix; under the assumption that the sampling density $p$ is $C^3$ and bounded away from zero, the same convergence rates hold. We numerically demonstrate the performance of the proposed estimator on simulated data.

Diffusion models have shown promise in learning to solve constraint optimization problems. However, they are mostly restricted to problems with binary variables and rely on graph neural networks, hindering their application to a broader range of problems such as those with general discrete variables or constraint structures that necessitate global rather than local reasoning. We investigate the use of Diffusion Transformers to address the aforementioned limitations. A naive implementation performs poorly due to a fundamental mismatch between the standard diffusion process and constraint solving: while the former applies small, incremental denoising across all variables, the latter requires substantially altering specific subsets of variables to attain feasibility or optimality. Our method, Blocked Gibbs Diffusion Transformer (BloGDiT), is the first to address this limitation by replacing standard joint Gaussian denoising with blocked Gaussian denoising. BloGDiT uses iterative block resampling and anneals the block size over time to facilitate large, targeted edits within a block of variables. Across Sudoku, Graph Coloring, Maximum Independent Set, and MaxCut, BloGDiT matches or outperforms existing methods, demonstrating that blocked Gibbs-style diffusion provides a highly effective inductive bias for Transformer-based constraint satisfaction and optimization.

Pre-propagation graph neural networks (PPGNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch training without inter-node dependencies, avoids repeated sparse matrix--matrix multiplications, and better matches modern accelerators optimized for dense compute. However, their expressivity remains unclear, and empirical results show a gap between PPGNNs and their message-passing counterparts on commonly used graph benchmarks, especially heterophilic ones. In this paper, we propose a suite of robust graph diffusion operators for preprocessing and a few-shot hidden-state re-propagation scheme during training. Our methods improve the validation and test accuracy of PPGNNs, enabling them to match the accuracy of message-passing GNNs while maintaining training efficiency.

EEG-based emotion recognition holds significant promise for objective diagnosis of mood disorders. Graph neural networks (GNNs) have emerged as the dominant paradigm for modeling inter-channel dependencies in EEG, yet existing approaches rely on symmetric adjacency matrices derived from spatial proximity or functional correlations that fundamentally capture statistical associations rather than directed causal influences, which conflicts with the inherently asymmetric, causally-driven nature of neural information flow. To bridge this gap, we propose GL-LFGNN, a Global-Local Dual-branch Causal Graph Neural Network grounded in Liang-Kleeman information flow theory. Unlike Granger causality that merely assesses temporal precedence, our approach rigorously quantifies causal strength from a dynamical systems perspective, yielding neurophysiologically interpretable directed graphs. A dual-branch architecture further integrates whole-brain connectivity with region-specific processing aligned to established functional neuroanatomy. On the MEEG dataset, GL-LFGNN achieves 86.17% (Arousal) and 86.71% (Valence) accuracy with only 37K parameters -- approximately 10% of the current state-of-the-art -- demonstrating that principled causal modeling can simultaneously enhance interpretability, generalization, and computational efficiency. Code will be released.

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a $k$-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the $k$-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.

Submodular optimization has become a fundamental paradigm for data selection, retrieval, summarization, and representation learning due to its ability to model coverage, diversity, and representativeness. However, classical submodular objectives optimize only the selected subset and do not explicitly preserve structural information between the selected subset and the remaining data. In many modern machine learning applications, including train/validation/test splitting, benchmark construction, and robust subset selection, the quality of a selection depends critically on preserving balanced structure across both the selected subset and its complement. In this work, we introduce Complement Submodular Information (CSI), a new class of complement-aware submodular objectives that quantify shared structural information between a subset and its complement. Our framework induces complement-aware variants of several classical submodular functions including Facility Location, Graph Cut, LogDet, Saturated Coverage, Set Cover, Probabilistic Set Cover, and Feature Based Functions. We analyze the theoretical properties of CSI objectives and show that they exhibit approximate monotonicity under bounded curvature conditions, leading to near-$(1-1/e)$ greedy approximation guarantees. Empirically, CSI objectives consistently outperform standard submodular objectives on robust hidden-slice-aware subset selection. In particular, CSI objectives significantly improve preservation of coherent rare/tail semantic structure while simultaneously suppressing noisy and isolated outliers, leading to substantially improved downstream predictive performance. Synthetic experiments further illustrate how different CSI instantiations capture complementary notions of representativeness, diversity, connectivity, and balanced neighborhood preservation.

Tabular synthesis is critical for privacy-preserving sharing and augmentation, yet diffusion models rely on implicit mechanisms to capture inter-column relationships. We introduce Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. Our MLP instantiation achieves state-of-the-art benchmark performance while using 3.5x fewer parameters on average (up to 25x for classification tasks): on ten datasets, it wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility (F1/RMSE), reducing Shape and Trend error by 27% and 20%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset cells. A matched ablation shows supervision (not extra inputs or capacity) drives the gain. This shows explicit relational supervision is a portable inductive bias for tabular diffusion.

Multimodal Attributed Graph Learning (MAGL) integrates intrinsic node attributes with structural topology via graph aggregation. However, as pretrained encoders evolve into Large Foundation Models (LFMs), the landscape of MAGL fundamentally shifts: under high-confidence LFM priors, mandatory aggregation introduces topological noise that overwhelms discriminative signals, triggering a counter-intuitive performance inversion where sophisticated MAGL architectures underperform simple topology-agnostic MLPs. Through systematic empirical and theoretical analysis, we identify that this inversion stems from a fundamental aggregation dilemma characterized by two concurrent pathologies: (1) Representational Pathology (SNR Degradation) - mandatory aggregation dilutes robust intrinsic features with topological noise, causing the noise penalty to outweigh its collaborative benefit; and (2) Optimization Pathology (Gradient Starvation) - topological aggregation attenuates gradient flow, while a shared task loss causes dominant modalities to prematurely suppress weaker ones. To resolve this dilemma, we propose SUPRA (Shared-Unique Prior-Retaining Architecture), a decoupled dual-pathway paradigm. SUPRA processes modality-specific features through topology-agnostic MLPs while capturing structural synergy via a lightweight shared GNN, with auxiliary deep supervision counteracting gradient starvation. Extensive evaluations demonstrate that SUPRA achieves state-of-the-art performance while requiring 3.5x lower peak GPU memory and up to 4.4x faster training time than Multimodal Graph Transformers.

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.

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.

The exponential growth of data has intensified the gap between the availability of unlabeled data and the high cost of manual annotation. Graph Neural Networks (GNNs) have emerged as a promising solution, as they exploit relational structures and learn from both labeled and unlabeled data, performing semi-supervised learning. A crucial component of many of these models is degree-based normalization, which influences message propagation but typically assumes uniform importance among neighboring nodes. In image classification, graphs are usually constructed from feature similarity, where treating all neighbors equally may overlook important variations in relevance. Motivated by this gap, we propose GRaNDe (Gaussian Rank-based Neighborhood Degree). This novel degree measure integrates neighborhood ranking with Gaussian distance weighting to better capture node importance. Experiments on five public image classification datasets show consistent accuracy improvements and competitive or superior results compared to state-of-the-art methods.

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.

Deep learning over relational databases is conventionally realized by translating data into graph representations and applying graph-based neural networks within external frameworks. This round-trip between the database and external machine learning (ML) systems introduces non-trivial engineering overhead. In effect, these graph neural networks operate on tuple embeddings and manipulate them in ways that capture the interactions induced by relational joins. Given this natural correspondence, there is no fundamental reason why specifying a neural network over relational data should be substantially harder than querying it. We propose an approach that naturally integrates deep learning with database queries. The key idea is to associate each tuple with provenance, represented as a vector embedding with learnable parameters. Queries are lifted to operate jointly on data and embeddings, mapping input relations with embedded tuples to output relations with embedded tuples. This approach provides a declarative foundation for relational deep learning, facilitating integration with database systems, optimization, and wide adoption. We describe RelaNN, a proof-of-concept implementation of this approach built on top of PyTorch and cuDF. We illustrate the utility of RelaNN by implementing various graph-learning models, including graph convolutional networks, heterogeneous graph transformers, hypergraph neural networks and deep homomorphism networks. The simplicity of the programs and their competitive runtime performance demonstrate a concrete path toward making the implementation of state-of-the-art neural networks over databases as simple as writing a query.

Biological systems are governed by structured molecular interactions, where pathways, regulatory circuits, and functional gene relationships shape cellular behavior and disease progression. Much of this knowledge is naturally represented as graphs. However, most biomedical AI models cannot directly use graph-encoded biological knowledge and instead require compressed low-dimensional representations, which can lose important structure and reduce performance, especially in limited-sample clinical studies. Here, we introduce Graph-in-Graph (GiG), a knowledge graph-modulated deep learning framework for data-efficient clinical prediction. GiG represents each patient as a standalone modular graph, in which curated biological knowledge graphs define edges and patient-specific measurements, such as gene expression, define node features. This design allows multiple biological knowledge graphs to be integrated while preserving gene-gene interactions and pathway topology during patient-level representation learning. Across cohorts comprising nearly 9,700 patients and five clinical tasks, including liquid biopsy cancer detection, prostate cancer diagnosis, and 32-class pan-cancer classification, GiG consistently outperforms traditional and state-of-the-art methods, with the largest gains in limited-sample settings. On the challenging prostate cancer diagnosis task, GiG improves macro-F1 by up to 49 percentage points relative to competing methods. Control experiments replacing real pathway graphs with random topologies confirm that these gains arise from biologically grounded knowledge graph structure rather than graph modeling alone. These findings show that knowledge graph-modulated deep learning can improve robustness, interpretability, and sample efficiency in clinical data analysis, and provide a principled framework for integrating biological knowledge graphs into predictive modeling.

Bradley-Terry-Luce (BTL) model estimation is a well-established strategy to rank a collection of items given a dataset of pairwise comparisons. Although the theoretical performance of BTL estimation methods, such as spectral and maximum likelihood estimation, is well studied in the regime of uniformly sampled graphs, generalizing such results to a wider class of random graphs has proved challenging. In this work, we investigate the entry-wise error of spectral algorithms against a semi-random adversary that can arbitrarily boost the sampling probabilities of certain edges. We find that the performance of the unweighted spectral method is heavily dependent on the spectral properties of the generated graph. Furthermore, we show that asymptotic performance approaching that of uniformly sampled graphs can be recovered by appropriately reweighting the observed edges to counteract the adversary and restore the spectral gap. Finally, we provide numerical simulations that support our theoretical findings.

The communication complexity of a voting rule is the worst-case number of bits that n voters must transmit to a central authority under the most efficient elicitation protocol in an election with m candidates. We study the communication complexity of Instant-Runoff Voting (IRV). Conitzer and Sandholm [2005] established an upper bound of O(n (log m)${}^2$), but did not provide a matching lower bound beyond $Ω$(n log m). We resolve this open problem by raising the lower bound to $Ω$(n (log m)${}^2$) using the fooling set technique, thereby showing that the communication complexity of IRV is $Θ$(n (log m)${}^2$). We further show that this complexity drops to $Θ$(n log m) under the single-peakedness restriction, and that both the IRV-Average variant and Single Transferable Vote (STV), the multiwinner extension of IRV, have the same asymptotic communication complexity as IRV.

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of \emph{walks} to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires {\em exponential} computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose {\em polynomial-time} algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the \emph{max-product} algorithm -- a common tool for finding the maximum likelihood configurations in probabilistic graphical models -- and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under \href{https://github.com/xiong-ping/rel_walk_gnnlrp}{github.com/xiong-ping/rel\_walk\_gnnlrp}.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Graphs with a simple spectrum admit cubic-time isomorphism testing, yet we prove that for every natural number $k$, the $k$-Weisfeiler-Leman ($k$-WL) test cannot distinguish all non-isomorphic graphs with a simple spectrum. As the WL hierarchy upper-bounds the distinguishing power of widely-used Graph Neural Networks (GNNs), this incompleteness applies to all such GNNs, ruling out completeness for every $k$-WL-aligned GNN family. To close this gap, we introduce PRiSM (Partition, Refine, Solve, Match), the first provably complete canonicalization of simple-spectrum eigendecompositions. PRiSM obtains the completeness guarantee that prior canonicalizations provably lack, and resolves the open problem of achieving complete expressivity on simple-spectrum graphs. When composed with DeepSets or a Transformer, PRiSM achieves universal approximation on simple-spectrum graphs, justifying the use of canonicalized Laplacian positional encodings. Empirically, PRiSM performs comparably to or outperforms existing spectral canonicalizations on graph regression, classification, and expressivity

Generating graph ensembles with precisely controlled structural properties is central to investigating how network structure shapes function. Canonical ensembles impose constraints only in expectation (soft constraints), letting individual realizations fluctuate around the target, whereas enforcing hard constraints with prescribed precision in every realization remains challenging beyond fixing the degree sequence. Here we show that a reinforcement learning framework can drive a graph through degree-preserving rewirings to satisfy a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. By replacing the entropically dominated Metropolis--Hastings random walk with directed transport, the learned policy reduces generation cost by at least an order of magnitude while retaining over 98% of configurational diversity. Trained on small graphs, the framework generalizes across sizes and topologies without retraining, enabling quantitative isolation of secondary observables such as the clustering coefficient. These results establish reinforcement learning as a practical paradigm for hard-constrained graph generation.

Relational databases (RDBs) remain the cornerstone of modern data systems and support diverse predictive tasks. Recent relational deep learning (RDL) methods enable end-to-end prediction by converting RDBs into graphs, where rows are represented as nodes and inter-table interactions are represented as edges, and then applying graph-based models for representation learning. Despite the strong capability of RDL, effective self-supervised pre-training for RDBs remains non-trivial. RDB tasks often require multi-faceted information across different perspectives and granularities. For example, user churn classification may rely more on interaction patterns, whereas consumption value prediction requires both user-item behaviors and intrinsic user attributes for fine-grained regression. Such heterogeneous needs challenge RDB representation learning, as pre-training objectives should cover comprehensive information for downstream adaptation. However, existing SSL methods typically derive supervision from a single facet, such as node-level intrinsic attributes or subgraph-level relational structures, providing limited adaptability. To this end, we propose RelPrism, a multi-faceted self-supervised learning framework for RDBs. RelPrism constructs intrinsic, relational, and hybrid attributes from distinct perspectives, and applies multi-granularity clustering to each perspective to form corresponding pseudo-task pools. Pre-training over these pools exposes representations to broader perspectives and granularity levels, yielding a stronger basis for downstream adaptation. Experiments on 14 tasks across 5 real-world datasets show that RelPrism improves ROC-AUC by 4.15% for classification and reduces MAE by 10.75% for regression over state-of-the-art baselines. Our code is available at https://anonymous.4open.science/r/RelPrism.

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.

Hyper-relational knowledge graphs (HKGs) effectively represent complex facts. While inferring new knowledge in HKGs is a critical problem, current methods cast it as a simple link prediction, assuming that nearly all entities and relations within a fact are known, leaving only a single blank to be filled. However, this restricted assumption may not hold in real-world scenarios in which multiple, or even all, constituent components of a fact may be missing simultaneously. To bridge this gap, we introduce a task called fact generation: generating a valid hyper-relational fact from an arbitrarily masked query, i.e., completing a partially observed fact or generating a fact from scratch. We propose KREPE, the first generative representation learning method for HKGs that learns to model the probability distributions of missing components conditioned on the local fact components and global structure of HKGs via a masked discrete diffusion. KREPE models both the intra-fact dependencies by contextual message passing and inter-fact correlations by aggregating stochastically sampled contexts. KREPE seamlessly unifies link prediction and fact generation within a single training framework, achieving state-of-the-art performance on standard HKG link prediction benchmarks and outperforming LLM-based baselines in generating novel and correct facts.

Fast and reliable optimal power flow (OPF) approximation is essential for reliable smart-grid operation, yet many learning-based surrogates either flatten the native heterogeneous structure of power networks, target a limited set of grid topologies, or lack scalable infrastructure for graph foundation model (GFM) training. This paper presents a scalable heterogeneous graph neural network (GNN) workflow, built on HydraGNN, for data-driven OPF surrogate modeling and OPF-GFM development. The workflow preserves the distinct node and edge types of power grids -- buses, generators, loads, shunts, AC lines, transformers, and device-to-bus couplings -- and supports distributed preprocessing, training, hyperparameter optimization (HPO), and downstream fine-tuning on leadership-class supercomputers. Using three million heterogeneous graph instances spanning ten PGLib-OPF cases, from 14 to 13,659 buses, we conduct DeepHyper-driven HPO on the ORNL Frontier supercomputer. The campaign identifies compact models ($\sim$1.6--1.7M parameters) with the lowest validation losses. Downstream experiments on feasibility classification and N-1 contingency regression show that fine-tuning pretrained OPF GFM improves low-data accuracy, stabilizes training, accelerates convergence, and reduces adaptation cost when partial or head-only fine-tuning is used.

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.

Deep learning has brought significant progress to medical image classification, yet most existing methods still rely on isolated visual evidence and cannot effectively leverage similar cases or external knowledge. In clinical practice, diagnosis is typically supported by similar historical cases and their associated symptoms. To explicitly model this evidence-based diagnostic process, we propose a case-aware reasoning framework driven by multimodal knowledge graphs for medical image classification. Specifically, we construct a case-aware multimodal knowledge graph as a structured diagnostic memory, where diseases, images, and symptoms are hierarchically organized. Given an input image, our method adaptively retrieves similar cases from this memory and extracts their corresponding case-centered subgraphs. We further introduce a knowledge propagation and injection mechanism, in which an image-centric Graph Attention Network aggregates heterogeneous semantics into case-based features, followed by a bidirectional cross-modal attention mechanism that injects these features into visual representations for cross-modal alignment. To mitigate noisy retrieval, we design a confidence-calibrated decision refinement scheme that estimates the reliability of each retrieved case by jointly considering prediction confidence and sample similarity, and reweights its contribution to the final prediction, providing interpretable case-level evidence. Extensive experiments on multiple medical imaging datasets demonstrate that our approach consistently outperforms strong baselines, while ablation and qualitative analyses validate its effectiveness and interpretability. The code is available at https://anonymous.4open.science/r/MKG-CARE-8B7B.

Mini-batch training of Graph Neural Networks (GNNs) is fundamentally different from training on i.i.d. data: sampling a subgraph alters the topology and introduces boundary effects, leading prior work to develop structure-aware samplers that preserve local connectivity and reduce embedding variance. Surprisingly, we demonstrate that the simplest possible scheme, Random Node Sampling (RNS), training on the induced subgraph of uniformly sampled nodes, matches or outperforms full-graph training on 8 of 10 datasets at a fraction of the wall-clock time and memory. To explain this, we apply backward error analysis to graph mini-batch Stochastic Gradient Descent (SGD) and show that it implicitly minimizes the sampled loss plus a regularizer proportional to the mini-batch gradient variance, a quantity directly shaped by the sampler. Although RNS discards local structure, it produces mini-batches whose expected loss is closer to the full-graph loss, and whose per-batch gradients have lower variance, yielding a better implicit objective. Our analysis reframes the choice of graph sampler as a form of implicit regularization, and identifies RNS as a strong, theoretically grounded method for scalable GNN training.

Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.

Explaining graph neural networks (GNNs) has become more and more important recently. Higher-order interpretation schemes, such as GNN-LRP (layer-wise relevance propagation for GNN), emerged as powerful tools for unraveling how different features interact thereby contributing to explaining GNNs. GNN-LRP gives a relevance attribution of walks between nodes at each layer, and the subgraph attribution is expressed as a sum over exponentially many such walks. In this work, we demonstrate that such exponential complexity can be avoided. In particular, we propose novel algorithms that enable to attribute subgraphs with GNN-LRP in linear-time (w.r.t. the network depth). Our algorithms are derived via message passing techniques that make use of the distributive property, thereby directly computing quantities for higher-order explanations. We further adapt our efficient algorithms to compute a generalization of subgraph attributions that also takes into account the neighboring graph features. Experimental results show the significant acceleration of the proposed algorithms and demonstrate the high usefulness and scalability of our novel generalized subgraph attribution method.

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.

Video Capsule Endoscopy (VCE) poses a challenging multi-label temporal classification problem, requiring simultaneous localization of 8 anatomical regions and detection of 9 pathological findings across tens of thousands of frames. We present GALAR-TemporalNet v2, a hierarchical temporal model that addresses three core challenges: extreme class imbalance, long-range temporal dependencies, and pathology--anatomy entanglement. Our architecture combines windowed self-attention for local modeling, a Dual-Graph GCN for global frame relationships, and Bidirectional Mamba for selective boundary context encoding. A novel anatomy prototype residual pathway decouples pathological deviation signals from normal organ appearance, and a frame-level GCN skip connection stabilizes training of visually confusable rare classes. The competition version, GALAR-TemporalNet, achieved an overall mAP@0.5 of 0.2644 and mAP@0.95 of 0.2353 on the RARE-VISION test set. Following the competition, the redesigned GALAR-TemporalNet v2 -- incorporating a restructured pathology branch, refined loss functions, and extended post-processing -- improved these results to mAP@0.5 of 0.3409 and mAP@0.95 of 0.3333.

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.

Blind image quality assessment (BIQA) for ultrahighdefinition (UHD) images remains challenging because native-resolution inference is computationally expensive, whereas aggressive resizing or isolated cropping may suppress scale-sensitive distortions and weaken the relationship between local artifacts and global scene context. This paper aims to improve UHD-BIQA by explicitly modeling the structural dependencies among sampled image regions rather than treating them as independent views, and a graph representation learning framework UHD-GCN-BIQA is proposed. The framework samples aspect-ratio-aligned patches from each UHD image, encodes them as graph nodes, and constructs a hybrid k-nearest-neighbor graph using spatial proximity and feature similarity. Residual graph convolution is used to propagate contextual information across regions, and gated attention pooling aggregates patchlevel evidence into an imagelevel quality prediction. An exponential moving average normalized multiobjective loss function is adopted to stabilize the joint optimization of regression, correlation, and ranking objectives. Experiments on the UHD-IQA benchmark show that UHD-GCN-BIQA achieves PLCC = 0.7784, SRCC = 0.8019, and RMSE = 0.0519, obtaining competitive correlation performance and the lowest RMSE among the compared methods. These results indicate that graph-based region relation modeling is effective for UHD image quality assessment, particularly for improving absolute quality score estimation under high-resolution visual content.

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.

GraphRAG conditions language models on subgraphs retrieved from knowledge graphs, encoded via message-passing GNNs. Because these encoders entangle node contributions through iterated neighborhood aggregation, there is no closed-form way to determine how much each retrieved entity influenced the encoder's output, and therefore no way to faithfully audit what structural evidence actually reached the model. We introduce Ex-GraphRAG, which replaces the GNN encoder with a Multivariate Graph Neural Additive Network (M-GNAN), an extension of additive graph models to high-dimensional embedding spaces that yields an exact decomposition of the encoder's output across individual nodes and feature groups, without post-hoc approximation. On STaRK-Prime, this auditable encoder matches black-box performance. Using it to audit evidence routing, we uncover a semantic-structural mismatch: the nodes that dominate the encoder's output are structurally disconnected in the retrieved subgraph, held together by low-attribution intermediaries whose removal degrades multi-hop QA by up to 28%. This mismatch, invisible to any opaque encoder, reveals that semantic importance and structural connectivity are governed by disjoint sets of nodes, with direct implications for retrieval pruning, context construction, and failure diagnosis in graph-augmented LLMs.

We study fixed-cardinality maximization of the inverse-matrix Solow--Polasky diversity, equivalently finite metric magnitude for the exponential kernel, on one-dimensional and ordered metric sets. The analysis starts from the known finite-line gap formula for the exponential kernel, which writes the excess inverse-matrix diversity as a sum of functions of consecutive gaps. Building on this formula, the main interval theorem proves that, for every $k\geq 2$, the unique maximizing $k$-point subset of $[0,1]$ is the equally spaced set. Thus the objective selects a uniform gap representation on the real line. A converse kernel proposition shows that, among normalized non-increasing distance kernels, requiring the corresponding adjacent-gap additive structure forces the exponential family. Further results transfer the interval theorem to ordered $\ell_1$ (L1, or Manhattan) curves by isometry: the maximizing sets are uniform in accumulated $\ell_1$ length. As a consequence, monotone biobjective Pareto fronts admit Solow--Polasky optimal finite approximations that are uniformly spaced in accumulated objective-space change, a natural representation when all parts of a continuous front should be covered. Examples, including a dense connected front and a finite disconnected ZDT3 front, illustrate how the continuous uniform-gap result appears on discrete candidate sets. Solow-Polasky diversity; diversity measures; finite metric magnitude; L1 distance; uniform spacing; Pareto-front approximation; multiobjective optimization; fixed-cardinality subset selection

Real-time jet tagging is critical for identifying short-lived particle decays in the high-throughput detectors of the Large Hadron Collider, where real-time trigger systems responsible for deciding which collision events to store impose strict latency and accuracy constraints. While transformer architectures achieve the highest jet tagging accuracy when compute is unconstrained, their quadratic self-attention cost makes inference restrictive on trigger budget. Existing efficient variants reduce the computational cost, but hinder the classification performance. To address this limitation, we introduce the Patch Hierarchical Attention Transformer (PHAT-JeT), which combines two mechanisms: a physics-inspired geometric message-passing module that encodes local detector-plane structure, and a hierarchical patch-based attention scheme that computes exact attention within small particle groups while preserving global context through lightweight patch-token communication. Within a restricted budget, PHAT-JeT achieves state-of-the-art accuracy and background rejection among all resource-constrained jet tagging models on four benchmarks (\textsc{hls4ml}, JetClass, Top Tagging, and Quark--Gluon). Our code is available at https://github.com/aaronw5/PHAT-JeT.

Equivariant graph neural network (GNN) methods for antibody complementarity-determining region (CDR) design achieve the highest sequence recovery but suffer from severe vocabulary collapse. The current best GNN methods over-predict very few amino acids, such as tyrosine and glycine, while ignoring functionally important residues. We trace this failure to GNN encoders learning amino acid distributions de novo from limited structural data, discarding substitution patterns encoded in evolutionary databases. To resolve this, we propose EvoStruct, which bridges a frozen protein language model (PLM) with 3D structural context from an E(3)-equivariant GNN via a cross-attention adapter. Unlike prior PLM-structure adapters for general protein design, EvoStruct targets the vocabulary collapse problem specific to CDR design through progressive PLM unfreezing and R-Drop consistency regularization. On the CHIMERA-Bench dataset, EvoStruct achieves the highest amino acid recovery and lowest perplexity among several antibody design methods, improving sequence recovery by 16% and reducing perplexity by 43% relative to the best GNN baselines, while recovering 2.3x greater amino acid diversity and the highest binding-pair correlation with ground truth.

Precise measurement of the kinematic Sunyaev-Zel'dovich (kSZ) effect - a probe of the large-scale distribution of baryonic matter, a key observable for cosmological inference - requires accurate reconstruction of galaxy velocities from spectroscopic surveys. The signal-to-noise ratio (SNR) of kSZ measurements scales directly with the correlation coefficient $r$ between reconstructed and true velocities. We introduce Velocityformer, an equivariant graph transformer architecture designed to match the specific symmetry of the observational data. While the underlying physics is equivariant with respect to translations and rotations, observational effects break this symmetry due to the preferred line-of-sight direction. Matching the model's inductive bias to the data's broken symmetry consistently improves performance across all model sizes and training volumes, with Velocityformer improving $r$ by 35% over the standard linear theory baseline and outperforming ML baselines at every data volume. By matching the model's inductive bias to the data and conditioning on the physics-based long-wavelength solution, Velocityformer is highly data-efficient, training to high accuracy on as few as 4 low-fidelity simulations, and generalises zero-shot across input geometry, cosmological parameters, and galaxy sample. On high-fidelity simulated galaxy catalogues, this yields a 30% improvement in $r$ over the physical baseline, directly translating to the same SNR gain on observational data.

Relational prediction tasks are fundamental in many real-world applications, where data are naturally stored in relational databases (RDBs). Relational Deep Learning (RDL) addresses this problem by modeling RDBs as graphs and applying graph neural networks (GNNs) for end-to-end learning. However, the full-resolution property is commonly adopted as a design principle in graph construction for RDBs to preserve relational semantics, which leads most existing methods to rely on fixed graph structures. In this paper, we propose FROG, a Full-Resolution and Optimizable Graph Structure Learning} framework for RDL that formulates relational structure learning as a learnable table role modeling problem, allowing tables to contribute as nodes and edges in message passing. We further design role-driven message passing mechanisms to capture relational semantics, enabling joint optimization of graph structure and GNN representations. To ensure semantic consistency, we introduce functional dependency constraints that regularize representations across table and entity levels. Extensive experiments demonstrate that our method outperforms existing approaches and reveal how table roles impact downstream tasks, offering new insights into graph construction for RDL

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing. However, these approaches inherently suffer from the oversmoothing problem, where node features become indistinguishable as the network depth increases. Inspired by the Navier Stokes equations, we introduce Graph Navier Stokes Networks (GNSN), a novel architecture that transcends conventional diffusion-based message passing by incorporating convection into graph structures. GNSN defines a dynamic velocity field on the graph to govern convection, enabling more efficient and direct message propagation. By adaptively balancing convection and diffusion, GNSN is able to efficiently handle datasets with varying levels of homophily. Extensive evaluations across twelve real-world datasets demonstrate that GNSN consistently outperforms state-of-the-art baselines in classification accuracy. Moreover, experimental results further emphasize its effectiveness in alleviating the oversmoothing problem.

Subterranean (SubT) environments have been a frontier for autonomous robotics, driven by the push for automation of mining operations and the interest in planetary exploration (Martian Lava Tubes). Due to the challenges involved in accessing real SubT environments, rigorous hardening of autonomy stacks in realistic simulation environments is critical. This article fills a well-known gap, which relates to the unavailability of a large-scale simulation-based benchmarking infrastructure for rigorous statistical evaluation of robotic autonomy, due to which it is common for SubT research articles to present validation results in a few environments at best. This article presents SubTGraph, a novel framework for rapid synthesis of multi-level SubT environments with high variability, incorporating user specifications related to topology, dimensionality, textures, etc., to generate distinct environments such as operational mines, natural caves and lava tubes. SubTGraph builds a cost matrix from user-specified structural constraints to guide the classical Dijkstra algorithm to procedurally generate SubT worlds utilizing topometric tiles from the DARPA World Generator. Three robotics case-studies are investigated to demonstrate the utility of SubTGraph for rigorous validation of different layers in the robotic autonomy stack. Structural semantic segmentation is validated against topometric ground truths, multi-agent path planning is widely tested for identification of patterns and trends in the algorithm behavior and LIO SLAM is stress-tested in challenging subterranean sections to identify failure cases. The SubTGraph world creation codebase is open-sourced (https://github.com/LTU-RAI/SubTGraph.git) along with a database consisting of 150 highly variable underground worlds.

Machine learning interatomic potentials (MLIPs) achieve excellent accuracy when trained on large Density Functional Theory (DFT) data. To be useful in practice, they must often be adapted to target chemistries using small and expensive task-specific datasets. However, MLIPs transfer inconsistently across domains, with representations that often loose accessible composition and structure information. To address this, we present TriForces, a model-agnostic three-stream framework that separates composition and structure information, combined with self-supervised learning to preserve transferable representations. TriForces improves performance on MatBench and QM9 over baselines without needing DFT labels and enables efficient similar structure retrieval through its learned latent space. On OMat24, in limited-data training regime, TriForces reduces energy MAE by 57% at 20K samples only and improves force MAE across sample sizes. We release pretrained TriForces variants across multiple MLIP architectures with code at https://github.com/Ramlaoui/triforces.