Graph Neural Networks

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each recommended item is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens nodes evaluations.

We study the contradiction graphs associated with binary concept classes. For a class $H \subseteq \{0,1\}^X$, the order-$m$ contradiction graph $G_m(H)$ has as vertices the $H$-realizable labeled sequences of length $m$, with two vertices adjacent when the two sequences assign opposite labels to some common domain point. Our main result is that the single graph $G_m(H)$ determines the threshold predicate $\mathrm{VCdim}(H)\ge m$. Consequently, the full sequence $(G_m(H))_{m \ge 1}$ determines the exact VC dimension and, in particular, detects finite versus infinite VC dimension, answering a question posed by Alon et al. (2024).

Distillation transfers knowledge from a large model trained on broad data to a smaller, more efficient model suitable for deployment. In structured prediction settings, prior knowledge about the task can guide the choice of a target architecture that is algorithmically aligned with the underlying problem. Building on recent learning-theoretic analyses of decision-tree (DT) distillation (Boix-Adsera, 2024), we study when distillation succeeds for combinatorial optimization tasks. We focus on the case where the target model is a graph neural network whose architecture is aligned with a dynamic programming (DP) algorithm for the task. Assuming that the source model is sufficiently rich, formalized through the linear representation hypothesis (LRH) (Elhage et al., 2022; Park et al., 2024), we show that the distillation problem can be solved efficiently in the complexity parameters of the DP transition function, represented as a DT. Our results provide a rigorous sufficient condition for successful distillation in the flavour of algorithmic alignment.

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

We introduce Contrastive FUSE, a fast and unified framework for scalable node representation learning in graphs with partially available pairwise node labels and no available node features. Unlike existing methods, we directly optimize a spectral contrastive objective that integrates community-aware structural signals with signed pairwise constraints. To support large-scale training, we replace the expensive modularity gradient with a lightweight approximation, which preserves the structure-seeking behavior of modularity while reducing the computational cost significantly. This yields an efficient optimization scheme with a natural gradient decomposition and adaptive learning-rate scaling, enabling fast iterative updates even on million-edge graphs. Extensive experiments on benchmark citation networks, large co-purchase graphs, and OGB datasets show that Contrastive FUSE achieves competitive or superior contrastive classification performance without relying on node features, while offering substantial runtime gains over existing baselines. These results highlight the effectiveness of coupling modularity-inspired structural learning with contrastive supervision for efficient and scalable contrastive node representation learning.

Predicting protein-ligand binding affinity remains intractable for multi-domain proteins, where inter-domain dynamics govern molecular recognition. Existing geometric deep learning methods typically treat proteins as monolithic static graphs, suffering from rigid-body assumptions and aleatoric noise in flexible regions. To address this, we introduced HCLBind, a self-supervised framework that decouples geometric representation learning from affinity regression. HCLBind leverages a general-to-specific pre-training paradigm on the Q-BioLiP database to learn a robust physical grammar of binding. We propose a novel hierarchical decoy strategy: the model learns local physicochemical constraints through protein coordinate perturbation in single-domain proteins and global conformational geometry through inter-domain rotation in multi-domain complexes. Our hybrid architecture integrates a domain-gated graph attention network and cross-modal attention to explicitly prioritize domain interfaces. Furthermore, we employ LoRA on protein and ligand foundation models, ensuring efficient optimization while preserving evolutionary knowledge. Experiments on PDBBind demonstrate that HCLBind effectively learns discriminative interface features and provides robust uncertainty estimation, overcoming the limitations of standard supervised learning. The code is available at https://github.com/jiankliu/HCLBind.

We introduce B-cos GNNs, an inherently explainable class of graph neural networks whose predictions decompose exactly into per-node, per-feature contributions via a single input-dependent linear map. B-cos GNNs use linear (sum-based) aggregation and replace non-linear message and update functions with B-cos transforms. This induces meaningful, task-specific weight-input alignment that is directly accessible through the model's dynamic linearity. Instance-level explanations follow from a single forward and backward pass, requiring no auxiliary explainer, modified learning objective, or perturbation procedure. Instantiated as a GIN, our approach trades small losses in predictive accuracy for state-of-the-art explainability across diverse synthetic and real-world benchmarks, producing explanations orders of magnitude faster than post-hoc baselines.

Community detection is a central problem in graph analysis, with applications ranging from network science to graph signal processing. In recent years, Graph Neural Networks (GNNs) have emerged as effective tools for learning low-dimensional representations of graph-structured data and have shown strong performance in clustering tasks, particularly on large and high-dimensional graphs. This paper investigates the use of GNN-based community detection within a graph signal interpolation framework. After reviewing the main classes of GNN architectures for community detection according to a standard taxonomy, we integrate the resulting graph communities into a Partition of Unity Method (PUM) for interpolation with Graph Basis Functions (GBFs). In this approach, GNN-derived communities are used to construct local subdomains on which GBF interpolants are computed and subsequently combined into a global approximation. Numerical experiments on benchmark %graph datasets, including geometric and urban network examples demonstrate that the proposed combination of GNN-based clustering and GBF-PUM interpolation yields accurate signal reconstructions. The results indicate that deep learning-based community detection can provide effective graph partitions for localized interpolation schemes, supporting its use in scalable graph signal analysis.

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

Dental aerosol procedures produce sub-50 micrometre nuclei that can remain airborne for long periods in enclosed clinics, creating pathways for airborne pathogen transmission. Reynolds-Averaged Navier-Stokes (RANS) simulations with Euler-Lagrange particle tracking capture this transport accurately but require very long run times per scenario, which precludes real-time clinical decision support in 3D. We present the Eulerian-Lagrangian Graph Interaction Network (ELGIN), a physics-informed graph surrogate that jointly predicts carrier-flow dynamics on the OpenFOAM polyhedral mesh and the per-parcel motion of the polydisperse spray cloud. ELGIN couples a multi-head Graph Transformer with Jacobi-preconditioned learnable pressure projection and a turbulence-closure head to a sigmoid-gated Lagrangian Interaction Network through differentiable inverse-distance mesh-parcel coupling, and advances parcels with a symplectic Stormer-Verlet integrator. A four-stage physics-informed curriculum stabilises 260-step autoregressive rollouts without gradient explosion. A parameter sweep with foam-extend 4.1 OpenFOAM reactingParcelFoam across clinically relevant ventilation rates and handpiece spray speeds provides CFD ground truth. This article reports a single-case demonstration in which both ELGIN and a Lagrangian-only baseline (M0) are trained and evaluated on Sweep_Case_03 of a twenty-case sweep; full 16/2/2 retraining is in progress and will replace all reported metrics. On this case, ELGIN tracks the foam-extend particle cloud much more closely than M0: mean parcel displacement error falls from 19.56% to 16.20% of room width and cloud radius-of-gyration error from 9.85% to 6.58%. A 26-second rollout completes in ~64 s on a 4 GB GPU, approximately 37x faster than the foam-extend reference pipeline, toward per-appointment infection-risk screening once the multi-case checkpoint is in place.

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S&P 500 equities from 2015-2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph weighted by pairwise distances, without requiring any prior vector representation of the data. The embedding is obtained by solving a variational problem that matches local, on-graph distances to the Euclidean metric, induced by the differentials of the embedding functions. The resulting Euler-Lagrange equations are derived in a coordinate-free form, enabling direct evaluation of all operators from the distance graph alone. Though non-linear and missing an explicit expression for their non-linearity, these equations are shown to be resolved as an iteratively updated sparse linear problem. The main contributions of the proposed approach are (a) the derivation of the functional equations governing the optimal Euclidean embedding in the continuum, (b) a representation-free formulation that requires only a neighborhood distance graph and no feature vectors and (c) an estimation procedure based exclusively on local graph operations. We experimentally evaluate the resulting non-parametric algorithm on synthetic manifolds and real datasets, demonstrating consistent preservation of local metric structure and neighboring relations, while approximating the global isometric embedding.

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

Deep Graph Neural Networks (GNNs) are essential for capturing complex dependencies in graph-structured data. However, scaling GNNs to depth remains challenging, as stacking layers leads to representation collapse and diminishing sensitivity due to repeated aggregation. While Neural Sheaf Diffusion (NSD) provides strong theoretical guarantees against such collapse, these guarantees do not translate to practice: as depth increases, the disagreement signal of the sheaf Laplacian vanishes, limiting the contribution of deeper layers. We identify mechanisms that hinder NSD effectiveness at depth and propose \emph{Deep Neural Sheaf Diffusion} (DNSD), which replaces the sheaf Laplacian with a sheaf adjacency operator to maintain informative signals across layers. This is complemented by normalization, odd nonlinearities, and gating. To provide a principled explanation of the expected performance improvement, we contrast sheaf diffusion to graph attention mechanisms, highlighting that DNSD replaces scalar attention scores with matrix-valued edge functions and normalizes node representations rather than attention scores. We demonstrate empirically that DNSD effectively utilizes deep aggregation in graph tasks, outperforming GNN and NSD baselines with up to 30pp accuracy on synthetic long-range datasets, and consistently outperforming them on real-world benchmarks. These results position sheaf-based architectures as a promising building block for graph foundation models by supporting effective deep architectures.

Pre-training on text-attributed graphs (TAGs) is central to building transferable graph foundation models, where LLM-as-Aligner methods align graph and text representations through the semantic knowledge of large language models. However, these methods usually assume that node texts provide sufficient and reliable supervision, an assumption often violated in real-world sparse TAGs. When textual anchors are missing, noisy, or uneven across domains, graph structures must be aligned with weak semantic evidence, leading to unreliable structure-semantics correspondence and sparsity-induced transfer bias. This paper presents S2Aligner, a sparsity-aware and structure-enhanced LLM-as-Aligner framework for graph-text pre-training on sparse TAGs. The key idea is to decouple semantic alignment from structural modeling, allowing topology-aware signals to enhance alignment without contaminating the shared semantic space. Specifically, S2Aligner decomposes graph-text representations into semantic and structural components, uses structure-oriented reconstruction with consistency control to inject reliable topology cues into text representations, and suppresses inconsistent structural signals under textual sparsity. Moreover, S2Aligner introduces sparsity-aware cross-domain risk balancing, which calibrates domain risks through a global-domain density ratio and downweights unreliable sparse samples via graph reliability estimation. Theoretical analysis shows that this objective reduces cross-domain generalization gaps by controlling domain risk discrepancy. Extensive experiments across diverse graph domains, sparsity levels, and downstream tasks demonstrate that S2Aligner consistently outperforms existing baselines.

Graph Neural Networks (GNNs) and Graph Transformers (GTs) are now a fundamental paradigm for graph learning, combining the representation-learning capabilities of deep models with the sample efficiency induced by their inductive biases. Despite their effectiveness, a large body of work has shown that these models still face fundamental limitations in tasks that require capturing correlations between distant regions of a graph. To address this issue, we introduce Graph Hierarchical Recurrence (GHR), a novel framework that operates jointly on the input graph and on a hierarchical abstraction obtained through pooling. We also show that the limitations of existing models are even more pronounced in out-of-range generalization, where test instances involve interactions over distances longer than those observed during training. By contrast, despite its simple design, GHR provides three key advantages: strong performance on long-range dependencies, improved out-of-range generalization, and high parameter efficiency. To corroborate these claims, we show that across a broad set of long-range benchmarks, GHR consistently outperforms existing graph models while using as little as 1% of the parameters of current state-of-the-art models. These results suggest a complementary direction to the current trend of scaling architectures to obtain graph foundation models, indicating that increased model capacity alone may not be sufficient for generalization.

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and structural anomalies that break standard metric properties. We show that such misspecification pushes the data-generating distribution outside the model class, causing Bayesian inference to become overconfident and poorly calibrated. To address this, we propose a generalized posterior framework for random geometric graphs. We introduce Link-Sequential R-SafeBayes, a method that exploits dyadic conditional independence to estimate prequential risk and adaptively tune posterior regularization. Experiments on synthetic and real-world networks demonstrate improved calibration, better link prediction performance, and a reliable criterion for selecting latent geometries across Euclidean, spherical, and hyperbolic spaces.

We introduce Graph-Augmented Sequence-to-Sequence (GA-S2S), a novel framework that integrates a T5-small encoder-decoder with a Relational Graph Attention Network (RGAT) to improve link prediction in knowledge graphs. While existing Seq2Seq models rely solely on surface-level textual descriptions of entities and relations and at best, flatten the neighborhoods of a query entity into a single linear sequence, thereby discarding the inherent graph structure, GA-S2S jointly encodes both textual features and the full $k$-hop subgraph topology surrounding the query entity. By integrating raw encoder outputs with RGAT's relation-aware embeddings, our model captures and leverages richer multi-hop relational patterns and textual information. Our preliminary experiments on the CoDEx dataset demonstrate that GA-S2S outperforms competitive Seq2Seq-based baseline models, achieving up to a 19% relative gain in link prediction accuracy.

Existing Multivariate Time Series Anomaly Detection (MTSAD) frameworks increasingly rely on integrating Graph Neural Networks (GNNs) with sequence models to capture complex spatio-temporal dependencies. However, less attention is paid to the spatial over-generalization problem, where unconstrained structural modeling indiscriminately reconstructs anomalies, inevitably degrading detection recall. To tackle this problem, we propose a novel framework that unifies spatio-temporal modeling through a joint prior-observation adversarial learning paradigm. In the spatial dimension, the model alternately learns adjacency matrices as structural prior and models the association discrepancy between prior and data-driven observation in a minimax manner during training. Such adversarial optimization not only improves the model sensitivity for time-wise detection, but also enables the model to localize anomalies to specific channels. To systematically evaluate this anomaly localization capability, we further construct a synthetic benchmark equipped with precise channel-wise annotations. Extensive experiments across public datasets and our dedicated benchmark demonstrate that the proposed framework establishes a new state-of-the-art in both time-wise detection and spatial localization tasks. Our code, pre-trained models, and benchmark are publicly available at https://github.com/anocodetest1/POST.

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

Acquisition and creation of 3D assets have been largely view- or appearance-driven. As a result, existing digital 3D models often lack the requisite structural components to function as intended, such as joints, supports, interiors, or interaction elements. At the same time, even human-annotated motions are frequently error-prone, leading to physically implausible behavior. We introduce object functionalization, a novel task aimed at transforming visually plausible but non-functional 3D models into functional and physically operable ones. We formulate functionalization as a graph completion problem over a new functional graph representation, where labeled nodes represent object parts, labeled edges encode functional and contact relations, and movable nodes carry motion attributes, so that structural functional deficiencies manifest as missing nodes or incorrect edges. We develop a neural Graph Functionalizer (GraFu) to complete an incomplete graph representing a non-functional 3D object. The completed graph then drives a geometry realization stage that instantiates predicted connectors and structural elements in 3D, with the compelling side effect of rectifying erroneous human-annotated and predicted motions. To support training and evaluation, focusing on furniture as a rich and challenging target category, we introduce FurFun-233, a dataset of 233 paired non-functional and functionalized furniture models. On PartNet-Mobility ("zero-shot") and HSSD test sets, our method matches state-of-the-art methods in motion prediction accuracy while substantially improving functionality in terms of collision and connectivity.

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

The expressive limitations of message-passing Graph Neural Networks (GNNs) have motivated a wide range of more powerful graph learning architectures. We advocate Deep Homomorphism Networks (DHNs) as a model particularly well-suited for learning over relational databases, due to their close connection to important fragments of SQL such as conjunctive queries. We study the precise expressive power of DHNs by relating them to various natural fragments and extensions of first-order logic (FO). For DHNs with max, sum, and mean aggregations, we establish connections to the unary negation fragment (UNFO) and to the extensions of UNFO with counting quantifiers and with ratio quantifiers. We further relate sum-aggregation DHNs to the unary quantifier alternation fragment of FO and to an extension of FO with expressive counting. Through the classical correspondence between FO and SQL, these results also illuminate the relation between DHNs and SQL. They also enable us to study the decidability of two fundamental static analysis problems for DHNs, the emptiness problem and the subsumption problem. Finally, we confirm through experiments that the established differences in expressive power are reflected in the performance on suitable prediction tasks.

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

The U.S. financial system processes approximately 1.3 million interbank transactions daily, yet no system in the reviewed literature models fraud propagation across the interbank network using fraud co-occurrence edge features. Prior interbank GNN architectures model credit contagion using credit distress supervision signals, producing systems misaligned for fraud forensics. No existing system generates SAR narratives with per-assertion forensic traceability to specific numerical detection outputs, creating regulatory auditability gaps in FinCEN-submitted reports. This paper introduces SCAFDS (Systemic Contagion-Aware Fraud Detection System), a seven-stage integrated surveillance pipeline addressing five structural limitations of prior art: (1) fraud-specific interbank topology encoding using fraud co-occurrence frequency metrics f(u,v,t) derived from FinCEN SAR registry records; (2) edge-feature-informed graph attention where coefficients are computed from both node representations and fraud co-occurrence edge features; (3) bilinear fraud co-occurrence risk fusion producing institution-level systemic fraud risk scores; (4) attribution-conditioned SAR narrative generation with per-assertion significance thresholds ensuring each FinCEN SAR assertion is traceable to a specific numerical pipeline output; and (5) topology-aware adaptive forensic feedback updating graph attention weights from regulatory dispositions. Experiments on the IEEE-CIS Fraud Detection Dataset (590,540 transactions) and a synthetic FDIC-aligned interbank network (8,103 institutions, 169,800 edges) show SCAFDS achieves AUPRC=0.515+/-0.032 and AUROC=0.802+/-0.018, representing +15.9pp and +13.7pp improvements over GraphSAGE-AML. Partial validation on FDIC enforcement action records (n=4,279) confirms consistent model ranking. USPTO Provisional Patent Application No. 64/061,083, filed May 8, 2026.

Learning causal relations from observational data is challenging because the graph search space grows super-exponentially with the number of variables. Ordering-based methods reduce this space by first identifying the topological ordering, whereas continuous optimization methods explore most likely regions of the space by casting DAG learning as a differentiable objective with an acyclicity constraint. Despite their conceptual appeal, both paradigms face significant scalability limitations in high-dimensional settings, restricting their practical applicability. In this work, we introduce a new formulation for linear causal discovery that tightly integrates these two paradigms to achieve substantial gains in scalability without sacrificing accuracy. Our approach, TriOpt, decomposes the problem into two efficient stages. First, it recovers the topological ordering by exploiting the Sherman-Morrison rank-1 downdate together with the additive structure of linear kernels, enabling fast and scalable ordering estimation. Second, given this ordering, we reformulate structure learning as a convex continuous optimization problem that entirely avoids the need for enforcing costly acyclicity constraints. We theoretically show that, under the true ordering, TriOpt exactly recovers the underlying linear DAG. Empirically, across synthetic, semi-synthetic, and real-world datasets, TriOpt achieves orders-of-magnitude speedups over state-of-the-art linear causal discovery methods in high-dimensional regimes, while maintaining comparable or superior accuracy.

Coordination graphs are a central abstraction in cooperative multi-agent reinforcement learning (MARL), yet existing sparse-graph learners lack a theoretically grounded mechanism to decide which edges should exist and how much information each edge should carry. Current methods rely on heuristic criteria that offer no formal guarantee on the learned topology, and no principled way to allocate different communication capacities to structurally different agent relationships. To address this, we propose Heterogeneous Information-Bottleneck Coordination Graphs (HIBCG), which learns a group-aware sparse graph in which both edge existence and message capacity are theoretically justified. With the graph information bottleneck (GIB) serving as the underlying tool, HIBCG first constructs a group-aligned block-diagonal prior that provides a closed-form criterion for edge retention -- determining which edges should exist and at what density per group block -- and then controls per-agent feature bandwidth on the resulting topology, compressing messages to retain only task-relevant content. We prove that the group-aligned prior strictly tightens the variational bound on topology learning, that the objective decomposes per group block, enabling differential edge control, and that capacity allocation follows a water-filling principle.

Sparse matrix reordering can significantly reduce the fill-in during matrix factorization, thereby decreasing the computational and storage requirements in sparse matrix computations. Finding a minimal fill-in ordering is known to be an NP-hard problem. Moreover, there is a paradox: matrix reordering is applied before matrix factorization, but fill-ins that matrix reordering methods aim at are generated from matrix factorization. To bridge the gap between reordering and factorization, we propose a deep learning framework to minimize a fill-in surrogate function based on spectral embedding. First, we employ a multi-grid-like GNN architecture to learn to approximate the smallest eigenvectors of its graph Laplacian matrix, i.e. spectral embedding, and capture the global structural information of the matrix. Then, another multi-grid-like GNN architecture is used to minimize the potential space where fill-in can occur based on the rank distribution. Experimental results indicate that our approach achieves competitive performance compared with traditional graph-theoretic algorithms and deep learning methods.

Graph Neural Networks (GNNs) are powerful tools for learning from graph-structured data, but their scalability is increasingly strained by the size of real-world graphs in domains like recommender systems, fraud detection, and molecular biology. Graph condensation -- the task of generating a smaller synthetic graph that retains the performance of models trained on the original -- has emerged as a promising solution. However, the dominant approach of gradient matching introduces a fundamental contradiction: it requires training on the full dataset to create the compressed version, thereby undermining the goal of efficiency. Worse still, these methods suffer from high computational overhead, poor generalization across GNN architectures, and brittle reliance on specific model configurations. Equally concerning is the community's reliance on misleading evaluation protocols such as node compression ratios, which fail to reflect true resource savings, condensation overhead, and illusory application to neural architecture search. These shortcomings are not incidental -- they are systemic, and they obstruct meaningful progress. In this position paper, we argue that graph condensation, in its current form, needs a reset. We call for moving beyond full-dataset training and model-dependent design, and instead advocate for methods that are lightweight, architecture-agnostic, and practically deployable. By identifying key methodological flaws and outlining concrete research directions, we aim to reorient the field toward approaches that deliver on the true promise of condensation: efficient, generalizable, and usable GNN training at scale.

Node representation learning, such as Graph Neural Networks (GNNs), has emerged as a pivotal method in machine learning. The demand for reliable explanation generation surges, yet unsupervised models remain underexplored. To bridge this gap, we introduce a method for generating counterfactual (CF) explanations in unsupervised node representation learning. We identify the most important subgraphs that cause a significant change in the k-nearest neighbors of a node of interest in the learned embedding space upon perturbation. The k-nearest neighbor-based CF explanation method provides simple, yet pivotal, information for understanding unsupervised downstream tasks, such as top-k link prediction and clustering. Consequently, we introduce UNR-Explainer for generating expressive CF explanations for Unsupervised Node Representation learning methods based on a Monte Carlo Tree Search (MCTS). The proposed method demonstrates superior performance on diverse datasets for unsupervised GraphSAGE and DGI.

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

Social engineering attacks exploit human trust rather than software vulnerabilities, making them difficult to detect using conventional filters. We propose a two-stage filter-then-verify framework combining inductive Graph Neural Networks (GNNs) for structural anomaly detection with a co-attention ModernBERT model for content verification. The GNN identifies anomalous sender-receiver patterns, while BERT analyzes message context to reduce false positives. Using the Enron dataset augmented with realistic synthetic campaigns, we show that the framework achieves 86% recall in structural filtering and over 92% precision after BERT refinement, effectively detecting both external attacks and insider threats. Our results demonstrate that combining structural and content analysis allows practical, scalable detection of multi-stage social engineering attacks in email networks.

Scientific artifacts such as models and datasets are foundations for research. With the rapid growth of platforms like HuggingFace, researchers now have access to a large number of artifacts. Yet, a key challenge remains: how can we automatically discover the state-of-the-art (SOTA) model for a given dataset by fully leveraging existing artifacts? We formalize this task as automatic SOTA discovery by modeling HuggingFace as an artifact graph, where nodes are models/datasets and edges represent evaluations. We propose ArtifactLinker, a two-stage framework: (1) ranking promising unobserved model--dataset links using Graph Neural Networks (GNNs) or graph-augmented Large Language Models (LLMs), and (2) verifying top-ranked links via coding experiments with LLM-based agents. We further introduce a benchmark named ArtifactBench with 14,053 artifacts and 51,337 relations to evaluate the performance of both stages. Results show that (1) graph structures between existing artifacts are effective for missing link prediction; (2) end-to-end ranking and verification with ArtifactLinker help discover potential SOTA results and research insights.

We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2 tensor channels aligned with the decomposition of polarizability into isotropic and anisotropic components. In contrast to approaches that construct tensor outputs only at readout, our model propagates tensor structure throughout message passing using geometrically motivated tensor bases. This yields a target-aligned architecture for tensor-valued molecular prediction. On optimized QM7-X geometries, the proposed model achieves lower full-tensor and anisotropic error than both a PaiNN-style readout baseline and a dielectric MACE baseline under matched training conditions and at nearly identical parameter count. In this controlled setting, it also outperforms MACE while remaining substantially faster at inference. Ablation studies show that the gain does not arise from increased capacity alone, but from the combination of explicit tensor propagation and a traceless target parameterization matched to the anisotropic part of the polarizability tensor. Among the tensor bases considered, the strongest results are obtained from interactions between learned directional features, indicating that these are particularly effective for modeling molecular polarizability. Rotational equivariance tests further confirm that all compared models are numerically equivariant, so the observed improvements are attributable to better learning of the target tensor itself. Overall, our results show that for structured tensor-valued targets, propagating target-aligned tensor features can outperform both readout-only tensor construction and a more general higher-order equivariant model in the present training setting.

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

Graph neural networks (GNNs) have achieved remarkable success in relational learning. However, their vulnerability to graph backdoor attacks (GBAs) poses a significant barrier to broader adoption in high-stakes applications. Despite recent advances in graph backdoor defense (GBD), existing methods primarily focus on subgraph-based GBAs, relying on the assumption that poisoned target nodes are explicitly connected to subgraph triggers. Our empirical results reveal that such structure-centric approaches fail to defend against emerging feature-based GBAs that preserve graph topology. Therefore, in this paper, we study a novel problem of universal graph backdoor defense. First, we investigate the shared effects of both attack types from a feature-based homophily perspective, which characterizes local feature consistency between nodes and their neighborhoods. Thorough theoretical and empirical analyses demonstrate that, regardless of trigger mechanisms, backdoors induced by GBAs exhibit lower feature-based homophily than clean nodes, indicating a discrepancy in local feature similarity. Motivated by this insight, we propose to leverage node-level local feature consistency, modeled by a neighbor-aware reconstruction loss, to distinguish backdoors from clean nodes. Then, a robust training strategy is developed to eliminate trigger effects while reducing noise induced by detection uncertainty. Extensive experiments demonstrate that our framework significantly degrades the attack success rate and maintains competitive clean accuracy under both subgraph-based and feature-based attacks.

The quality of graph-structured data is fundamental to the success of modern graph analysis techniques such as Graph Neural Networks (GNNs). However, real-world graph data is often suboptimal, suffering from issues such as noise and incomplete connections. Graph Structure Learning (GSL) has emerged as a promising technique that adaptively optimizes node connections. However, we observe that the effectiveness of GSL often comes at the cost of a dramatic expansion in edge count, resulting in significant storage and computational overhead. In this work, we reveal that this limitation stems from the prevalent use of similarity-based edge construction, which predominantly connects highly similar neighbors based on their embeddings, introducing substantial structure redundancy. To address this, we propose a novel Informative Graph Structure Learning method (InGSL), which jointly considers both similarity and diversity in edge construction by incorporating a mutual-information-guided learning strategy. Notably, InGSL serves as a plug-in module that can be seamlessly integrated into existing GSL frameworks. Through extensive experiments on six representative GSL methods, we demonstrate that InGSL achieves significant performance improvements at a reduced number of edges.

Traffic forecasting is a significant part of intelligent transportation systems. One of the critical challenges of traffic forecasting is to find spatio-temporal correlations. In recent years, graph convolutional networks and graph attention networks have replaced traditional statistical models to predict future traffic. However, it is complicated for both of them to allow vertices to have far different characters. To address this, we propose the Global-Local Graph Attention Network (GLGAT) with pairwise encoding and the event-based adjacency matrix. The GLGAT allows vertices to have a global attention matrix set for the whole graph and assigns local attention matrix sets to each vertex. Experiments on two real-world traffic datasets show that GLGAT can effectively capture spatio-temporal correlations and has competitive performance against other state-of-the-art baselines.

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

Relational databases store much of the world's structured information, and they are essential for driving complex predictive applications. However, deep learning progress on relational data remains limited, as conventional approaches flatten databases into single tables via manual feature engineering, discarding relational context. Relational deep learning (RDL) addresses this by modeling databases as relational entity graphs (REGs) for graph neural networks (GNNs), but remains task- and database-specific. To combine the strengths of both paradigms, we propose a hybrid architecture combining a fine-tuned BART encoder to capture intra-row semantics with a GraphSAGE-based GNN over REGs to inject relational context. Experiments on RelBench show that the GNN substantially enriches BART's row embeddings, achieving a ROC-AUC of 67.40 on the driver-dnf task from the rel-f1 dataset. This performance is competitive with supervised baselines such as LightGBM (68.86) and narrows the gap to RDL (72.62) to within 5.22 points, though a substantial gap remains to state-of-the-art foundation models such as KumoRFM (82.63). These results suggest that lightweight hybrid LM-GNN architectures offer a promising and resource-efficient path towards foundation models for relational databases.

Heterogeneous Graph Prompt Learning (HGPL)has emerged as a promising paradigm for bridging the gap between the objectives of pre-training foundation models and their downstream applications in heterogeneous graph settings. However, existing HGPL methods are primarily designed for in-domain scenarios, whereas real-world deployments often span multiple domains, and the data used for pre-training and downstream tasks may originate from different distributions. Consequently, the applicability of current HGPL approaches is limited to in-domain settings, and their performance typically degrades when application domains shift. To address this serious limitation, we develop CHoE, a cross-domain HGPL method built upon an expert network. During pre-training, we introduce and train structure-conditioned experts, and during prompt tuning, we adopt a structure-aware expert routing and load balancing mechanism to select structurally compatible experts for each meta-path view. In addition, we design a prompt-based semantic fusion module to integrate representations across multiple views for downstream prediction. Extensive experiments show that CHoE consistently improves performance in few-shot cross-domain applications, outperforming all baseline approaches.

Multimodal alignment is commonly learned from isolated image-text pairs via CLIP-style dual encoders, leaving the relational context among entities largely unused. Multimodal attributed graphs (MAGs), where nodes carry multimodal attributes and edges encode corpus structure, provide a natural setting for refining frozen vision-language embeddings. This refinement is challenging: visual, textual, and cross-modal relations often induce different neighborhood geometries, while unrestricted graph propagation can quickly over-smooth retrieval representations. Effectively leveraging graph context therefore requires simultaneously breaking modality-specific topological barriers, controlling the smoothing regime, and preserving informative smoothing before semantic boundaries collapse. We propose Graph-Optimized Multimodal Alignment (GOMA), a structure-driven post-alignment framework that views frozen multimodal embeddings as graph signals and addresses these requirements through a unified retrieval-oriented design. GOMA decouples three key design choices: where messages should flow, how multimodal evidence should propagate, and which smoothing depth should be retained. Concretely, it learns modality-aware propagation operators, performs finite-step coupled smoothing without diagonal cross-modal shortcuts, and adaptively reads out node-specific smoothing trajectories to preserve useful smoothing before collapse. All experiments follow a transductive MAG retrieval protocol where the graph serves only as unlabeled context and diagonal self-pair edges are removed. On seven MAG benchmarks, GOMA achieves state-of-the-art or tied state-of-the-art retrieval and remains substantially more stable than the strongest graph competitor, demonstrating that MAG structure can serve as an effective post-encoder for frozen multimodal embeddings.

Data selection seeks to identify a compact yet informative subset from large-scale training corpora, balancing sample quality against collection diversity. We formulate this problem as a Weighted Independent Set (WIS) on a similarity graph, where nodes represent data samples weighted by influence, and edges connect semantically redundant pairs. This formulation naturally yields subsets that are simultaneously high-quality and diverse. However, two challenges arise in practice: naive node weights fail to distinguish informative signals from gradient noise, and edge construction under heterogeneous domain distributions produces structurally imbalanced graphs that bias selection toward sparse regions. To address these issues, we introduce two principled refinements from a unified graph perspective: (1) \textit{node value calibration} that restricts influence estimation to the bilateral salient subspace to ground node importance in task-relevant signals rather than surface-level statistics; (2) \textit{local scale normalization} that adapts edge thresholds to local neighborhood density, mitigating graph imbalance induced by cross-domain distribution shifts. Together, these components yield a robust and scalable data selection pipeline dubbed SEED. We further construct \texttt{Honeybee-Remake-SEED-200K}, a compact multimodal dataset curated by SEED. Extensive experiments show that SEED consistently outperforms state-of-the-art methods on instruction tuning, visual instruction tuning, and semantic segmentation across diverse model families.

Macro placement is a pivotal stage in VLSI physical design, fundamentally determining the overall chip performance. Recent data-driven placement methods have demonstrated significant potential, yet they often struggle to handle sequential dependencies and to balance topological connectivity with physical constraints. To bridge this gap, we propose MacroDiff+, a physics-guided geometric diffusion framework. Specifically, we design a dual-domain denoising architecture that couples topological connectivity encoded by heterogeneous GNNs with global geometric context modeled by a Transformer. Furthermore, we introduce Physics-Guided Sampling, an inference strategy that actively steers the generation using explicit gradients to ensure both statistical plausibility and physical validity. On the ISPD2005 MMS benchmarks, MacroDiff+ outperforms state-of-the-art baselines with a 6.1-6.2% reduction in wirelength. Notably, it exhibits superior stability and scalability on large-scale designs where prior methods fail to converge. The source code is available at https://github.com/jhy00n/MacroDiff-plus.

Relational graph learning models relational databases as graphs and has demonstrated superior performance on a wide range of relational predictive tasks. However, existing methods struggle to capture long-range dependencies due to information decay in their message-passing mechanisms, and recent relational graph transformers remain limited in jointly modeling structural, semantic, and temporal information. In this paper, we propose GelGT, a Gaussian relational graph transformer that explicitly addresses these challenges. GelGT introduces a structure-semantic collaborative sampling strategy to preserve structural connectivity while filtering irrelevant semantic information, and incorporates a Gaussian graph attention mechanism with a learnable Gaussian bias on the sampled subgraphs to dynamically encode temporal dependencies. Extensive experiments on various real-world datasets demonstrate that GelGT achieves state-of-the-art downstream task performance, with up to a 13.8% improvement in predictive performance.

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

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

Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass. We apply Njord globally at 0.25° resolution and regionally to the Baltic Sea at 2 km resolution. To scale to these large ocean grids we introduce K-means cluster meshes that adapt to irregular sea surface geometry. Experiments demonstrate strong performance on both domains compared to deterministic machine learning baselines, while also providing uncertainty estimates from the sampled ensemble forecasts. On the global OceanBench benchmark, Njord achieves the lowest errors on average across upper-ocean variables when evaluated against real-world observations, with the largest improvements in surface temperature prediction.

Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability. While reinforcement learning (RL) offers a natural post-training mechanism for task-specific optimization, applying it to graph generative models is hindered by the vast atom-wise action spaces and chemically invalid intermediate states. We propose \textbf{Co}ntrollable \textbf{Mole}cular Generative Foundation Models (CoMole), built with a unified motif-aware graph diffusion pipeline. By learning a motif-aware graph space, CoMole transfers pretrained structural priors into controllable generation, where RL optimizes conditional reverse policies over chemically meaningful decisions. We theoretically characterize the bottleneck of atom-level RL and justify motif-aware policy optimization. Across three heterogeneous benchmarks spanning materials and drug discovery, CoMole ranks first in controllability on all nine targets, reduces MAE by up to 48.2% relative to the strongest baselines, and maintains validity above 0.94 without rule-based correction or post-hoc filtering. We further show that CoMole transfers controllability to unseen properties by optimizing only task embeddings with the generator frozen, achieving performance competitive with strong task-specific baselines.

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

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

Forecasting within signal processing pipelines is crucial for mitigating delays, particularly in predicting the dynamic movements of objects such as NBA players. This task poses significant challenges due to the inherently interactive and unpredictable nature of sports, where abrupt changes in velocity and direction are prevalent. Traditional approaches, including (S)ARIMA(X), Kalman filters (KF), and Particle filters (PF), often struggle to model the non-linear dynamics present in such scenarios. Machine learning (ML) methods, such as long short-term memory (LSTM) networks, graph neural networks (GNNs), and Transformers, offer greater flexibility and accuracy but frequently fail to explicitly capture the interplay between temporal dependencies and contextual interactions, which are critical in chaotic sports environments. In this paper, we evaluate these models and assess their strengths and weaknesses. Experimental results reveal key performance trade-offs across input history length, generalizability, and the ability to incorporate contextual information. ML-based methods demonstrated substantial improvements over linear models across forecast horizons of up to 2s. Among the tested architectures, our hybrid LSTM augmented with contextual information achieved the lowest final displacement error (FDE) of 1.51m, outperforming temporal convolutional neural network (TCNN), graph attention network (GAT), and Transformers, while also requiring less data and training time compared to GAT and Transformers. Our findings indicate that no single architecture excels across all metrics, emphasizing the need for task-specific considerations in trajectory prediction for fast-paced, dynamic environments such as NBA gameplay.

Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.

The reliability of Healthcare Information Systems (HIS) is frequently compromised by human-induced data entry errors, which existing statistical anomaly detection methods fail to distinguish from legitimate clinical extremes. This paper proposes Logic-GNN, a novel neuro-symbolic framework that treats clinical records as a structured private language'' governed by latent logical games. By integrating Temporal Graph Neural Networks (TGNN) with Graph Kolmogorov Complexity, we induce a symbolic grammar that represents the underlying logic of medical interactions. We define anomalies as grammatical violations'' that cause a significant expansion in the Minimum Description Length (MDL) of the clinical graph. Evaluated on the Sina System dataset (2M+ records), Logic-GNN achieves an F1-score of 0.94, outperforming state-of-the-art baselines by 12% in distinguishing between life-threatening medical outliers and data corruption. Our approach introduces a self-healing mechanism that suggests logical corrections to maintain data integrity in real-time HIS environments.

Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent sampling. We consider strong mixing dependent observations and ask whether dependence changes the scale of nearest-neighbor neighborhoods. We establish distribution-free almost sure convergence under polynomial mixing and sharp non-asymptotic moment bounds under geometric mixing. The moment bounds depend on the local intrinsic dimension rather than the ambient dimension, making the results applicable to high-dimensional data concentrated near lower-dimensional manifolds. Synthetic experiments and real-world time-series benchmarks support the theory, showing that nearest-neighbor geometry remains informative under dependence sampling.

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

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative. Message-passing GNNs are widely used for mesh simulation, and their shared node and edge update functions are relatively generalisable across varying graph structures. By contrast, non-shareable edge-specific aggregation layers can capture nonlinear relationships more accurately but usually require fixed graph connectivity, which limits generalisability. This paper presents Mask-Morph Graph U-Net (MMGUNet), a practical approach to addressing the limitation of hierarchical Graph U-Net architectures that use edge-specific downsampling and upsampling layers. Fixed coarse graph connectivity is required for edge-specific layers. To retain this while improving spatial correspondence, the proposed method morphs the coarsened graph hierarchy to each input mesh using feature-aligned barycentric parameterisation before constructing cross-graph edges. It further applies node masking during supervised pretraining, followed by parameter-efficient fine-tuning in which high-parameter edge-specific layers are frozen. The proposed approach is evaluated in in-distribution, out-of-distribution, and cross-component transfer settings using mean Euclidean distance and maximum intrusion percentage error. Results show that coarse-graph morphing improves test accuracy relative to a fixed-coarse-graph baseline, while masked supervised pretraining reduces the train-test discrepancy and improves data efficiency during transfer. The proposed model also achieves lower prediction error compared with external baselines. These results demonstrate a practical route toward reusable, data-efficient mesh-based surrogate modelling for crashworthiness design exploration.

The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be adapted further to its specific objective function and constraints. In this article, we introduce such an adapted graph neural network architecture in which features are assigned only to edges, and the computation of messages is based on triangles in the underlying graph. Experiments with synthetic and real-world instances with up to 200 nodes show that our method outperforms state-of-the-art heuristic solvers in terms of solution quality while maintaining feasible runtimes. For some instances, our method finds optimal solutions in seconds whereas exact solvers need hours to find and certify optimal solutions.

Graph convolutional networks (GCNs) are widely used for 3D hand pose estimation, where the hand skeleton is encoded as a fixed adjacency graph. We revisit whether this is the most effective way to incorporate hand topology in 2D-to-3D lifting. In this paper, we perform controlled, parameter-matched ablations on the FPHA benchmark and show that standard multi-head self-attention consistently outperforms GCN baselines. Even when the GCN is strengthened with multi-hop adjacency and matched parameter count, self-attention reduces MPJPE from 12.36 mm to 10.09 mm. A skeleton-constrained graph attention network recovers most of this gap, indicating that input-dependent aggregation is a major source of improvement, while fully connected attention yields additional gains. We further show that hand topology is most effective when introduced as a soft structural prior through graph-distance positional encoding, rather than as a hard adjacency constraint. These results suggest that, for hand pose lifting, adaptive spatial attention is a more effective inductive bias than fixed graph convolution.