Graph Neural Networks

While signed-directed graphs have been studied using linear Laplacians in the design of graph neural networks, relatively little research has focused on developing non-linear Laplacian operators for such networks. We introduce a non-linear Laplacian operator specific to signed and directed networks (NLSD). This non-linear operator extends the concepts of the signed Laplacian for signed graphs and the Laplacian for directed graphs. The NLSD calculates node-specific potentials based on features More precisely, if the potential discrepancy is not aligned with the edge direction, we ignore it (and vice versa) leveraging message-passing techniques only across edges where potential discrepancies align with the edge's direction. Utilizing this novel operator, we propose an efficient spectral GNN framework (NLSD-GNN). We conducted comprehensive evaluations focusing on node classification and link prediction, examining scenarios involving signed, directional, or both types of information. Our findings reveal that this spectral GNN framework not only integrates signed and directional data effectively but also achieves superior performance across diverse datasets.

Multimodal-attributed graphs (MAGs), whose nodes carry heterogeneous attributes such as text and images over a relational structure, have become a fundamental substrate for label-free entity grouping tasks, including community discovery and product segmentation. Existing MAG clustering methods effectively integrate complementary modalities when attributes are clean and complete, but degrade substantially under noisy or missing attributes because they implicitly assume equal modality reliability across all nodes. In practice, modality reliability is inherently node-specific: images may be corrupted or absent, while textual descriptions are incomplete or noisy. We argue that, under attribute homophily, graph neighborhoods naturally provide supervision-free evidence for estimating node-specific modality reliability. Based on this insight, we propose RHEA, a reliability-aware framework for MAG clustering that estimates node-specific modality reliability from neighborhood consensus and propagates this signal throughout the clustering pipeline. RHEA reconstructs unreliable or missing modalities from graph neighborhoods, adaptively weights modalities during reliability-aware fusion, and performs topology-aware optimal transport clustering with reliability-aware transport assignment and neighbor-consensus assignment distillation. Furthermore, the confidence of reconstructed representations is incorporated into the clustering objective, allowing uncertain reconstructions to contribute proportionally during optimization. Experiments on four MAG benchmarks under five attribute conditions show that RHEA consistently outperforms the strongest baseline, with NMI gains increasing as attribute quality deteriorates.

Graph self-supervised learning aims to learn transferable representations from large-scale unlabeled graph data. Joint-embedding predictive architectures (JEPAs) avoid explicit negative-pair construction and raw-input reconstruction by predicting masked targets directly in latent space. However, existing graph JEPAs typically rely on a single predefined graph partition, biasing the learned representations toward one structural granularity and limiting their ability to capture complementary patterns at different graph scales. To address this limitation, we propose HP-JEPA, a hierarchical partitioning framework for multi-resolution graph joint-embedding prediction. HP-JEPA organizes each graph into an ordered bank of coarse-to-fine partition resolutions and performs context-target latent prediction separately at each resolution using an online encoder, an exponential-moving-average target encoder, and a latent predictor. The resulting resolution-specific graph representations are subsequently integrated through concatenation or task-specific resolution weighting, allowing downstream models to combine complementary local, regional, and global structural information. Experiments on seven graph classification benchmarks and one graph regression benchmark show that HP-JEPA outperforms the fixed-resolution Graph-JEPA baseline on 6 of 8 tasks, improving upon Graph-JEPA on most evaluated benchmarks. Size-stratified analyses further show that HP-JEPA achieves higher accuracy than Graph-JEPA in most evaluated graph-size quartiles on three representative datasets. These results highlight the effectiveness of hierarchical multi-resolution partitioning for transferable graph representation learning.

High-entropy perovskite oxides (HEPOs) represent a chemically complex class of materials with promising functional properties, yet their vast compositional space and, chemical/structural disorder pose significant challenge for accurate property prediction. Graph neural networks (GNNs) enable rapid exploration of materials space but are often limited by the availability of representative training data. Here, we investigate ordered-to-disordered transfer learning using GNNs for formation-energy and HOMO-LUMO gap prediction in HEPOs by transferring knowledge learned from chemically ordered perovskites. Four representative GNN models, including CGCNN, GATGNN, ALIGNN and M3GNet are evaluated to understand the role of structural representations, spanning pairwise two-body and angular three-body interactions in transfer performance. We find strong property-dependent transfer behavior: formation-energy prediction transfers effectively to disordered HEPOs, whereas HOMO-LUMO gap prediction shows limited transferability due to its sensitivity to local chemical environments. Incorporating a small HEPO-specific training dataset substantially improves HOMO-LUMO gap prediction. Representation-level analysis using UMAP further highlights the importance of encoding three-body geometric information such as in ALIGNN for capturing complex structure-property relationships and improving transferability.

Accurate fault location is critical for distribution network reliability. However, increasing distributed energy resource (DER) penetration complicates fault location due to intermittent generation and bidirectional power flows that reshape fault signatures. Spatio-Temporal Graph Neural Networks (STGNNs) have shown promise by jointly modeling spatial and temporal dependencies, but their behavior under increasing DER penetration has not been studied rigorously. In this paper, we (i) systematically benchmark spatio-temporal graph attention network (STGATv2) against purely temporal (gated recurrent unit, GRU), purely spatial (GATv2) and traditional machine learning baselines, and (ii) evaluate how well models generalize across increasing DER penetration levels (10%, 25%, 50%) on a reconfigured IEEE 123-bus feeder with multiple DER injection points and moderate-to-high impedance faults. Results show that STGATv2 consistently outperforms neural baselines, achieving 92-94% macro F1 in-distribution. Notably, generalization across penetration levels is asymmetric: training at 50% penetration retains near in-distribution F1 score at lower levels, whereas training at 10% degrades considerably at 50% - with STGATv2 retaining 81-84% F1 under these drastic shifts, substantially higher than GATv2 and GRU which drop to 69-74% F1 and 73-75% F1 respectively. Under realistic measurement noise, STGATv2 maintains > 85% F1, while GRU drops as low as 33.5% F1, highlighting the critical role of topological awareness for robust fault location in active distribution networks.

Multi-label node classification is an important yet challenging task in graph learning, where nodes exhibit multiple semantics simultaneously. Existing methods for multi-label node classification can effectively model multiple labels, while only considering in-domain scenarios where the model needs to be trained and tested within the same graph domain, resulting in limited cross-domain generalization. Recently, Graph Foundation Models (GFMs) have emerged as a promising paradigm for learning transferable graph representations across diverse graph domains and downstream tasks. However, existing GFMs are built upon single-label assumption, where all nodes are arbitrarily regarded as containing only one class of semantic and embedded into a single representation. For multi-label nodes, such a representation essentially approximates multiple semantics with a single point in the representation space, inevitably leading to semantic entanglement and making simultaneous discrimination of multiple labels difficult. To address these limitations, we propose a Multi-Semantic Basis Graph Foundation Model (MSB-GFM), a framework for cross-domain multi-label node classification. Specifically, we introduce a multi-semantic basis representation learning paradigm that models each multi-label node as an adaptive composition of semantic bases, thereby enabling flexible representational capacity for modeling multiple semantics. Furthermore, we develop a semantic-structure dual-channel architecture with domain adversarial training for effective cross-domain knowledge transfer. Extensive experiments demonstrate the effectiveness of our model.

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for enabling knowledge transfer across diverse domains. Unlike traditional graph learning methods that are typically designed for in-domain settings, GFMs aim to learn transferable knowledge that can generalize to unseen graph domains. However, unlike language or visual data, graphs lack intrinsic and unified representation units, such as tokens in language and patches in vision, making it challenging to identify transferable knowledge units for building graph foundation models. Existing graph foundation models mainly focus on mitigating domain discrepancies through feature alignment and structure alignment, while overlooking the exploration of transferable knowledge units underlying graph data. Moreover, these methods generally rely on fixed propagation mechanisms during message passing, overlooking the heterogeneity in propagation patterns, as different edges may exhibit distinct propagation patterns for different feature dimensions. To address these limitations, we propose a Propagation-aware Graph Foundation Model (ProGFM), which regards the propagation relationships between edges and feature dimensions as transferable knowledge units. Through a propagation relationship prototype bank, ProGFM learns cross-domain transferable propagation knowledge, enabling adaptive information aggregation in unseen graph domains. Extensive experiments across various cross-domain transfer scenarios demonstrate that ProGFM possesses strong cross-domain knowledge transfer capability and exhibits superior generalization performance compared with existing methods.

Dynamic matching markets require decisions about whom to match and when: matching now yields value but removes participants who may create better future opportunities. We develop a value-based reinforcement-learning framework for this problem on finite, evolving weighted graphs. We study an infinite-horizon continuous-time model with stochastic arrivals, node-type transitions, edge realizations, and exogenous exits. We prove an event-time reduction: without loss of optimality, the planner acts immediately after each exogenous event and then waits for the next one. We further show that the optimal edge-wise $Q$-function is characterized by a single continuation-value function on post-decision residual graphs, reducing the learned object from state-action values to graph values. Exact action selection still requires combinatorial matching optimization; we approximate the value with a graph neural network, train it by temporal-difference learning, and use it in a forward-greedy matching heuristic. In a binary-type benchmark, the learned policy substantially outperforms immediate and threshold-greedy rules by preserving common nodes for rare arrivals of valuable matches while forming lower-value matches only in thick pools. In a kidney paired donation benchmark, it performs similarly to immediate greedy when exits are unpredictable, recovers the logic of patient matching when warnings are reliable, and outperforms the better of Immediate Greedy and Patient Greedy across intermediate warning probabilities. These results show that residual-graph value learning yields state-dependent dynamic matching policies that adapt to realized connectivity and exit information.

Metallic magnets exhibit complex spin dynamics governed by electronically generated interactions. Predictive simulations of such dynamics typically require repeated solutions of an underlying electronic problem throughout the time evolution, creating a major computational bottleneck. Here we introduce a graph neural network (GNN) magnetic force-field framework that learns the effective magnetic energy functional governing itinerant spin dynamics directly from electronic calculations. Conceptually analogous to machine-learned interatomic potentials, the proposed framework enables efficient evaluation of spin torques while capturing the nonlinear and spatially extended interactions generated by itinerant electrons. We benchmark the method on representative metallic magnetic systems exhibiting collinear, noncollinear, and noncoplanar magnetic order. The learned force fields accurately reproduce electronically generated spin torques and yield nonequilibrium spin dynamics in excellent agreement with direct electronic simulations. Our results establish graph neural networks as a powerful framework for machine-learned magnetic force fields, providing a pathway toward predictive large-scale simulations of nonequilibrium magnetism across multiple length and time scales.

Many real-world graphs support multiple predictive tasks over the same underlying structure, creating an opportunity to reuse supervision across node classification (NC) and link prediction (LP). However, existing evaluations often rely on incompatible splits, observed-graph assumptions, and negative sampling rules, making conclusions about same-graph cross-task transfer unreliable. We formalize same-graph NC-LP transfer and propose a leakage-free protocol that fixes node and edge splits, uses a shared message-passing graph that excludes evaluated edges, and employs fixed negatives for LP. Across three backbones (GCN, GraphSAGE, GPS), we find that transfer is strongly directional and predictable: NC $\to$ LP is consistently beneficial on homophilic graphs, while LP $\to$ NC is fragile and can even degrade accuracy under naive representation reuse. LP $\to$ NC becomes reliably positive mainly in a structure-dominant regime where LP is easy but NC is unsaturated, suggesting that LP acts as structural pretraining. Finally, we introduce the CoTask Score (CTS) to summarize joint NC+LP utility when a shared encoder must serve both tasks, and show that simple dataset statistics, especially homophily, can guide mechanism choice and help avoid negative transfer.

Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning. While classical methods such as algebraic multigrid (AMG) are highly scalable, their robustness can degrade on indefinite or nonsymmetric systems where heuristics originally developed for elliptic PDEs are less reliable. Recently, Graph Neural Networks (GNNs) have emerged as data-driven preconditioners; yet, the practical impact of imposing an AMG-style hierarchy remains underexplored for general sparse matrices. In this work, we propose a Graph Neural Multilevel Preconditioner (GMP) that adopts an AMG hierarchy as a structural prior and learns smoothing, restriction, and interpolation operators in a unified framework. Our method targets general sparse systems and is instantiated as a drop-in preconditioner for standard Krylov solvers. On a benchmark of over 800 sparse matrices, we compare against classical AMG, single-level ILUT, and state-of-the-art GNN preconditioners, and characterize the regimes where multilevel graph neural preconditioning improves convergence or, conversely, introduces overhead relative to strong single-level baselines. These results highlight both the promise and the limitations of enforcing AMG-style multilevel structure in learned preconditioners for large-scale scientific simulations.

Multimodal federated graph learning enables clients to collaboratively train graph models over structural, textual, and visual signals without sharing private local data. However, the presence of heterogeneous multimodal content also makes unlearning requests more frequent and fine-grained: users may delete accounts or interactions, remove a particular image or text while retaining the associated entity, or revoke the learned correspondence between retained modalities or graph attributes. Existing federated graph unlearning mainly handles entity/relation or client removal and cannot directly satisfy these multimodal requests. They introduce three challenges: removing only the requested information without damaging retained content, preventing the target from being recovered through remaining modalities or graph neighborhoods, and stopping related traces on other clients from re-entering the global model after aggregation. To address them, we propose \textsc{\textbf{MMFGU}}, a multimodal federated graph unlearning framework built around target-specific representation decoupling. \textsc{MMFGU} maps heterogeneous requests into unified target carriers, decouples requested representations while anchoring retained semantics, exposes and repairs propagated residuals with lightweight probes, and selectively purges affected clients through compact prototype and response signals. Experiments show that \textsc{MMFGU} effectively removes requested information, preserves retained graph utility, and achieves a $\boldsymbol{41.5\times}$ speedup over full retraining.

Query optimization of Basic Graph Patterns (BGP) SPARQL queries over Knowledge Graphs (KG) requires accurate cardinality estimation. Recently published learned estimators outperform statistics- and sampling-based approaches, but share a limitation preventing their adoption in real-world triplestores: they are transductive and require retraining when the underlying graph changes or when applied to new graphs. We present FICE (Fully Inductive Cardinality Estimation), the first learned cardinality estimator for BGP queries over KGs that generalizes to entirely unseen graphs (including unseen relations), without any retraining. FICE is a graph neural network (GNN) with two coupled components. First, an encoder GNN over a factor-graph view of the KG produces entity and relation embeddings. We prove that BGP cardinality is a local function of the 2-hop neighborhood around bound terms in this view, motivating the local message-passing encoder. A decoder GNN then composes these embeddings along the join topology of the query to predict log-cardinality. The encoder and decoder are trained jointly, making the embeddings specialized for cardinality estimation. FICE is trained using neighborhood sampling to scale to KGs with millions of triples, and decouples embedding generation from cardinality decoding to enable estimation latency below a millisecond. Compared to learned and non-learned baselines over 10 KGs, FICE reduces the overall median q-error from 13.54 (for the best competitor) to 5.34 and dominates all approaches in tail behavior.

We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is Topo-Scan, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, Topo-Scan is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that Topoformer matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace. This phenomenon limits the effective depth of message-passing architectures and motivates the search for mechanisms that preserve representation diversity. In this paper, we study a recurrent graph neural network in which independent Gaussian noise is injected after every propagation step and analyze the resulting architecture as a stochastic dynamical system. Under a standard global contraction assumption on the deterministic update, we prove that the hidden representations form a geometrically ergodic Markov chain admitting a unique invariant probability measure. Our main theoretical result establishes an explicit positive lower bound on the expected stationary Dirichlet energy, proportional to both the noise variance and the spectral gap of the underlying graph. Consequently, the stationary representations cannot collapse onto the constant manifold, providing a rigorous guarantee that asymptotic oversmoothing is prevented in the sense of non-vanishing Dirichlet energy. Our analysis reveals persistent stochastic perturbations as a fundamentally different mechanism for combating oversmoothing, complementing existing deterministic approaches based on residual connections, normalization, and graph rewiring. Finally, numerical experiments on both linear and nonlinear recurrent graph neural networks closely match the theoretical predictions, illustrating the emergence of a stationary distribution and the predicted dependence of the limiting Dirichlet energy on the noise intensity.

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for general-purpose graph learning, aiming to learn reusable knowledge that generalizes across diverse graph domains and downstream tasks, reducing the need for specific model development. Achieving this goal requires reconciling the substantial heterogeneity in node features, graph structures, and semantic information across domains. Among them, heterogeneous node features constitute a fundamental input-level barrier, as their dimensionality and semantics vary substantially across datasets. Existing studies typically project or map heterogeneous node features into a fixed-dimensional space, often implicitly equating dimensional uniformity with effective feature unification. Yet dimensional consistency alone does not ensure that the unified features preserve informative semantics and capture transferable patterns that can support cross-domain knowledge transfer. To bridge this conceptual gap, we distill four desiderata for cross-domain graph feature unification: formal uniformity, cross-domain transferability, information preservation, and backbone compatibility. Guided by these principles, we propose SliGFM, a graph foundation model built upon topology-aware sliding-window feature encoding and generative reconstruction. SliGFM orders feature dimensions by topological smoothness and scans the reordered features with a shared sliding-window feature encoder, transforming heterogeneous features into a common space of ordered fixed-dimensional feature tokens. This formulation enables a smoothness-aware transformer to capture transferable relational patterns among feature tokens within each node, while the generative reconstruction objective encourages preservation of the original feature information.

SHACL shapes enable data graph validation, making automatic shape learning essential for knowledge graph applications. We investigate the well-known fitting approach to this task: given sets P and N of positive and negative example nodes from an input graph, compute a shape expression C, possibly using shape names defined in a recursive shape catalogue, that validates at every node in P and none in N. We focus on the case where C is written in a core fragment of SHACL corresponding to the Description Logic ELI. For the catalogue, we consider the well-founded, stable, and supported semantics. We address fitting existence and most specific fitting computation, establish tight exponential-time upper bounds for both problems, and obtain polynomial bounds for relevant special cases.

Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs. This raises a central question: when can a model trained on a smaller, scaled-down replica of a graph be deployed on the full-resolution graph without retraining? We introduce a zero-shot transfer protocol in which a GNN is trained on a graph coarse-grained by geometric renormalization (GR), and the resulting weights are transferred directly to the original network. Across synthetic and real-world networks, training on GR scaled-down replicas preserves much of the original-scale predictive performance while significantly reducing training cost. We further find that learned representations and predictive trajectories remain aligned across scales. These findings suggest that structural similarity may be more important than network size in determining GNN transferability, opening a path toward scale-equivariant graph architectures.

Reinforcement learning (RL) search agents commonly model retrieval as free-form natural-language query generation and optimize multi-turn interactions using final-answer rewards. Current studies mainly improve training with denser or more structured credit signals, but rarely examine whether retrieval is properly formulated at the policy-environment interface. We observe pronounced retrieval aliasing during Search-R1 training: rollouts for the same question continue to generate distinct query strings, yet their accumulated evidence sets increasingly overlap. We call this phenomenon retrieval-equivalence collapse; in this regime, trajectories approach utility equivalence with respect to retrieval decisions, leaving within-group returns with little effective retrieval contrast. To address this problem, we propose Harness-G, a graph-structured retrieval framework that redesigns this interface. It reformulates free-form query generation as finite action selection: the policy selects an evidence sentence or entity, or chooses to answer, while the environment constructs the menu, tracks retrieval state, and validates and executes each choice. This interface reduces linguistic aliasing and makes same-state alternatives directly comparable. Building on this interface, we introduce Structured Non-myopic Credit (SNC), which uses a frozen answer scorer to compare the selected action with its alternatives and assigns downstream gains to the earlier actions that enabled them. Across six QA benchmarks, Harness-G achieves the highest average F1 at both evaluated model scales, outperforming the strongest baseline, Graph-R1, by 10.74 points at 1.5B and 3.98 points at 3B.

Functional magnetic resonance imaging (fMRI) is a widely used technique for studying the brain. Recent methods that utilize graph neural networks (GNNs) for analysis of brain functional connectivity have shown great potential for the classification of brain disorders, such as Alzheimer's disease (AD). However, these methods often assume a preset number of functional modules across all subjects, which overlooks inter-subject variability. In addition, the discovered modules are rarely used to directly guide the learned connectivity patterns. Here, to address these issues, we propose a Meta Probabilistic Pooling GNN (MPP-GNN). We frame the model's task as a coupled, bilevel optimization that performs adaptive graph partitioning hierarchically to discover subject-specific modules and then uses the discovered brain modules as an explicit prior to guide edge refinement and representation learning. We validate MPP-GNN on two public datasets for AD classification, achieving the highest AUC in comparison to established baselines for both datasets. Furthermore, our analysis demonstrates that MPP-GNN shows significant alignment with the canonical functional-network organization defined by the Yeo brain atlas and reveals a network-level dedifferentiation pattern for AD.

The information flow in the graph neural networks (GNNs) is fundamentally constrained by over-squashing, where structural bottlenecks impede long range information propagation. Graph-rewiring methods, which modify graph topology, have been extensively used to alleviate this. However, existing approaches often introduce prohibitive structural and computational bottlenecks, fail to preserve the critical properties of original graphs, and increase the edge counts massively. We introduce a novel method Schreier-Coset Graph Rewiring , a group-theoretic rewiring method that augments the input graph with a Schreier-Coset graph derived from a special linear group. Our method provides theoretical guarantees, a graph that exhibits spectral gap and a bounded effective resistance, creating a low-resistance bypass for long-range communication. Empirical evaluations demonstrate that SCGR reduces effective resistance by 5-40% across various learning tasks, effectively mitigating connectivity bottlenecks while maintaining competitive accuracy.

Large language model (LLM) agents have been widely applied in automating data science tasks. However, existing methods typically rely on a limited set of provided datasets, and they face challenges in data-intensive scenarios that require discovering and leveraging relevant information from large-scale and heterogeneous data repositories. Urban tasks are representative examples of such scenarios, as urban data are not only large-scale and multi-sourced, but also exhibit complex spatial, temporal, and semantic relationships. To address these challenges, we propose UrbanDS, a graph-guided LLM multi-agent system for data-intensive urban tasks. We first construct a unified dataset graph to organize reusable dataset skills and the relationships among datasets. Specifically, we develop a Data Profiling Agent that constructs a skill for each dataset. Moreover, a Relation Agent identifies relationships among datasets and integrates these relationships into the dataset graph. At runtime, a Planner Agent retrieves task-relevant datasets from the graph and generates execution plans. Multiple Execution Agents then perform data processing and analysis, while their execution progress and intermediate results are shared through a common memory. Finally, a Report Agent synthesizes the experimental logs into a report, which can be further refined based on user feedback. To systematically evaluate the capability of agents in handling data-intensive urban scenarios, we further construct UrbanDS-Bench, an urban data science benchmark covering representative data analysis and modeling tasks. Experiments on both general and urban benchmarks demonstrate that UrbanDS consistently outperforms existing data science agents on data-intensive tasks. Furthermore, UrbanDS has been deployed on the urban operations platform of Dongxihu District, Wuhan, demonstrating its effectiveness in real-world urban applications.

We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically. Here, we establish a novel universality result focusing on permutation-equivariant neural networks (PENNs), a class of GNNs built from feedforward neural network components that subsumes many prominent GNN architectures. We show that PENNs, combined with partially random node features, can approximate arbitrarily well in probability any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size with multidimensional node and edge features. For $k$-times continuously differentiable functions, $k\geq 2$, we also derive upper bounds on the approximation rates, relating the complexity of the feedforward components of a PENN in terms of layer depth and number of nonzero weights to the desired approximation accuracy.

Organizational digitalization expands cybersecurity risks, making cybersecurity an increasingly important research area in Information Systems (IS). Among these risks, malware has become a pervasive and destructive threat. Byte-based machine learning (ML) methods are widely used for malware detection but remain vulnerable to evasive behaviors that manipulate raw bytes to evade detection. Graph-based methods are less affected by such manipulations because they represent software as program graphs that capture execution behavior. However, they do not explicitly identify cohesive groups of basic blocks that jointly realize meaningful program behaviors, nor do they learn sufficiently expressive program graph representations for accurate detection. To this end, we propose MalGuard, a graph-based malware detection method for organizational malware risk management. MalGuard introduces two methodological innovations: an operational role identification approach and a program graph representation learning method. The former identifies these cohesive groups of basic blocks as operational roles, enabling the detector to capture program behaviors that may not be visible from isolated basic blocks. The latter learns expressive program graph representations by modeling interactions among operational roles, preserving sparse malicious signals, and capturing hierarchical graph structure. Extensive experiments show that MalGuard improves detection performance and reduces the expected cost of undetected malware.

Graph Foundation Models (GFMs) aim to learn transferable knowledge from multi-domain graphs and adapt to unseen scenarios. As a fundamental source of relational semantics in graphs, the transferability of topological patterns has long been central to GFM research. However, local structural patterns may vary across graphs and even among nodes within the same graph. Despite such structural variation, most existing GFMs rely on manually designed propagation schemes and apply them to new graphs largely unchanged. Such fixed schemes may not suit the diverse structural patterns of different nodes. This raises a key question: can each node autonomously determine how information should be propagated through the graph? We refer to this capability as information-flow control. Inspired by recent advances in agent technology, we formulate this problem as agent-based decision making and treat each node as an agent. Accordingly, we propose AgentGFM, in which all node agents follow a shared end-to-end trainable policy rather than using independent models. For adaptive information-flow control, each node interacts with the graph through a predict-act-observe-correct process. During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting. The resulting observation is compared with the prediction and their discrepancy is used to correct the node state and guide subsequent interactions. Extensive experiments across node-level, graph-level and large-scale transfer scenarios demonstrate the effectiveness of AgentGFM across diverse graph topologies.

Graph Neural Networks (GNN) facilitate effective prediction on graph data such as molecules, media networks and neural network blueprints. GNNs facilitate prediction through message passing techniques which define how information flows from a node to its neighbors. Due to the ubiquity of the graph data type, the development of newer and better GNNs has garnered much interest in the machine learning community. However, GNN evaluation and benchmarking is primarily driven by classification tasks. Thus, prospective GNN message passing layers are evaluated on their ability to outperform prior work in classification contexts. In contrast, GNNs are equally capable of performing scalar regression prediction, yet this class of problem is often overlooked when proposing new GNNs while the best classification GNNs are utilized in an a priori or off-the-shelf manner for regression problems. In response, this paper studies the efficacy of GNN layers in a slew of regression contexts from rank ordering, error minimization and insight extraction. Results show that deep convolutional GNNs, particularly GEN, are more effective at these tasks than attention-based GNNs, while other classical, theoretically-inspired GNNs remain competitive and efficient.

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.

The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC). While generally undecidable, several families of infinite non-abelian groups exhibit solvable or algorithmically fast word problems, making them attractive platforms for cryptographic design. This paper introduces WPNet, a novel Graph Neural Network architecture capable of solving the Word Problem heuristically, which is demonstrated on the Baumslag-Solitar group $BS(1,2)$ and on an Artin group. By mapping unreduced words to dynamic graph structures, the model learns to cluster algebraically equivalent elements in a continuous embedding space, effectively identifying the geodesic representative of a word without executing discrete reduction steps. As an application, a model variant is developed that can predict the geodesic length of an unreduced word in both groups. To demonstrate the cryptographic severity of this structural leakage, WPNet is successfully deployed against the Wagner-Magyarik public-key cryptosystem.

Graph foundation models (GFMs) have emerged as a promising paradigm for transferring knowledge across graph domains and tasks. Real-world graphs associate nodes with text, images, and other modalities, making multimodal graphs essential for representing complex entities and relations. Moreover, collecting labels and adapting models for every new graph domain is costly and often infeasible, motivating zero-shot transfer. Unfortunately, zero-shot transfer on multimodal graphs remains underexplored. Existing GNN-based graph foundation models typically require downstream adaptation, whereas LLM-based graph methods mainly address unimodal graphs or tasks within a single domain. This setting presents two key challenges. First, models must generalize knowledge from individual modalities while capturing transferable cross-modal relations. Second, without target-domain fine-tuning, node representations remain entangled with domain-specific structures and modality-specific characteristics, obscuring shared concepts in unseen domains. To address these challenges, we propose CHARM, a multimodal graph foundation model with hierarchical context modeling for zero-shot transfer. CHARM replaces isolated raw nodes with hierarchical graph contexts that capture multimodal semantics and cross-modal relations. These contexts map domain-specific node patterns to shared high-level concepts, reducing reliance on target-domain supervision or adaptation. A modality-aware graph context encoder integrates multimodal information with graph structure and converts the resulting representations into graph tokens for a large language model . Experiments show consistent improvements on zero-shot multimodal graph tasks.

The Information Dynamics of Music model (IDyOM) has played a central role in computational accounts of musical expectation by providing event-by-event estimates of uncertainty and surprise from symbolic musical sequences. However, its reference implementation is difficult to integrate with contemporary Python workflows, and its internal memory structures are not easily accessible for inspection or modification. We introduce GraphIDyOM, a graph-native Python reimplementation of IDyOM that represents long-term and short-term predictive memories as explicit graph objects while preserving the model's variable-order, multiple-viewpoint architecture. GraphIDyOM returns event-wise information content and entropy, exposes internal memory structures for analysis and export, and supports access through a local server. We validate the implementation against the original Lisp IDyOM across single, projected, and multiple-viewpoint configurations, and benchmark its coverage and computational performance against a recent reimplementation. We then demonstrate how the explicit memory representation supports network analysis of learned memories, projection of expectation values onto musical networks, recency-sensitive memory retrieval, and interactive applications. GraphIDyOM therefore provides both a faithful and accessible reimplementation of a widely used model and a platform for studying musical expectation through memory, topology, and interaction.

Graph Neural Networks (GNNs) and Large Language Models (LLMs) have each advanced recommendation systems by modeling structural and semantic signals, respectively. However, integrating their complementary strengths remains challenging, particularly in sparse settings where maintaining semantic precision is critical. We propose TRWH (Text-driven Random Walk Heterogeneous Graph Neural Network), a novel framework that fuses LLM-generated textual profiles with heterogeneous graph structures through strategic random walk augmentation. TRWH consists of three core components: (1) Embedding Creation, which produces user and item representations using both Word2Vec and LLM-based profiling; (2) a Heterogeneous Graph Neural Network (HeteroGNN) that propagates information across multi-relational edges; and (3) Random Walk-based Path Construction, which enriches sparse graphs with second-order user-user and item-item links. Experiments on the Amazon-2023 Fashion (2M users, 825K items) and Beauty (631K users, 112K items) datasets demonstrate that TRWH achieves substantial performance gains over state-of-the-art methods, including 80.0% RMSE and 52.6% MAE reductions on Fashion, and 25.7% and 10.8% improvements on Beauty. Notably, while random walks improve performance with traditional embeddings, they can dilute the nuanced representations learned by LLMs, underscoring the importance of adaptive integration strategies.

Learned restriction maps in sheaf graph neural networks are often treated as proof that the model has discovered useful edge geometry. That conclusion does not follow from parameter movement or from a post-hoc ablation: both can show how one checkpoint is organized while leaving open whether learned transport still helps after the rest of the model adapts. We separate these claims with two estimands. Checkpoint reliance intervenes on the maps of a fixed predictor; protocol-relative replacement retrains matched families that remove map capacity, edge variation, or persistent edge assignment. A task-null theorem shows why the claims can diverge: labels identify only the transported classifier directions, leaving $d^2-d$ invisible degrees of freedom in every full $d\times d$ map. An exact frame model then gives the boundary at which reliance becomes unreplaced task value. Label-only training realizes the predicted separation, while audits of public NSD, DNSD, and Directed Sheaf Neural Network (DSNN) implementations recover both replaceable and unreplaced transport regimes on real graphs. All five DNSD benchmarks exhibit fixed-checkpoint reliance. After retraining, assignment-breaking or shared-map controls recover Full performance on four; Roman-Empire retains a $.0675$ advantage over continually resampled assignment and a $.0391$ advantage over a parameter-matched shared map across ten official splits. Thus, a learned map can govern a fitted computation without constituting indispensable edge geometry. Claims of learned transport should pair checkpoint interventions with matched retraining.

Amyotrophic lateral sclerosis (ALS) progressively impairs speech motor control, making acoustic analysis a promising biomarker for severity and progression estimation. We propose a subject-level graph framework that aggregates multiple phonation recordings into a unique k-nearest-neighbor graph built from pretrained SSL embeddings of 2s segments. We compare four SSL front-ends (wav2vec 2.0, HuBERT, data2vec-audio, and UniSpeech-SAT) and five graph neural networks (GCN, residual GCN, GAT, GraphSAGE, and GIN) on the SAND dataset tasks (339 participants: 205 ALS, 134 control): 5-class dysarthria severity and 4-class ALSFRS-R progression prediction. On the official validation set, the best configuration (HuBERT+GIN) achieves macro-F$_1$ of 0.73 for Task 1 and 0.69 for Task 2, outperforming SAND validation baselines (0.61 and 0.58). These results highlight the potential of combining GNNs with pretrained cross-lingual speech representations for low-resource ALS detection and progression monitoring.

Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient $λ$. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-$γ$, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at $p<0.01$ (paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer ($p=0.23$). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.

Integrating heterogeneous industrial knowledge, including factual relations and decision constraints, remains a core challenge in industrial information systems. Machining process planning exemplifies this problem because engineers must select operations by combining material properties, feature characteristics, and quality requirements. Existing methods rely mainly on similarity retrieval or classification, without a unified ranking objective or standardized evaluation. We propose PCA-GAT, which formulates machining process plan recommendation as a knowledge graph enhanced collaborative filtering problem. Bayesian Personalized Ranking provides the learning objective, while Recall@K and NDCG@K define evaluation. The knowledge graph supplies semantic structure when collaborative signals are sparse. Four domain constraints, material compatibility, precision requirements, feature applicability, and operation sequencing, are introduced as attention biases during graph propagation. Type-specific weights learn their importance, and an adaptive gate adjusts their influence using local context. On a real aerospace dataset with 115 parts and 507 plans, PCA-GAT achieves Recall@1 = 0.9087 and strong cold-start robustness, with about half the degradation of the strongest baseline under severe sparsity. Ablation studies show that knowledge graph enrichment is essential, constraints add value, and ungated constraint injection can hurt performance. The learned weights identify material-operation compatibility as the dominant factor, consistent with domain expertise. Results on three public benchmarks show no degradation when constraints are absent, supporting generalization beyond manufacturing. This study establishes a standardized recommendation protocol for engineering process planning and benchmarks seven methods across three categories, showing that knowledge representation is the main bottleneck.

Modern System-on-Chip (SoCs) often contain hundreds of millions to tens of billions of gates, making existing Hardware Trojan (HT) detection methods impractical due to their immense scale. The proposed approach incorporates symbolically enabled learning by modeling flattened gate-level netlists as Boolean networks represented as And-Inverter Graphs (AIGs), where all internal nodes are 2-input AND gates and inversions reside on the edges. Each directed connection is expressed as a triple within a Knowledge Graph Embedding (KGE) framework, producing compact, constant-size per-node representations that retain multi-hop structural context. The AIG's bounded fan-in and uniform semantics ensure training and inference complexity scale linearly with edge count, addressing major scalability bottlenecks in HT detection. Symbolically enabled learning across deep datapaths enables the model to differentiate circuit structures from rare and functionally inconsistent connections that signify potential Trojan triggers and payloads. Experiments on large-scale SoC benchmarks demonstrate clear geometric separation between Trojan and benign nodes and practical scalability.

Question answering (QA) over complex documents requires models to retrieve and integrate evidence distributed across distant document regions and modalities. Multimodal GraphRAG provides a promising direction by organizing document evidence with graph structures. However, existing methods often suffer from unreliable cross-modal evidence indexing and expensive graph traversal. To address these issues, we propose HVM-GraphRAG, a holistic-view multimodal GraphRAG framework on complex document. HVM-GraphRAG uses a holistic view to guide graph construction, thereby reducing noisy and conflicting graph updates and building reliable indices between concept-level graph nodes and supporting multimodal chunks. During retrieval, HVM-GraphRAG searches over a compact concept-level graph and directly accesses supporting evidence through the constructed index, avoiding costly traversal over dense entity-level graphs. After obtaining the retrieved evidence, HVM-GraphRAG further reorganizes chunks into modality-specific groups, enabling the answering model to better integrate heterogeneous evidence. Experiments on three datasets show that HVM-GraphRAG achieves the best answer performance in most evaluated settings while substantially improving online retrieval efficiency over representative graph-based baselines.

Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming. We present a machine-checked formalization of the method for finite simple graphs, together with a certificate-to-proof compiler that turns externally generated certificate data into algebraic proofs checked by Lean. The formalization covers the foundations of the method: partially labeled graphs, their densities in large graphs, the quotient algebra of density expressions, graph-limit semantics through positive homomorphisms, and the downward operators used to average out labels. The compiler treats the external semidefinite programming output as candidate data rather than trusted input: Lean independently computes the required density and multiplication facts, verifies positive semidefiniteness exactly over $\mathbb{Q}$, and carries out the algebraic normalization steps of flag-algebra proofs. Our case studies yield formal proofs of seven Turán-type upper bounds, including Mantel's theorem and the Erdős pentagon theorem, a $C_4$-density bound for triangle-free graphs, and edge-density bounds for $K_4$-free, $K_5$-free, and $C_5$-free graphs. Independently of the compiler, we formalize the matching constructions that complete the exact Turán densities of Mantel's theorem and the Erdős pentagon theorem, and prove two inequalities of Goodman. Our constrained semantics also prompted a meta-theoretic comparison of two ways of imposing graph constraints: building a hereditary constraint into the flag algebra from the start, or testing inequalities afterward on constrained graph limits with labels chosen at random. We state the resulting root-plantability criterion characterizing when the two approaches agree; a forthcoming paper will present the complete account.

We study an integrated pickup-and-delivery problem on sparse, non-Euclidean networks that jointly optimizes cyclic routing, cargo flow allocation, and cross-cycle service. The tight coupling of these operational constraints creates a complex discrete-continuous decision space with highly restricted feasible regions. To overcome these computational challenges, we propose Double-Channel Graph Attention (DCGA), an end-to-end reinforcement learning framework. DCGA isolates network reachability and demand-service logic into separate graph channels and constructs valid routes using a simulator-coupled, constraint-informed decoder. Experiments on LinerLib benchmarks demonstrate that DCGA achieves seconds-level inference and delivers state-of-the-art solution quality on instances beyond a specific scale, with its advantage over existing baselines widening significantly as problem size increases. Supported by extensive stability and ablation analyses, our results demonstrate that this structure-aware learning approach provides an effective, low-latency engine for realistic routing-and-flow optimization.

Graph compression reduces the computational cost of graph learning, but its effect on signal propagation remains largely underexplored. Existing work evaluates compression through downstream task performance or structural preservation, neither of which directly captures how propagation dynamics change after compression. We study two fundamental compression paradigms, coarsening and sparsification, and ask whether they preserve the propagation behavior of the original graph. Across five datasets, varying compression rates, and propagation depths, we measure signal behavior through three complementary metrics. Our results reveal a consistent tension between the two compression families. Sparsification retains higher signal diversity and mitigates oversmoothing, but its propagation trajectory progressively diverges from that of the original graph. Coarsening more faithfully preserves propagation behavior, but at the cost of stronger smoothing and rank collapse. These findings demonstrate that two propagation-centric objectives, preserving signal diversity and preserving propagation fidelity, are distinct and empirically at odds under graph compression, highlighting the need for evaluation protocols that jointly consider both dimensions. The code and results are available at: https://github.com/KawshikBanerjee/Compression-Propagation-Duality

Multi-hop question answering requires coordinating relational and textual evidence across reasoning steps, a combination neither a text corpus nor a knowledge graph can supply alone. Prior work often emphasizes only part of this loop: graph-augmented RAG retrieves from a pre-built or query-updated graph, KGQA systems search within topic-centered subgraphs, and memory-augmented agents maintain evolving memories without continuously reconciling graph memory with textual context. We propose Co-E, a training-free system built around synchronized bidirectional graph-text working memory. A synchronization cycle consolidates textual memory, extracts relational triples into graph memory, and injects graph facts back into the generation context. Because both memories are maintained, they shape subsequent retrieval and generation. Evaluated on six multi-hop QA benchmarks, Co-E improves over comparable training-free open-backbone baselines and is competitive with larger or trained systems.

Anomaly detection on multivariate sensor time series is critical for industrial monitoring of cyber-physical systems (CPS), where even subtle deviations from normal behavior can indicate process disruption. Recent graph-based approaches have made significant progress, but they often struggle in small-scale physical systems with scarce labeled anomalies and limited normal data. In such settings, graph-based models tend to capture spurious correlations and produce unstable sensor topologies. We propose DPR-GM (Domain-Prior-Regularized Graph Modeling), a forecasting-based framework that incorporates system design knowledge into graph construction. DPR-GM leverages a large language model (LLM) to extract directed physical couplings between sensor pairs from system documentation, which are encoded as a binary domain adjacency matrix serving as a structural gate over sensor relations. This gate is then modulated by Pearson correlations estimated from normal training data. The anomaly score is further weighted by sensor-level reliability derived from the coefficient of variation. All graph and weighting components are fixed prior to training and add no learnable parameters. On the SKAB benchmark, DPR-GM outperforms graph-based, statistical, and deep learning baselines across F1, AUROC, and AUPRC, showing that domain-structured graph priors are a practical alternative to fully learned topologies in data-scarce CPS.

Learning causal graphs from interventional data is a challenging problem with broad applications. In molecular biology, for example, a central goal is to uncover gene regulatory networks from large-scale perturbation data. An ideal algorithm for this task should scale to thousands of nodes, incorporate interventions even when their targets are unknown, quantify uncertainty, and provide identifiability guarantees. However, existing approaches---e.g. approaches using score-based optimization or approximate Bayesian inference---often fail to meet all of these criteria. To address these limitations, we develop Amortized Bayesian Causal Discovery of Extended Factor Graphs (ABCDEFG). Our method guarantees exact acyclicity, scales to graphs with thousands of nodes, and naturally handles interventions even when their targets are unknown. Additionally, ABCDEFG estimates a posterior distribution whose maximum a posteriori estimate provably identifies the true causal graph up to an equivalence class. On simulated datasets, ABCDEFG achieves state-of-the-art accuracy, producing a well-calibrated posterior distribution while outperforming previous score-based and approximate Bayesian methods. Applied to large-scale single-cell perturbation data, ABCDEFG identifies both established and novel gene targets of growth factors.

This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures. We propose a novel convex optimization framework in which an initial matrix is projected onto an elliptope under a positive semidefiniteness constraint. Several numerical schemes are implemented and compared. The problem falls within the broader class of matrix completion, where off-diagonal entries corresponding to absent edges are fixed to zero and diagonal entries are fixed to one. Beyond this structural constraint, the approach offers greater flexibility than existing methods by allowing control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that better reflect realistic data. This procedure is not designed to yield a uniform distribution over the feasible set; rather, it provides a principled and tunable way to construct correlation matrices suitable for benchmarking statistical methods for graphical model inference. Theoretical guarantees on the existence of solutions are established, both in the general setting and under the additional mean constraint. Simulation studies illustrate the properties of the generated matrices with respect to graph structure. The methodology is applied to two real-world datasets from neuroscience and finance, and a comparison with GAN-based correlation matrix generation is provided.

Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances. We introduce Entropic Curvature, a global, transport-based curvature obtained by extending the Lott-Sturm-Villani framework to graphs through the displacement convexity of entropy along Wasserstein geodesics. We define a tractable Weak Entropic Curvature proxy that lower-bounds the global entropic curvature, and from it derive (i) a Poincare-type inequality controlling oversmoothing, (ii) a transport-entropy generalization bound, and (iii) an expansion paradox proving that sparsity, strong spectral expansion, and positive entropic curvature cannot coexist in large graphs, unifying oversmoothing and oversquashing as opposite ends of a single curvature spectrum. We translate the theory into three practical mechanisms, the E-Gate aggregator, the ENT structural encoding, and Midpoint-Completion Rewiring (MCR), and benchmark them against SDRF, FoSR, BORF, LCP, and Graph Ricci Flow on six node-classification benchmarks, and graph-classification.

Graph-based recommendations are widely adopted in real-world industrial applications. However, graphs in these systems often reach a massive scale, posing notable scalability and efficiency challenges. This requires techniques that can effectively balance predictive quality with computational cost. One promising approach is graph coarsening, an adaptive graph reduction technique that offers a way to systematically construct smaller, yet structurally representative, versions of the original large-scale graphs. In this work, we propose a flexible two-stage diffusion framework that combines graph coarsening with multi-step label propagation in the telecommunications domain. Domain-specific heuristics are applied to first aggregate nodes into meaningful communities, reducing graph size while preserving essential business-relevant relationships. An initial diffusion process done by a Label Propagation Algorithm (LPA) or a Graph Neural Network (GNN) propagates labels across the coarsened graph to produce coarse-grained predictions. Finally, a second LPA within subgraphs generates the final recommendations for individual users. On a real-world telecommunications dataset, when using LPA in both stages, our method achieves up to +24% NDCG@5 over the full-graph LPA baseline. Incorporating a lightweight GNN in the first stage further boosts NDCG@5 by more than 50%, but requires substantial training and inference time. Through extensive experiments and a detailed ablation, we quantify these trade-offs and demonstrate that our coarsening-driven approach delivers an optimal balance between scalability, latency, and recommendation quality.

Accurate yet low-latency depth is essential for radar-camera perception in autonomous systems. Cameras provide rich appearance but lack metric scale, whereas automotive radar offers metric range but is sparse and noisy. Many pipelines are multi-stage or depend on auxiliary annotations, increasing latency and limiting portability. We introduce JustDepth, a single-stage radar-camera depth estimator trained only with radar, camera, and single-scan LiDAR. All radar returns are aggregated into a fixed-width 1D representation, decoupling runtime from point count. A Height Fusion Block fuses modalities, a lightweight GNN propagates depth globally, and a training-only confidence decoder stabilizes learning with zero test-time cost. We mitigate stripe artifacts via simple augmentations and quantify them using the Vertical-Horizontal Gradient Ratio (VHGR). On nuScenes, compared to recent state-of-the-art methods, JustDepth maintains accuracy while reducing inference time by 39.7x and stripe artifacts by 66% as measured by VHGR.

Chemists and materials scientists increasingly use machine learning models, such as graph neural networks (GNNs), to predict properties of molecules and the outcomes of their reactions. Beyond predictive performance, understanding how these models organize chemical information internally in their latent spaces, i.e., the embeddings of the molecules, is critical. Analyzing latent spaces helps diagnose model behavior and assess whether the learned embeddings are organized in ways that reflect meaningful chemical relationships. Unfortunately, existing methods provide limited support for analyzing latent spaces across layers and across different model states (e.g., training epochs, model configurations, and input data), making it difficult to understand how these latent spaces evolve throughout a model or relate to chemical concepts. We present LatentFlow, a visual analytics system developed in collaboration with a domain expert for analyzing latent spaces in molecular GNNs. LatentFlow groups embeddings into clusters and supports exploration of latent spaces by tracking how these clusters change across layers and model states using a modified Sankey diagram. To support interpretation, LatentFlow links these clusters to representative molecules and their shared substructures, and it allows scientists to introduce their own domain knowledge and compare it with the patterns found in the latent spaces. We evaluate LatentFlow through two case studies. The results show that LatentFlow helps scientists understand how latent spaces evolve, identify meaningful molecular patterns, and better interpret model behavior.

Coarsening-based training for graph neural networks (GNNs), i.e.\ training on coarsened graphs rather than the original large ones, has become a promising direction for scaling GNNs to massive graphs. However, prior work has been evaluated almost exclusively on \textit{homophilic} graphs, leaving the more challenging \textit{heterophilic} settings underexplored. We show, both empirically and theoretically, that existing coarsening-based training methods suffer significant performance degradation on heterophilic graphs due to inevitable loss of graph information during coarsening. To address this, we propose {\bf A}daptive {\bf C}omplementary {\bf E}nhancement, a plug-and-play, model-agnostic strategy that reintegrates the information discarded in coarsening: ACE learns a projector for re-constructing original node features and applies \textit{anisotropic structural regularization} to embed local heterophily. We further adopt \textit{homoscedastic uncertainty weighting} to adaptively balance the combined training objective of primary coarsened-graph training loss and full-graph auxiliary loss with augmented node features re-constructed by the heterophily-aware projector. Extensive experiments show that ACE drives consistent gains on heterophilic benchmarks while preserving competitive results on homophilic graphs with minimal computational overhead. Code is available at the GitHub repository: https://github.com/vasile-paskardlgm/ACE.

We present a traffic-signal control interface in which a shared graph neural network assigns scores to individual traffic movements. Each junction converts these scores into its own variable-sized set of legal signal phases using a deterministic incidence matrix. Directed corridor nodes provide traffic context, while movement nodes represent controlled input-to-output paths through junctions. Typed mean aggregation produces one scalar per movement; phase definitions and signal timing remain outside the learned network. This makes graph size and junction-specific action count independent of the learned parameter shapes. PPO experiments evaluate the interface on unseen synthetic grid geometries, altered signal coverage, and five heterogeneous city graphs. The policies retained performance across unseen geometries within the synthetic grid family, while changes in signal coverage exposed sensitivity to a signal-coverage distribution shift. A single trained city-policy instance executed across all five city graphs, with heterogeneous outcomes. These results provide feasibility evidence rather than a general estimate of transfer to arbitrary road networks.

Molecular property prediction from structure often uses a single representative conformation, even though many molecules exist as conformational ensembles in solution. We introduce EnsembleEGNN, a molecular ensemble foundation model that encodes an ensemble by first encoding each conformer with shared Equivariant Graph Neural Network (EGNN) layers, then pooling the resulting conformer representations with a Set Attention Block. We pretrain the model on CREMP, a cyclic peptide ensemble dataset, using a multi-task self-supervised objective combining masked token recovery, noisy-coordinate reconstruction, and pairwise distance reconstruction. On the CREMP-CycPeptMPDB dataset, training EnsembleEGNN from scratch fails entirely ($R^2=0.005$). However, the pretrained model reaches $R^2=0.477$ and Pearson $r=0.699$, outperforming the sequence-only BERT baseline ($R^2=0.439$, Pearson $r=0.667$). When EnsembleEGNN is co-trained end-to-end with the BERT sequence encoder, the hybrid model improves further to $R^2=0.538$ and Pearson $r=0.737$. These results demonstrate that encoding conformational ensembles into a single thermodynamically informed embedding improves cyclic-peptide property prediction.

The Shannon capacity $Θ(G)$ of a graph $G$ quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel. It is lower bounded by $α(G^d)^{1/d}$ for any $d$, where $α(G^d)$ is the independence number of the $d$-th strong product of $G$. We construct independent sets of size $134753$ in $C_7^{10}$, $21909$ in $C_{11}^{6}$, $62530$ in $C_{13}^{6}$, and $8076974$ in $C_{15}^{8}$, improving the best known lower bounds for the Shannon capacity of these graphs to $Θ(C_7)\geq 134753^{1/10}>3.258020$, $Θ(C_{11})\geq 21909^{1/6}>5.289773$, $Θ(C_{13})\geq 62530^{1/6}>6.300109$, and $Θ(C_{15})\geq 8076974^{1/8}>7.301399$. We also improve the best known lower bounds on the independence numbers of several individual strong products of odd cycles that do not improve the Shannon capacity lower bound. The constructions were discovered through iterative interactions with a Large Language Model (LLM), illustrating the potential of LLMs for finding explicit combinatorial constructions.

Instance-level explanations aim to reveal the rationale behind a model's decisions for a specific graph. Previous methods explain graph neural networks (GNNs) by selecting important edges to induce subgraphs, where edge importance is assessed by perturbing each edge and observing changes in the model predictions. However, they often neglect the synergistic effects among edges, which are crucial for accurately characterizing edge importance. To address this issue, we propose SeeExplainer, a parameter-free explainer to interpret GNNs. Specifically, we first introduce a granular-ball graph refinement mechanism that decomposes a graph into several disjoint granular-balls with no fixed size, and utilize them as nodes to construct a structural graph. This process can better capture the synergistic effects among edges. Then, we perturb nodes and edges in the structural graph to generate explanatory subgraphs based on their respective contributions. Experiments on several graph classification datasets of different networks show that SeeExplainer outperforms state-of-the-art baselines.

Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations. We formulate SFL as a statistical learning problem in which optimal subgraph operators are inherently data-dependent. To address the difficulty of directly estimating such operators, we develop a subgraph filter algebra based on distance-aware Laplacian constructions, defining a structured and controllable class of filters for effective approximation. We further establish performance risk bounds under the least squares loss, quantifying how well the learned operator approximates the restricted ambient mapping. Experiments real-world datasets show that, for SFL tasks, the proposed algebraic models consistently outperform polynomial filters, distribution-agnostic operators, and direct numerical filter learning baselines that attempt to recover the underlying structure from data.

We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution. Path-integral methods such as Integrated Gradients provide an axiomatic formulation of attribution, but their practical use in deep GNNs typically relies on finite-sample numerical approximations to the path integral, requiring a trade-off between quadrature error and computational cost. This paper proposes APEX, a model-attribution co-design framework that makes the attribution integral exactly computable under a polynomial GNN architecture. The key component is PolyGIN, a GIN-style graph network whose message-passing, normalization, and transformation operations preserve a bounded multivariate polynomial form for scalar model scores, such as pre-softmax logits. We show that, for a PolyGIN with $L$ polynomial transformation blocks, the derivative along the attribution path has degree at most $2^L-1$. Therefore, Gauss--Legendre quadrature can evaluate the Aumann--Shapley path integral exactly, up to floating-point precision, with $2^{L-1}$ deterministic evaluation points. The resulting attributions can be computed at the feature level and then aggregated into node-level scores while preserving completeness. Experiments on synthetic and real-world graph benchmarks show that PolyGIN maintains competitive predictive performance, while the complete APEX framework achieves higher attribution fidelity than the compared baselines and substantially reduces the number of evaluations required for path integration.

Stress is a dynamic process characterized by significant individual variability in facial expression. Traditional architectures, such as Recurrent Neural Networks (RNNs) and Convolutional Neural Networks (CNNs), often overlook person-specific baselines or lack the representational capacity to model the non-linear temporal progression of distress due to sequential bottlenecks and rigid grid-based constraints. Furthermore, many deep learning models lack the interpretability required for clinical deployment. This study introduces StressGAT, a Graph Attention Network that leverages the relational inductive bias of graph modeling to capture complex facial dynamics that indicate acute stress. By using Differential Action Units, the framework normalizes individual responses relative to neutral baselines to achieve personalized recognition. The proposed model achieves 88.62% accuracy on a diverse stress-induction cohort (58 participants) using a subject-independent, Leave-One-Subject-Out (LOSO) cross-validation protocol. Beyond predictive accuracy, the architecture integrates a Multiple Instance Learning (MIL) attention mechanism to identify peak stress intervals and reveal distinct expressivity phenotypes. By simultaneously optimizing for accuracy and interpretability, this framework provides a robust, explainable solution for personalized affective monitoring.

Graph Neural Networks trained on heterogenous bipartite graphs form a common basis in recommendation systems. These graphs often express relations that vary in cardinality, for example, user-item preferences are one-to-many and user-attribute features are one-to-one. Traditionally, a unique loss function is applied for all of the network components which is often Bayesian Personalized Ranking (BPR). While BPR works well for the recommendation task, we find that it causes attribute embeddings to collapse to near-random geometry -- a silent failure that leaves standard ranking metrics largely unaffected and therefore invisible to conventional evaluation. This in turn pollutes user node embeddings, which are shaped by both edge types simultaneously, hurting downstream tasks like personalization, segmentation, etc. Here we propose a Cardinality-Decomposed Loss (CDL) that combines both Cross Entropy (CE) and BPR to enable the model to collectively optimize for relations across cardinalities. We confirm this CE-BPR conflict by showing the two losses compete in the shared encoder's parameter space. We evaluate CDL on five datasets spanning two structural configurations -- one-to-one attributes on user nodes (MovieLens-1M, Last.fm-360K, PayPal Audience Factory, BookCrossing) and on item nodes (Yelp) -- and find that CDL consistently improves discriminability in attribute embeddings. We also show that ranking (NDCG) improves when attributes carry meaningful preference signal, but conflicts with it when the correlation is weak. We use a lambda parameter to navigate this trade-off, and a lambda-sweep reveals that dataset behavior is governed by two graph properties -- semantic alignment and topology leakage. Semantic alignment measures whether the attribute predicts preferences, while topology leakage measures whether the graph's connectivity already encodes it.

Machine Learning models are widely used for automating classification tasks by extracting statistical patterns from data. However, their performance deteriorates if the data distribution changes, making them ill-suited to handle uncertain and evolving information. Moreover, they provide limited support for integrating prior knowledge. To address these limitations, we present CLARK (Closed-loop Learning for Adaptive Reasoning over Knowledge Graphs), a framework that integrates knowledge graphs, symbolic rule mining, and probabilistic reasoning under the Logic Programs with Markov Logic Networks (LP$^{\text{MLN}}$) formalism. Starting from CACTUS-derived KGs, CLARK translates graph structure into an LP$^{\text{MLN}}$ program and iteratively enriches it with candidate rules proposed by symbolic learners. These rules are calibrated through probabilistic weight learning, enabling reasoning under uncertainty and refinement of the underlying graph structure. We evaluate CLARK on two medical datasets, analysing both rule quality and downstream classification performance. Results demonstrate that CLARK leads to improved classification performance and more generalisable inference. Overall, CLARK provides a principled approach to constructing adaptive, interpretable, knowledge-driven models for classification.

The HIPE-2026 shared task introduces person-place relation extraction from multilingual historical newspapers as a new evaluation track, classifying the at and isAt relations between pre-annotated person and location mentions in English, French, and German. Motivated by the cost of processing historical archives at scale, our team (DS@GT HIPE, team 2 in the official results) investigates how far a lightweight, interpretable system can go without any pretrained language model at the relation classification stage. Our approach builds a document-level graph from dependency parses, extracts proximity-based and part-of-speech features for each entity pair, and classifies them with small scikit-learn ensembles or compact Graph Attention Networks, keeping every submitted run under 847K parameters. On the official evaluation (Test A, the newspaper test set), our best run reached a macro recall of 0.5142, ranking 3rd on the Efficiency profile while placing mid-table on Accuracy among the 17 participating teams. Two findings stand out. First, minimum character distance alone captures most of the classification signal; adding further engineered features yields inconsistent gains and sometimes degrades performance, echoing prior evidence that argument distance dominates relation extraction. Second, document-grouped cross-validation is essential on this corpus: pair-level splits inflate scores by 25-37 percentage points because entity mentions recur across documents, a data-leakage effect that grouped cross-validation removes.

The Traffic Assignment Problem is a fundamental but computationally expensive component of transportation planning. While Graph Neural Networks have emerged as fast, data-driven surrogates, their practical deployment is severely constrained by a spatial generalization gap. Standard models rely on transductive feature initializations that tie travel demand to fixed network topologies, preventing seamless transfer to new urban environments. To overcome this structural limitation, this research proposes a network-agnostic initialization layer, termed Geometrically Unconstrained Inductive Demand EmbeDding (GUIDED). By injecting travel demand as a scalar attribute on auxiliary virtual links rather than as specific node features, this modular framework standardizes the input space regardless of network scale. Extensive experimental evaluation across multiple urban topologies demonstrates that a Heterogeneous Graph Attention Network (HetGAT) model integrated with the proposed GUIDED layer maintains state-of-the-art predictive accuracy on single-network tasks, while demonstrating superior robustness to out-of-distribution demand patterns and maintaining a distinct performance advantage over the baseline even under severe data scarcity. Notably, the proposed feature initialization enables highly parameter-efficient domain adaptation for inter-network transfer learning without artificial input homogenization, establishing a robust foundation for truly inductive models. At the same time, the optimized scatter operations of the initialization layer yield an approximate 50% reduction in training time per epoch compared to the baseline approach. Furthermore, while demonstrated on vehicular traffic, this fundamental abstraction of spatial topology provides a versatile blueprint for generalized origin-destination spatial problems, such as freight logistics and multimodal network optimization.