Graph Neural Networks

Legal precedent retrieval is a fundamental task in legal case preparation, planning, litigation strategy, and legal research. Current approaches for automatic precedent retrieval map legal documents to a low-dimensional semantic space and compute similarity based on the proximity of their representations. These approaches treat legal documents as monolithic texts, ignoring the rhetorical organization of the legal technicalities. Ergo, they overlook nuanced legal meanings and fail to distinguish the contextual significance of legal entities and concepts that vary based on their rhetorical roles within the document. To address this insufficiency, we propose the PRecG pipeline that computes the similarity between pairs of legal judgments by hierarchically learning their representations. The process begins by decomposing each document into distinct semantic units (segments) based on the rhetorical roles of sentences. For each rhetorical segment, a knowledge graph is constructed to capture the legal entities and their relationships within the segment. Contextual representations of the entities are then learned and aggregated to derive segment-level embeddings. These embeddings are further integrated to produce a unified document-level representation, and finally, the semantic similarity between a pair of documents is computed. We validate the performance of the proposed approach through extensive experiments on a benchmark Indian legal dataset, comparing it against state-of-the-art baselines to demonstrate its effectiveness.

Graph Neural Networks have emerged as a powerful tool for the fast and accurate prediction of various crystal properties. These models often encode domain-specific knowledge into their graph encoding modules, which increases their parameter size and makes their performance heavily dependent on domain expertise. Added to this, explicitly incorporating all chemical and structural features, that might influence a specific crystal property into the GNN encoder, is a challenging task. In this work, we propose a soft prompt learning framework that captures latent features essential for property prediction, which are not explicitly provided to the GNN. We introduce a novel multilevel graph prompt learning framework comprising both node-level and graph-level soft prompts. At the node level, we capture the local chemical semantics of different atom types, while at the graph level, we encode the global structural symmetry of the crystal graph. Our proposed prompt learning framework is lightweight and seamlessly integrates with any existing GNN encoder. Extensive experiments on popular benchmark datasets show that incorporating prompt learning significantly improves (3% - 15%) the performance of state-of-the-art GNN models in crystal property prediction tasks. Furthermore, the learned soft prompts enable cross-property knowledge transfer, enhancing prediction performance for properties with limited training data. Code is available at https://github.com/shrimonmuke0202/Prompt.git

Time series reasoning is essential for real-world problem-solving. While both Large Language Models (LLMs) and Vision-Language Models (VLMs) can reason about time-series data, their capabilities are complementary: LLMs process time series as text sequences and thus preserve exact numerical understanding, but struggle with global patterns, whereas VLMs efficiently capture these patterns by visualizing time series but may lose fine-grained details. Moreover, models vary significantly in task-specific expertise and inference costs. Dynamically selecting the most suitable modality and model for each query is therefore crucial, yet challenging because it requires modeling the complex interactions among tasks, queries, modalities, and models, which carry rich contextual signals. To this end, we introduce TSRouter, a graph-based dynamic routing framework. TSRouter constructs a heterogeneous graph of task, query, modality, and model nodes to contextualize the interactions among query characteristics, modality attributes, and model capabilities. TSRouter formulates routing as a candidate scoring problem, where each modality-model pair is evaluated based on user-defined performance-cost preferences to select the optimal candidate. Comprehensive evaluations on 4 distinct time series reasoning tasks reveal that TSRouter substantially outperforms diverse baselines with 16% to 46% relative improvements. Furthermore, TSRouter demonstrates robust zero-shot plug-and-play generalization to unseen models and novel tasks and preserves high performance while reducing computational overhead through cost-aware optimization. Our code is available at https://github.com/tianyi-lab/TSRouter.

Missing data is ubiquitous in real-world datasets. Traditional methods either discard incomplete samples or apply imputation techniques that ignore potentially informative missingness patterns, implicitly assuming that missingness occurs randomly. However, missingness patterns might provide additional information. We propose pattern-aware graph neural networks that explicitly encode which features are missing alongside observed values. We used four encoding strategies -- learned embeddings, frozen random embeddings, statistical features, and hierarchical representations -- across seven UCI datasets with naturally occurring missingness. Our Pattern-aware methods achieve substantial improvements over baselines, with an average improvement of 17% in balanced accuracy and 22% in F1-macro across all datasets. The benefits vary significantly by dataset: annealing shows dramatic improvement (+80% balanced accuracy), while hepatitis and soybean show minimal gains (+4--5%). Notably, even simple random pattern embeddings perform comparably to learned embeddings (0.650 vs 0.663 balanced accuracy), suggesting that distinguishing between patterns may be more important than task-specific optimization. Our ablation study reveals that attention mechanisms, while helpful, are not critical when pattern information is available -- simple mean aggregation with pattern awareness achieves 0.640 balanced accuracy compared to 0.645 for attention-based variants.

While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP's 2D projection introduces. We demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions versus sparse periphery, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).

Graph Neural Networks (GNNs) have shown considerable success in learning from graph-structured data, but their use in privacy-sensitive areas remains difficult because graph structure can leak sensitive link information. To satisfy edge-level differential privacy, a common approach is to inject noise into all elements of the graph's adjacency matrix, thereby obfuscating the existence of any single edge. However, stronger privacy requires more noise, and excessive noise reduces utility, making the privacy-utility balance a major barrier to practical privacy-preserving graph learning. To address this issue, we propose EdgeRefine, a local differential privacy framework that improves this trade-off through adaptive edge refinement. EdgeRefine first estimates edge-existence probabilities using Jaccard similarity and ranks edges for noisy edge removal. To ensure the sparsity and reliability of the final graph, it uses the privacy budget $ε$ to determine the ratio of true to false edges, samples them separately based on this probability ranking, and controls the total number of edges with a separate sampling rate $k$. Extensive experiments show that EdgeRefine achieves accuracy comparable to the noise-free baseline and substantially outperforms other privacy-preserving methods across datasets and GNN architectures. Under privacy budget $ε= 2.5$, EdgeRefine improves node classification accuracy over state-of-the-art baselines by 17.8% on ACM under GAT and 19.7% on Cora under GCN. In graph classification, it achieves an average accuracy degradation of around 5% compared to the noise-free baseline. Under graph reconstruction attacks, EdgeRefine maintains relative absolute error levels above 1 across all privacy budgets, averaging 1.962 on Cora and 1.472 on AMAP, indicating strong resilience against privacy leakage.

Heterogeneous graph built on notes, lyric syllables, and accompaniment events is a natural representation of symbolic music score, providing a substrate for both philological analysis and computational tasks. Music features are therefore well-captured by graph geometry and its properties. This representation has proved effective for analytical tasks as cadence detection, voice separation, and stylistic classification. In the present work, the reduction of harmonic complexity of a music score on graph, by preserving task-relevant information, relation between notes, and graph structure is investigated. A compression scheme for the piano subgraph of vocal-pianistic scores, built on binary wedge partitioning trees, is proposed. The wedges are generated through a fully adaptive greedy algorithm that recursively minimizes the $L^2$-error within a six-dimensional Tonnetz embedding of musical notes. The partitioning process employs a splitting criterion based on harmonic distance, resulting in regions that accurately reflect the intrinsic harmonic relationships among notes. The reconstructed music scores obtained through piecewise-constant functions and the mean values of the notes inside each wedge are used as a new simplified scores human-readable and playable. Some experiments on a corpus of symbolic music scores of three different composers are performed to assess the proposed approach.

The problem of learning constant-depth circuits holds profound implications for computational learning theory. In a seminal result, by introducing the low-degree algorithm, Linial, Mansour, and Nisan (J. ACM 1993) presented a quasipolynomial-time learner for $\mathsf{AC}^0$ under the uniform distribution. However, obtaining comparable learning guarantees for broader classes of correlated distributions has remained a longstanding challenge. Recently, Chandrasekaran, Gaitonde, Moitra, and Vasilyan (arXiv 2026) extended these guarantees to Gibbs distributions on bounded-degree graphical models with both strong spatial mixing and polynomial growth. In this paper, we give a quasipolynomial-time learner for $\mathsf{AC}^0$ under graphical models that admit efficient local samplers, circumventing the polynomial-growth requirement in prior work. The key ingredient is a new low-degree approximation for Gibbs distributions, established by simulating and suitably truncating the classical Glauber dynamics. As applications, this framework yields learners for two-spin systems, including the hard-core model and Ising model, on arbitrary bounded-degree graphs, in regimes approaching their respective sampling thresholds.

Existing retrieval-augmented generation (RAG) systems treat web pages as flat text, losing the structural and semantic signals encoded in HTML. We present PolyUQuest, a verifiable, structure-aware web RAG framework built on a heterogeneous graph that unifies hyperlink topology between pages, DOM hierarchy within pages, and entity-relation knowledge across pages. A two-tier router dispatches each query to one of three retrieval modes matched to its structural need, including direct block retrieval, cross-page graph traversal, and multi-hop entity reasoning. Every answer is fully verifiable, as each cited block carries its source page, heading path, and entity links so that users can trace any claim back to its structural evidence. We evaluate on the official websites of the Hong Kong Polytechnic University (PolyU), comprising 4,240 pages, 31,086 DOM blocks, 29,119 entities, and 37,680 relations, together with a multi-type evaluation benchmark. PolyUQuest outperforms existing RAG systems in answer correctness, coverage, and faithfulness, while consuming significantly fewer LLM tokens per query. The demonstration provides an interactive interface for inspecting cited answers, comparing retrieval traces across routing modes, and exploring evidence graph paths. PolyUQuest is being prepared for deployment as a student-facing QA service at PolyU.

Recent algorithmic advances have made directed acyclic graph (DAG) structure learning scalable for causal discovery. Yet, the currently available techniques assume a completely homogeneous population, precluding their application to clustered data where cluster-specific variations (e.g., patient-specific effects) are common. We address this issue by introducing a new approach that estimates a global structure while accounting for local cluster-level effects. The key idea is to extend the fixed- and random-effects framework of classical mixed models to the structure learning setting. Towards this end, we present a differentiable graph coupling mechanism that guarantees the union of the fixed- and random-effects graphs remains acyclic. Computationally, we provide a provably convergent first-order method and leverage efficient batched updates across clusters. Statistically, we establish identifiability of the model and show that our approach recovers the true structure asymptotically. In experiments on real and synthetic data, our proposal detects dependencies missed by alternative estimators, underscoring its value for structure learning in clustered settings.

We present path_boost, a Python package for interpretable supervised learning on graph-structured input data. The package implements PathBoost, a gradient boosting algorithm that automatically discovers predictive labeled paths within graphs during the learning process. Unlike graph neural networks, which are generally difficult to interpret, PathBoost produces an additive prediction model over path-based features that explicitly reveals which substructures drive predictions. To avoid an exhaustive enumeration of all possible paths, the algorithm iteratively selects and extends paths during learning based on their predictive power, using boosting to combine weak learners into a strong ensemble. The package supports both regression and binary classification. Key features include compatibility with scikit-learn workflows, support for custom base learners and selectors, automatic starting node selection, parallel training across anchor nodes, and built-in variable importance computation. We demonstrate PathBoost on molecular property prediction of transition metal compounds, where atoms serve as nodes and bonds as edges, and further benchmark PathBoost against an established graph neural network and a graph kernel method across six molecular datasets. The package is available on PyPI and GitHub under an open-source license.

For seemless control of advanced hand prostheses and augmented reality, accurate and immediate hand gestures recognition is essential. Surface electromyography (sEMG) signals obtained from the forearm are commonly employed for this purpose. In this paper, we present a novel approach for sEMG representation that utilizes graph networks which contain information about muscle activation patterns in the forearm. Based on these graph networks, we have developed a machine learning algorithm capable of real-time hand gesture recognition using a graph neural network. The algorithm's performance was evaluated using sEMG signals acquired from myoband, which has 8 electrodes placed around the forearm, involving 8 healthy subjects. The proposed method demonstrated an average classification accuracy of 99%, surpassing the performance of state-of-the-art techniques. The average time for both graph construction and prediction stood at 48ms utilizing a M1 pro CPU, rendering the approach well-suited for real-time applications.

EEG-based emotion recognition is critical for mental health monitoring and affective brain-computer interfaces, yet existing deep learning approaches often treat emotion classes as isolated labels, ignoring their psychological interdependencies. We propose a graph-regularized learning framework that conceptualizes emotions as nodes in a graph where edges encode proximity based on dimensional emotion theories. We adapt three complementary regularization strategies--Graph Label Smoothing (intuitive soft labeling), Commuting distance on graph via Graph Laplacian (spectral graph theory), and Sliced Wasserstein Distance (optimal transport on graph)--ordered by increasing computational complexity. These strategies penalize model predictions that deviate from the established emotion topology. Our framework is evaluated across three representative backbone architectures: AudioTransformer (pure transformer), Conformer (CNN-transformer hybrid), and DCGNN (causal graph neural network), demonstrating architecture-agnostic benefits. Experiments on SEED-IV (4 classes) and SEED-V (5 classes) datasets show consistent improvements: best case up to +5.42% accuracy and 39% reduction in psychologically implausible misclassifications. Ultimately, our framework help raise the upper bound of performance achievable with standard approaches. Code will be released.

Alzheimer's disease (AD) is a common neurodegenerative disorder, and early diagnosis is of great significance for delaying disease progression and enabling timely intervention. Mild cognitive impairment (MCI), which represents an intermediate clinical stage between cognitively normal aging and AD. Structural magnetic resonance imaging (sMRI) provides detailed characterization of anatomical structures and plays an important role in AD-related brain analysis. However, existing sMRI-based brain network methods typically rely on a single graph construction strategy, limiting their ability to jointly capture spatial relationships and morphological similarities between brain regions. To address these issues, this paper proposes an sMRI-based multi-view masked graph neural network model (MVMGNN) for AD diagnosis. A joint node-edge masking mechanism is proposed to simultaneously select radiomics feature dimensions and structural connections, reducing redundancy during graph learning. Furthermore, a patient-level cross-view gated fusion mechanism is proposed to integrate multi-view representations. Experimental results on the ADNI dataset demonstrate that MVMGNN outperforms several competing approaches in AD classification. Interpretability analysis further demonstrates that MVMGNN is able to identify key brain regions associated with AD, providing useful insights into discriminative patterns in sMRI-based brain networks.Our implementation is publicly available at https://github.com/chenzhao2023/MVMGNN_AD

Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation. We provide one. Data augmentation induces a similarity graph on the unlabeled data, so downstream learning on that graph is graph-Laplacian-regularized learning. We prove a fast transductive rate, $O(1/n_L)$ in the number of labels, in place of the supervised $O(1/\sqrt{n_L})$, by carrying the leave-one-out stability apparatus of Johnson and Zhang (JMLR 2007) over to the augmentation graph, and without the unrealistic assumptions of limit-based analyses (exact kernel, generalizing features). The bound makes augmentation quality explicit: the expected error is at most $C/n_L + R_{\mathrm{DA}}(y)$, where the data-augmentation alignment error $R_{\mathrm{DA}}(y)$ is proportional to the graph-cut mass of augmentations that cross a label boundary, so good augmentations let few labels suffice. The analysis uses a streamlined loss that drops the projector, negative-sample, and orthogonality overhead of standard objectives yet still recovers the top-$K$ ideal features in the infinite-data limit, the augmentation-kernel eigenspace studied by Zhai et al. The bound gives a mechanistic account of the accuracy-versus-label-count curve through augmentation quality, verified in a controlled model where the constants are known.

Logical Multi-Hop Query Answering over Knowledge Graphs (KGs) can be formulated as querying, with an implicit completeness assumption. Current works mainly focus on Existential First Order Logic (EFO) queries. These EFO queries contain conjunction, disjunction, and negation operators. Most existing works employ transductive reasoning, meaning they are not capable of reasoning over entities unseen during training. In the real world, there is a resource scarcity, and we cannot train a model with all the nodes of a large KG. Hence, we propose InductWave, a wavelet-based inductive embedding method for logical query answering on large KGs. Here, the training graph consists of fewer nodes than the test graph. Our model performs on par with the baseline models while having half the number of message-passing layers. It outperforms all of them in most cases, with 75% of the layers. These fewer resource requirements enable us to evaluate InductWave on massive graphs, such as Wiki-KG. We test our model using extensive experiments across varying train-test graph proportions of the FB15k-(237) dataset, comparing it with the state-of-the-art models. The code and datasets for the model are available at https://github.com/kracr/inductwave/.

Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures. We propose learnable spectral PEs of the form $h_θ(A_q)\,R$, where $A_q$ is a normalized magnetic operator, $h_θ$ a learnable scalar spectral response, and $R$ a block of random probes. Because the PE is a \emph{matrix function} of the operator, it is gauge-invariant by construction. We compute it in a Hermitian block Krylov subspace from sparse matrix--vector products only, prove that $k = O(\log(1/\varepsilon))$ block steps suffice uniformly over heat--resolvent response families, and give a covering-number argument for why low-dimensional structured families generalize where free per-eigenvalue weights overfit. On a directed SBM whose symmetrization is uninformative by construction, direction-blind PEs stay at chance while magnetic Krylov PEs converge to the exact-eigendecomposition oracle as the depth grows. The same probes yield gauge-invariant pairwise features with $1/\sqrt{s}$ Monte-Carlo error, and the undirected $q{=}0$ case improves heterophilous benchmarks over no-PE and polynomial baselines.

Event-based cameras are gaining popularity as the sensor of choice for mobile robotics, due to their high performance in dynamic environments. However, these applications require efficient real-time data processing with low latency and power consumption. One strategy to meet these stringent requirements is hardware acceleration of efficient algorithms that preserve the temporal sparsity of event data. In this work, we propose an optimization strategy for Graph Convolutional Neural Networks models aimed at adapting their architecture to the limited resources of embedded heterogeneous FPGA platforms. Our method incorporates hardware-aware pruning and quantization, taking into account the trade-off between on-chip memory savings and inference accuracy. Strategic exploration of the design space with Fine Grid Search and Greedy layer-wise Iterative Deepening Search methods enables flexible adaptation of the model architecture to the target platform. Our approach was evaluated across various network configurations and multiple datasets, resulting in BRAM memory reductions of 28.8% for CIFAR-10 (with a 1.65% decrease in accuracy), 31.4% for MNIST-DVS (accuracy drop of 3.55%), and 26.5% for N-Caltech101 (with a 5.18% accuracy reduction).

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att

We introduce EntroPath, a manifold learning method that recovers geodesic geometry from data graphs through ensembles of diffusion paths. Many existing graph-based embeddings rely either on locally normalised random walks or on shortest-path distances. The former can concentrate diffusion in densely sampled regions, while the latter are sensitive to spurious shortcut edges in the graph. EntroPath instead builds its dissimilarities from the maximum entropy random walk (MERW), which aggregates the full ensemble of k-step paths between points rather than relying on any single trajectory. We show that the resulting free-energy dissimilarity converges to squared geodesic distance in the short-time limit, via Varadhan's heat-kernel formula. The diffusion depth k interpolates smoothly between local neighbourhood structure and global manifold geometry, and the symmetrised kernel admits an exact Gram factorisation connecting EntroPath to kernel methods. We further provide scalable extensions via landmark projection and diffusion-potential pseudotime. Across synthetic manifolds and single-cell benchmarks, EntroPath consistently matches or outperforms diffusion- and shortest-path-based methods, while remaining competitive with neighbourhood-preserving embeddings (UMAP, t-SNE) on local-structure metrics. Its gains are most pronounced on manifolds with non-uniform sampling density and well-separated branching trajectories, where path-ensemble diffusion more faithfully preserves the underlying geodesic geometry.

This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport. While traditional Gromov-Wasserstein and semi-relaxed variants (srGW, srFGW) capture graph structure, they often struggle with sparse, noisy, or partially observed graphs. Inspired by Graph Diffusion Distance, which posits graphs are similar if they enable similar information transmission patterns, DsrFGW incorporates diffusion processes allowing information propagation across nodes, capturing local and global structural patterns while reducing sensitivity to noise or missing edges. An extensive evaluation on 36 synthetic pairwise graph matching tasks (easy, medium, hard) demonstrates consistent superiority over srFGW, achieving accuracy improvements of 0-20 percentage points and dramatic Adjusted Rand Index (ARI) gains: in medium-difficulty scenarios, srFGW often achieves negative ARI (worse than random) while DsrFGW offers better performance in terms of both internal and external clustering quality measures (i.e., Adjusted Rank Index and Accuracy with respect to the true underlying clusters, respectively). Even under severe noise, DsrFGW improves clustering quality in 92% of the synthetic tasks with optimal diffusion scales adapting to problem difficulty, establishing DsrFGW as a robust framework for graph comparison under structural uncertainty.

Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets. In particular, sampling mechanisms based on DPPs are believed to demonstrate better approximation properties compared to classical i.i.d. samplers, even at the scale of the exponent. One of the key strengths of DPP based samplers is that they can be deployed over very general spaces, in contrast to more classical sampling methods beyond i.i.d. which tend to work in very well-structured settings, principally Euclidean spaces. In this work, we establish explicit rate guarantees for determinantal sampling in spaces that extend far beyond known Euclidean setups, focusing on spectral kernels obtained from eigenspaces of naturally associated Laplacian and other Markov diffusion operators. This includes, in particular, Riemannian manifolds and weighted networks. In determinantal sampling from compact Riemannian manifolds, we establish sampling rates that automatically pick up the intrinsic dimensionality $d_{\text{int}}$ of the underlying manifold. In the setting of networks, we investigate DPP-based samplers on the celebrated k-nearest neighbour graphs, as well as weighted random geometric graphs, and demonstrate a similar improved dependence on the intrinsic dimensionality of the data. Overall, our approach achieves guarantees of $\big(\text{sample size}\big)^{-\frac{1}{2}-\frac{1}{2d_{\text{int}}}}$ that match known rates on Euclidean spaces of comparable dimension. In terms of techniques, we connect to the celebrated Weyl's Law for manifold spectra, and leverage tools from the theory of Markov diffusions and Dirichlet forms as well as certain ingredients from the theory of pseudodifferential operators, which could be of independent interest in this area.

Molecular property prediction often relies on isolated data modalities, where continuous 3D graph neural networks (GNNs) struggle to efficiently capture long-range topological dependencies and exact macroscopic heuristics. In this work, we introduce a parameter-efficient Tri-Branch Modular Fusion Neural Network that synthesizes three orthogonal modalities: 3D spatial geometry (SchNet), discrete topological grammar (SMILES via ChemBERTa), and explicit macroscopic physicochemical descriptors (Deep & Cross Network). By bypassing standard scalar readouts and employing a shared late-fusion architecture, the framework establishes a mathematically rigorous multimodal latent space that effectively resolves the arithmetic and oversmoothing limitations of local message passing. We evaluate the proposed architecture on the QM9 benchmark, targeting the extensive thermodynamic property of atomization energy at 0 K ($U_0^{\mathrm{atom}}$). Through systematic combinatorial ablation and latent bottleneck optimization ($d_e=64$), the tri-modal framework achieves a validation Mean Absolute Error (MAE) of 0.0207 eV. Operating with fewer than one million parameters, this architecture decisively surpasses the sub-chemical accuracy threshold and yields a substantial 20.6% error reduction over a strictly controlled geometric baseline. Ultimately, our findings demonstrate that integrating orthogonal macroscopic and topological data streams provides a synergistic, $\mathcal{O}(1)$ physical shortcut. This multimodal alignment offers a highly efficient alternative to brute-force parameter scaling, establishing a robust surrogate model for high-throughput virtual screening (HTVS) pipelines.

Random Vector Functional Link (RVFL) networks are popular due to their fast training and universal approximation capabilities. However, RVFL models face challenges in preserving geometric relationships and utilizing multiple feature views effectively. To address these limitations we propose the Intuitionistic Fuzzy Graph Embedded Random Vector Functional Link with Multiview Learning (IFGRVFL-MV) model. The proposed approach comprises three key components: intuitionistic fuzzy sets for uncertainty handling, graph embedding to capture intrinsic geometric structures, and multiview learning to use complementary information from multiple feature spaces. The model assigns intuitionistic fuzzy membership and non-membership values to data points making it robust to outliers. Also, the graph embedding framework preserves topological structures, increasing the generalization performance. We performed experiments on benchmark datasets from UCI and KEEL repositories which concludes that IFGRVFL-MV outperforms existing models in classification accuracy. Our results establish that IFGRVFL-MV is a promising advancement in the domain of uncertainty and multiview environments.

For robots to work reliably in commercial and industrial applications, can recent advances in agentic coding systems combine interpretable robot programming with the open-world adaptability of model-free policies? We focus on "Variational Automation" (VA), a class of tasks that have larger variations in object geometry and pose than fixed automation. Model-free policies often struggle to close the reliability gap for VA tasks, which must be executed persistently and reliably in commercial and industrial applications. Motivated by prior work on Task and Motion Planning (TAMP) and the Robot Operating System (ROS), we introduce Graph-as-Policy (GaP), a multi-agent coding harness that generates directed computation graphs with perception, planning, and control nodes from a Modular Open Robot Skill Library (MORSL). GaP then generates an internal simulation environment to rehearse task instances with different graphs in parallel to iteratively refine the graph structure and parameters to improve success rates and throughput. Evaluation with 8 new open VA task benchmarks, 4 in-simulation and 4 in real-world, suggests that GaP can achieve success rates that significantly outperform baselines. Details, code, and data can be found online: https://graph-robots.github.io/gap

Open-vocabulary 3D scene understanding aims to segment 3D scenes beyond predefined categories by transferring semantic knowledge from vision-language models. Existing methods have advanced this task by lifting language-aligned 2D features into 3D, yet they often rely on context-independent semantic representations, leaving object relationships underexplored for contextual refinement. We propose RelGraphOV, a relationship-aware framework that uses 3D scene graphs to enhance open-vocabulary 3D understanding. Our method constructs relational scene graphs from multi-view observations by leveraging vision-language reasoning to infer object relationships and prune geometrically implausible connections, without manual relationship annotations. To aggregate relational context while avoiding feature interference, we introduce an Adaptive Gated Dual-Stream Contextual GAT that separates dense geometric features and semantic CLIP embeddings, performs edge-guided message passing, and adaptively fuses complementary semantics. A hierarchical contrastive objective further promotes instance-level consistency and category-level discrimination. Experiments on ScanNetV2, ScanNet200, ScanNet$++$, and Replica demonstrate strong performance and generalization ability. Project Page: https://cxavireh.github.io/relgraphov-projectpage

Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes. Examples include utility networks such as water distribution systems or gas networks, electrical grids, and traffic flow networks. Such systems are naturally modeled as metric graphs, where edges correspond to one-dimensional Euclidean subspaces connected at vertices. Metric graphs are independent of an underlying global Euclidean space, limiting direct application of typical PINNs and operator-learning methods. Especially transport dynamics like advection require a methodology able to capture antisymmetric and long-range dependencies on graphs, which is itself a challenge. We propose a novel physics-informed message passing operator that encodes linear advection on metric graphs as an inductive bias. In the purely advective setting, the operator provably recovers the exact dynamics up to a theoretically derived discretization error without any training. Combined with trainable components like MLPs, our message passing operator extends to realistic advection-reaction dynamics in water distribution systems, where we achieve superior performance compared to baselines and zero-shot generalization across different graph topologies.

The performance of deep learning models crucially depends on the settings of hyperparameters like learning rate, initialization scale, and weight decay. Hyperparameter transfer aims to make near-optimal hyperparameter settings consistent across model scale, so that large models can be optimized by proxy tuning their smaller, cheaper-to-optimize counterparts. While transfer principles are well-studied in the context of dense neural networks in language and vision tasks, they remain comparatively under-explored for graph neural networks (GNNs). We develop and validate a transfer parameterization for GNNs trained with SGD, Adam, and AdamW. Through theoretical scaling analyses and controlled experiments, we show that the proposed parameterization yields stable feature updates, learning rate transfer, and improved performance as width and depth increase. For SGD, we identify graph-dependent first-layer correction factors and show that their use can accelerate early training in graphs with sparse bag-of-words inputs. For Adam, we explore how different message passing normalizations affect early- and late-training transfer behavior, illustrating the importance of message passing normalization and advocating for an associated hyperparameter. For AdamW, we adapt a parameterization that allows for the joint transfer of weight decay and learning rate. Together, these results provide a practical recipe for scaling GNNs across a variety of learning tasks and training scenarios.

In patients with breast cancer, pathological complete response (pCR) has been established as a clinically meaningful surrogate marker for long-term outcomes. While commonly treated with neoadjuvant chemotherapy (NACT), effective treatment decision-making remains challenging, as therapeutic response can vary substantially across patients, calling for predictive models capable of accurately estimating individualized treatment response. To address this, we propose an imaging-based 3D spatio-temporal framework for treatment response prediction that integrates a state-of-the-art graph neural network with relational modeling of temporal interactions across timepoints alongside three novel complementary self-supervised treatment trajectory representation learning objectives. Experiments across a cohort of 585 patients from the public ISPY-2 dataset demonstrate that our method substantially outperforms both vision and self-supervised learning baselines across several classification metrics. Alongside establishing a breast cancer pCR prediction benchmark, we include a principled ablation of our method and further introduce and empirically assess the impact of the available number of DCE-MRI timepoints per patient trajectory and the inclusion of inter-scan time-differences. Overall, our study substantiates the utility of clinically meaningful longitudinal medical imagaging modeling for predicting NACT-induced pCR. We will publicly share our code repository and a user-friendly PyPI library for dataset curation upon publication, effectively promoting reproducible open-source research.

Motivated by real-world scenarios where malicious entities tamper with existing networks, we define a model where an adversary seeks to hide a set of \emph{corrupted vertices} inside a graph $G^*$. To this end, the adversary can add edges between the corrupted vertices, as well as edges between the corrupted vertices and $G^*$, and its power is then measured by the size of the \emph{neighborhood} of the corrupted vertices in $G^*$. Our goal is to design an active learning algorithm that efficiently finds the subset of corrupted vertices using a small number of label queries. We devise an efficient algorithm that approximately recovers the corrupted vertices with a query complexity that depends polynomially on both the power of the adversary and the \emph{vertex expansion} of $G^*$, a fundamental measure of graph connectivity. At the heart of this result is a polynomial-time algorithm, obtained by carefully adapting sum-of-squares algorithms for approximating minimum expansion, that finds a set with small vertex expansion subject to cardinality constraints. To the best of our knowledge, this is the first time that the vertex expansion is shown to play a key role in determining the query complexity of active learning algorithms robust to structural adversarial attacks.

Graph-structured data is increasingly generated and stored in decentralized environments, such as social platforms, mobile applications, and edge networks, where users maintain control over their local graph data. However, collecting and analyzing such decentralized graph data for downstream learning tasks raises significant privacy concerns, as nodes and their attributes often contain sensitive personal information. Local Differential Privacy (LDP) has emerged as a promising solution for privacy-preserving data collection without relying on trusted servers. Nevertheless, existing LDP-based graph learning methods typically assume uniform privacy requirements across users, ignoring the heterogeneous and personalized privacy preferences commonly observed in real-world systems. This uniform treatment leads to inflexible noise injection at the data collection stage, resulting in substantial distortion of graph data and degraded utility in subsequent analysis. To address this limitation, we propose PPGNN, a personalized differentially private framework for decentralized graph data. PPGNN enables user-specific privacy budgets during local perturbation while preserving analytical utility. To handle heterogeneous privacy levels and noise distortion, we design a two-stage solution consisting of a Personalized Perturbation Mechanism (PPM) and a weighted calibration strategy, FlexProp. Extensive experiments on six real-world graph datasets demonstrate that PPGNN effectively balances personalized privacy protection and data utility in decentralized graph learning scenarios.

Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks. Although Graph Contrastive Learning has demonstrated promising performance, existing methods often suffer from the "structural isolation" issue during mini-batch training, making it challenging to capture cohesive community structures that characterize the global topological distribution. To address these challenges, we propose SCISE, a Scalable unsupervised graph Clustering framework that preserves structural Integrity by synergizing community-aware sampling with constrained Structural Entropy. Specifically, we first introduce the Structural Entropy Community Constraint operator (SECC), which optimizes structural information within a constrained solution space to mitigate community fragmentation and enhance partition cohesion. Second, to prevent global information loss during batch training, we design a Community-Aware Sampling Expansion (CSampE) mechanism that incorporates the community context of target nodes into sampling batches, effectively breaking structural barriers and preserving topological integrity. Finally, we devise a Structural Contrastive Learning (StructCL) module that refines edge weights based on intra-batch structural similarity, guiding the encoder to learn representations in a higher-order structural space. Extensive experiments on six mainstream benchmark datasets demonstrate that SCISE significantly outperforms state-of-the-art algorithms, with ablation studies and robustness analyses further validating its effectiveness and reliability for real-world large-scale graphs.

Graph eXplainable AI (G-XAI) is increasingly important for making Graph Neural Networks interpretable and accountable. While a growing number of explainers are available, choosing the right method and assessing the trustworthiness of its outputs remains unclear. Consistent evaluation practices and actionable guidance are still missing, hindering practical adoption. In this paper, we introduce a unified, quantitative benchmarking framework for G-XAI that requires no ground-truth assumptions. We formalize tabular explainability metrics for graph data, evaluating topological structure and node features as independent components. Our large-scale benchmarking study identifies explainers that consistently lie on the Pareto front across metric pairs and tasks, establishing robustly non-dominated solutions - while confirming that no single explainer achieves universal superiority. We distill our findings into actionable G-XAI usability guidelines to support Machine Learning practitioners in evaluating and deploying trustworthy GNN-based pipelines.

Convolutional Neural Network (CNN) and Vision Transformer (ViT) for image classification exploit a dense grid of pixels containing redundant information. Consequently, for a larger image dataset, CNNs and ViTs face deployability challenges due to high computational complexity. Representing images as graphs of superpixels offers an efficient alternative that preserves key information while eliminating pixel-level redundancy. Graph Neural Networks (GNNs) have been utilized on such graphs to perform image classification. However, GNNs are known to struggle with capturing long-range dependencies which is important in the domain of image classification. Furthermore, a majority of these superpixel-based image classification approaches do not explicitly preserve translation/rotation invariance. Nevertheless, preserving translation/rotation invariance is important for robust image classification. Thus, this paper proposes SuperGT, a Graph Transformer-based framework for image classification, which captures the long range dependencies, along with a pre-processing scheme that preserves translation/rotation invariance. We evaluate SuperGT on CIFAR-10 dataset and observe that it performs significantly better than many baselines. Furthermore, we note that the overall performance of SuperGT is comparable to the previous state-of-the-art model, namely, ShapeGNN, without relying on coordinates of the boundary points of each superpixel required by ShapeGNN.

Graph Neural Networks (GNNs) have achieved remarkable performance in graph representation learning, yet their inherent vulnerability to adversarial attacks poses severe security risks. Especially, black-box node injection attacks have become a major threat to GNNs since they inject malicious nodes without altering the original graph topology. However, they typically decouple the generation of malicious node features and edge connections, thereby resulting in suboptimal attack efficacy under stringent budgets. To address this critical issue, this study proposes a novel Target-aware Interaction-guided Reinforcement learning for Black-box node injection Attacks on GNNs (TIRBA), which formulates the attack as a Markov Decision Process and jointly optimizes node feature generation and edge construction in a heterogeneous action space. Firstly, TIRBA designs a target-aware interaction encoder to fuse information of node features and edges. Further, it introduces a class-center guidance mechanism to utilize prior class distribution information, thereby guiding efficient exploration of the high-dimensional feature space. Finally, a topology difference-aware state value evaluation is adopted to explicitly capture local structural anomalies caused by injected nodes, thereby stabilizing the reinforcement learning training process. Experimental results demonstrate that the proposed TIRBA significantly outperforms state-of-the-art black-box node injection attack methods.

We propose NetinfoGC, a framework for graph classification that extends the Network Usable Information (NUI) paradigm to graph-level learning. Unlike conventional graph neural network approaches that rely on end-to-end training of black-box embeddings, NetinfoGC constructs a family of permutation-invariant graph representations derived from propagation-based mechanisms and classical structural descriptors, including graph centrality measures. To evaluate representation quality, we introduce a training-free NUI estimation procedure based on clustering consistency with ground-truth labels, providing a proxy for task-relevant information without supervised learning. We further exploit the same representations using sparse-group LASSO regularization, enabling automatic selection of informative structural descriptors while suppressing redundant ones. Experiments on benchmark datasets show that classical centrality measures are highly competitive with learned propagation-based representations, and in several cases yield superior performance. Moreover, we observe a strong correlation between estimated NUI and downstream classification accuracy, validating NUI as an effective measure of representation utility. Overall, NetinfoGC provides a unified and interpretable framework for evaluating and exploiting graph representations without requiring end-to-end neural training.

Graph-based semi-supervised learning (SSL) propagates a few labels over a similarity graph by minimizing a Dirichlet-type energy. The standard quadratic ($p=2$) energy reduces to a single graph-Laplacian solve, but it degenerates exactly where SSL is most useful when labels are scarce: gathering more unlabeled data drives the $p=2$ estimate to a near-constant function whenever $d\ge2$ (Nadler-Srebro-Zhou). Well-posedness requires the nonlinear $p$-Laplacian energy with $p>d$. Existing solvers reduce this to a sequence of weighted Laplacian solves, but their reference implementations use a direct sparse factorization or ichol-preconditioned CG instead. Plugging a near-linear Laplacian solver is not straightforward: at large $p$ the conductance weights degenerate near flat-gradient edges, making the system nearly singular and causing stagnation without a damped outer iteration. We close this gap. Recasting $p$-Laplacian SSL as a source-form nonlinear Laplacian flow $Bρ_p(B^\top x)=b$ and solving by damped chord-Newton continuation in $p$, every linearized system stays well-conditioned and can be delegated to a near-linear Laplacian engine. On size-scaled graph families the wall-clock is empirically $m^{0.96}$-$m^{1.02}$ per family (approximate Cholesky default), and a pooled fit across 228 SuiteSparse graphs gives $m^{1.19}$ vs.\ $m^{1.45}$ for direct factorization; the solver handles a $6.8\times10^7$-edge social network in minutes. Memory is the binding constraint: Cholesky fill reaches $10$-$280\times$ the graph nonzeros vs.\ our $O(m)$ hierarchy. Against the released FCL solver we are $1.5$-$14\times$ faster at matched accuracy. On MNIST $10$-NN, $p=3$ scores $64\%$ at one label per class vs.\ $36\%$ for $p=2$. Code: https://github.com/orenlivne/np.

Knowledge graphs (KGs) that underpin Graph-based Retrieval-Augmented Generation (Graph-RAG) are increasingly built automatically by LLM-driven extraction rather than curated by experts. Proper evaluation would require instrumenting all pertinent stages: extraction, graph construction, and inference, coherently enough to localize failures, so that a failure at one stage is not discovered as a wrong answer at the end. We introduce TRIAGE, a stage-aware instrumentation framework for automated, document-grounded graph-RAG that asks not only whether the underlying graph can be trusted but at what cost it can be queried. TRIAGE attaches stage-specific, independently interpretable metrics to three stages: the KG Implementation (triple confidence, source coverage, and schema and canonicalization checks), the KG Validation by expert (graph-level structural quality, with correctness and completeness computed only as offline calibration when a reference is available), and the KG Usage (retrieval coverage, faithfulness, and retrieval cost); the deployed metrics need no gold annotations, the gold-requiring ones serving only as offline calibration. At usage time these metrics form a diagnostic chain of necessary conditions whose first broken link localizes the failure, and the diagnosis maps to the stage levers that can remedy it: extraction, graph and schema, or retrieval. TRIAGE is a theoretical framework with a proof of concept and a reproducible evaluation protocol.

Malicious Python packages have become a major threat to software supply chain ecosystems due to the widespread adoption of open-source repositories such as PyPI. Existing learning-based detection methods struggle to capture the hierarchical organization and heterogeneous interactions among different program entities. Although Large Language Models (LLMs) have demonstrated strong capabilities in code understanding and semantic reasoning, they are rarely integrated with structural program representations for fine-grained malicious behavior analysis. In this paper, we propose an LLM-enhanced hierarchical heterogeneous graph representation learning framework for malicious Python package detection. The framework constructs a hierarchical heterogeneous code graph that explicitly models heterogeneous code entities and different types of structural dependencies. LLMs are further leveraged to infer function-level semantic roles, introducing an additional layer of semantic heterogeneity. Based on this graph, we develop a hierarchical heterogeneous graph neural network that performs type-aware message passing over different node and edge categories, effectively modeling malicious behavior propagation for accurate package-level classification. The framework also incorporates a function-level attribution mechanism which, combined with LLM reasoning, automatically identifies suspicious functions and localizes fine-grained malicious behaviors without human expert intervention. Extensive experiments on real-world datasets show that our framework consistently outperforms traditional machine learning methods, graph-based detectors, and state-of-the-art LLMs across packages with varying sizes and dependency complexities, while providing accurate, robust, and interpretable malicious behavior localization.

In this study, we propose a layout-independent control allocator capable of zero-shot deployment across diverse actuator configurations. The proposed method utilizes a learning pipeline that integrates a Graph Neural Network (GNN) and a Transformer to represent the robot's geometric layout as a graph, along with a Mixture Density Network (MDN) to predict multi-modal control command distributions. Furthermore, by incorporating a differentiable physics surrogate model, we achieve command refinement during inference to minimize target wrench tracking error and energy consumption. A single generalized model using randomly generated actuator layout data demonstrated high trajectory tracking performance on different actuator layout robots outside the training distribution. Additionally, in real-world pool experiments, our approach achieved performance nearly equivalent to conventional controllers designed to specific layouts.

We study a graph classification problem involving over 20 million graphs, arising from high-order perturbative computations of correlators in planar $\mathcal{N}=4$ super-Yang--Mills, a model closely related to the theory of the strong nuclear force. We benchmark graph neural networks, including graph transformers, achieving robust generalization to larger graphs with up to $99.996\%$ ROC AUC. Then, we analyze how the models can be used to gain a computational speedup compared to the traditional graphical bootstrap algorithm, through shrinking the redundant data by up to $85.5\%$ at the level of denominator graphs. Finally, we study the embeddings of the models to investigate their interpretability.

Heterogeneous Graph Neural Networks (HGNNs) have exhibited remarkable efficacy in modeling complex systems with multiple types of nodes and relations, yet their training on large-scale heterogeneous graphs remains computationally prohibitive. Although graph condensation methods can effectively improve learning efficiency on large-scale graphs, existing condensation processes are mainly designed for homogeneous graphs and typically rely on computationally expensive gradient matching or bilevel optimization paradigms, rendering them impractical for heterogeneous settings. To address these limitations, we propose HGC-RC, a simple yet effective role-aware heterogeneous graph condensation framework. Specifically, HGC-RC first extracts semantically enhanced node embeddings via lightweight propagation. It then introduces a role-aware hybrid clustering strategy consisting of class-partitioned clustering for labeled target nodes to preserve class distributions and unsupervised type-wise clustering for non-target nodes to retain critical cross-type connectivity. Finally, a compact heterogeneous graph is efficiently reconstructed based on the resulting cluster assignments. Extensive experiments demonstrate that HGC-RC outperforms state-of-the-art baselines, offering a practical pathway to accelerate HGNN training on large-scale heterogeneous graphs without sacrificing task performance

Recent advances in molecular large language models have led to strong performance on molecular understanding and generation tasks, yet these gains often come without reliable structural grounding. In particular, existing approaches conflict with the chemistry principle that structure determines function: despite their downstream success, current molecular LLMs perform poorly on basic structure recognition, suggesting that they fail to capture molecular graphs from canonical SMILES. To remedy this, we propose MolBasic, a structure-first framework that strengthens structural comprehension via SMILES-Graph translation. MolBasic is built around a multi-level structure perception benchmark, where bidirectional SMILES-Graph conversion serves as the core task to align sequential and topological representations. On top of this foundation, we employ a progressive learning scheme with a standardized Chain-of-Thought (CoT) to steer models from structure acquisition toward higher-level molecular reasoning. Experiments show that MolBasic substantially improves structural understanding and yields robust gains on downstream tasks, including property prediction and objective optimization, supporting our structure-first paradigm.

We propose MABLE (Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning), a self-supervised framework for learning node and graph embeddings from large, heterogeneous graphs, demonstrated here on geospatial mineral-exploration data. MABLE combines masked reconstruction with fixed cosine-similarity losses that align matched augmented views while keeping unpaired embeddings well spread. A bi-Lipschitz feature decoder ties a low-dimensional reconstruction component of each node embedding to feature similarity, while matched-node consistency shapes the remaining context used by graph pooling. Lipschitz-controlled pooling helps stabilize graph-level representations under perturbations of retained node embeddings, while augmentation alignment trains robustness to masking, node dropping, and sampling variation. Across local copper and regional Arabian Shield studies, MABLE embeddings provide complementary downstream signal and produce coherent embedding-derived layers for hypothesis generation without learned discriminators or hard-negative selection.

Recent advancements in the Internet of Things (IoT) emphasize the urgent need for advanced network security, as IoT networks feature dynamic topologies, imbalanced traffic, and complex attack patterns. Unlike general IT networks, IoT environments exhibit extreme heterogeneity and sparse topologies. Traditional GNN-based intrusion detection methods often struggle to efficiently model node and edge features or capture fine-grained anomalies in such settings. To address this, we propose SKGFusionKAN, a novel IoT-tailored approach enhancing GraphSAGE with a multi-scale selective kernel attention mechanism. This enables adaptive extraction of node and edge features under diverse traffic conditions. Specifically, our edge-oriented message passing strengthens information propagation, while selective kernel attention adaptively weights edge-derived information from different scales to handle heterogeneity. We also introduce a gated fusion process to dynamically integrate multi-scale features, improving robustness against evolving attacks. Finally, we leverage Kolmogorov-Arnold Networks (KAN) for classification, offering superior nonlinear modeling capabilities essential for detecting intricate, low-frequency attacks. To our knowledge, this work presents a comprehensive integration of GNNs and KAN with dedicated architectural innovations for IoT intrusion detection. Extensive experiments on four NIDS benchmarks show that SKGFusionKAN consistently outperforms state-of-the-art approaches in binary and multiclass tasks, demonstrating its potential for IoT security.

Hierarchical Navigable Small World (HNSW) graphs serve as the industry standard due to their logarithmic complexity and strong empirical performance. However, HNSW relies on greedy graph traversal, a heuristic that provides no theoretical guarantees of correctness. In this paper, we propose a novel "Certify-then-Rectify" framework that bridges the gap between the speed of heuristic search and the rigor of exact retrieval. Rather than discarding HNSW, our approach first employs a distribution-free statistical certifier to dynamically evaluate the quality of a standard HNSW search with minimal overhead. If certification indicates that the retrieved neighbors are of low quality, the framework safely escalates to a rigorous exact recovery algorithm. To make this exact recovery computationally feasible, we reinterpret the HNSW graph as a geometric spanner and utilize Extreme Value Theory to stochastically estimate its maximum empirical stretch factor. This allows us to mathematically bound the maximum distance of true nearest neighbors. Extensive evaluations on benchmark datasets demonstrate that our tiered framework delivers the average-case speed of HNSW while ensuring the worst-case correctness of exact search and outperforming other applicable approaches.

Modern automotive software architectures comprise large sets of mixed-criticality functions executing on shared multi-core platforms with strict real-time and end-to-end timing requirements. Sensor-to-actuator data propagation in such systems is typically expressed via cause-effect chains with worst-case data-age budgets. Job-level dependencies (JLDs) have been introduced to provide a schedule-agnostic mechanism for bounding the data age independently of the underlying scheduler. The state-of-the-art methods for synthesizing JLDs, however, do not check whether the produced JLDs are enforceable under a concrete scheduling policy or jointly schedulable at the system level. In this paper we propose the first machine-learning-based JLD synthesis method, built around a two-level Graph Neural Network with temperature-controlled sampling that learns the structural patterns connecting cause-effect chain configurations to their JLD solutions. Since learned outputs may not be correct by construction, we embed the GNN in a novel Generate-and-Verify architecture in which a safe DP data-age checker, together with a per-chain EDF feasibility checker and a system-level demand-bound test, accept or reject each candidate. We show that the ML-based generator substantially outperforms the original greedy heuristic while achieving orders-of-magnitude lower synthesis time, demonstrating that learned structural priors can effectively replace exponential propagation-tree enumeration on this class of real-time scheduling problems.

Fault trees are a widely used as effective risk models for complex systems, answering the question "what can go wrong?", especially through minimal cut set analysis. We study fault trees from the perspective of Halpern & Pearl's theory of actual causality. This allows us to use fault trees to answer the question "why has it gone wrong?", which is fundamental to failure diagnostics. We give a complete classification of each of the different notions of actual causality in terms of the fault tree's graph structure and logical structure, and show how minimal cut sets give rise to actual causes.

Radio frequency (RF) maps provide a compact representation of multipath propagation characteristics and are fundamental to channel modeling, coverage analysis, and environment-aware wireless optimization. This paper proposes a unified RF map construction framework based on a physics-informed neural network (PINN) and a graph neural network (GNN), supporting both cross-scene generation and in-scene completion with 2D and 2.5D environmental representations. The PINN embeds electromagnetic propagation constraints to establish a physically consistent mapping from receiver locations to multipath parameters, including path gain, time of arrival, and angles, while the GNN enforces spatial consistency by modeling correlations among neighboring receivers. To comprehensively evaluate multipath reconstruction quality, we propose a peak-weighted dynamic time warping metric that jointly accounts for amplitude errors and peak delay misalignment in channel impulse responses. Extensive experiments demonstrate that the proposed method consistently outperforms image-based, diffusion-based, and interpolation baselines across both map-level and multipath-level metrics, achieving robust generalization and high-fidelity RF map construction under sparse observations.

Fine-scale rainfall reconstruction is critical for urban flood modeling, but real rainfall sensing systems observe the field through incompatible spatial supports: gauges measure points, microwave links measure paths, and radar/satellite products measure gridded areas. These differences in measurement support impose geometrically distinct constraints on the rainfall field, yet existing heterogeneous graph approaches reconcile such sources in feature space, giving each its own embedding while discarding the geometry of its support. We propose a geometry-aware multi-support heterogeneous graph neural network that represents each observation according to its support type (0D point, 1D line, or 2D grid) as a distinct node layer, and fuses them through cross-support message passing into a point-support prediction layer from which the field is reconstructed. An inductive masked-node formulation decouples prediction resolution from sensing resolution, allowing the same trained model to reconstruct the field at user-defined target locations or display grids. On Singapore data, the proposed method reduces RMSE by 23.2% over the classical interpolation baseline, inverse-distance weighting, and consistently outperforms other neural architectures such as convolutional fusion and support-agnostic heterogeneous graph baselines. A generalization study using data from Sydney, Australia lets us characterize when multi-support fusion helps: the available skill appears to depend on gauge spacing relative to the spatial correlation length of the field, so fusion delivers the largest gains where the field is under-sampled relative to its correlation length and little when it is already resolved. Code and models will be open-sourced upon paper acceptance.

Transformers have become general-purpose architectures, but their all-to-all self-attention is poorly matched to graph data, whose interactions are sparse, structured and multi-scale. Existing Graph Transformers address this mismatch through structural encodings, hybrid message-passing modules or learned attention constraints, often introducing additional complexity and limited interpretability. Here we introduce X-LogSMask, an explainable multi-head logarithmic structural mask that injects symmetrically normalized graph topology directly into attention logits. The logarithmic transform converts structural connectivity into a topology-aware gating signal, suppressing unsupported node interactions while preserving feature-dependent attention. By assigning different powers of the normalized adjacency matrix to different attention heads, X-LogSMask gives each head a defined structural radius and supports multi-hop information propagation within a single layer. We further show that a standard Transformer encoder can be interpreted as one-step message passing on a complete graph, motivating X-LogSMask as a topology-constrained alternative to unrestricted self-attention. Across 20 node-, edge- and graph-level benchmarks, Transformers equipped with X-LogSMask achieve state-of-the-art performance on 13 datasets and remain competitive in a lightweight one-layer configuration. These results show that simple, interpretable structural masks can make self-attention an effective graph-learning operator without changing the Transformer architecture. The code is available at https://github.com/LiLeyan-0120/X-LogSMask.

Mode shape recognition is a fundamental task in automotive NVH development, yet it remains dependent on manual visual inspection by experienced engineers. Existing approaches based on engineering heuristics, Modal Assurance Criterion (MAC), or geometry-dependent AI representations often exhibit limited robustness across different vehicle architectures, finite element (FE) meshes, and experimental measurement layouts, restricting their industrial applicability. This paper presents a Canonical Engineering Graph Representation and region-aware graph learning framework for robust and explainable 3D mode shape recognition. Rather than learning directly from vehicle-specific FE meshes, heterogeneous FE models and experimental measurements are transformed into a common graph whose nodes represent semantically meaningful structural regions connected through engineering-informed relationships. Geometry-independent regional descriptors are combined with graph attention learning and region-aware pooling to capture structural interactions while preserving engineering semantics and enabling physically interpretable predictions. The resulting representation decouples engineering knowledge from numerical discretization, allowing transfer across different vehicle programs without requiring identical mesh topology or sensor configurations. The proposed framework is validated using FE and experimental datasets from four vehicle programs under severe label scarcity. Results demonstrate high classification accuracy, cross-vehicle transferability, and physically meaningful explanations by directly relating predictions to engineering-defined structural regions used in NVH analysis. Beyond mode shape recognition, the proposed Canonical Engineering Graph Representation provides a reusable engineering abstraction for trustworthy and transferable AI across heterogeneous simulation and experimental workflows.

While inference-time scaling has improved the reasoning abilities of large language models (LLMs), the need to generate long chains-of-thought (CoTs) is a computational bottleneck. Thus, in contrast to sequential scaling methods like CoT, recent parallel scaling techniques instead use fork and join (FJ) primitives to divide work across multiple LLM threads. However, in the fork-join paradigm, threads are typically transient and do not communicate pointwise with one another which limits scalability. To tackle this, we introduce Message Passing Language Models (MPLMs), a framework for LLM reasoning in which threads communicate directly via lightweight send and receive primitives. MPLMs enable efficient scaling through two key mechanisms: (1) reduced communication costs, achieved by avoiding redundant context sharing, and (2) preemption, which allows threads to terminate early based on partial information from their peers. We demonstrate the promise of MPLMs on 3 classes of tasks. First, on Sudoku puzzles, we show that MPLMs require an asymptotically smaller context than both serial CoT and parallel FJ. We then fine-tune a single model to solve 25 x 25 puzzles that remain challenging for standard CoT and FJ approaches, as well as frontier reasoning models without tools. Second, on 3-SAT puzzles, the capability of preemption allows termination of unpromising branches, which results in improved efficiency. Finally, we show that appropriately prompted large pre-trained models follow the MPLM protocol, achieving competitive results on long-context question answering relative to popular fork-join approaches.

We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms. In particular, we introduce separable graphs, in which each missing edge implies the existence of a separating set for its endpoints, and essentially separable graphs, those graphs separation equivalent to a separable graph. We show that these models include many existing graph families used to define graphical models an provide several characterizations of separable graphs and essentially separable graphs. We also provide multiple characterizations of separation equivalence for separable graphs. One is a graphical characterization in terms of ordinary graph properties, extending earlier results for specific subfamilies Another is a separational characterization depending only on graph separation properties. Finally, we provide a canonical representation for the equivalence classes of essentially separable graphs and develop an algorithm that, under suitable assumptions, identifies the equivalence class of any essentially separable graph.

The stable coloring of the Weisfeiler-Leman (1-WL) test is a cornerstone of Graph Neural Networks because it provides an upper bound to the expressive power of message-passing architectures. Unfortunately, computing it presents two fundamental bottlenecks. First, classic algorithms are inherently sequential and cannot exploit modern massively parallel hardware. Second, these are \emph{global} algorithms, i.e., they require availability in memory of the full graph, severely limiting applicability to real-world instances. We leverage a linear-algebraic interpretation of 1-WL stable coloring and introduce two key contributions: (i)~a randomized refinement algorithm with tight probabilistic guarantees and (ii)~a correctness-preserving batching scheme that decomposes the graph into independently processable subgraphs while provably returning a stable coloring of the original graph. This approach maps directly to GPU-efficient primitives. In numerical experiments, our CUDA implementation delivers speedups up to two orders of magnitude over classical CPU-based partition refinement and, for the first time, successfully computes stable colorings on web-scale graphs with over 30 billion edges, where CPU baselines time out or fail.

Neoadjuvant chemotherapy (NAC) response prediction is clinically important for treatment stratification in breast cancer. However, robust pre-treatment pathological complete response (pCR) prediction remains challenging due to insufficient cross-modal modeling, multicenter imaging heterogeneity, and weak evidence-grounded interpretability. We propose ClinRAG-GRAPH, a Clinically informed Retrieval-Augmented Generation Graph framework, for pre-treatment pCR prediction from DCE-MRI, structured clinical variables, and biopsy-derived pathological biomarkers. ClinRAG-GRAPH constructs an intra-patient clinical-prior graph and applies a prior-guided relation-aware graph convolutional network for structured multimodal representation learning. To improve cross-center robustness, we introduce a dual-branch domain-adversarial learning strategy to suppress protocol-related MRI bias while preserving pCR-relevant features. To enhance interpretability, we further incorporate large language model (LLM)-driven subgraph RAG module that retrieves clinically analogous historical cases and integrates retrieved evidence for pCR inference. We assemble a large-scale multicenter NAC breast cancer cohort for extensive validation, drawing from two public sources and three in-house centers.Results show that ClinRAG-GRAPH achieves AUCs of 0.815 on the internal test set and 0.774/0.712 on two external test sets, demonstrating robust pre-treatment pCR prediction across centers. The code is available at the anonymized https://github.com/miccai26-1181/ClinRAG-GRAPH.

Skeleton-based action recognition has achieved remarkable success by exploiting joint coordinates and their topological connections, yet prevailing methods overwhelmingly assume complete and clean skeleton inputs. In real-world deployments, such as egocentric vision, crowded surveillance, wearable devices, or edge robotics, limited field-of-view (FoV) frequently causes substantial joint visibility dropout, leading to severe performance degradation that existing models are largely unprepared to handle. To bridge this critical yet underexplored gap, we introduce PartialVisGraph, a novel hypergraph framework tailored for robust skeleton action recognition under constrained FoV. We first construct highly expressive hypergraphs by introducing learnable virtual hyperedges that form a soft incidence matrix, capturing flexible high-order dependencies beyond conventional pairwise graphs. We then propose the Single-Head Sample-Adaptive Transformer, which adaptively aggregates joint features onto hyperedges while explicitly incorporating a visibility prior. This prior selectively gates information flow, preventing occluded or out-of-view joints from corrupting reliable feature propagation. We further establish rigorous evaluation protocols with realistic FoV simulation benchmarks on NTU RGB+D 60 and 120. Extensive experiments demonstrate that PartialVisGraph consistently achieves state-of-the-art accuracy under partial visibility, with gains of up to 68.8% on subsets with severe FoV restrictions compared to recent strong baselines, while remaining superior on full-visibility settings. Our approach offers a principled and practical pathway toward deployable skeleton-based action understanding in unconstrained environments.

Graphs are a complex and versatile data structure used across various domains, with possibly multi-label nodes playing a particularly crucial role. Examples include proteins in PPI networks with multiple functions and users in social or e-commerce networks exhibiting diverse interests. Tackling multi-label node classification (MLNC) on graphs has led to the development of various approaches. Some methods leverage graph neural networks (GNNs) to exploit label co-occurrence correlations, while others incorporate label embeddings to capture label proximity. However, these approaches fail to account for the intricate influences between labels in non-Euclidean graph data. To address this issue, we decompose the message passing process in GNNs into two operations: propagation and transformation. We then conduct a comprehensive analysis and quantification of the influence correlations between labels in each operation. Building on these insights, we propose a novel model, Label Influence Propagation (LIP). Specifically, we construct a label influence graph based on the integrated label correlations. Then, we propagate high-order influences through this graph, dynamically adjusting the learning process by amplifying labels with positive contributions and mitigating those with negative influence. Finally, our framework is evaluated on comprehensive benchmark datasets, consistently outperforming SOTA methods across various settings, demonstrating its effectiveness on MLNC tasks.

In light of strides in Arti cial Intelligence (AI) and its wide spread application, challenges persist in the interpretability of AI models, particularly within specialized domains like healthcare, such as electro cardiograph (ECG) recognition. Rather than relying solely on end-to-end convolutional neural networks, this paper introduces a novel approach using a domain knowledge-based graph convolution network for ECG recognition. Key landmarks points of PRQST, vital to ECG interpreta tion, are incorporated as domain knowledge. The double-stream directed graph is employed to model both intra and inter ECG cycles. Speci cally, spatial directed graphs capture the positional relationships among key points, while temporal directed graphs delineate temporal dependencies between adjacent cycles in extended ECG sequences. Experimental re sults on the First Chinese ECG Intelligent Competition dataset, which speci cally classify ECG into nine categories, prove the e cacy of the proposed model. The overall average F1 score is 88.1%, the average F1 score of rare categories is 76.3%, both outperform the state-of-the-art models. The introduction of domain knowledge did enhance the detec tion performance, especially for rare categories.

Self-supervised Continual Graph Learning (CGL) aims to successively learn from a graph sequence with different tasks without label supervision - a paradigm that has attracted widespread attention. Most existing self-supervised CGL methods rely on instance-level consistency objectives that enforce stability of individual node (or node-pair) embeddings. Due to optimizing nodes in isolation, these methods fail to maintain global relational structure, causing inter-node correspondences to progressively distort under continual learning. To this end, we propose a novel Structure-Aware Optimal Transport (SAOT) framework that explicitly captures and preserves relational structure within graph representations across sequential tasks. Specifically, SAOT leverages optimal transport theory to capture global inter-node correspondences, thereby facilitating and enhancing graph representation learning. Simultaneously, SAOT incorporates a cross-task knowledge distillation mechanism to preserve the previous structural knowledge. Extensive experiments on four CGL benchmark datasets demonstrate that SAOT outperforms existing self-supervised baselines. In particular, SAOT achieves significant performance gains, improving average accuracy by up to 5% on CoraFull-CL and over 15% on Products-CL compared with state-of-the-art methods in the Class-IL setting.