Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical states. Learning these maps is difficult, especially for time-dependent systems that must assimilate history and remain stable under autoregressive rollout. Many neural operators work best on regular, structured grids, while realistic simulations often require unstructured meshes or point clouds to resolve complex geometries; in such settings, grid-centric representations can lose accuracy. Graph neural operators handle these domains through message passing or spectral graph filtering, but pairwise edges do not directly capture group-wise couplings among mesh cells, local neighborhoods, or conservation volumes. We introduce the Hypergraph Adaptive waveLet Operator (HALO), which lifts the domain to a hypergraph and learns in its spectral wavelet domain. HALO avoids explicit hypergraph-Laplacian eigendecomposition through Chebyshev polynomial wavelet filters, giving localized spectral kernels at linear sparse-matrix cost. Its trainable dyadic wavelet scales are regularized toward tight-frame coverage, allowing the frequency response to adapt to each PDE while encouraging stable multi-scale spectral coverage. Across 2D and 3D benchmarks on structured and unstructured discretizations, HALO achieves best or near-best accuracy among frequency-, transformer-, DeepONet-, state-space-, and graph-based baselines and sustains stable multi-step rollouts. The same model scales to industrial aerodynamic geometries: on meshes of a few hundred thousand points it is on par with, or better than, the strongest fixed-discretization transformers, while remaining resolution-equivariant.

Hypergraph-based Multimodal Retrieval-Augmented Generation with Incremental Refinement

Modern Multimodal Retrieval-Augmented Generation (M-RAG) systems are fundamentally limited by the binary connectivity paradigm of traditional simple graphs, which fails to capture the intricate, high-order correlations among heterogeneous entities, such as the N-ary relationships between a visual chart, its scattered textual descriptions, and underlying numerical data. Furthermore, existing refinement strategies often rely on exhaustive, full-page reconstruction to align cross-modal information, leading to prohibitive computational redundancy and the introduction of contextual noise in long-form document processing. In this paper, we propose Hyper-M2RAG, a novel framework that redefines multimodal document retrieval through High-order Hypergraph Representation Learning. We first formalize the document structure as a Multimodal Hypergraph, utilizing hyperedges as unified semantic containers to encapsulate multi-way associations across text, images, and tables, thereby transcending point-to-point modeling. To mitigate semantic fragmentation caused by physical pagination, we introduce an Anchor-driven Incremental Refinement mechanism. Rather than performing a global sweep, our approach identifies boundary-crossing anchor nodes and reconstructs their local hyper-topology using one-hop neighborhood contexts. This targeted refinement effectively bridges cross-page knowledge gaps with minimal computational footprints. Extensive evaluations on multimodal benchmarking datasets demonstrate that Hyper-M2RAG significantly outperforms state-of-the-art methods in both retrieval precision and generation coherence. Our code is available at https://github.com/ShenAoChen2001/MMHRAG.

Modality Agreement- and Conflict-Aware Prototype Hypergraph Learning for Multimodal Intent Understanding

Multimodal intent recognition requires understanding not only what textual, acoustic, and visual signals share, but also how they disagree. Such disagreement is frequently class-informative; for example, lexical positivity accompanied by incongruent vocal or facial behavior may indicate sarcasm or taunting, yet most fusion methods either encourage modality alignment or treat inconsistency as uncertainty to be suppressed. We propose MACH (Modality Agreement- and Conflict-aware prototype Hypergraph), a hierarchical prototype-hypergraph framework that represents multimodal agreement and conflict as distinct, recurring relational structures. MACH progressively composes unimodal representations into bimodal and trimodal abstractions. At each applicable level, modality-composition anchors activate sparse agreement prototype hypergraphs that capture reusable consensus patterns, while a separate conflict pathway maps cross-modal discrepancies to dedicated conflict prototype hypergraphs. The two pathways are combined through a feature-wise, sample-adaptive arbitration mechanism, enabling the model to preserve informative disagreement while suppressing incidental modality noise. A progressive optimization strategy stabilizes the interdependent hierarchy before joint agreement-conflict learning. Experiments on benchmark datasets demonstrate the effectiveness of the proposed formulation, while component and robustness analyses validate the distinct roles of hierarchical composition, prototype-mediated semantic refinement, and agreement-conflict arbitration.

HyCoRec: Hypergraph-Enhanced Multi-Preference Learning for Alleviating Matthew Effect in Conversational Recommendation

The Matthew effect is a notorious issue in Recommender Systems (RSs), \emph{i.e.}, the rich get richer and the poor get poorer, wherein popular items are overexposed while less popular ones are regularly ignored. Most methods examine Matthew effect in static or nearly-static recommendation scenarios. However, the Matthew effect will be increasingly amplified when the user interacts with the system over time. To address these issues, we propose a novel paradigm, Hypergraph-Enhanced Multi-Preference Learning for Alleviating Matthew Effect in Conversational Recommendation (HyCoRec), which aims to alleviate the Matthew effect in conversational recommendation. Concretely, HyCoRec devotes to alleviate the Matthew effect by learning multi-aspect preferences, \emph{i.e.}, item-, entity-, word-, review-, and knowledge-aspect preferences, to effectively generate responses in the conversational task and accurately predict items in the recommendation task when the user chats with the system over time. Extensive experiments conducted on two benchmarks validate that HyCoRec achieves new state-of-the-art performance and the superior of alleviating Matthew effect. Our code is available at https://github.com/zysensmile/HyCoRec.

ChemHyperMag: Physics-informed magnetic hypergraph learning improves molecular ADMET prediction

Accurate prediction of ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) is important for drug discovery. Most predictors use undirected molecular graphs and pairwise edges. This choice misses asymmetric interactions, nonreversible dynamics, and motif level effects from functional groups and ring systems. We propose ChemHyperMag for multitask ADMET prediction under missing labels. ChemHyperMag builds a functional group hypergraph from rings, BRICS fragments, Bemis-Murcko scaffolds, and bonds. It also defines a potential driven nonreversible flow guided by electronegativity and Gasteiger partial charges. The resulting circulation is encoded by a Hermitian magnetic Laplacian and processed with a magnetic Chebyshev encoder. We perturb magnetic phases to form stochastic views and train with an InfoNCE objective. Experiments on multiple ADMET benchmarks show improvements over recent methods with fewer labeled samples and no conformers. ChemHyperMag is scalable and provides interpretable directional signals through its magnetic phases.

Beyond Pairwise Relations: Dynamic Manipulation Hypergraphs for Vision-Based Human Activity Recognition

Fine-grained manipulation recognition requires modeling evolving relations among hands, objects, tools, and supporting surfaces. Conventional graph-based methods use pairwise edges that can fragment a coordinated event into disconnected binary relations. We propose a dynamic manipulation hypergraph framework that represents multi-entity configurations as higher-order relational units. At each temporal step, relevant entities are encoded using appearance, spatial, motion, and semantic-role features. Hyperedge candidates are instantiated and ranked using proximity, contact, and motion-coupling predicates. A hypergraph reasoning network performs node-to-hyperedge and hyperedge-to-node message passing, followed by temporal attention over the evolving interaction structure. The framework provides class-agnostic hyperedge-importance scores that identify entity configurations and temporal intervals emphasized by the model without treating them as causal explanations. Quantitative evaluation is conducted on EPIC-KITCHENS-100/VISOR and Assembly101 under an annotation-assisted entity-localization protocol. Video-only and entity-based methods provide contextual comparisons, while a matched pairwise graph and a static hypergraph serve as the principal controlled baselines because they use identical entity inputs and comparable relational settings. The proposed method improves HO-F1 over the matched pairwise graph by 6.9 percentage points on EPIC-KITCHENS-100/VISOR and 9.5 points on Assembly101, and exceeds the static hypergraph by 4.4 and 5.8 points, respectively. Qualitative analysis on ARCTIC further shows correspondence between highly ranked hyperedges and contact-rich manipulation intervals. These results demonstrate the value of time-varying higher-order relational modeling for fine-grained manipulation activity recognition.

Dual-Correlation Hypergraph Network for Unaligned RGBT Video Object Detection and A Large-scale Benchmark

RGB-Thermal (RGBT) Video Object Detection (VOD) has gained significant traction due to its ability to overcome the limitations of conventional RGB-based VOD under challenging conditions. However, spatial misalignment commonly exists between RGBT image pairs. To address this, we propose a Dual-Correlation Hypergraph Network (DHNet) that captures high-dimensional complementary information by explicitly modeling two types of correlations: temporal correlation across consecutive frames and spatial correlation from cross-modal features. Specifically, we first design a Patch-based Spatial Alignment Module (PSAM) to sequentially align the multimodal features at the local region level. Subsequently, we introduce a Dual Hypergraph Fusion Module (DHFM), which constructs separate temporal and multimodal hypergraphs to enhance object discriminability through dual-correlation learning. Furthermore, the field currently lacks a large-scale, scene-diverse benchmark dataset for comprehensive evaluation. To address this gap, we construct DVT-VOD1000, a large-scale RGBT VOD dataset containing 1,000 video sequences with 103,464 RGBT image pairs. The dataset covers diverse scenarios, including campuses, parks, transportation, rural areas, night scenes, rain, and snow. Comprehensive experiments on VT-VOD50 and our DVT-VOD1000 demonstrate that DHNet achieves state-of-the-art detection accuracy. The dataset and source code will be made publicly available on https://github.com/tzz-ahu/ to support academic research.

A Framework for Directed Acyclic Hypergraph Learning

Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.

HYolo: An Intelligent IoT-Based Object Detection System Using Hypergraph Learning

This paper presents HYolo, an intelligent IoT-based object detection framework that integrates hypergraph learning into the YOLO architecture. Traditional YOLO-based object detection models primarily capture pairwise feature interactions and may fail to model complex high-order relationships among objects and contextual features. To address this limitation, HYolo incorporates hypergraph learning to capture richer contextual dependencies and improve object representation. Experimental evaluation on the COCO dataset demonstrates significant performance improvements over baseline YOLO models. The proposed approach achieves approximately 12% improvement in mAP@50 while enhancing overall detection accuracy and robustness. By modeling high-order feature relationships, HYolo provides improved contextual understanding and more reliable object detection performance in IoT-based environments. The results indicate that integrating hypergraph learning into object detection pipelines offers a promising direction for intelligent and context-aware IoT vision systems.

Learning Multi-Scale Hypergraph for High-Order Brain Connectivity Analysis

Understanding complex interactions between brain regions is critical for early neurodegenerative disease classification such as Alzheimer's Disease (AD) and Parkinson's Disease (PD). While graph-based models are widely used to analyze brain networks, most existing approaches primarily focus on pairwise interactions between directly connected nodes, limiting their ability to capture higher-order dependencies across multiple regions. Although hypergraph-based methods have been proposed to model higher-order relations, many rely on predefined hyperedges or restrict learning to hyperedge weights, reducing flexibility and limiting their capacity to capture multi-resolution structural patterns. In this regard, we introduce an adaptive multi-scale hyperedge learning framework, i.e., MuHL, which constructs hierarchical node features and dynamically learns high-order interactions through continuous hyperedge construction over multi-resolution graph signals. Extensive experiments on multiple brain network benchmarks demonstrate that MuHL consistently improves disease classification performance across different stages, and further identifies key regions of interest (ROIs) and their group-wise interactions from the learned hyperedges that are associated with disease progression, highlighting its potential as a powerful tool for brain network analysis in neurodegenerative disorders.

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

Unsat Core Prediction through Polarity-Aware Representation Learning over Clause-Literal Hypergraphs

Graph neural networks have been widely used in Boolean satisfiability (SAT) tasks to learn structural information from SAT formulas. The goal of these studies is to solve SAT instances or to enhance SAT solvers, including tasks such as unsat-core prediction. However, most existing approaches model a SAT formula as a bipartite graph or a directed acyclic graph, which are less expressive in capturing higher-order interactions among literals and clauses. Moreover, these approaches are limited in modeling intrinsic polarity-related properties of SAT, such as the complementary relationship between the positive and negative literals of a variable. To address these limitations, we propose a polarity-aware representation learning framework over clause-literal hypergraphs. We model SAT formulas as clause-literal hypergraphs augmented with a clause incidence graph to capture higher-order structural interactions. We then introduce a polarity-aware decomposed mechanism that separates variable representations into polarity invariant and equivariant components, explicitly modeling the relationship between positive and negative literals, with the resulting literal representations propagated along the hypergraph structure. We further incorporate a polarity-inversion consistency regularization to reinforce polarity-consistent representations during training. Experimental results on multiple SAT datasets demonstrate the effectiveness of the proposed approach.

UHR-Net: An Uncertainty-Aware Hypergraph Refinement Network for Medical Image Segmentation

Accurate lesion segmentation is crucial for clinical diagnosis and treatment planning. However, lesions often resemble surrounding tissues and exhibit ill-defined boundaries, leading to unstable predictions in boundary/transition regions. Moreover, small-lesion cues can be diluted by multi-scale feature extraction, causing under- or over-segmentation. To address these challenges, we propose an Uncertainty-Aware Hypergraph Refinement Network (UHR-Net). First, we introduce an Uncertainty-Oriented Instance Contrastive (UO-IC) pretraining strategy that couples geometry-aware copy-paste augmentation with hard-negative mining of lesion-like background regions to improve instance-level discrimination for small and visually ambiguous lesions. Second, we design an Uncertainty-Guided Hypergraph Refinement (UGHR) block, which derives an entropy-based uncertainty map from a coarse probability map to guide hypergraph refinement. By splitting hyperedge prototypes into foreground and background groups, UGHR decouples higher-order interactions and improves refinement in ambiguous regions. Experiments on five public benchmarks demonstrate consistent gains over strong baselines. Code is available at: https://github.com/CUGfreshman/UHR-Net.