Hypergraphs

Volume-based multimodal retrieval jointly scores a text query with a candidate's video, audio, and subtitle embeddings. While this approach captures higher-order within-candidate alignment, the score remains candidate-local, and semantically related training samples primarily serve as contrastive negatives. This work introduces Hypergraph-Regularized Gramian Volumes (HyVol), a training-time module that incorporates these semantic relations prior to evaluating the original volume loss. Document hyperedges connect the observed modalities of each candidate, whereas semantic hyperedges link candidates whose detached captions are mutual top-k neighbors. A shallow gated hyper-graph network applies residual corrections to the modality embeddings. Presence masks exclude unavailable streams from message passing, and identity padding preserves the determinant of the observed Gram submatrix without feature imputation. As refinement operates on embeddings rather than scores, the same construction applies to both Gram and HyperGram. We remove the hypergraph after training, leaving the backbone-only architecture, original scoring function, and retrieval cost unchanged. We train both backbones on a 150K-clip subset of VAST-27M and evaluate zero-shot performance on six benchmarks. Under the paired protocol, HyVol improves R@1 across all five retrieval benchmarks, with video-to-text gains reaching +8.3 on MSR-VTT and +7.6 on VATEX. Under missing-modality masking, the V2T margin remains positive in all experimental settings, although the T2V margin becomes slightly negative in four.

Existing graph-clustering methods typically improve clustering performance by optimizing model parameters and node representations. Effective means of further improving the clustering results of an already trained and frozen model, however, remain limited. We study post-processing for frozen graph clustering. After checkpoint fixation, the procedure uses no labels and updates neither model parameters, node representations, nor the original graph structure. Instead, it exploits an attribute hypergraph to supplement higher-order relations that ordinary graphs cannot readily express, thereby refining existing cluster assignments. Because global hypergraph refinement can yield both performance gains and erroneous updates, we propose Selective Hypergraph Refinement (SHR). The method generates candidate residual directions from the hypergraph and evaluates their reliability using graph structure, node attributes, and matched-null evidence. It updates only nodes with sufficient support and otherwise retains their original assignments. Further analysis shows that whether a node changes cluster is jointly governed by its native assignment gap and the directional strength of the refinement. In a controlled common-suite evaluation, 13 of 15 backbone-dataset cells had a positive mean macro gain, one produced exact no-action, and one was negative. The cell-equal macro gain was 0.066 pp (95% bootstrap CI, [0.030, 0.107] pp), while only 0.209% of hard assignments changed on average. A broader 15-combination native-interface evaluation yielded a macro gain of 0.137 pp at a mean change ratio of 0.375%. These results indicate that frozen clustering outputs retain a limited but measurable refinement space after training. The effect is heterogeneous across backbone-dataset pairs, and broader coverage also increases exposure to negative transfer.

Tables are ubiquitous across diverse domains, yet reasoning over them remains a significant challenge for modern large language models (LLMs). Current approaches typically linearize tables into sequences, inherently overlooking their intrinsic two-dimensional and hierarchical structure. To address this, we propose H2Table (Hierarchical Hypergraph-Enhanced Table Reasoning), a novel framework that represents complex tables as hierarchical nested hypergraphs. To process this representation, we design a tailored hypergraph encoder to facilitate message passing between hyperedges (headers) and nodes (cells), thereby perceiving the semantic entailment relationships between them within complex tables. Furthermore, we introduce a set of learnable query vectors acting as a lightweight bridge to extract representative structural embeddings from the encoder into the LLM. Experimental results demonstrate that our approach effectively handles complex table question answering tasks with hierarchical nested headers. Notably, on the HiTab dataset, H2Table achieves an average improvement of 22.88% over state-of-the-art baselines on highly complex tables with a nesting depth of four. Our code is available at: https://github.com/lila120/h2table.

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

We provide an expository introduction on the importance of higher-arity tensor operations to deep learning. Then, we conduct a novel empirical investigation of higher-arity phenomenon in trained neural networks, introduce a hypergraphical generalization of the multilayer perceptron, and explore connections to evolutionary algorithms. We conclude with a discussion of promising directions for future research.

We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information, without node features, labels, seed matches, or side information. Direct higher-order formulations can represent hyperedge interactions faithfully, but they can be computationally demanding and cumbersome for non-uniform hypergraphs. Graph-reduction approaches introduce a different challenge: clique expansions keep the alignment problem on the original node set but collapse all hyperedge evidence into one pairwise graph, whereas bipartite expansions preserve incidence structure but enlarge the problem from nodes to nodes plus hyperedges. We introduce FALCON (Filtration-based hypergrAph aLignment via Cross-scale Optimal traNsport), an unsupervised optimal-transport framework for hypergraph alignment. Instead of representing each hypergraph by a single collapsed clique graph, FALCON constructs a filtration-induced sequence of clique-based co-occurrence dissimilarity matrices and jointly aligns all levels through one shared multi-scale Gromov--Wasserstein (GW) objective. The shared transport plan enforces a globally consistent node correspondence across filtration levels while avoiding the auxiliary hyperedge nodes introduced by bipartite expansion. Experiments on perturbation benchmarks derived from real-world hypergraphs show that FALCON is robust to structural noise and in almost all cases outperforms strong graph- and hypergraph-alignment baselines.

While retrieval-augmented generation (RAG) has proven effective at giving LLMs access to external knowledge, mainstream dense-retrieval implementations remain inherently limited in handling structured constraints and multi-hop reasoning. Graph-based methods address this by constructing knowledge graphs offline, but they often fragment semantics, incur high maintenance, and complicate incremental updates. We propose SAG (SQL-Retrieval Augmented Generation), a structured retrieval architecture that organizes documents into an event-entity index without building a global knowledge graph. SAG represents each chunk as a semantically complete event paired with its entities, forming a latent hyperedge that preserves n-ary relations without decomposing them into triples. At query time, SAG treats shared entities as join keys to connect related chunks. This dynamically yields a query-scoped neighborhood of events, and yet every piece of evidence remains the original chunk throughout. Experiments on HotpotQA, 2WikiMultiHopQA, and MuSiQue show that SAG achieves the best retrieval and end-to-end QA performance on every benchmark, with gains that widen as reasoning-chain complexity increases. On MuSiQue, where multi-hop evidence chaining is most demanding, SAG reaches 80.36% Recall@5, outperforming the strongest baseline by 11.52 points. This work paves the way for knowledge infrastructure that enables LLM agents to retrieve and reason over continually growing organizational knowledge.

Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare. We benchmark 13 unsupervised hyperbolic graph embedders under a unified protocol for link prediction and topology reconstruction on synthetic and empirical networks. The protocol captures both missing-link recovery and the preservation of local and global network structure. Maximum-likelihood and representation-learning-based approaches, including hybrid variants, achieve the strongest overall performance, although no method dominates across all tasks and structural regimes. Performance is more strongly associated with embedding paradigm than with disciplinary origin. We identify the network regimes in which different paradigms succeed or fail and provide practical guidance for method selection in downstream applications.

Hyperdimensional computing (HDC) is an approach from the cognitive science literature for solving information processing tasks using data represented as high-dimensional random vectors. The technique has a rigorous mathematical backing, and is easy to implement in energy-efficient and highly parallel hardware like FPGAs and "processing-in-memory" architectures. The effectiveness of HDC in machine learning largely depends on how raw data is mapped to high-dimensional space. In this work, we propose NysHD, a new method for constructing this mapping that is based on the Nyström method from the literature on kernel approximation. Our approach provides a simple recipe to turn any user-defined positive-semidefinite similarity function into an equivalent mapping in HDC. There is a vast literature on the design of such functions for learning problems. Our approach provides a mechanism to import them into the HDC setting, expanding the types of problems that can be tackled using HDC. Empirical evaluation against existing HDC encoding methods shows that NysHD can achieve, on average, 11% and 17% better classification accuracy on graph and string datasets respectively.

Particle swarm optimization (PSO) has been widely applied to solve complex optimization problems from real-world applications due to its efficient exploration of large solution spaces and the ability to converge towards optimal solutions without requiring gradient information. Common swarm topologies in standard PSO and its variants, e.g., Ring and Star, can be regarded as graphs, where each edge connects only two particles. Such topology structures allow direct interactions only between connected particle pairs, and thus often fail to directly capture the higher-order social relationships that are necessary for navigating complex search landscapes. Therefore, this article proposes a novel PSO variant termed Hypergraph-assisted Particle Swarm Optimization (HPSO). In HPSO, the topology of the particles in a swarm is modeled by a hypergraph, in which hyperedges are used to connect multiple particles. This allows multiple particles within a hyperedge to interact directly. Furthermore, an adaptive hypergraph updating strategy is designed to periodically reconstruct the topology based on cumulative average particle displacement, thereby maintaining swarm diversity throughout the evolutionary process. In the experiments, the effectiveness of HPSO is verified on the IEEE CEC'17 benchmark suite, and the results demonstrate that HPSO achieves promising performance across various types of functions. Furthermore, the ablation experiment demonstrates that HPSO has excellent search capabilities.

Hypergraph neural networks (HGNNs) have demonstrated remarkable capabilities in processing complex higher-order relationships. However, their performance is highly dependent on labeled data, making them vulnerable to label noise. Despite advances in learning with label noise (LLN) and graph learning with label noise (GLN), noisy-label learning on hypergraphs remains underexplored. In this paper, we present a systematic study of hypergraph node classification under label noise. First, we adapt representative LLN and GLN methods to hypergraphs and evaluate them under a unified benchmark, revealing the limitations of existing robust learning strategies for hypergraphs. Building on this, we propose a new hypergraph robust framework, HyperTrust, which first estimates hyperedge trustworthiness through a pretraining-based, entropy-aware strategy, and then incorporates the HyperedgeBoost module to enhance reliable supervision by connecting unlabeled nodes to trustworthy hyperedges, as well as the HyperedgePrune module to suppress noisy propagation by removing untrustworthy node-hyperedge incidences. Finally, two modules work collaboratively to adjust the hypergraph structure and generate final predictions. Extensive experiments and theoretical analysis demonstrate the effectiveness and robustness of HyperTrust on multiple hypergraph datasets under various noisy settings. Our work provides a unified benchmark and an effective solution for hypergraph learning with label noise and lays a foundation for future research in this direction.

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.

We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations. As fair we consider the allocations that are envy-free-up-to-any-good (EFX). Finding if EFX alloca- tions always exist, even for agents with additive valuations, is a major open problem in Fair Division. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph, respectively, and only the endpoints of an edge may have non-zero marginal value for it. We show that for hypergraphs with girth at least 4 and agents with general monotone valuations there always exists an EFX allocation and can be constructed in polynomial time. We generalize our approach to also show that multi-hypergraphs with girth (on the simple hypergraph) at least 4 always admit an EFX allocation, as long as there exists a single vertex whose incident edges have multiplicity at most the size of that edge minus 2; our construction in this case needs pseudo-polynomial time.

Fixed-layout indoor furniture styling requires selecting assets that form a coherent room without changing the prescribed furniture categories, positions, orientations, or scales. Existing approaches typically retrieve each asset independently or rely on static local relations, making them prone to shape, material, and color conflicts after scene composition. We introduce StyleForge, a scene-level structured selection framework built on a dynamic hypergraph style field. A frozen multimodal large language model extracts structured style priors from an open-ended style request and the fixed layout, while StyleForge maintains a learnable candidate distribution for each furniture slot. Conditioned on the target style, the dynamic hypergraph style field adaptively activates and weights layout-induced hyperedges to capture higher-order dependencies among furniture. Counterfactual style preference learning then treats each candidate as a local substitution in the current style field and evaluates its contextual compatibility using Mahalanobis energies. Training alternates between optimizing the style field and the candidate logits. At inference, the model remains frozen and test-time training updates only room-specific candidate logits, progressively correcting cross-slot style conflicts as the global scene context evolves. Experiments on 3D-FRONT demonstrate state-of-the-art furniture retrieval and scene-level style coherence, producing more coherent fixed-layout furniture arrangements than object- and scene-level retrieval baselines.

Large language model (LLM) agents increasingly rely on external tools to complete complex real-world tasks. However, reliable tool-use planning remains challenging due to the limitations of implicit reasoning and the evolving nature of real-world execution environments. Existing tool-use agents typically rely on LLMs to infer tool compositions from textual descriptions, which can lead to inefficient exploration and unreliable execution in complex tasks. To address these challenges, we model tool relations at the schema level and construct a directed Tool--Schema Hypergraph, in which tools are represented as hyperedges from their required input-schema nodes to their output-schema nodes. Furthermore, we propose HyperAgent, a Tool--Schema Hypergraph-guided framework for dynamic planning and execution. Given a task, HyperAgent first extracts a task-relevant tool context graph and uses it to guide the construction of a schema-aware Task DAG. During execution, HyperAgent dynamically realizes each subtask by constructing a state-conditioned tool support graph through deficit-oriented expansion, which identifies unresolved requirements and retrieves supporting producer tools according to the current agent state. Experiments on AppWorld demonstrate that HyperAgent improves task completion performance while reducing redundant API calls, LLM interactions, and token consumption compared with existing agent baselines.

Falls represent a critical public health challenge, and accurate detection of the impact moment when an individual hits the ground is crucial for timely intervention. Existing skeleton-based methods rely on graph neural networks modeling only pairwise joint connections, failing to capture multi-joint coordination characteristic of fall impacts, while transformer-based temporal models suffer from quadratic complexity limiting real-time deployment. We propose FLASH, a novel framework integrating single-matrix hypergraph representations with Mamba's selective state-space models through adaptive feedback mechanisms for efficient impact detection. Our approach constructs biomechanically-grounded hyperedges to model functional joint coordination while leveraging Mamba's linear-time complexity to capture temporal dynamics. Experiments on UP-Fall and UMAFall datasets demonstrate that FLASH achieves state-of-the-art accuracy with real-time inference capability and strong zero-shot cross-dataset generalization, while significantly reducing computational cost compared to dual-representation and transformer-based methods. The model provides interpretable feedback through learned attention patterns aligned with biomechanical principles. Code is available at https://github.com/Tresor-Koffi/FLASH-Impact-Fall-Detection.

Large language model (LLM) agents increasingly rely on invoking external tools to complete real-world tasks. Tool retrieval, which selects a small task-relevant subset from a library of thousands of tools before the agent acts, has therefore become a critical component of LLM agent pipelines. However, existing retrievers either score each tool in isolation or assemble the tool set sequentially, so the joint utility of a candidate set is never evaluated as a whole. In this paper, we propose HYSET, short for HYperedge-based SEt-level Tool retrieval. Our contributions are threefold: (i) we formulate tool retrieval as query-conditioned hyperedge prediction on a tool co-invocation hypergraph, under which the tool set itself becomes the unit of scoring and most existing retrieval paradigms reduce to restricted instances; (ii) we capture size-dependent tool compatibility through cardinality-specific interactions; and (iii) we design HYSET as a pre-selection module requiring no modification to the downstream agent. Experiments on ToolBench demonstrate that HYSET consistently outperforms state-of-the-art baselines in both tool retrieval performance and end-to-end task success. Beyond the in-domain setting, HYSET further supports zero-shot/few-shot transfer, generalizing to held-out tools/categories and unseen domains with minimal supervision.

Recently, cross-domain few-shot facial expression recognition (CF-FER) has received considerable attention. However, the performance of existing CF-FER methods is still unsatisfactory due to inferior transferable feature learning under large domain discrepancy and limited target samples. Fortunately, the action units (AUs), which indicate the movements of different facial muscles, provide consistent conceptual semantics for describing expressions within and across domains. Inspired by this, we propose a novel Action Unit-based Consistency-aware Hypergraph Network (AUCH-Net), which constructs consistency-aware hypergraphs on AUs, for CF-FER. Specifically, AUCH-Net presents a new AU feature learning (AFL) module and a new visual feature learning (VFL) module. The AFL module learns AU features under the guidance of a novel relation consistency loss and an AU regularization loss, while the VFL module learns visual features supervised by a relation consistency loss and a classification loss. By learning consistent AU features, AUCH-Net effectively models the connections between AUs and expression categories. As a result, we can bridge the gap between fine-grained facial variations and high-level expression categories, greatly facilitating the learning of transferable feature representations.Extensive experiments on both in-the-lab and in-the-wild datasets show that our method consistently outperforms several state-of-the-art methods. Our results clearly show that modeling the relationships among AUs holds significant potential for FER under cross-domain few-shot scenarios.

Hypergraph-based RAG systems surpass traditional graph-based approaches by organizing complex n-ary atomic facts among entities, rather than relying solely on binary relationships. Despite the advancements in multimodal large language models (MLLMs) with enhanced visual capabilities, current hypergraph-based RAG frameworks predominantly restrict knowledge retrieval and reconstruction to a unimodal, text-centric paradigm. This limitation prevents them from fully leveraging the powerful visual perception capabilities of modern MLLMs. To address this gap, we systematically explore the integration of hypergraph awareness in RAG systems through visual cues. By incorporating visual representations of hypergraphs into the RAG pipeline, we introduce VizRAG, the first RAG system to support visual hypergraph structure awareness. Experimental results demonstrate that VizRAG significantly outperforms strong baselines, validating the promising potential of hypergraph visualization as a novel approach for RAG systems.

Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

The Matthew effect is a big challenge in Recommender Systems (RSs), where popular items tend to receive increasing attention, while less popular ones are often overlooked, perpetuating existing disparities. Although many existing methods attempt to mitigate Matthew effect in the static or quasi-static recommendation scenarios, such issue will be more pronounced as users engage with the system over time. To this end, we propose a novel framework, Multi-Hypergraph Boosted Multi-Interest Self-Supervised Learning for Conversational Recommendation (HiCore), aiming to address Matthew effect in the Conversational Recommender System (CRS) involving the dynamic user-system feedback loop. It devotes to learn multi-level user interests by building a set of hypergraphs (i.e., item-, entity-, word-oriented multiple-channel hypergraphs) to alleviate the Matthew effec. Extensive experiments on four CRS-based datasets showcase that HiCore attains a new state-of-the-art performance, underscoring its superiority in mitigating the Matthew effect effectively. Our code is available at https://github.com/zysensmile/HiCore.

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.

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.

Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.

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.

We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $Σ_{\mathrm{HG}}$. The encoding is executed by a small virtual machine comprising a sparse hypergraph, a circular doubly-linked list (CDLL) of node references, and $k$ traversal pointers, where $k$ bounds the hyperedge arity. Instructions either move a pointer through the CDLL or insert a hyperedge, optionally together with new nodes, into the hypergraph. Every string over $Σ_{\mathrm{HG}}$ decodes to a valid hypergraph; the alphabet is closed. A greedy \emph{HypergraphToString} (h2s) algorithm encodes any connected hypergraph into a string; a backtracking variant seeded at nodes of lexicographically maximal structural tuple produces a \emph{canonical string} $w^{*}$, which we conjecture to be a complete isomorphism invariant. Canonical-string equality then decides hypergraph isomorphism natively, without the standard reduction to the Levi incidence graph followed by a graph-isomorphism engine. We verify the round-trip property $s2h(h2s(H)) \cong H$ on 150 connected random uniform hypergraphs and on named combinatorial designs, and we benchmark the canonical algorithm against the three practically available exact baselines -- nauty, Traces, and bliss operating on the 2-coloured Levi graph -- across a $(n, c)$ grid with ten seeds per cell. All four methods agree on every one of 600 isomorphism verdicts, consistent with the completeness conjecture. On wall-clock time the Levi baselines dominate every tested cell by three to five orders of magnitude (geometric-mean ratio $311\times$ to $117{,}672\times$), which we report as measured. We contribute the representation framework, a conjecture of canonical completeness, and the first native-versus-Levi benchmark for hypergraph isomorphism.

RGB-Thermal (RGBT) Video Object Detection (VOD) has gained significant attention because of the limitations of conventional RGB-based VOD methods under challenging conditions, such as low light, heavy fog, and adverse weather, etc. However, spatial misalignment commonly exists between RGBT image pairs. To address this, we propose a Dual-Correlation Hypergraph Network (DCHNet) 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 propose a Dual Hypergraph Fusion Module (DHFM), which constructs temporal and multimodal hypergraphs, respectively, to enhance object characteristic through dual-correlation learning. Furthermore, the field currently lacks a large-scale, scene-diverse benchmark dataset for comprehensive evaluation. Therefore, 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, traffics, rural areas, night scenes, rainy weather, and snowy weather. Comprehensive experiments on VT-VOD50 and our DVT-VOD1000 demonstrate that DCHNet 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.

Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored. Unlike pairwise graphs, uncertainty in hypergraphs arises not only from noisy attributes and ambiguous labels, but also from variations in node-hyperedge incidence structures and complex higher-order dependencies. Existing approaches mainly estimate uncertainty from final predictions or rely on computationally expensive ensembles and Bayesian inference, limiting their ability to capture uncertainty evolution during representation learning. In this paper, we propose Hypergraph Neural Stochastic Diffusion(HyperNSD), a stochastic differential equation framework for uncertainty estimation on hypergraphs. HyperNSD models hypergraph representations as stochastic processes evolving over node-hyperedge incidence structures. A learnable drift function captures deterministic higher-order diffusion dynamics, while a learnable stochastic forcing function characterizes structural ambiguity and representation noise. Predictive uncertainty is directly quantified through the variability of stochastic representation trajectories, providing an intrinsic uncertainty measure beyond post-hoc confidence scores. We formulate HyperNSD with neural drift and diffusion networks, enabling joint learning of prediction and uncertainty propagation. Theoretical analyses establish well posedness, perturbation stability,permutation equivariance, and numerical convergence of the proposed stochastic dynamics. Experiments on multiple hypergraph benchmarks demonstrate that HyperNSD achieves reliable uncertainty estimation for out-of-distribution and misclassification detection while preserving competitive prediction accuracy. These results provide a principled stochastic-dynamical framework for trustworthy higher-order representation learning.

The rapid advancement of deepfakes necessitates robust face forgery detection. Although forged faces may lack obvious artifacts, they often contain subtle disharmony among different facial regions. We propose SGF-CDNet, a Consistency-Discrepancy Graph Network (CD-GNN) over Semantic-Geometric Fused (SGF) nodes. First, SGF-CDNet constructs SGF nodes by deeply fusing semantic regions from face parsing with geometric information from facial landmarks, allowing nodes to capture both high-level concepts and precise geometric constraints. Next, a dual-path CD-GNN performs parallel relational reasoning on these nodes across two dimensions: consistency and discrepancy. The consistency path evaluates if facial components follow natural biological patterns, while the discrepancy path mines for structural tensions and feature conflicts introduced by forgeries. By integrating these processes, our model effectively identifies disharmonious relationships between facial components. Extensive experiments on public datasets demonstrate that SGF-CDNet achieves superior performance, establishing it as a reliable solution for face forgery detection.

Falls among the elderly represent a significant public health concern due to their prevalence, consequences, and societal burden. While deep learning has improved fall detection, accurately identifying impact moments (when an individual hits the ground) remains challenging. Additionally, current algorithms often rely on complex models with high computational demands, limiting real-time deployment feasibility. In this work, we propose DistillH-Mamba, a novel architecture for impact fall detection that addresses these challenges through three key innovations: First, we introduce a hypergraph-based approach that captures higher-order relationships between multiple joints simultaneously, enabling more accurate modeling of complex interactions during impact falls. Second, we integrate the Mamba architecture with hypergraphs for impact detection, significantly accelerating processing speed while efficiently capturing both long-term dependencies and sudden skeletal motion changes. Third, we employ relational knowledge distillation that preserves crucial spatial-temporal relationships while reducing computational demands for real-time impact fall detection. Evaluated on the 3D Skeletons UP-Fall and UMAFall datasets, our DistillH-Mamba model achieves 97.38% accuracy in detecting impact within fall events and 73.8% reduction in inference time compared to its teacher model, outperforming state-of-the-art methods in both precision and efficiency.

Fast estimation of the size of the largest overlap between tables enables blocking and query-by-table retrieval in large table repositories. The first and the state-of-the-art estimator Armadillo improves efficiency by embedding each table independently and approximating overlap ratio via embedding similarity. However, accurate estimation in heterogeneous repositories remains limited by three challenges: (C1) overlap depends on row-column structure, i.e., each matched cell must preserve both its row and column membership under a joint alignment of the two tables, but existing encodings leave this structure to be inferred indirectly; (C2) independent encoding provides no explicit channel for inter-table alignment signals, biasing prediction toward global similarity; (C3) naive value encodings overfit to corpus-specific distributions, causing cross-domain degradation. Hence, we propose ALORE, a scalable and domain-robust overlap ratio estimator built on three principles: (P1) explicitly represent row-column structure; (P2) expose inter-table alignment signals during training without expensive alignment search; (P3) reduce sensitivity to corpus-specific value distributions. ALORE instantiates these principles with a Two-View Row-Column Hypergraph encoder, alignment-guided objectives with inexpensive interaction signals, and a domain-robust value mapping. Experiments on multiple datasets spanning diverse domains and scales, including a large real-world corpus beyond prior benchmarks, show that ALORE outperforms the state of the art. ALORE reduces MAE by up to 55% overall and 69% in zero-shot transfer, while achieving up to 89x speedup. We further validate its effectiveness for query-by-table retrieval.

Effective brain disease diagnosis requires the synergy of brain connectivity patterns and high-level semantic knowledge. Existing methods, however, largely treat semantics from large language models (LLMs) as auxiliary features or supervision, limiting their direct role in decision-making and constraining classification stability and robustness. To overcome this, we propose a semantic-aligned brain network framework that actively integrates LLM-derived semantics into the prediction process. Specifically, ROI-level semantics are first incorporated via global self-attention to enrich node representations and provide whole-brain context. Multi-scale hypergraphs are then constructed to explicitly model functional subnetworks and multi-ROI interactions, addressing the locality limitations of traditional GNNs and capturing high-order dependencies. Finally, a decision-level semantic alignment mechanism selectively injects patient-specific textual embeddings into graph representations, enabling semantics to directly guide predictions without perturbing the underlying network structure. Experiments on public brain network datasets ABIDE and ADHD-200 demonstrate state-of-the-art performance, enhanced stability, and improved interpretability, particularly in small-sample settings.

Next activity prediction helps service-oriented processes anticipate upcoming steps before delays, exceptions, or service-level risks occur. Most existing methods assume classical single-case event logs, whereas real service processes often involve events shared by multiple typed business objects. Object-centric event logs (OCELs) capture such interactions, but current predictors remain limited. Flattening-based approaches lose cross-object context, and native OCEL graph-based approaches encode multi-object events through pairwise relations. Existing models also do not jointly capture event-driven object state changes, inter-event timing, and global execution patterns. We propose EHHN, an Event-driven Heterogeneous Hypergraph Network for object-centric next activity prediction. EHHN represents each prediction prefix as a heterogeneous hypergraph, where event--object hyperedges bind retained co-participating objects and a lifecycle hyperedge groups the primary object's observed lifecycle events. Based on this representation, EHHN uses a dual-stream architecture in which a micro-spatial stream models event-driven object-state evolution and a macro-evolution stream captures temporal dynamics using retrieved global prototypes. The two streams are fused to predict the next activity. Experiments on four public OCEL benchmarks against nine baselines show that EHHN achieves the best accuracy and macro F1-score on all datasets, with improvements of up to 8.1 and 12.4 percentage points over the strongest baselines. Compared with the strongest OCEL-native graph baseline, EHHN also reduces peak GPU memory by up to 24 times. Code is available at https://github.com/chenkaitao1112/EHHN.

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.

With the increasing deployment of heterogeneous robot fleets in industrial environments, efficient coordination remains a critical challenge. Real-time path planning must simultaneously accommodate high robot densities and heterogeneous motion capabilities, while communication delays, execution uncertainties, and other disturbances may cause robots to deviate from the temporal assumptions underlying planned paths. Such deviations can lead to excessive waiting and congestion propagation across the fleet. This paper presents SCALE, a reactive online coordination framework that enables real-time planning while maintaining robust execution. Within this framework, we introduce a motion-induced conflict reduction mechanism to support the online generation of feasible paths for online conflict resolution. To mitigate the effects of disturbances, we further design a generalized Conjugate Action-Precedence Hypergraph (CAPH) that adaptively adjusts precedence relations among robots. Extensive validation experiments, together with a three-day deployment in a warehouse, demonstrate the

We introduce Directed Hypergraph Signal Processing (DHGSP), a unified framework that extends graph signal processing to accommodate both higher-order (polyadic) and asymmetric (directional) relationships simultaneously. Using the tensor singular value decomposition (t-SVD) within the t-product algebra, we define a novel adjacency tensor for directed hypergraphs, a topologically faithful shift operator, and a lossless Directed Hypergraph Fourier Transform (t-DHGFT). Experiments on real traffic networks demonstrate that DHGSP outperforms matrix-based (graph and digraph) and undirected tensor-based (hypergraph) baselines in denoising tasks.

Parameter-efficient fine-tuning (PEFT) has become a practical solution for adapting large pretrained vision transformers (ViTs) to downstream tasks while updating only a small subset of parameters. However, existing adapter-based methods perform adaptation independently for each token, implicitly assuming that token refinements should be learned in isolation. This token-wise formulation overlooks the structured relationships among tokens that naturally arise in visual scenes, potentially leading to redundant updates and spatially inconsistent feature refinement. In this work, we revisit the design of parameter-efficient adapters and propose to perform adaptation in hyperedge space rather than token space. We introduce HyperAdapter, a hypergraph-based adapter architecture that enables structured, group-aware adaptation through soft token routing. HyperAdapter constructs a soft hypergraph over ViT tokens using prototype-based assignments, aggregates token features into latent hyperedge representations, applies lightweight bottleneck adaptation at the hyperedge level, and diffuses the resulting updates back to tokens via the hypergraph incidence structure. This design injects an explicit structural inductive bias into PEFT while preserving the modularity and efficiency of standard adapters. Extensive experiments across diverse visual benchmarks demonstrate that structured hyperedge adaptation consistently outperforms strong PEFT baselines under comparable parameter budgets, with particularly pronounced gains on tasks requiring structured reasoning. Our results suggest that the choice of adaptation space is a critical yet underexplored dimension in parameter-efficient transfer for ViTs.

Abnormality detection in complex systems faces two practical barriers: abnormal labels are scarce, and binary labels do not quantify how far an event has departed from normal behavior. We study a normal-world modeling formulation for this setting. Instead of learning a large and incomplete space of abnormal classes, the model learns the normal world from abundant normal events and uses a few abnormal examples only to calibrate the boundary of normality. We instantiate this idea as a Hypergraph Entropic Normal-World Model. The model represents multivariate sensor windows as context-conditioned hypergraphs, where hyperedges capture high-order relations among groups of variables. It then defines abnormality by an entropy-aware normal-world energy that combines temporal prediction surprise, hypergraph consistency surprise, and latent normal-manifold departure. On the NASA C-MAPSS turbofan degradation benchmark, the proposed full energy achieves strong zero-shot and few-shot performance across all four subsets and reaches AUROC 0.9983 on FD004, the most complex setting with multiple operating conditions and fault modes. Beyond standard detection metrics, we introduce mechanistic validation tests to probe whether the energy encodes normal-world structure rather than a superficial input-output mapping. The learned energy accepts unseen healthy engines, increases along degradation trajectories, and sharply penalizes context-mismatched cross-variable coupling breaks. These results suggest that normal-world energy can serve as an anomaly score, a graded risk measure, and a testable representation of normal system behavior under severe abnormal-label scarcity.

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.

Semantic-aware communication has emerged as a transformative paradigm for next-generation communication systems, shifting the fundamental goal from transmitting bit-level symbols to reliably recovering and understanding the semantic meaning of information. Previous studies have demonstrated that representing the semantic content of source messages as graph-based structures can significantly improve communication efficiency and the accuracy of semantic inference at the receiver. However, existing solutions typically employ graphs that capture only pairwise relationships, thereby neglecting higher-order implicit correlations commonly observed in real-world scenarios, such as group interactions, multi-entity associations, and complex relational contexts. This limitation reduces semantic expressiveness and makes semantic inference susceptible to ambiguity and performance degradation, particularly under noisy or corrupted channel conditions. To address these issues, this paper proposes a novel hypergraph-based implicit semantic reasoning framework, HISR, which leverages hypergraphs to represent complex multi-entity relationships among semantic knowledge entities. In HISR, entities and their associated higher-order relations are mapped into dedicated semantic subspaces tailored to distinct relational contexts. This design not only disentangles diverse semantic interactions to mitigate the over-smoothing effects commonly found in traditional graph embedding methods but also enables robust semantic inference even when partial information loss occurs during transmission. Numerical results show that the proposed HISR achieves up to a 36.6% improvement in implicit semantic interpretation accuracy over the state-of-the-art benchmarks.

Retrieval-Augmented Generation (RAG) offers an effective approach for large language models to access external knowledge. However, existing methods rely on dense similarity retrieval and face inherent limitations in handling structured constraints and multi-hop reasoning. Incorporating knowledge graphs partially alleviates these issues, but at the cost of semantic fragmentation, high maintenance overhead, and difficult incremental updates. This paper introduces SAG (SQLRetrieval Augmented Generation), a structured architecture for retrieval and agent systems. Instead of pre-building a global static graph, SAG converts each chunk into one semantically complete event and a set of indexing entities, then uses SQL join queries to dynamically link events that share entities into local hyperedges,constructing, at query time, a dynamically instantiated local index structure. This design avoids the need for global graph rebuilding and ongoing maintenance; the system naturally supports incremental writes, concurrent processing, and continuous scaling through its reliance on standard database infrastructure. Across HotpotQA, 2WikiMultiHop, and MuSiQue, three standard multi-hop benchmarks,SAG achieves the best results on 8 out of 9 Recall@K metrics, reaching 80.0% Recall@5 on MuSiQue, the benchmark with the highest multi-hop reasoning demands.SAG has also been deployed at a production scale of hundreds of millions of data items, with online retrieval latency kept within seconds. Project site and code are available at https://github.com/Zleap-AI/SAG-Benchmark.

Tabular data embeddings have become a cornerstone of data profiling and data integration pipelines, enabling tasks such as entity annotation and resolution; schema matching; column type detection; and table search, among others. Existing approaches embed rows, columns, or entire tables into a vector space and rely on nearest-neighbor search to retrieve candidate matches. A fundamental limitation of current embedding methods is the lack of interpretable similarity scores: the concrete similarity value between a query and its nearest neighbour carries no intrinsic meaning, making it impossible to determine whether that neighbour is a true match or simply the least-dissimilar item in a corpus that contains no valid answer. This inability to set principled thresholds for retrieval undermines practical deployment, particularly for zero-match detection. We investigate the use of HyperDimensional Computing (HDC), specifically the Holographic Reduced Representations (HRR) model, as a framework for tabular row embeddings when the retrieval task corresponds to answering structured select-project queries in vector space. Exploiting the algebraic properties of HDC operations, we derive closed-form expected similarity values for both equality and non-equality retrieval predicates, which converge to interpretable values as dimensionality increases, and use these to identify suitable retrieval thresholds. We evaluate HDC against EmbDI, a graph-based baseline, on two real-world datasets across varying table sizes and predicate lengths. Our results show that HDC matches or outperforms EmbDI for row retrieval across all configurations, handles non-equality predicates more robustly, and achieves perfect attribute projection accuracy at sufficient dimensionality -- while uniquely enabling reliable identification of zero-match predicates through its principled thresholds.

Persona-grounded dialogue systems aim to produce responses consistent with a speaker's persona, yet existing methods treat personas as a flat set of sentences and fail to model the high-order relations among persona attributes-e.g., that several persona sentences share a topical category. We propose HyPE (Hypergraph Persona Encoder), a framework that (i) analyzes each persona-bearing text as a (Core, Expression, Sentiment, Category) quadruple, and (ii) organizes persona elements into a hypergraph whose hyperedges are induced by shared category labels. An HyperGCN hypergraph neural network propagates this structure into a persona summary vector and a soft-memory bank that condition the response generator. We further propose Persistent Edge Embeddings (PEE), lightweight per-category learnable priors fused into the HyperGCN message-passing step. On PersonaChat under greedy decoding, HyPE consistently outperforms sentence-level pooling baselines across GPT-2, LLaMA-3.2-3B, and Qwen2.5-3B backbones by demonstrating that structured hyperedge-level persona encoding provides a transferable advantage across model scales.

Long-document question answering (QA) requires large language models (LLMs) to reason over evidence scattered across lengthy documents, where answers often depend on event order, section-level context, and cross-part evidence connections. Although retrieval-augmented generation (RAG) reduces the input context by retrieving relevant evidence, existing structured RAG methods still face three limitations: costly query-agnostic knowledge organization, insufficient use of original document structure, and no reuse of historical reasoning experience. To address these limitations, we propose DocTrace, a multi-agent RAG framework for long-document QA that supports query-triggered knowledge organization, document-structure-aware and experience-guided reasoning. DocTrace preserves document hierarchy with a lightweight document structural tree index, constructs agent-shared hypergraph-structured working memory on demand during reasoning, and stores successful reasoning plans in graph-structured experience memory for future reuse, enabling adaptive exploration across related long-document questions. Experiments on four long-document QA datasets show that DocTrace achieves the best performance on three datasets, surpassing the strongest baseline, ComoRAG, by up to 8.85% in F1 and 4.40% in EM, while reducing the overall computational cost by 53.32%

Local Hyper-Flow Diffusion (HFD) gives an edge-size-independent Cheeger-type guarantee for seeded clustering in general submodular hypergraphs, but existing HFD solvers do not keep intermediate computation local at every iteration. We introduce Thresholded Local HFD (TL-HFD), a first-order method that maintains an active region around the seeds, performs projected subgradient updates on that region and its immediate boundary, and expands via thresholded (top-k) boundary activation. We prove that the local update is exact: the degree-preconditioned projected subgradient step restricted to the active region and its boundary coincides with the unrestricted global update. We establish finite-time dual suboptimality for both exact and thresholded updates, treating the latter as inexact projected subgradient steps with explicit skipped-boundary error. We further derive an additive activated-volume bound controlled by realized local subgradient norms and the minimum boundary-push among newly activated vertices, and translate approximate dual optimality with localized support into a robust sweep-cut guarantee for early-stopped iterates. For general submodular cut-costs, each iteration is local in the scanned region and oracle-sensitive in the hyperedge primitive. Empirically, TL-HFD often matches or improves over HFD while activating less volume, with the largest gains on noisy instances where diffusion tends to absorb non-target vertices.

Convolutions have successfully transitioned from image processing to the complex realm of non-Euclidean higher-order domains, particularly in hypergraphs. Despite the success in convolution, the exploration of a popular architecture named U-Net remains largely unexplored for hypergraph data due to the lack of well-defined pooling and unpooling operations. This work pioneers the study of U-Net architectures for hypergraph data, addressing the critical challenge of designing effective pooling and unpooling operations that retain maximal structural information from the input hypergraph. Motivated by hierarchical clustering, we propose to construct the pooling and unpooling operators all at once by cutting the clustering dendrogram at different granularities, named the Parallel Hierarchical Pooling (PHPool) and Unpooling (PHUnpool) operators. Unlike existing pooling methods that risk local structural damage through a sequential learning procedure, our PHPool operators are designed in a global and parallel manner to ensure fidelity to the original hypergraph structure with efficient computation while the PHUnpool operators are tailored to perform inverse operations of the PHPools for hypergraph reconstruction. We validate our model through hypergraph reconstruction simulation, hypergraph classification, and node-level anomaly detection, where it demonstrates superior performance over existing state-of-the-art graph and hypergraph deep learning methods.

Hypergraph knowledge distillation aims to retain the predictive performance of a hypergraph neural network (HNN) teacher while reducing inference costs through a lightweight student model. In this work, we observe that HNNs exhibit substantially lower prediction performance on heterophilic nodes connected through semantically diverse hyperedges, indicating that the reliability of teacher knowledge varies across nodes. Motivated by this observation, we propose HADES, a heterophily-aware adaptive distillation method for hypergraph neural networks. HADES quantifies node heterophily and leverages it as an estimate of teacher reliability to modulate the transfer of teacher knowledge during distillation. Experimental results on real-world hypergraphs demonstrate that HADES consistently improves student performance across different HNN teachers and distillation objectives. In many cases, the resulting student models surpass the predictive performance of their teachers while achieving up to 12.3 times faster inference.

Novel class discovery in point cloud segmentation aims to transfer knowledge from known classes to automatically identify and segment unlabeled novel classes in point clouds. Existing methods mainly rely on pairwise associations for class assignment and novel class reasoning, which limits their ability to capture complex relationships among known and novel classes and may lead to inaccurate semantic segmentation. To address this issue, we introduce a hypergraph-based framework that models high-order associations among classes and enables collaborative reasoning from known classes to novel classes beyond traditional pairwise relations. Moreover, existing methods tend to focus on semantic feature extraction while paying insufficient attention to geometric information in point clouds. To better exploit spatial structure, we propose Geometric-Aware Prototypes to enhance the representation of class-level geometric cues. By propagating geometric information through hyperedges, the proposed method improves the understanding of spatial distributions across classes and leads to more accurate segmentation. Experiments on the SemanticKITTI and SemanticPOSS datasets demonstrate the effectiveness and superiority of our method.

Multi-hop RAG poses a data-engineering problem beyond passage matching: under fixed retrieval budgets, a system must organize retrieved text into evidence units that expose answer chains. Dense retrievers score passages independently, while graph-based memories make associations explicit but often rely on pairwise or entity-centered keys that fragment multi-hop evidence. We present HKVM-RAG, a key-value-separated evidence-organization layer. It assembles answer-path hyperedges from cached passage-level LLM evidence tuples and uses them as retrieval keys, while retaining passage text as answer values. To isolate key-space design, our fixed-substrate protocol holds the tuple cache, candidate passages, reader, and evaluation budget constant across pairwise graph and hypergraph variants. Weighted hypergraph key-value retrieval improves over KG-PPR by +3.426 F1 on 2WikiMultiHopQA and +3.592 F1 on MuSiQue; HotpotQA shows that higher structured support coverage need not yield standalone answer-F1 gains. We therefore study WHG-KV as an evidence-control signal rather than a dense-retrieval replacement. Oracle and train-to-dev analyses identify support selection as repairable, and a dense-aware controller combines frozen ColBERTv2 and HKVM rank/score features using out-of-fold HKVM predictions. It reaches 88.846, 65.073, and 85.810 F1 on the three benchmarks, improving over ColBERTv2 by +11.084, +6.763, and +5.966 F1. Source-level ablations show that matched non-WHG structured signals do not match the WHG-KV gains. These results provide bounded evidence that key-value-separated hypergraph organization can serve as a reusable evidence-control mechanism for multi-hop RAG.

Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes. Latent factorization of tensors (LFT) extracts target knowledge from DWDNs via low-rank embedding. However, similar to many machine learning models, the performance of LFT heavily depends on the selection of hyperparameters. In practice, these parameters are often tuned manually or through grid search, which requires significant computational resources and human effort. Motivated by this challenge, this paper proposes an automated hyperparameter optimization framework based on Differential Evolution (DE) for LFT (DE-LFT). The proposed method integrates DE into the training process of the LFT model to automatically learn optimal regularization parameters $λ_1$, $λ_2$ and $λ_3$. As a result, the model can adaptively search the hyperparameter space and improve prediction accuracy. Experimental results on four real-world datasets demonstrate that the proposed approach achieves lower MAE and RMSE compared with manually tuned baselines while reducing the need for extensive parameter tuning.

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.

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.

Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabilities of GFMs. Specifically, the introduced Hyperbolic Knowledge Indexing module retains the tree-like hierarchies of the external knowledge base by modeling them within hyperbolic space. The Multi-granularity Retrieval module then provides GFMs with the global semantic anchors and local semantic nuances through coarse-grained and fine-grained knowledge retrieval, respectively. Finally, the Dual-path Fusion module achieves effective knowledge integration for graph tasks at both the feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in the zero-shot setting, highlighting the generalization of our method for robust GFMs inference.

Deep learning has revolutionized medical image analysis, delivering exceptional diagnostic accuracy across diverse applications. Yet, the lack of interpretability in its decision-making hinders clinical adoption, particularly in high-stakes medical contexts where transparency is paramount for trustworthiness. For example, in Placenta Accreta Spectrum (PAS), subtle cues in ultrasound imaging challenge reliable diagnosis, rendering black-box models untrustworthy for accurate scoring. To address this, Concept Bottleneck Models (CBMs) offer a promising avenue by embedding clinically meaningful intermediate concepts into the diagnosis pipeline, enabling clinicians to scrutinize and refine model outputs. However, conventional CBMs falter in capturing complex inter-concept dependencies and demand costly, expert-driven concept annotations, limiting their scalability. This study introduces a novel semi-supervised CBM framework designed for medical imaging, which leverages dual-level hypergraph learning to model high-order concept dependencies and generate domain-adaptive pseudo-labels. Our approach achieves superior interpretability and performance by integrating a concept-level hypergraph for enhanced reasoning and an image-level hypergraph for robust pseudo-label generation. Experiments on a newly annotated PAS ultrasound dataset and a breast ultrasound public dataset demonstrate the effectiveness of the proposed concept label-efficient interpretable framework. Its universality is further validated on the dermoscopic image dataset SkinCon. The code is available at https://github.com/scott-yjyang/HyperCBM.

LLM-driven social bots can generate fluent, human-like text, reducing the discriminative advantage of content-based detection alone. However, coordinated campaigns still leave relational patterns -- interactions, behavioral similarity, shared neighborhoods, community positions, and coordinated activity -- that graph-based methods can exploit. Existing graph detectors face two challenges when exploiting such evidence. First, Euclidean GNNs distort hierarchical and scale-free social graphs; while hyperbolic geometry addresses this volume-growth mismatch, fixed-curvature models still assign uniform geometric resolution to structural directions with different densities and separation needs. Second, relational evidence is not always reliable: sophisticated bots forge heterophilic connections with genuine users, causing neighborhood aggregation to mix bot and human signals and dilute account-level evidence. We propose SAHG (Sector-Anisotropic Hyperbolic Graph), addressing both challenges. SAHG learns a direction-dependent curvature field $γ(u)$ that adapts geometric resolution across structural directions, and uses sector prototypes to convert angular concentration and alignment into classifier-readable features. To prevent contaminated aggregation from overwhelming account-level evidence, SAHG encodes per-account features and graph-neighborhood representations in two independent SAH channels, fusing them only at the classifier. Experiments on Fox8-23, BotSim-24, and MGTAB show that SAHG achieves the highest accuracy and F1 on all three benchmarks, outperforming feature-based, graph-based, LLM-based, and isotropic hyperbolic baselines. Ablation and geometric analyses confirm the effectiveness of the anisotropic geometry and dual-channel design.

Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and implicitly couple word occurrence and repetition within one probabilistic mechanism. However, this formulation restricts the dependence structure among words and overlooks informative higher-order interactions, particularly in dynamic corpora with overlapping semantics. To address these limitations, we introduce a hypergraph representation of text where each document is modeled as a hyperedge connecting all co-occurring words, with repetition intensities encoded as node weights. This representation naturally separates word occurrence from repetition and induces a novel hypergraph-based multinomial distribution with a nonlinear normalization depending on the observed word set of each document. Building on this likelihood, we develop a dynamic topic modeling framework via structured low-rank factorizations with explicit temporal regularization on topic-word profiles. Moreover, we establish local convergence guarantees and derive non-asymptotic error bounds despite the intrinsic nonconvexity induced by bilinear factorization and document-specific nonlinear normalization. Numerical experiments on synthetic data and an application to the International Conference on Learning Representations (ICLR) corpus demonstrate consistent improvements over existing multinomial-based topic models.

Predicting Internet round-trip time (RTT) is critical for routing optimization, quality-of-service (QoS) provisioning, and traffic engineering, yet remains challenging due to long-term temporal dependencies, evolving routing dynamics, and heavy-tailed latency distributions. While Temporal Graph Neural Networks (TGNNs) can model evolving network topologies, most existing approaches operate in Euclidean space, which poorly captures the hierarchical and scale-free structure of Internet routing graphs. Hyperbolic geometry provides a more suitable representation space. We propose HERMIT (Hyperbolic Edge-aware RTT Modeling via Integrated Topology), a hybrid framework combining a hyperbolic manifold-preserving temporal GNN with a Random Forest regressor for joint link prediction and RTT prediction. Built on HMPTGN, HERMIT introduces RTT-aware edge features and a learnable edge encoder to improve modeling of evolving link states and routing behavior. The resulting hyperbolic node representations are combined with historical RTT statistics for robust latency prediction. We evaluate HERMIT on a large-scale real Internet dataset spanning 2015-2024. HERMIT consistently outperforms a strong Random Forest baseline using only historical RTT statistics, achieving a 6% RMSE improvement while reducing large errors on heavy-tailed samples. It also surpasses prior hyperbolic TGNN models, including HMPTGN and HTGN, in link prediction performance. These results demonstrate that combining hyperbolic temporal graph learning with tree-based regression provides a scalable solution for RTT prediction in real-world Internet topologies.

As a core task in intelligent transportation systems, traffic forecasting plays a critical role in urban traffic management. Accurate traffic forecasting relies on modeling complex spatiotemporal dependencies, which is inherently challenging due to spatial heterogeneity in traffic systems.Despite significant progress, most existing methods are still limited to pairwise spatial dependency modeling, making it difficult to capture dynamic high-order interactions among nodes with similar traffic patterns. To address this issue, we propose PHGNet, a novel spatiotemporal forecasting framework based on prototype-guided hypergraph construction. At the core of PHGNet, a prototype learning mechanism is designed to adaptively assign pattern-similar nodes to hyperedges, thereby capturing high-order interactions with time-varying structures. To improve the reliability of dynamic hypergraph construction, we further develop a global-local node representation module to extract time-consistent features. For forecasting, iterative residual refinement and Temporal Query Attention are introduced to improve forecasting accuracy while supporting efficient parallel decoding. Extensive experiments on multiple real-world datasets demonstrate that PHGNet achieves superior predictive performance compared with state-of-the-art methods.

Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down in edge environments, where knowledge is fragmented across devices, raw data cannot be shared, and repeated LLM calls are prohibitively expensive. We propose FD-RAG, a federated dual-system RAG framework that decouples lightweight memory access from on-demand LLM reasoning for decentralized deployment. Specifically, FD-RAG learns semantic-aware adaptive hypergraphs over local corpora and distills them into compact QA memories. At inference time, it answers well-covered queries via direct memory matching and invokes LLM-based reasoning only when necessary, while tracing retrieved memories to hypergraph-grounded evidence. To mitigate cross-device knowledge fragmentation, FD-RAG aggregates anonymized memories across devices without exposing raw documents. Experiments on QA benchmarks show that FD-RAG improves accuracy by up to 7.8% while reducing latency by 8.4$\times$ compared with strong local and federated baselines. We also provide theoretical analysis establishing an $\mathcal{O}(1/ε^{2})$ convergence rate for the proposed hypergraph learning, supporting its tractable deployment in edge settings.

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