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20 pages, 551 KB  
Article
Long-Horizon Constraint-Aware Collaborative Scheduling for Multiple Phased-Array Radars Using Mamba Temporal Encoding and Structured Hybrid Actions
by Jianan Liu, Jie Xu, Wenge Xing and Mingrui Li
Sensors 2026, 26(15), 4772; https://doi.org/10.3390/s26154772 - 27 Jul 2026
Viewed by 324
Abstract
Phased-array radar networks require real-time collaborative scheduling of search, tracking, and identification tasks under coupled resource, beam, time-window, and power constraints. Current decisions affect future residual power, task refresh intervals, and tracking uncertainty, making long-horizon scheduling particularly challenging. This paper proposes CS-Mamba, a [...] Read more.
Phased-array radar networks require real-time collaborative scheduling of search, tracking, and identification tasks under coupled resource, beam, time-window, and power constraints. Current decisions affect future residual power, task refresh intervals, and tracking uncertainty, making long-horizon scheduling particularly challenging. This paper proposes CS-Mamba, a long-horizon constraint-aware collaborative scheduling framework for homogeneous multiple phased-array radars. The scheduling problem is formulated as a finite-horizon constrained decision process with structured hybrid actions, where the discrete component represents radar–task matching and the continuous component represents transmit-power allocation. A Mamba-based temporal encoder is introduced to summarize long scheduling histories with linear sequence complexity. Based on the encoded representation, the scheduler predicts task priorities, constructs a masked radar–task bipartite graph, solves a constrained maximum-weight matching problem, and projects raw transmit powers onto the feasible power domain. In addition, an action-dependent radar model is incorporated to link transmit power, effective SNR, detection probability, measurement noise, and tracking covariance. The model is trained using behavioral cloning from constraint-aware heuristic trajectories followed by actor–critic fine-tuning. Experiments on the proposed MRSched-Bench show that CS-Mamba improves the normalized cost-effectiveness score from 0.62 to 0.78 compared with MAPPO in the Medium scenario, while reducing end-to-end decision latency from 24.5 ms to 12.8 ms per step. Additional ablation studies verify the contributions of temporal encoding, structured matching, feasible power projection, and two-stage training. Full article
(This article belongs to the Section Radar Sensors)
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36 pages, 1214 KB  
Article
Explainable Graph Neural Networks Towards Data-Driven Inverse Kinematics in Industrial Robot Motion Planning
by Ali Jlidi, Rabab Benotsmane and László Kovács
Electronics 2026, 15(14), 3071; https://doi.org/10.3390/electronics15143071 - 13 Jul 2026
Viewed by 386
Abstract
Inverse kinematics (IK) is fundamental to robot motion planning. Classical analytical solvers require complete Denavit–Hartenberg (DH) parameters that are often proprietary or degraded by mechanical wear, and numerical solvers based on damped least squares (DLS) are sensitive to initialization, particularly near singularities. We [...] Read more.
Inverse kinematics (IK) is fundamental to robot motion planning. Classical analytical solvers require complete Denavit–Hartenberg (DH) parameters that are often proprietary or degraded by mechanical wear, and numerical solvers based on damped least squares (DLS) are sensitive to initialization, particularly near singularities. We propose XGNN, an explainable graph neural network positioned as a model-free, interpretable warm-start initializer for downstream numerical IK refinement rather than as a standalone replacement for analytical solvers. Each IK query is encoded as a 12-node graph in which six pose nodes and six joint nodes are connected through bipartite pose-to-joint attention edges and chain edges along the kinematic structure. GATv2 message passing aggregates information at each joint node; two ablation-validated design contributions (a learnable node-type embedding and an angle-aware composite loss) enable training to convergence. Evaluated on 300,000 trajectory-style samples generated from the ABB IRB 2400 kinematic model, XGNN achieves 3.66 joint mean absolute error (MAE), comparable to a multilayer perceptron baseline (3.09) and a bidirectional LSTM (3.14) under identical training. The standalone joint accuracy of all learned models is too coarse for direct industrial use, but XGNN provides the strongest warm start for DLS refinement: the convergence rate improves from 98.4% to 100%, mean iterations drop from 14.6 to 3.2, and wall-clock time per pose drops 5.0× on the IRB 2400. The benefit transfers cross-platform to the Universal Robots UR5 collaborative manipulator (convergence rate 82.2% to 100%, 10.0× speedup) and survives DH parameter perturbation of up to ±10%, simulating calibration drift or mechanical wear. The GATv2 attention coefficients additionally provide an interpretability signal at zero inference cost. XGNN therefore complements analytical and numerical IK methods as an interpretable, calibration-robust warm start when DH parameters are unavailable, proprietary, or degraded. Full article
(This article belongs to the Special Issue Recent Advances in Mobile Robot Navigation and Motion Planning)
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26 pages, 966 KB  
Article
A Statistical Modeling and Monitoring Framework for Dynamic Processes Based on Knowledge Graph and Dissimilarity Analysis
by Yunhan Hao and Shanliang Zhu
Mathematics 2026, 14(12), 2047; https://doi.org/10.3390/math14122047 - 8 Jun 2026
Viewed by 231
Abstract
Dynamic industrial processes often exhibit complex variable interactions, and time-varying behaviors, which pose significant challenges to conventional multivariate statistical monitoring methods. To address these issues, this paper proposes a novel data-driven monitoring framework that integrates knowledge-informed bipartite graph embedding with multi-scale dissimilarity analysis. [...] Read more.
Dynamic industrial processes often exhibit complex variable interactions, and time-varying behaviors, which pose significant challenges to conventional multivariate statistical monitoring methods. To address these issues, this paper proposes a novel data-driven monitoring framework that integrates knowledge-informed bipartite graph embedding with multi-scale dissimilarity analysis. First, a bipartite graph-embedding strategy is developed to incorporate mechanistic knowledge into the modeling process, enabling a more interpretable representation of dynamic relationships among process variables. On this basis, a multi-scale recursive dissimilarity monitoring method is further designed to enhance detection performance by capturing process variations across different temporal scales while reducing sensitivity to sliding window selection. The effectiveness of the proposed framework is validated through a numerical example and a benchmark simulation process. The results demonstrate that the proposed method achieves improved fault detection performance and robustness compared with conventional approaches. Full article
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28 pages, 871 KB  
Article
Prediction Pipeline Selection for Incomplete Clinical Data via Missingness Fingerprints and Instance Augmentation
by Runze Li, Zhuyi Shen, Chengkai Wu, Jingsong Li and Yu Tian
Bioengineering 2026, 13(5), 497; https://doi.org/10.3390/bioengineering13050497 - 24 Apr 2026
Viewed by 1053
Abstract
Clinical prediction from electronic health records (EHRs) is complicated by pervasive missingness and label scarcity, which make performance sensitive to the match between data conditions and pipeline choice. Choosing the best pipeline for a new incomplete dataset still requires costly trial-and-error. We cast [...] Read more.
Clinical prediction from electronic health records (EHRs) is complicated by pervasive missingness and label scarcity, which make performance sensitive to the match between data conditions and pipeline choice. Choosing the best pipeline for a new incomplete dataset still requires costly trial-and-error. We cast this as an algorithm selection problem and address two bottlenecks—instance scarcity and distance quality—that have so far prevented meta-learning from reaching clinical settings. Graph neural networks offer diverse strategies (patient similarity networks, bipartite imputation graphs, attention-driven feature interaction), yet no single architecture dominates across missingness patterns, and selecting the best pipeline for a new dataset remains a trial-and-error approach. Formal algorithm selection could automate this choice but requires many characterized meta-instances—more than clinical settings typically provide. We propose two solutions: (1) constructive instance augmentation, applying controlled quality perturbations (MCAR and MNAR missingness injection, label trimming) to 20 base EHR datasets to expand the meta-knowledge base to 83 characterized meta-instances, each described by a 10-dimensional missingness fingerprint, without additional model training; and (2) dynamic-supervised metric learning, using differential evolution to optimize fingerprint feature weights so that static distances preserve method-performance similarity captured by dynamic fingerprints, which require model sweeps and are unavailable at deployment. Under base-dataset-level leave-one-dataset-out cross-validation over 21 pipelines, the resulting metric-learned kNN recommender attains the highest win rate (20.5%) among non-oracle strategies on the augmented store, selecting the correct pipeline more often than any fixed default. At deployment, the recommender needs only the 10-dimensional static fingerprint with pre-learned weights; no sweep data is required for new datasets. Cross-domain evaluation on 25 external subsets (colorectal cancer, kidney disease, MIMIC-IV) demonstrates framework modularity: when the fingerprint module is adapted (standard meta-features in place of the missingness-specific set), the recommender achieves regret of 0.025 (55% below random selection). Full article
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26 pages, 7247 KB  
Article
Fast Unconstraint Convex Symmetric Matrix for Semi-Supervised Learning
by Wenhao Wang, Kaiwen Chen, Wenjun Luo, Nan Zhou and Yanyi Cao
Symmetry 2026, 18(4), 698; https://doi.org/10.3390/sym18040698 - 21 Apr 2026
Viewed by 477
Abstract
Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex [...] Read more.
Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex symmetric matrix factorization framework, termed FUCSMF, for semi-supervised learning. By incorporating label information into the symmetric factorization formulation, the proposed model is transformed into a convex objective, which guarantees global optimality and enables efficient optimization using standard unconstrained solvers. To further improve scalability, a bipartite graph structure is introduced into SMF from a hypergraph-inspired perspective, significantly reducing the computational burden. The resulting computational complexity is reduced to O(nmd), which is substantially lower than the O(nmd+m2n+m3) complexity required by existing bipartite graph-based methods, where n, m, and d denote the numbers of samples, anchor points, and feature dimensions, respectively. In addition, we propose a correntropy-based graph construction strategy to alleviate the sensitivity of conventional adaptive neighbor bipartite graph methods. Extensive experiments on six benchmark datasets, involving comparisons with eleven state-of-the-art methods, demonstrate that FUCSMF achieves superior clustering performance while requiring significantly less computational time. Empirical results further show that the proposed method converges rapidly, typically within ten iterations. Full article
(This article belongs to the Section A: Computer Science)
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32 pages, 2911 KB  
Article
End-to-End Personalization via Unifying LLM Agents and Graph Attention Networks for Entertainment Recommendation
by Danial Ebrat, Sepideh Ahmadian and Luis Rueda
Information 2026, 17(4), 344; https://doi.org/10.3390/info17040344 - 2 Apr 2026
Viewed by 1726
Abstract
Recommender systems are central to helping users navigate the rapidly expanding entertainment ecosystem, yet achieving strong personalization with limited feedback while maintaining interpretability remains difficult, particularly under cold-start conditions and heterogeneous item metadata. This work presents an end-to-end hybrid recommendation framework that unifies [...] Read more.
Recommender systems are central to helping users navigate the rapidly expanding entertainment ecosystem, yet achieving strong personalization with limited feedback while maintaining interpretability remains difficult, particularly under cold-start conditions and heterogeneous item metadata. This work presents an end-to-end hybrid recommendation framework that unifies a Large Language Model (LLM) with Graph Attention Network (GAT)-based collaborative filtering to improve both ranking accuracy and explanation quality across movies, books, and music. LLM-based agents first transform raw metadata such as titles, genres, descriptions, and auxiliary attributes into semantically grounded user and item profiles, which are embedded and used as initial node features in a user–item bipartite graph processed by a GAT-based recommender. Model optimization relies on a hybrid objective combining Bayesian Personalized Ranking, cosine-similarity regularization, and robust negative sampling to better align semantic and collaborative signals. Finally, in the post-processing stage, an LLM-based agent re-ranks the GAT outputs using a proposed Hybrid Confidence-Weighted Binary Search Tree, and another LLM-based agent that produces natural-language justifications tailored to each user. Experiments on diverse benchmark datasets and extensive ablations demonstrate that the proposed methodology increases precision, recall, NDCG, and MAP across various values of K. In addition, the post processing step is especially effective in cold-start scenarios, consistently strengthening recommendation metrics and enhancing transparency at smaller values of K. Overall, integrating LLM-enriched representations with attention-based graph modeling enables more accurate and explainable entertainment recommendations. Full article
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22 pages, 1335 KB  
Article
Temporal Graph Neural Networks for Modeling Student Knowledge Evolution and Predicting Learning Trajectories
by Deborah Olaniyan and Ruth Wario
Algorithms 2026, 19(4), 263; https://doi.org/10.3390/a19040263 - 1 Apr 2026
Cited by 1 | Viewed by 1067
Abstract
Accurately modeling student knowledge evolution is a central challenge in personalized learning and adaptive educational systems. Traditional sequential or static approaches often fail to capture both the temporal dynamics of learning and the relational structure between students and concepts. This study introduces a [...] Read more.
Accurately modeling student knowledge evolution is a central challenge in personalized learning and adaptive educational systems. Traditional sequential or static approaches often fail to capture both the temporal dynamics of learning and the relational structure between students and concepts. This study introduces a Temporal Graph Neural Network (TGNN) framework for modeling student knowledge acquisition and predicting learning trajectories using fine-grained interaction data from the ASSISTments_skill dataset. The TGNN represents students and skills as nodes in a dynamic bipartite graph, with temporal edges encoding correctness, attempts, hints, and interaction timestamps. Experiments demonstrate that TGNN significantly outperforms state-of-the-art baselines, including Deep Knowledge Tracing (DKT), Self-Attentive Knowledge Tracing (SAKT), and static graph convolutional networks, achieving an Area Under the Curve (AUC) of 0.892, Accuracy of 0.846, F1 score of 0.842, and a Mean Absolute Error (MAE) of 0.078 for trajectory prediction. Ablation studies reveal the critical role of temporal encoding, edge features, and graph connectivity in accurately modeling learning dynamics. Concept-level analysis indicates high prediction accuracy across both high-frequency and low-frequency skills, while temporal attention mechanisms enable interpretable insights into the influence of prior interactions on future performance. These results highlight the effectiveness of integrating temporal dynamics, graph-based relational modeling, and pedagogically meaningful features in predicting student learning outcomes. These results demonstrate the potential of temporal graph-based modeling for capturing student–skill relationships and learning dynamics in educational interaction data. Rather than introducing a fundamentally new graph architecture, this study systematically adapts the Temporal Graph Network (TGN) framework to educational data and evaluates its effectiveness for modeling knowledge evolution and forecasting student learning trajectories. The findings provide practical insights for applying temporal graph learning methods to personalized learning, adaptive intervention design, and real-time performance forecasting. Full article
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15 pages, 2942 KB  
Article
When Wholes Resist Decomposition: A Spectral Measure of Epistemic Emergence
by Mark Bailey and Susan Schneider
Entropy 2026, 28(4), 380; https://doi.org/10.3390/e28040380 - 28 Mar 2026
Viewed by 1191
Abstract
Multi-agent and distributed dynamical systems can exhibit coordinated behavior that is difficult to summarize in terms of independent parts. Integrated Information Theory (IIT) provides one influential notion of system-level irreducibility, but exact computation of causal Φ remains intractable except in very small systems. [...] Read more.
Multi-agent and distributed dynamical systems can exhibit coordinated behavior that is difficult to summarize in terms of independent parts. Integrated Information Theory (IIT) provides one influential notion of system-level irreducibility, but exact computation of causal Φ remains intractable except in very small systems. In this work, we introduce Φspectral, a scalable observer-relative statistic defined on pairwise mutual information networks extracted from multivariate time-series data. A normalized graph Laplacian and its Fiedler vector identify a bipartition of the mutual information graph, and Φspectral reports the normalized weight of informational coupling crossing that cut. The measure is inspired by IIT’s concern with irreducibility but is not equivalent to intrinsic causal Φ: it is pairwise, undirected, and functional/statistical rather than intervention-based. We evaluate it on four exploratory simulation regimes: random oscillators, a transitional Kuramoto-like synchronization regime, a perfectly synchronized regime, and a combinatorial threshold-linear network (CTLN). Across these cases, Φspectral is most useful as a measure of observer-relative integration under second-order dependencies, separating redundancy-dominated from transiently differentiated regimes. The current results should be read as a proof-of-concept rather than as a formal validation against exact IIT. We discuss relations to weak IIT, Integrated World Modeling Theory (IWMT), and the perturbational complexity index (PCI), and we outline the stationary benchmarking and small-system validation needed for stronger causal claims. Full article
(This article belongs to the Section Complexity)
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15 pages, 403 KB  
Article
Sharp Choice Number Thresholds for Complete Bipartite Graphs
by Julian Allagan, Benkam Bobga, Jianning Su, Weizheng Gao and Shanzhen Gao
Axioms 2026, 15(4), 252; https://doi.org/10.3390/axioms15040252 - 27 Mar 2026
Viewed by 811
Abstract
Fix m3. The choice number ch(Km,n) of the complete bipartite graph Km,n has two sharp thresholds as n grows. We give complete proofs of the Hoffman–Johnson values at levels [...] Read more.
Fix m3. The choice number ch(Km,n) of the complete bipartite graph Km,n has two sharp thresholds as n grows. We give complete proofs of the Hoffman–Johnson values at levels m+1 and m, and we pin down the extremal list assignments at the lower threshold n0=(m1)m1(m2)m1. Specifically, ch(Km,n)=m+1,nmm,m,n0n<mm,m1,n<n0. Our method centers on a transversal obstruction principle and a dichotomy for how the M-side lists can intersect when all lists have size m1: Case I, in which some m1 of the M-lists are pairwise disjoint, and Case II, in which three M-lists pairwise intersect with all remaining lists mutually disjoint. For m5 we show that the three-way intersection pattern (three pairwise intersecting M-lists) is strictly non-extremal, and we prove the uniqueness of extremal configurations: we classify all uniformly critical assignments at n0 and show that, up to relabeling, there are exactly two extremal types for m5, while a third type appears for m{3,4}. Finally, we propose a fixed-k block model for deeper levels ch(Km,n)=mk+1 and contrast this unbalanced setting with the balanced case m=n, where ch(Km,m)log2m, highlighting the shift from polynomial to logarithmic threshold growth. Full article
(This article belongs to the Special Issue Combinatorics and Graph Theory with Applications in Computer Science)
31 pages, 4857 KB  
Article
Who Reaches the Consumer? A Network Analysis of Market Reach Factors of Slovakia’s Short Food Supply Chains
by Lukáš Varecha, Jana Jarábková and Michal Hrivnák
Agriculture 2026, 16(6), 649; https://doi.org/10.3390/agriculture16060649 - 12 Mar 2026
Viewed by 728
Abstract
The aim of this study is to identify the factors that shape the ability of producers in short food supply chains in Slovakia to utilize different types of distribution channels and to penetrate higher-demand markets. The analysis was based on a database compiled [...] Read more.
The aim of this study is to identify the factors that shape the ability of producers in short food supply chains in Slovakia to utilize different types of distribution channels and to penetrate higher-demand markets. The analysis was based on a database compiled from a public SFSC platform, comprising 986 agri-food producers, 1434 points of sale, and 1908 producer–point of sale ties. The data were analyzed as a two-mode network using ERGM models. The results show that most producers remain tied to local direct sales, while access to more demanding channels and distant markets is concentrated among a small group of actors. The study shows that the functioning of SFSCs in Slovakia is strongly shaped by producer size, value added, and the form of production organization. Organic certification emerges as a key tool of product differentiation that enhances ability to access distant and urban markets, although its importance in a post-socialist context is highly dependent on market characteristics. Family farms are selectively able to supply distant markets, while cooperatives, despite their expected association with commodity-oriented production, are able to overcome capacity and logistical barriers within SFSCs, indicating the emergence of new collaborative structures and business models. Full article
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33 pages, 13524 KB  
Article
MVGAE: A Multi-View Graph Auto-Encoder Model for Drug Prediction of Non-Small Cell Lung Cancer Based on Synthetic Lethality
by Shaobo Hu, Runsheng Jiang and Ning Zhao
Curr. Issues Mol. Biol. 2026, 48(3), 269; https://doi.org/10.3390/cimb48030269 - 3 Mar 2026
Viewed by 948
Abstract
Identifying therapeutic target genes and their corresponding targeted drugs is of significant importance for the treatment of non-small cell lung cancer (NSCLC). This study proposes a multi-view graph auto-encoder model (MVGAE), which, together with the network-informed adaptive positive-unlabeled (NIAPU) and synthetic lethality multi-view [...] Read more.
Identifying therapeutic target genes and their corresponding targeted drugs is of significant importance for the treatment of non-small cell lung cancer (NSCLC). This study proposes a multi-view graph auto-encoder model (MVGAE), which, together with the network-informed adaptive positive-unlabeled (NIAPU) and synthetic lethality multi-view graph auto-encoder (SLMGAE) model, constitutes an integrated computational framework. The framework integrates multi-source biological network data, including protein–protein interaction networks, disease-gene association information, and gene-drug bipartite graphs, for data mining. Through systematic analysis and computational screening, we ultimately predicted seven potential driver genes associated with NSCLC using the NIAPU model. The SLMGAE model predicted nine genes with synthetic lethality (SL) interactions to these driver genes as candidate therapeutic targets. Based on these SL targets, the MVGAE model further predicted corresponding targeted drugs. Notably, among the prioritized targets, existing studies indicate that ATR and RAD51 exhibit conditional SL effects in the context of functional impairment. Furthermore, several of the predicted candidate drugs (such as PAZOPANIB) have been previously reported to play a positive role in NSCLC treatment. This study highlights MVGAE as a novel computational framework for drug repurposing and demonstrates how its integration with complementary models can effectively prioritize potential therapeutic targets and candidate drugs, providing a robust computational basis for precision treatment strategies. Full article
(This article belongs to the Special Issue Advances in Drug Design and Drug Discovery)
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26 pages, 10514 KB  
Article
Vulnerability in Bank–Asset Bipartite Network Systems: Evidence from the Chinese Banking Sector
by Zikang Wang
Systems 2026, 14(2), 198; https://doi.org/10.3390/systems14020198 - 12 Feb 2026
Viewed by 809
Abstract
The interdependence inherent in interbank networks amplifies vulnerability to systemic risk, particularly through correlated asset exposures during exogenous negative shocks. This study employs exponential random graph models (ERGMs) to reconstruct a bipartite network of asset-holding correlations based on the balance sheets of Chinese [...] Read more.
The interdependence inherent in interbank networks amplifies vulnerability to systemic risk, particularly through correlated asset exposures during exogenous negative shocks. This study employs exponential random graph models (ERGMs) to reconstruct a bipartite network of asset-holding correlations based on the balance sheets of Chinese commercial banks from 2016 to 2022. The reconstructed network closely approximates the topological features of the actual banking system. We then introduce a novel framework for measuring aggregate network vulnerability, which incorporates bank size, initial shocks, interconnectedness, leverage, and asset fire sales to capture key channels of financial contagion. Our results indicate that the reconstructed network aligns closely with empirical data in both link structure and weight distribution. Furthermore, cumulative systemic vulnerability increases non-linearly with the severity of the initial shock and the discount depth of fire sales. For individual banks, indirect vulnerability driven by contagion via deleveraging and fire sales significantly exceeds direct losses from initial shocks. Systemic risk contributions are concentrated in large state-owned banks and nationwide joint-stock commercial banks, whereas the institutions most susceptible to risk shocks are predominantly small and medium-sized rural and urban commercial banks. Full article
(This article belongs to the Section Systems Practice in Social Science)
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20 pages, 1842 KB  
Article
TLFormer: Scalable Taylor Linear Attention in Transformer for Collaborative Filtering
by Dongdong Hao, Dongxiao Yu and Xiaowen Hou
Electronics 2026, 15(4), 759; https://doi.org/10.3390/electronics15040759 - 11 Feb 2026
Viewed by 796
Abstract
Graph Neural Networks (GNNs) have become foundational models in recommender systems due to their ability to propagate information over user–item bipartite graphs via neighborhood aggregation. Despite their empirical success, GNNs are inherently constrained by their reliance on local connectivity, which limits their ability [...] Read more.
Graph Neural Networks (GNNs) have become foundational models in recommender systems due to their ability to propagate information over user–item bipartite graphs via neighborhood aggregation. Despite their empirical success, GNNs are inherently constrained by their reliance on local connectivity, which limits their ability to capture global interaction patterns, particularly in large-scale recommendation scenarios characterized by severe data sparsity. To address these challenges, we propose the Taylor Linear attention in Transformer (TLFormer), which enhances recommendation performance by enabling global attention across all user–item pairs while preserving graph structural information. Unlike existing Transformer-based recommendation approaches that focus on local attention patterns, TLFormer introduces a novel linear attention mechanism derived from the first-order Taylor approximation, allowing efficient computation of all-pair interactions. TLFormer integrates spatial topology as positional encoding while maintaining linear complexity, effectively balancing computational efficiency with model expressiveness for large-scale recommendation scenarios. Extensive experiments across multiple datasets demonstrate that TLFormer significantly outperforms state-of-the-art methods, particularly in scenarios with sparse interactions and long-tail distributions. Full article
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17 pages, 5202 KB  
Article
A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs
by Bin Li, Yan Zhang, Hongle Du and Yeh-Cheng Cheng
Mathematics 2026, 14(3), 500; https://doi.org/10.3390/math14030500 - 30 Jan 2026
Cited by 1 | Viewed by 1217
Abstract
Whether learners can correctly complete exercises is influenced by multiple factors, including their mastery of relevant knowledge concepts and the interdependencies among these concepts. To investigate how the structure of the knowledge space—particularly the complex relationships among learners, exercises, and knowledge points—affects learning [...] Read more.
Whether learners can correctly complete exercises is influenced by multiple factors, including their mastery of relevant knowledge concepts and the interdependencies among these concepts. To investigate how the structure of the knowledge space—particularly the complex relationships among learners, exercises, and knowledge points—affects learning outcomes, this study proposes the Hierarchical Heterogeneous Graph Knowledge Tracing model (HHGKT). A hierarchical heterogeneous graph was constructed to capture two types of interactions—“learner–knowledge concept” and “exercise–knowledge concept”—and incorporate the interdependencies among knowledge concepts into the graph structure. By leveraging this hierarchical representation, the model’s ability to characterize learners and exercises was enhanced. A hierarchical heterogeneous graph encompassing users, exercises, and knowledge concepts was built based on the ASSISTments dataset, and simulation experiments were conducted. The results indicate that the proposed structure effectively represents the complexity of the knowledge space. Incorporating knowledge concept interdependencies improves prediction accuracy by 1.79%, while the hierarchical heterogeneous graph outperforms traditional bipartite graphs by approximately 1.5 percentage points in accuracy. These findings demonstrate that the model better integrates node and relational information, offering valuable insights for knowledge space modeling and its application in educational contexts. Full article
(This article belongs to the Special Issue Applied Mathematics for Information Security and Applications)
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20 pages, 6090 KB  
Article
Returnformer: A Graph Transformer-Based Model for Predicting Product Returns in E-Commerce
by Qian Cao, Ning Zhang and Huiyong Li
Entropy 2026, 28(1), 72; https://doi.org/10.3390/e28010072 - 8 Jan 2026
Viewed by 1597
Abstract
E-commerce retailers bear substantial additional costs arising from high product return rates due to lenient return policies and consumers’ impulsive purchasing. This study aims to accurately predict product return behavior before payment, supporting proactive return management and reducing potential losses. Based on the [...] Read more.
E-commerce retailers bear substantial additional costs arising from high product return rates due to lenient return policies and consumers’ impulsive purchasing. This study aims to accurately predict product return behavior before payment, supporting proactive return management and reducing potential losses. Based on the Graph Transformer, we proposed a novel return prediction model, Returnformer, which focuses on capturing user–product connections represented in topological structures of bipartite graphs. The Returnformer first integrates global topological embeddings into original node features to alleviate structural information loss caused by graph partitioning. It then employs a Graph Transformer to capture long-range user–item dependencies within local subgraphs. In addition, a graph-level attention mechanism is introduced to facilitate the propagation of global return patterns across different subgraphs. Experiments on a real-world e-commerce dataset show that the Returnformer outperforms four machine learning models in terms of prediction accuracy, demonstrating superior performance compared to the state-of-the-art models. The proposed model enables retailers to identify potential return risks prior to payment, thereby supporting timely and proactive preventive interventions. Full article
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