{"title":"核化超图神经网络","authors":"Yifan Feng;Yifan Zhang;Shihui Ying;Shaoyi Du;Yue Gao","doi":"10.1109/TPAMI.2025.3585179","DOIUrl":null,"url":null,"abstract":"Hypergraph Neural Networks (HGNNs) have attracted much attention for high-order structural data learning. Existing methods mainly focus on simple mean-based aggregation or manually combining multiple aggregations to capture multiple information on hypergraphs. However, those methods inherently lack continuous non-linear modeling ability and are sensitive to varied distributions. Although some kernel-based aggregations on GNNs and CNNs can capture non-linear patterns to some degree, those methods are restricted in the low-order correlation and may cause unstable computation in training. In this work, we introduce Kernelized Hypergraph Neural Networks (KHGNN) and its variant, Half-Kernelized Hypergraph Neural Networks (H-KHGNN), which synergize mean-based and max-based aggregation functions to enhance representation learning on hypergraphs. KHGNN’s kernelized aggregation strategy adaptively captures both semantic and structural information via learnable parameters, offering a mathematically grounded blend of kernelized aggregation approaches for comprehensive feature extraction. H-KHGNN addresses the challenge of overfitting in less intricate hypergraphs by employing non-linear aggregation selectively in the vertex-to-hyperedge message-passing process, thus reducing model complexity. Our theoretical contributions reveal a bounded gradient for kernelized aggregation, ensuring stability during training and inference. Empirical results demonstrate that KHGNN and H-KHGNN outperform state-of-the-art models across 10 graph/hypergraph datasets, with ablation studies demonstrating the effectiveness and computational stability of our method.","PeriodicalId":94034,"journal":{"name":"IEEE transactions on pattern analysis and machine intelligence","volume":"47 10","pages":"8938-8954"},"PeriodicalIF":18.6000,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kernelized Hypergraph Neural Networks\",\"authors\":\"Yifan Feng;Yifan Zhang;Shihui Ying;Shaoyi Du;Yue Gao\",\"doi\":\"10.1109/TPAMI.2025.3585179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Hypergraph Neural Networks (HGNNs) have attracted much attention for high-order structural data learning. Existing methods mainly focus on simple mean-based aggregation or manually combining multiple aggregations to capture multiple information on hypergraphs. However, those methods inherently lack continuous non-linear modeling ability and are sensitive to varied distributions. Although some kernel-based aggregations on GNNs and CNNs can capture non-linear patterns to some degree, those methods are restricted in the low-order correlation and may cause unstable computation in training. In this work, we introduce Kernelized Hypergraph Neural Networks (KHGNN) and its variant, Half-Kernelized Hypergraph Neural Networks (H-KHGNN), which synergize mean-based and max-based aggregation functions to enhance representation learning on hypergraphs. KHGNN’s kernelized aggregation strategy adaptively captures both semantic and structural information via learnable parameters, offering a mathematically grounded blend of kernelized aggregation approaches for comprehensive feature extraction. H-KHGNN addresses the challenge of overfitting in less intricate hypergraphs by employing non-linear aggregation selectively in the vertex-to-hyperedge message-passing process, thus reducing model complexity. Our theoretical contributions reveal a bounded gradient for kernelized aggregation, ensuring stability during training and inference. Empirical results demonstrate that KHGNN and H-KHGNN outperform state-of-the-art models across 10 graph/hypergraph datasets, with ablation studies demonstrating the effectiveness and computational stability of our method.\",\"PeriodicalId\":94034,\"journal\":{\"name\":\"IEEE transactions on pattern analysis and machine intelligence\",\"volume\":\"47 10\",\"pages\":\"8938-8954\"},\"PeriodicalIF\":18.6000,\"publicationDate\":\"2025-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE transactions on pattern analysis and machine intelligence\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/11063418/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE transactions on pattern analysis and machine intelligence","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/11063418/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hypergraph Neural Networks (HGNNs) have attracted much attention for high-order structural data learning. Existing methods mainly focus on simple mean-based aggregation or manually combining multiple aggregations to capture multiple information on hypergraphs. However, those methods inherently lack continuous non-linear modeling ability and are sensitive to varied distributions. Although some kernel-based aggregations on GNNs and CNNs can capture non-linear patterns to some degree, those methods are restricted in the low-order correlation and may cause unstable computation in training. In this work, we introduce Kernelized Hypergraph Neural Networks (KHGNN) and its variant, Half-Kernelized Hypergraph Neural Networks (H-KHGNN), which synergize mean-based and max-based aggregation functions to enhance representation learning on hypergraphs. KHGNN’s kernelized aggregation strategy adaptively captures both semantic and structural information via learnable parameters, offering a mathematically grounded blend of kernelized aggregation approaches for comprehensive feature extraction. H-KHGNN addresses the challenge of overfitting in less intricate hypergraphs by employing non-linear aggregation selectively in the vertex-to-hyperedge message-passing process, thus reducing model complexity. Our theoretical contributions reveal a bounded gradient for kernelized aggregation, ensuring stability during training and inference. Empirical results demonstrate that KHGNN and H-KHGNN outperform state-of-the-art models across 10 graph/hypergraph datasets, with ablation studies demonstrating the effectiveness and computational stability of our method.