{"type":"ScholarlyArticle","title":"AdaGeM: Adaptive Geometric Learning on Manifolds for Hyper-Relational Knowledge Graphs","authors":[{"name":"Ke-Jia Chen","slug":"ke-jia-chen","given":"Ke-Jia","family":"Chen","affiliation":"Jiangsu Key Laboratory of Big Data Security and Intelligent Processing , Nanjing University of Posts and Telecommunications , Nanjing , China; School of Computer Science , Nanjing University of Posts and Telecommunications , Nanjing , China"},{"name":"Yuzhe Hu","slug":"yuzhe-hu","given":"Yuzhe","family":"Hu","affiliation":"School of Computer Science , Nanjing University of Posts and Telecommunications , Nanjing , China"},{"name":"Yu Ni","slug":"yu-ni","given":"Yu","family":"Ni","affiliation":"School of Computer Science , Nanjing University of Posts and Telecommunications , Nanjing , China"},{"name":"Linfeng Liu","slug":"linfeng-liu","given":"Linfeng","family":"Liu","affiliation":"Jiangsu Key Laboratory of Big Data Security and Intelligent Processing , Nanjing University of Posts and Telecommunications , Nanjing , China; School of Computer Science , Nanjing University of Posts and Telecommunications , Nanjing , China"}],"abstract":"Hyper-relational Knowledge Graphs (HKGs) extend traditional knowledge graphs by introducing high-order dependencies, where auxiliary qualifiers provide detailed information. However, modeling such intricate topologies (e.g., mixtures of hierarchies, cycles, and chains) is challenging. Existing methods suffer from structural distortion due to reliance on a single geometric space and overlook dynamic semantics across entity roles. To address these issues, we propose AdaGeM (Adaptive Geometric Learning on Manifolds), an innovative space-adaptive framework that integrates geometric learning with a role-aware Transformer. First, we propose an adaptive geometric hypergraph encoder that projects entities into a product manifold and design a topology-aware gating mechanism to dynamically select optimal geometric spaces for each entity. Second, we develop a role-aware Transformer equipped with role-specific projections and micro-structural bias injection to refine embeddings by distinguishing entity semantics across different roles and focusing on valid n-ary interactions, respectively. Extensive experiments on benchmark datasets demonstrate that AdaGeM outperforms state-of-the-art baselines in entity/relation prediction tasks, with ablation studies validating the necessity of multi-manifold modeling for heterogeneous HKG structures.","doi":"10.24963/ijcai.2026/277","url":"https://ijcai.org/proceedings/2026/277","pdf":"https://ijcai.org/proceedings/2026/0277.pdf","markdown":"https://ijcai.org/proceedings/2026/277.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/277","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Data Mining","track":"Main Track","number":277,"pages":{"first":2492,"last":2500},"keywords":["Data Mining: Knowledge graphs and knowledge base completion"],"videos":[],"references":[{"position":1,"raw":"[Bronstein et al., 2017] Michael M. Bronstein, Joan Bruna, Yann Lecun, Arthur Szlam, and Pierre Vandergheynst. Ge- ometric Deep Learning: Going Beyond Euclidean Data. IEEE Signal Processing Magazine, 34(4):18-42, July 2017.","title":"Ge-ometric Deep Learning: Going Beyond Euclidean Data","authors":"M Michael, Joan Bronstein, Yann Bruna, Arthur Lecun, Pierre Szlam, Vandergheynst","year":"2017","venue":"IEEE Signal Processing Magazine","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Chami et al., 2019] Ines Chami, Rex Ying, Christopher Ré, and Jure Leskovec. Hyperbolic graph convolutional neu- ral networks. Advances in neural information processing systems, 32:4869, 2019.","title":"Hyperbolic graph convolutional neural networks","authors":"Ines Chami, Rex Ying, Christopher Ré, Jure Leskovec","year":"2019","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Chung et al., 2023] Chanyoung Chung, Jaejun Lee, and Joyce Jiyoung Whang. Representation learning on hyper- relational and numeric knowledge graphs with transform- ers. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 310-322, 2023.","title":"Representation learning on hyperrelational and numeric knowledge graphs with transformers","authors":"Chung","year":"2023","venue":"Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Di and Chen, 2023] Shimin Di and Lei Chen. Message function search for knowledge graph embedding. In Proceedings of the ACM Web Conference 2023, page 2633-2644, 2023.","title":"Message function search for knowledge graph embedding","authors":"Chen ; ] Shimin Di, Lei Di, Chen","year":"2023","venue":"Proceedings of the ACM Web Conference 2023","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Galkin et al., 2020] Mikhail Galkin, Priyansh Trivedi, Gau- rav Maheshwari, Ricardo Usbeck, and Jens Lehmann. Message passing for hyper-relational knowledge graphs. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pages 7346-7359, 2020.","title":"Message passing for hyper-relational knowledge graphs","authors":"Mikhail Galkin, Priyansh Trivedi, Gaurav Maheshwari, Ricardo Usbeck, Jens Lehmann","year":"2020","venue":"Proceedings of the Conference on Empirical Methods in Natural Language Processing","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Gu et al., 2018] Albert Gu, Frederic Sala, Beliz Gunel, and Christopher Ré. Learning mixed-curvature representations in product spaces. In International conference on learning representations, 2018.","title":"Learning mixed-curvature representations in product spaces","authors":"Albert Gu, Frederic Sala, Beliz Gunel, Christopher Ré","year":"2018","venue":"International conference on learning representations","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Guan et al., 2019] Saiping Guan, Xiaolong Jin, Yuanzhuo Wang, and Xueqi Cheng. Link prediction on n-ary re- lational data. In The World Wide Web Conference, page 583-593, 2019.","title":"Link prediction on n-ary relational data","authors":"Guan","year":"2019","venue":"The World Wide Web Conference","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Guan et al., 2020] Saiping Guan, Xiaolong Jin, Jiafeng Guo, Yuanzhuo Wang, and Xueqi Cheng. Neuinfer: Knowledge inference on n-ary facts. In Proceedings of the 58th annual meeting of the association for computational linguistics, pages 6141-6151, 2020.","title":"Neuinfer: Knowledge inference on n-ary facts","authors":"Guan","year":"2020","venue":"Proceedings of the 58th annual meeting of the association for computational linguistics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Han et al., 2025] Jiaqi Han, Jiacheng Cen, Liming Wu, Zongzhao Li, Xiangzhe Kong, Rui Jiao, Ziyang Yu, Tingyang Xu, Fandi Wu, Zihe Wang, et al. A survey of geometric graph neural networks: Data structures, mod- els and applications. Frontiers of Computer Science, 19(11):1911375, 2025.","title":"A survey of geometric graph neural networks: Data structures, models and applications","authors":"Jiaqi Han, Jiacheng Cen, Liming Wu, Zongzhao Li, Xiangzhe Kong, Rui Jiao, Ziyang Yu, Tingyang Xu, Fandi Wu, Zihe Wang","year":"2025","venue":"Frontiers of Computer Science","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hu et al., 2023] Zhiwei Hu, Víctor Gutiérrez-Basulto, Zhil- iang Xiang, Ru Li, and Jeff Z Pan. Hyperformer: En- hancing entity and relation interaction for hyper-relational knowledge graph completion. In Proceedings of the 32nd ACM international conference on information and knowl- edge management, pages 803-812, 2023.","title":"Hyperformer: Enhancing entity and relation interaction for hyper-relational knowledge graph completion","authors":"Zhiwei Hu, Víctor Gutiérrez-Basulto, Zhiliang Xiang, Ru Li, Jeff Z Pan","year":"2023","venue":"Proceedings of the 32nd ACM international conference on information and knowledge management","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Lee and Whang, 2025] Jaejun Lee and Joyce Jiyoung Whang. Structure is all you need: Structural representation learning on hyper-relational knowledge graphs. In Forty- second International Conference on Machine Learning, 2025.","title":"Structure is all you need: Structural representation learning on hyper-relational knowledge graphs","authors":"Lee, Whang ; ] Jaejun Lee, Joyce Jiyoung Whang","year":"2025","venue":"Fortysecond International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Li et al., 2024] Zhao Li, Chenxu Wang, Xin Wang, Zirui Chen, and Jianxin Li. Hje: Joint convolutional repre- sentation learning for knowledge hypergraph completion. IEEE Transactions on Knowledge and Data Engineering, 36(8):3879-3892, 2024.","title":"Hje: Joint convolutional representation learning for knowledge hypergraph completion","authors":"Zhao Li, Chenxu Wang, Xin Wang, Zirui Chen, Jianxin Li","year":"2024","venue":"IEEE Transactions on Knowledge and Data Engineering","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Li et al., 2025] Zhao Li, Xin Wang, Jun Zhao, Wenbin Guo, and Jianxin Li. Hycube: Efficient knowledge hypergraph 3d circular convolutional embedding. IEEE Trans. on Knowl. and Data Eng., 37(4):1902-1914, 2025.","title":"Hycube: Efficient knowledge hypergraph 3d circular convolutional embedding","authors":"Zhao Li, Xin Wang, Jun Zhao, Wenbin Guo, Jianxin Li","year":"2025","venue":"IEEE Trans. on Knowl. and Data Eng","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Liu et al., 2021] Yu Liu, Quanming Yao, and Yong Li. Role-aware modeling for n-ary relational knowledge bases. Proceedings of the Web Conference, pages 2660- 2671, 2021.","title":"Role-aware modeling for n-ary relational knowledge bases","authors":"Yu Liu, Quanming Yao, Yong Li","year":"2021","venue":"Proceedings of the Web Conference","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Luo et al., 2023] Haoran Luo, E Haihong, Yuhao Yang, Yikai Guo, Mingzhi Sun, Tianyu Yao, Zichen Tang, Kaiyang Wan, Meina Song, and Wei Lin. Hahe: Hier- archical attention for hyper-relational knowledge graphs in global and local level. In Proceedings of the Annual Meeting of the Association for Computational Linguistics, pages 8095-8107, 2023.","title":"Hahe: Hierarchical attention for hyper-relational knowledge graphs in global and local level","authors":"Haoran Luo, Yuhao Haihong, Yikai Yang, Mingzhi Guo, Tianyu Sun, Zichen Yao, Kaiyang Tang, Meina Wan, Wei Song, Lin","year":"2023","venue":"Proceedings of the Annual Meeting of the Association for Computational Linguistics","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nickel and Kiela, 2017] Maximilian Nickel and Douwe Kiela. Poincaré embeddings for learning hierarchical rep- resentations. In Proceedings of the International Con- ference on Neural Information Processing Systems, pages 6341-6350, 2017.","title":"Maximilian Nickel and Douwe Kiela. Poincaré embeddings for learning hierarchical representations","authors":"Kiela Nickel","year":"2017","venue":"Proceedings of the International Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Rosso et al., 2020] Paolo Rosso, Dingqi Yang, and Philippe Cudré-Mauroux. Beyond triplets: hyper-relational knowl- edge graph embedding for link prediction. In Proceedings of the web conference, pages 1885-1896, 2020.","title":"Beyond triplets: hyper-relational knowledge graph embedding for link prediction","authors":"Paolo Rosso, Dingqi Yang, Philippe Cudré-Mauroux","year":"2020","venue":"Proceedings of the web conference","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Shomer et al., 2023] Harry Shomer, Wei Jin, Juanhui Li, Yao Ma, and Hui Liu. Learning representations for hyper- relational knowledge graphs. In Proceedings of the In- ternational Conference on Advances in Social Networks Analysis and Mining, pages 253-257, 2023.","title":"Learning representations for hyperrelational knowledge graphs","authors":"Harry Shomer, Wei Jin, Juanhui Li, Yao Ma, Hui Liu","year":"2023","venue":"Proceedings of the International Conference on Advances in Social Networks Analysis and Mining","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Sun et al., 2019] Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie, and Jian Tang. Rotate: Knowledge graph embedding by relational rotation in complex space. In International Conference on Learning Representations, 2019.","title":"Rotate: Knowledge graph embedding by relational rotation in complex space","authors":"Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie, Jian Tang","year":"2019","venue":"International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Vaswani et al., 2017] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proceedings of the International Conference on Neural Information Processing Systems, page 6000-6010, 2017.","title":"Attention is all you need","authors":"Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, Illia Polosukhin","year":"2017","venue":"Proceedings of the International Conference on Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Wang et al., 2021] Quan Wang, Haifeng Wang, Yajuan Lyu, and Yong Zhu. Link prediction on n-ary relational facts: A graph-based approach. In Findings of the Association for Computational Linguistics, pages 396-407, 2021.","title":"Link prediction on n-ary relational facts: A graph-based approach","authors":"Quan Wang, Haifeng Wang, Yajuan Lyu, Yong Zhu","year":"2021","venue":"Findings of the Association for Computational Linguistics","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Wen et al., 2016] Jianfeng Wen, Jianxin Li, Yongyi Mao, Shini Chen, and Richong Zhang. On the representation and embedding of knowledge bases beyond binary rela- tions. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1300-1307, 2016.","title":"On the representation and embedding of knowledge bases beyond binary relations","authors":"Jianfeng Wen, Jianxin Li, Yongyi Mao, Shini Chen, Richong Zhang","year":"2016","venue":"Proceedings of the International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Xiong et al., 2023] Bo Xiong, Mojtaba Nayyeri, Shirui Pan, and Steffen Staab. Shrinking embeddings for hyper- relational knowledge graphs. In Proceedings of the Annual Meeting of the Association for Computational Linguistics, pages 13306-13320, 2023.","title":"Shrinking embeddings for hyperrelational knowledge graphs","authors":"Bo Xiong, Mojtaba Nayyeri, Shirui Pan, Steffen Staab","year":"2023","venue":"Proceedings of the Annual Meeting of the Association for Computational Linguistics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Yan et al., 2022a] Shiyao Yan, Zequn Zhang, Xian Sun, Guangluan Xu, Li Jin, and Shuchao Li. Hyper2: Hyper- bolic embedding for hyper-relational link prediction. Neu- rocomputing, 492:440-451, 2022.","title":"Hyper2: Hyperbolic embedding for hyper-relational link prediction","authors":"Yan","year":"2022","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Yan et al., 2022b] Shiyao Yan, Zequn Zhang, Xian Sun, Guangluan Xu, Shuchao Li, Qing Liu, Nayu Liu, and Shensi Wang. Polygone: Modeling n-ary relational data as gyro-polygons in hyperbolic space. Proceedings of the AAAI Conference on Artificial Intelligence, 36(4):4308- 4317, 2022.","title":"Polygone: Modeling n-ary relational data as gyro-polygons in hyperbolic space","authors":"Yan","year":"2022","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Yu and Yang, 2021] Donghan Yu and Yiming Yang. Im- proving hyper-relational knowledge graph completion. ArXiv, abs/2104.08167, 2021.","title":"Improving hyper-relational knowledge graph completion","authors":"Yang ; Yu, Donghan Yu, Yiming Yang","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zhang et al., 2018] Richong Zhang, Junpeng Li, Jiajie Mei, and Yongyi Mao. Scalable instance reconstruction in knowledge bases via relatedness affiliated embedding. In Proceedings of the World Wide Web Conference, page 1185-1194, 2018.","title":"Scalable instance reconstruction in knowledge bases via relatedness affiliated embedding","authors":"Zhang","year":"2018","venue":"Proceedings of the World Wide Web Conference","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}