Elamur Research⌕
☰
home / papers / 2026 / MAGIC: Deep Geometric Evolution with Structural Consensus for Temporal Knowledge Graph Reasoning

MAGIC: Deep Geometric Evolution with Structural Consensus for Temporal Knowledge Graph Reasoning

Paper · 2026 · Chengao Liu, Yuan Li, Yingze Wang et al.

Summary

Temporal knowledge graphs (TKGs) combine tree-like hierarchies with recurring events such as elections. Flat Euclidean embeddings distort both kinds of structure. Earlier multi-geometry models mix hyperbolic, spherical and Euclidean spaces, but they face two problems. First, Riemannian exponential and logarithmic maps become numerically unstable as depth grows, so these models stay shallow (two layers or fewer). Second, their learnable fusion gates tend to lock onto a single geometry early in training.

The authors propose MAGIC, a link-prediction model for queries of the form (s, r, ?, t). Each entity input adds a static embedding to periodic (sinusoidal) and trend (tanh) time features at year, month and day granularity. A Tangent-Residual Engine passes residual updates through the tangent space, which allows eight stable layers, each with its own learnable curvature. The authors observe curvature moving from nearly flat in early layers to stronger curvature in deeper ones, a pattern they call Geometric Annealing.

For fusion, MAGIC injects explicit geometric invariants (distance, norm and angle) and uses fixed consensus weights instead of learned gates. On ICEWS and GDELT benchmarks it reports state-of-the-art results. This shows that deep, balanced multi-geometry reasoning over TKGs is achievable.

Key points

  • MAGIC (Multi-geometry Annealing Graph Interaction with Consensus) trains stably with 8 geometric layers; prior geometric TKG encoders were limited to L ≤ 2.
  • MAGIC reports 82.5% MRR on ICEWS05-15 and gains of up to 2.9 MRR points over earlier methods. The evaluation uses the public ICEWS and GDELT datasets.
  • In a depth study, MAGIC stays above 0.84 MRR across depths. The Euclidean baseline remains below 0.72, and a hyperbolic-only baseline collapses as layers are added.
  • A learnable-gate baseline shows "gate collapse": around epoch 45 the hyperbolic weight jumps to 1.0, and MRR stalls near 0.675.
  • With fixed consensus weights (α, β), MRR stays above 0.83 across the hyperparameter grid, with variation under 1.5%. The authors list as limitations a small inference overhead from manifold projections and the restriction to snapshot-based (discrete-time) dynamics.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of Chinese Academy of SciencesBeijing · China147 works · 8,480 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksInformation Systems · 1,437 works

🧭 Topics 2Research subjects and languages the work is about.Reasoning · 1,426 worksKnowledge graphs & ontologies · 192 works

Cite

Cite as Chengao Liu, Yuan Li, Yingze Wang and Jianbin Jiao. 2026. MAGIC: Deep Geometric Evolution with Structural Consensus for Temporal Knowledge Graph Reasoning. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.acl-long.1011

@inproceedings{liu2026magic,
  title = {{MAGIC: Deep Geometric Evolution with Structural Consensus for Temporal Knowledge Graph Reasoning}},
  author = {Chengao Liu, Yuan Li, Yingze Wang and Jianbin Jiao},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.1011},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1011}
}

References

24 references, 6 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Julien Leblay and Melisachew Wudage Chekol. 2018. Deriving validity time in knowledge graph. In Proceedings of the Companion of the The Web Conference (WWW), pages 1771–1776. find
  2. Antoine Bordes, Nicolas Usunier, Alberto Garcia-Duran, Jason Weston, and Oksana Yakhnenko. 2013. Translating embeddings for modeling multi-relational data. In Advances in Neural Information Processing Systems (NIPS), volume 26.
  3. Ines Chami, Adva Wolf, Da-Cheng Juan, Frederic Sala, Sujith Ravi, and Christopher Ré. 2020. Low-dimensional hyperbolic knowledge graph embeddings. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics (ACL), pages 6901–6914.
  4. Shib Sankar Dasgupta, Swayambhu Nath Ray, and Partha Talukdar. 2018. HyTE: Hyperplane-based temporally aware knowledge graph embedding. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 2001–2011. find
  5. Patrick Lewis, Ethan Perez, Aleksandra Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Küttler, Mike Lewis, Wen-tau Yih, Tim Rocktäschel, Sebastian Riedel, and Douwe Kiela. 2020. Retrieval-augmented generation for knowledge-intensive nlp tasks. In Proceedings of the 34th Internation…
  6. Jiang Li, Xiangdong Su, and Guanglai Gao. 2023. TeAST: Temporal knowledge graph embedding via archimedean spiral timeline. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (ACL), pages 15460–15474. find
  7. Xiangyu Dong, Xingyi Zhang, Lei Chen, Mingxuan Yuan, and Sibo Wang. 2025. SpaceGNN: Multi-space graph neural network for node anomaly detection with extremely limited labels. In Proceedings of the International Conference on Learning Representations (ICLR). find
  8. Xueyuan Lin, Haihong E, Chengjin Xu, Gengxian Zhou, Haoran Luo, Tianyi Hu, Fenglong Su, Ningyuan Li, and Mingzhi Sun. 2023. Tflex: Temporal feature-logic embedding framework for complex reasoning over temporal knowledge graph. In Advances in Neural Information Processing Systems, volume 36, pages 73… find
  9. Alberto García-Durán, Sebastijan Dumančić, and Mathias Niepert. 2018. Learning sequence encoders for Chengao Liu, Yuan Li, Siheng Ning, Jianming Zhu, and Jianbin Jiao. 2025. PoinKI: A Poincaré-embedded knowledge-integrated model for dynamic link prediction. Knowledge-Based Systems, page 114879. find
  10. Johannes Messner, Ralph Abboud, and Ismail Ilkan Ceylan. 2022. Temporal knowledge graph completion using box embeddings. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 7779–7787. find
  11. Maximillian Nickel and Douwe Kiela. 2017. Poincaré embeddings for learning hierarchical representations. In Advances in Neural Information Processing Systems (NIPS), volume 30.
  12. Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, and Daisy Zhe Wang. 2021. ChronoR: Rotation based temporal knowledge graph embedding. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 6471–6479. find
  13. Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie, and Jian Tang. 2019. RotatE: Knowledge graph embedding by relational rotation in complex space. In Proceedings of the International Conference on Learning Representations (ICLR).
  14. Jiapu Wang, Zheng Cui, Boyue Wang, Shirui Pan, Junbin Gao, Baocai Yin, and Wen Gao. 2024. IME: Integrating multi-curvature shared and specific embedding for temporal knowledge graph completion. In Proceedings of the ACM Web Conference (WWW), pages 1954–1962. find
  15. Jiapu Wang, Boyue Wang, Junbin Gao, Xiaoyan Li, Yongli Hu, and Baocai Yin. 2023. QDN: A quadruplet distributor network for temporal knowledge graph completion. IEEE Transactions on Neural Networks and Learning Systems, 35(10):14018–14030. find
  16. Shen Wang, Xiaokai Wei, Cicero Nogueira Nogueira dos Santos, Zhiguo Wang, Ramesh Nallapati, Andrew Arnold, Bing Xiang, Philip S. Yu, and Isabel F. Cruz. 2021. Mixed-curvature multi-relational graph neural network for knowledge graph completion. In Proceedings of the Web Conference 2021, WWW ’21, pag… find
  17. Chengjin Xu, Mojtaba Nayyeri, Fouad Alkhoury, Hamed Shariat Yazdi, and Jens Lehmann. 2020b. TeRo: A time-aware knowledge graph embedding via temporal rotation. In Proceedings of the 28th International Conference on Computational Linguistics (COLING), pages 1583–1593. find
  18. Bishan Yang, Wen-tau Yih, Xiaodong He, Jianfeng Gao, and Li Deng. 2015. Embedding entities and relations for learning and inference in knowledge bases. In Proceedings of the International Conference on Learning Representations (ICLR).
  19. Rui Ying, Mengting Hu, Jianfeng Wu, Yalan Xie, Xiaoyi Liu, Zhunheng Wang, Ming Jiang, Hang Gao, Linlin Zhang, and Renhong Cheng. 2024. Simple but effective compound geometric operations for temporal knowledge graph completion. In Proceedings of the 62nd Annual Meeting of the Association for Computat… find
  20. Jiasheng Zhang, Shuang Liang, Yongpan Sheng, and Jie Shao. 2022. Temporal knowledge graph representation learning with local and global evolutions. Knowledge-Based Systems, 251:109234. (EvoExplore). find
  21. Sensen Zhang, Xun Liang, Zhiying Li, Junlan Feng, Xiangping Zheng, and Bo Wu. 2023. BiQCap: A biquaternion and capsule network-based embedding model for temporal knowledge graph completion. In International Conference on Database Systems for Advanced Applications (DASFAA), pages 673–688. find
  22. Weiyao Wang, Du Tran, and Matt Feiszli. 2020. What makes training multi-modal classification networks hard? In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 12695–12705. find
  23. Chengjin Xu, Yung-Yu Chen, Mojtaba Nayyeri, and Jens Lehmann. 2021. Temporal knowledge graph completion using a linear temporal regularizer and multivector embeddings. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language… find
  24. Chengjin Xu, Mojtaba Nayyeri, Fouad Alkhoury, Hamed Shakeri Yazdi, and Jens Lehmann. 2020a. Temporal knowledge graph completion based on time find

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/liu-2026-magic-deep-geometric-evolution-structural/