# HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings

arXiv: https://arxiv.org/abs/2511.10842 · HTML: https://mlsanity.com/paper/2511.10842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [OpenAlex: A fully-open index of scholarly works, authors, venues, institutions, and concepts](https://mlsanity.com/paper/2205.01833/) (2022)
- [Cross-lingual Entity Alignment via Joint Attribute-Preserving Embedding](https://mlsanity.com/paper/1708.05045/) (2017)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Knowledge Graph Embedding for Link Prediction: A Comparative Analysis](https://mlsanity.com/paper/2002.00819/) (2020)
- [Enhancing Knowledge Graph Construction Using Large Language Models](https://mlsanity.com/paper/2305.04676/) (2023)
- [Exploring Large Language Models for Knowledge Graph Completion](https://mlsanity.com/paper/2308.13916/) (2023)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [KnowledgeNavigator: Leveraging Large Language Models for Enhanced Reasoning over Knowledge Graph](https://mlsanity.com/paper/2312.15880/) (2023)
- [HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/1908.04895/) (2019)
- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [5* Knowledge Graph Embeddings with Projective Transformations](https://mlsanity.com/paper/2006.04986/) (2020)
- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://mlsanity.com/paper/2211.03635/) (2022)
- [Knowledge Graph Embeddings: A Comprehensive Survey on Capturing Relation Properties](https://mlsanity.com/paper/2410.14733/) (2024)

## Abstract (arXiv)

Knowledge graphs have emerged as fundamental structures for representing complex relational data across scientific and enterprise domains. However, existing embedding methods face critical limitations when modeling diverse relationship types at scale: Euclidean models struggle with hierarchies, vector space models cannot capture asymmetry, and hyperbolic models fail on symmetric relations. We propose HyperComplEx, a hybrid embedding framework that adaptively combines hyperbolic, complex, and Euclidean spaces via learned attention mechanisms. A relation-specific space weighting strategy dynamically selects optimal geometries for each relation type, while a multi-space consistency loss ensures coherent predictions across spaces. We evaluate HyperComplEx on computer science research knowledge graphs ranging from 1K papers (~25K triples) to 10M papers (~45M triples), demonstrating consistent improvements over state-of-the-art baselines including TransE, RotatE, DistMult, ComplEx, SEPA, and UltraE. Additional tests on standard benchmarks confirm significantly higher results than all baselines. On the 10M-paper dataset, HyperComplEx achieves 0.612 MRR, a 4.8% relative gain over the best baseline, while maintaining efficient training, achieving 85 ms inference per triple. The model scales near-linearly with graph size through adaptive dimension allocation. We release our implementation and dataset family to facilitate reproducible research in scalable knowledge graph embeddings.