# Geometry Interaction Knowledge Graph Embeddings

arXiv: https://arxiv.org/abs/2206.12418 · HTML: https://mlsanity.com/paper/2206.12418/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (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)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [Learning Symmetric Collaborative Dialogue Agents with Dynamic Knowledge Graph Embeddings](https://mlsanity.com/paper/1704.07130/) (2017)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Hypernetwork Knowledge Graph Embeddings](https://mlsanity.com/paper/1808.07018/) (2018)
- [Orthogonal Relation Transforms with Graph Context Modeling for Knowledge Graph Embedding](https://mlsanity.com/paper/1911.04910/) (2019)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [Attentional Graph Convolutional Networks for Knowledge Concept Recommendation in MOOCs in a Heterogeneous View](https://mlsanity.com/paper/2006.13257/) (2020)
- [TransG : A Generative Mixture Model for Knowledge Graph Embedding](https://mlsanity.com/paper/1509.05488/) (2015)
- [From One Point to A Manifold: Knowledge Graph Embedding For Precise Link Prediction](https://mlsanity.com/paper/1512.04792/) (2015)

## Built on by (most cited first, 18 of 18)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Prediction](https://mlsanity.com/paper/2306.11443/) (2023)
- [CompoundE: Knowledge Graph Embedding with Translation, Rotation and Scaling Compound Operations](https://mlsanity.com/paper/2207.05324/) (2022)
- [KRACL: Contrastive Learning with Graph Context Modeling for Sparse Knowledge Graph Completion](https://mlsanity.com/paper/2208.07622/) (2022)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Rethinking Regularization Methods for Knowledge Graph Completion](https://mlsanity.com/paper/2505.23442/) (2025)
- [Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold](https://mlsanity.com/paper/2307.04514/) (2023)
- [Knowledge Graph Reasoning with Self-supervised Reinforcement Learning](https://mlsanity.com/paper/2405.13640/) (2024)
- [Fully Hyperbolic Rotation for Knowledge Graph Embedding](https://mlsanity.com/paper/2411.03622/) (2024)
- [Knowledge Graph Completion with Mixed Geometry Tensor Factorization](https://mlsanity.com/paper/2504.02589/) (2025)
- [FMGNN: Fused Manifold Graph Neural Network](https://mlsanity.com/paper/2304.01081/) (2023)
- [CHAINSFORMER: Numerical Reasoning on Knowledge Graphs from a Chain Perspective](https://mlsanity.com/paper/2504.14282/) (2025)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [New Recipe for Semi-supervised Community Detection: Clique Annealing under Crystallization Kinetics](https://mlsanity.com/paper/2504.15927/) (2025)
- [Context-Driven Knowledge Graph Completion with Semantic-Aware Relational Message Passing](https://mlsanity.com/paper/2506.23141/) (2025)
- [Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions](https://mlsanity.com/paper/2605.10317/) (2026)
- [RTSKG: Building a Rail Transit Station Knowledge Graph Dataset](https://mlsanity.com/paper/2608.11080/) (2026)

## Abstract (arXiv)

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space, no matter the Euclidean space, hyperbolic space or hyperspheric space, cannot capture the complex structures of KGs accurately. To overcome this challenge, we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities. Experimental results on three well-established knowledge graph completion benchmarks show that our GIE achieves the state-of-the-art performance with fewer parameters.