# HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces

arXiv: https://arxiv.org/abs/2312.13680 · HTML: https://mlsanity.com/paper/2312.13680/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 11 of 11)

- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs](https://mlsanity.com/paper/1705.05742/) (2017)
- [Learning Sequence Encoders for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1809.03202/) (2018)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [Diachronic Embedding for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/1907.03143/) (2019)
- [TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation](https://mlsanity.com/paper/2010.01029/) (2020)
- [Temporal Knowledge Graph Completion using Box Embeddings](https://mlsanity.com/paper/2109.08970/) (2021)
- [DyERNIE: Dynamic Evolution of Riemannian Manifold Embeddings for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.03984/) (2020)
- [Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures](https://mlsanity.com/paper/2106.04311/) (2021)
- [NeuSTIP: A Novel Neuro-Symbolic Model for Link and Time Prediction in Temporal Knowledge Graphs](https://mlsanity.com/paper/2305.11301/) (2023)

## Built on by (most cited first, 10 of 10)

- [Rethinking Regularization Methods for Knowledge Graph Completion](https://mlsanity.com/paper/2505.23442/) (2025)
- [Time is Not a Label: Continuous Phase Rotation for Temporal Knowledge Graphs and Agentic Memory](https://mlsanity.com/paper/2604.11544/) (2026)
- [UniHR: Hierarchical Representation Learning for Unified Knowledge Graph Link Prediction](https://mlsanity.com/paper/2411.07019/) (2024)
- [Towards Foundation Model on Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2506.06367/) (2025)
- [Geometric Structural Knowledge Graph Foundation Model](https://mlsanity.com/paper/2512.22931/) (2025)
- [VITA: Versatile Time Representation Learning for Temporal Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2505.11803/) (2025)
- [DynaGen: Unifying Temporal Knowledge Graph Reasoning with Dynamic Subgraphs and Generative Regularization](https://mlsanity.com/paper/2512.12669/) (2025)
- [TKGB: A Comprehensive Benchmark for Temporal Knowledge Graph Forecasting](https://mlsanity.com/paper/2602.08353/) (2026)
- [FITTER: Vocabulary-Agnostic Cross-Domain Inference on Temporal Knowledge Graphs](https://mlsanity.com/paper/2608.10668/) (2026)
- [Biquaternionic Space with Complex-valued Attention for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2609.14279/) (2026)

## Abstract (arXiv)

Temporal knowledge graphs represent temporal facts (s,p,o,τ) relating a subject s and an object o via a relation label p at time τ, where τ could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e. Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.