# From Semantics to Hierarchy: A Hybrid Euclidean-Tangent-Hyperbolic Space Model for Temporal Knowledge Graph Reasoning

arXiv: https://arxiv.org/abs/2409.00149 · HTML: https://mlsanity.com/paper/2409.00149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [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)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (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)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion](https://mlsanity.com/paper/1811.04441/) (2018)
- [Temporal Knowledge Graph Reasoning Based on Evolutional Representation Learning](https://mlsanity.com/paper/2104.10353/) (2021)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Learning from History: Modeling Temporal Knowledge Graphs with Sequential Copy-Generation Networks](https://mlsanity.com/paper/2012.08492/) (2020)
- [Temporal Knowledge Graph Forecasting with Neural ODE](https://mlsanity.com/paper/2101.05151/) (2021)
- [TLogic: Temporal Logical Rules for Explainable Link Forecasting on Temporal Knowledge Graphs](https://mlsanity.com/paper/2112.08025/) (2021)
- [Knowledge Association with Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2010.02162/) (2020)
- [EvoKG: Jointly Modeling Event Time and Network Structure for Reasoning over Temporal Knowledge Graphs](https://mlsanity.com/paper/2202.07648/) (2022)
- [Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures](https://mlsanity.com/paper/2106.04311/) (2021)
- [Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces](https://mlsanity.com/paper/2209.05635/) (2022)

## Abstract (arXiv)

Temporal knowledge graph (TKG) reasoning predicts future events based on historical data, but it's challenging due to the complex semantic and hierarchical information involved. Existing Euclidean models excel at capturing semantics but struggle with hierarchy. Conversely, hyperbolic models manage hierarchical features well but fail to represent complex semantics due to limitations in shallow models' parameters and the absence of proper normalization in deep models relying on the L2 norm. Current solutions, as curvature transformations, are insufficient to address these issues. In this work, a novel hybrid geometric space approach that leverages the strengths of both Euclidean and hyperbolic models is proposed. Our approach transitions from single-space to multi-space parameter modeling, effectively capturing both semantic and hierarchical information. Initially, complex semantics are captured through a fact co-occurrence and autoregressive method with normalizations in Euclidean space. The embeddings are then transformed into Tangent space using a scaling mechanism, preserving semantic information while relearning hierarchical structures through a query-candidate separated modeling approach, which are subsequently transformed into Hyperbolic space. Finally, a hybrid inductive bias for hierarchical and semantic learning is achieved by combining hyperbolic and Euclidean scoring functions through a learnable query-specific mixing coefficient, utilizing embeddings from hyperbolic and Euclidean spaces. Experimental results on four TKG benchmarks demonstrate that our method reduces error relatively by up to 15.0% in mean reciprocal rank on YAGO compared to previous single-space models. Additionally, enriched visualization analysis validates the effectiveness of our approach, showing adaptive capabilities for datasets with varying levels of semantic and hierarchical complexity.