Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Siling Feng, Zhisheng Qi, Cong Lin

TL;DR

ETH addresses temporal knowledge graph reasoning by jointly modeling semantics and hierarchy through a hybrid Euclidean-Tangent-Hyperbolic space. It first encodes semantic information in Euclidean space with a relation-aware graph encoder and autoregressive temporal module, then refines hierarchical structure in tangent space before mapping to hyperbolic space, and finally blends Euclidean and hyperbolic scores via a learnable query-specific mixing coefficient. The approach yields strong extrapolation performance on four benchmarks, notably up to a 15% relative improvement in MRR on YAGO, and is supported by visualization analyses of tangent-space norms and hybrid scoring behavior. This hybrid geometric framework offers robust, adaptable reasoning across datasets with varying levels of semantic richness and hierarchical structure, advancing temporal knowledge graph reasoning beyond single-space models.

Abstract

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.

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

TL;DR

ETH addresses temporal knowledge graph reasoning by jointly modeling semantics and hierarchy through a hybrid Euclidean-Tangent-Hyperbolic space. It first encodes semantic information in Euclidean space with a relation-aware graph encoder and autoregressive temporal module, then refines hierarchical structure in tangent space before mapping to hyperbolic space, and finally blends Euclidean and hyperbolic scores via a learnable query-specific mixing coefficient. The approach yields strong extrapolation performance on four benchmarks, notably up to a 15% relative improvement in MRR on YAGO, and is supported by visualization analyses of tangent-space norms and hybrid scoring behavior. This hybrid geometric framework offers robust, adaptable reasoning across datasets with varying levels of semantic richness and hierarchical structure, advancing temporal knowledge graph reasoning beyond single-space models.

Abstract

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.
Paper Structure (35 sections, 15 equations, 5 figures, 3 tables)

This paper contains 35 sections, 15 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Static KG Reasoning Models
  4. Temporal KG Reasoning Models
  5. Hyperbolic Models
  6. Problem Formulation and Background
  7. Problem Definition
  8. Hyperbolic Geometry
  9. Methodology
  10. Euclidean Modeling
  11. Multi-Relational Graph Semantic Modeling.
  12. Autoregressive Temporal Semantic Modeling.
  13. Tangent Space Transformation
  14. Transformation for Candidate Entity.
  15. Transformation for Query Entity.
  16. ...and 20 more sections

Figures (5)

  • Figure 1: Illustration of a TKG from ICEWS14, with line styles indicating the time of events: dot-dash for September 4th, solid for the 5th, and double-line for the 6th, all in 2014.
  • Figure 2: An illustrative diagram of the proposed ETH model.
  • Figure 3: $Khs$ statistics for each dataset.
  • Figure 4: Density distribution of $L_2$ norms in Tangent space for candidate and query entities in ICEWS14 a and YAGO b.
  • Figure 5: ICEWS14 scoring examples.