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HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces
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Proposes HGE, which embeds temporal knowledge graph facts in a product space of complex, split-complex and dual subspaces with temporal-relational and temporal-geometric attention, and plugs it into complex-space TKGE backbones to improve link prediction.
Problem
Single-geometry temporal KG embedding models cannot capture all kinds of static and dynamic temporal patterns (symmetry, hierarchy, star structures), and existing multi-geometry product spaces need manual subspace dimension selection.
Approach
Share real and imaginary embedding vectors across complex, split-complex and dual subspaces (avoiding per-subspace dimension selection), then combine subspace scores with a temporal-geometric attention conditioned on a relation embedding that is mixed static/dynamic by a temporal-relational attention.
Key results
- TNTComplEx+HGE reaches 63.0 MRR on ICEWS14 (vs 60.7) and 37.1 MRR on GDELT (vs 34.1), 8.8% relative improvement on GDELT.
- TLT-KGE+HGE improves MRR on ICEWS14 from 63.0 to 63.4 and on GDELT from 35.6 to 37.1.
- On ICEWS05-15, TeRo+HGE slightly decreases MRR (58.6 to 57.8), while TNTComplEx+HGE improves MRR from 66.6 to 68.1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add HGE to TNTComplEx | TNTComplEx · ICEWS14, ICEWS05-15, and GDELT | MRR: 60.7 -> 63.0; 66.6 -> 68.1; 34.1 -> 37.1 | Helped |
| Add HGE to TLT-KGE | TLT-KGE · ICEWS14, ICEWS05-15, and GDELT | MRR: 63.0 -> 63.4; 68.6 -> 68.8; 35.6 -> 37.1 | Helped |
| Add HGE to TNTComplEx | TNTComplEx · Wikidata12k [a,b] and (-∞, b] | MRR: 27.4 -> 28.4; 51.7 -> 57.0 | Helped |
| Add HGE to TNTComplEx | TNTComplEx · Wikidata12k [a,∞) | MRR: 37.8 -> 37.8 | No clear effect |
| Integrate the geometric subspaces with HGE instead of stacking (ablation) | TNTComplEx · ICEWS14, ICEWS05-15, and GDELT | MRR: 62.0 -> 63.0; 67.3 -> 68.1; 35.6 -> 37.1 | Helped |
| Add temporal-relational attention to temporal-geometric attention (ablation) | TNTComplEx+tga · ICEWS14, ICEWS05-15, and GDELT | MRR: 62.6 -> 63.0; 67.5 -> 68.1; 36.4 -> 37.1 | Helped |
| Add temporal-geometric attention to temporal-relational attention (ablation) | TNTComplEx+tra · ICEWS14, ICEWS05-15, and GDELT | MRR: 62.0 -> 63.0; 67.4 -> 68.1; 36.9 -> 37.1 | Helped |
| Use temporal-relational attention only (ablation) | TNTComplEx · ICEWS14, ICEWS05-15, and GDELT | MRR: 60.7 -> 62.0; 66.6 -> 67.4; 34.1 -> 36.9 | Helped |
| Use temporal-geometric attention only (ablation) | TNTComplEx · ICEWS14, ICEWS05-15, and GDELT | MRR: 60.7 -> 62.6; 66.6 -> 67.5; 34.1 -> 36.4 | Helped |
Surprising findings
- TeRo+HGE decreases MRR on ICEWS05-15, which the authors attribute to that dataset being the sparsest.
- Pre-experiments show real and imaginary vectors across complex, split-complex and dual subspaces have cosine similarity above 0.95, motivating vector sharing.
Limitations
- Gains are inconsistent: TeRo+HGE decreases performance on ICEWS05-15 and gains are small on several TLT-KGE metrics.
- The authors note they plan to add more heterogeneous geometries in future work, so only three subspaces are covered.
- The theoretical pattern proofs are sketched for one-dimensional split-complex vectors and extended informally to higher dimensions.
Experimental setup
Datasets: ICEWS14 ICEWS05-15 GDELT Wikidata12k
Benchmarks: ICEWS14 ICEWS05-15 GDELT Wikidata12k
Metrics: MRR Hits@1 Hits@3 Hits@10
Baselines: TTransE TA-DistMult RotateQVS BoxTE LCGE TComplEx TNTComplEx TeRo TLT-KGE
Builds on: TeRo TNTComplEx TLT-KGE AttH
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