Research map / Graph learning / Knowledge and temporal graphs
Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization
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Proposes GoldE, a KGE framework that parameterizes relation transformations as products of generalized Householder reflections, unifying elliptic and hyperbolic geometries in a product manifold to extend orthogonal transformations to arbitrary dimension.
Problem
Existing orthogonal relation transformation KGE models are restricted to low dimensions (e.g., 2D rotations in hyperbolic space) and to a single homogeneous geometry, failing to capture both logical patterns and heterogeneous topologies (cyclic and hierarchical) of knowledge graphs.
Approach
A generalized Householder reflection under a quadratic inner product yields a universal parameterization of generalized orthogonal matrices (Cartan-Dieudonné-based covering theorem) for elliptic and hyperbolic spaces of any dimension; these are combined as components of a product manifold to unify geometries.
Key results
- GoldE achieves MRR .525 on WN18RR, .370 on FB15k-237 and .588 on YAGO3-10, outperforming HousE (.496, .348, .565) and HousE-pro (.511, .361, .571).
- With 32-dimensional embeddings, GoldE reaches MRR .482 on WN18RR, .335 on FB15k-237 and .420 on YAGO3-10, above the best baseline in each dataset.
- On WN18RR per-relation analysis, GoldE achieves the best MRR on all 11 relation types compared to RotH and HousE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GoldE's mixed elliptic-hyperbolic product manifold instead of HousE-pro | Knowledge graph embedding · WN18RR | MRR: .511 -> .525 | Helped |
| Use GoldE's mixed elliptic-hyperbolic product manifold instead of HousE-pro | Knowledge graph embedding · FB15k-237 | MRR: .361 -> .370 | Helped |
| Use GoldE's mixed elliptic-hyperbolic product manifold instead of RefH | Knowledge graph embedding · YAGO3-10 | MRR: .576 -> .588 | Helped |
| Replace Euclidean geometry with elliptic geometry (ablation) | GoldE · WN18RR | MRR: .496 -> .505 | Helped |
| Replace Euclidean geometry with hyperbolic geometry (ablation) | GoldE · WN18RR | MRR: .496 -> .513 | Helped |
| Use mixed elliptic and hyperbolic components instead of multiple hyperbolic components (ablation) | GoldE · WN18RR | MRR: .518 -> .525 | Helped |
| Use mixed elliptic and hyperbolic components instead of multiple elliptic components (ablation) | GoldE · FB15k-237 | MRR: .365 -> .370 | Helped |
| Use mixed elliptic and hyperbolic components instead of multiple hyperbolic components (ablation) | GoldE · YAGO3-10 | MRR: .585 -> .588 | Helped |
| Increase the dimension of orthogonal transformations (ablation) | GoldE · WN18RR and FB15k-237 | MRR | Helped |
Limitations
- Relation-specific geometric configuration (number and dimension of P and Q components) requires hyperparameter tuning.
- Evaluated only on three standard link prediction benchmarks; hyper-relational and temporal KGs left to future work.
Experimental setup
Datasets: WN18RR FB15k-237 YAGO3-10
Benchmarks: WN18RR FB15k-237 YAGO3-10
Metrics: MRR Hits@1 Hits@3 Hits@10 MR
Baselines: TransE DistMult ComplEx ConvE MuRP RotatE Rotate3D QuatE DualE ReflectE HousE CompoundE
Builds on: RotatE HousE AttH RotH RefH
Closest papers by meaning
- HousE: Knowledge Graph Embedding with Householder Parameterization (ICML 2022 · similarity 0.90)
- You CAN Teach an Old Dog New Tricks! On Training Knowledge Graph Embeddings (ICLR 2020 · similarity 0.89)
- TorusE: Knowledge Graph Embedding on a Lie Group (AAAI 2018 · similarity 0.88)
- Geometry Interaction Knowledge Graph Embeddings (AAAI 2022 · similarity 0.88)
- Towards Global-Topology Relation Graph for Inductive Knowledge Graph Completion (AAAI 2025 · similarity 0.86)
- Clustering then Propagation: Select Better Anchors for Knowledge Graph Embedding (NeurIPS 2024 · similarity 0.86)
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