Research map / Graph learning / Knowledge and temporal graphs
NestE: Modeling Nested Relational Structures for Knowledge Graph Reasoning
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Proposes NestE, a hypercomplex KG embedding that jointly models atomic triples and nested (quoted) triples via 1x3 fact matrices rotated by 3x3 hypercomplex relation matrices, unifying quaternion, hyperbolic and split-quaternion spaces.
Problem
Standard KG embeddings model only triple-shaped or atomic facts and cannot capture relations between facts (nested facts), such as temporal situations and non-first-order logical implications over facts.
Approach
Represent each atomic fact as a 1x3 matrix of 4D hypercomplex numbers and each nested relation as a 3x3 hypercomplex matrix that transforms the head fact via matrix-like Hamilton products; the family covers (spherical), hyperbolic and split quaternions, subsuming QuatE and generalizing BiVE-style MLP fact modeling.
Key results
- On triple prediction, NestE-SB reaches MRR 0.922 on FBH, 0.851 on FBHE and 0.862 on DBHE, outperforming BiVE-Q's 0.855, 0.711 and 0.687.
- On conditional link prediction, the best NestE variant surpasses the baselines by 11.8%, 13.9% and 8.5% in MRR on FBH, FBHE and DBHE.
- On base link prediction on FBHE and DBHE, NestE-QB achieves the best MR and MRR (0.371 and 0.289 MRR on FBHE and DBHE respectively, as reported in the table).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NestE-SB instead of BiVE-Q | triple prediction · FBH | MRR: 0.855 -> 0.922 | Helped |
| Use NestE-SB instead of BiVE-Q | triple prediction · FBHE | MRR: 0.711 -> 0.851 | Helped |
| Use NestE-SB instead of BiVE-B | triple prediction · DBHE | MRR: 0.718 -> 0.862 | Helped |
| Use NestE-QB instead of BiVE-B | conditional link prediction · FBH | MRR: 0.836 -> 0.935 | Helped |
| Use NestE-SB instead of BiVE-Q | conditional link prediction · FBHE | MRR: 0.761 -> 0.867 | Helped |
| Use NestE-QB instead of BiVE-B | base link prediction · DBHE | MRR: 0.274 -> 0.289 | Helped |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-Q · FBHE | MRR: 0.368 -> 0.365 | Hurt |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-Q · DBHE | Hit@10: 0.431 -> 0.446 | Helped |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-H · FBHE | MRR: 0.347 -> 0.349 | Helped |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-H · DBHE | MRR: 0.267 -> 0.266 | Hurt |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-S · FBHE | MRR: 0.347 -> 0.350 | Helped |
| Add nested fact embedding loss (λ1=0.5) (ablation) | NestE-S · DBHE | MRR: 0.272 -> 0.272 | No clear effect |
Surprising findings
- Hypercomplex variants of BiVE (BiVE-H, BiVE-S) do not significantly improve over BiVE-Q, which the authors attribute to concatenation and MLP disrupting geometric properties.
- The best hypercomplex space varies by dataset and by relation, with no single geometry dominating.
Limitations
- Scoring uses only the inner product; a distance-based scoring function is left unexplored.
- Hyperparameters were reused from prior work without further search.
- Nested-fact datasets are small, manually curated benchmarks built over FB15K237 and DB15K.
Experimental setup
Datasets: FBH FBHE DBHE
Benchmarks: FBH FBHE DBHE
Metrics: MR MRR Hit@10
Baselines: BiVE-Q BiVE-B QuatE BiQUE Neural-LP DRUM AnyBURL
Builds on: QuatE BiVE ComplEx BiQUE
Closest papers by meaning
- Structure Is All You Need: Structural Representation Learning on Hyper-Relational Knowledge Graphs (ICML 2025 · similarity 0.86)
- Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning (ICLR 2024 · similarity 0.86)
- Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties (NeurIPS 2025 · similarity 0.86)
- Graph-constrained Reasoning: Faithful Reasoning on Knowledge Graphs with Large Language Models (ICML 2025 · similarity 0.86)
- Reasoning of Large Language Models over Knowledge Graphs with Super-Relations (ICLR 2025 · similarity 0.86)
- Context-aware Inductive Knowledge Graph Completion with Latent Type Constraints and Subgraph Reasoning (AAAI 2025 · similarity 0.85)
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