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Lorentzian Distance Learning for Hyperbolic Representations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use squared Lorentzian distance with small curvature (β=0.01) instead of Poincaré distance, λ=0 | taxonomy embeddings · WordNet Nouns, MeSH, EuroVoc, ACM | MR and MAP: MeSH MR 12.4 to 1.30; MAP 79.9 to 90.5 | Helped |
| Increase curvature from β=0.01 to β=1 (λ=0) (ablation) | Lorentzian taxonomy embeddings · WordNet Nouns, MeSH | MAP: WordNet Nouns MAP 94.0 to 91.5; MeSH MAP 90.5 to 85.5 | Hurt |
| Add rank-order regularizer (λ=0.01) on embedding norms (ablation) | Lorentzian taxonomy embeddings (β=0.01) · WordNet Nouns | ρ: 45.2 to 71.1 | Helped |
| Add rank-order regularizer (λ=0.01) on embedding norms (ablation) | Lorentzian taxonomy embeddings (β=0.01) · WordNet Nouns | MR and MAP: MR 1.46 to 1.47; MAP 94.0 to 94.7 | No clear effect |
| Use Lorentzian distance (β=0.01, λ=0) instead of Poincaré-based classification for subtree classification | WordNet subtree binary classification · worker.n.01 and group.n.01 subtrees | F1: worker.n.01 66.83 to 96.32; group.n.01 91.91 to 99.86 | Helped |
| Use Lorentzian distance with β=0.01 and λ=0 for hierarchy embeddings in classification | WordNet subtree binary classification · mammal.n.01 subtree | F1: 91.37 to 97.73 | Helped |
| Replace hierarchical clustering with Euclidean distance on CIFAR-100 superclass centroids | CIFAR-100 taxonomy extraction · CIFAR-100 superclass taxonomy | qualitative taxonomy naturalness | Helped |
Closest papers by meaning
- Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry (ICML 2018 · similarity 0.91)
- The Numerical Stability of Hyperbolic Representation Learning (ICML 2023 · similarity 0.90)
- Robust Hyperbolic Learning with Curvature-Aware Optimization (NeurIPS 2025 · similarity 0.86)
- Hyperbolic Embeddings of Supervised Models (NeurIPS 2024 · similarity 0.86)
- Fast Hyperboloid Decision Tree Algorithms (ICLR 2024 · similarity 0.86)
- Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learning (ICML 2025 · similarity 0.85)
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