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HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings

Jugal Gajjar, Kaustik Ranaware, Kamalasankari Subramaniakuppusamy, Vaibhav Gandhi

TL;DR

This work addresses the challenge of heterogeneous relational patterns in large-scale knowledge graphs by proposing HyperComplEx, an adaptive multi-space embedding framework that unifies hyperbolic, complex, and Euclidean geometries. It introduces a relation-specific attention mechanism and a multi-space consistency loss, along with adaptive dimension allocation and scalable architecture (sharded embeddings, mixed precision) to enable near-linear scalability. Empirically, HyperComplEx achieves state-of-the-art link prediction across eight datasets, including a $0.612$ MRR on the 10M-paper CS dataset, with a near-linear training time $T \propto |\mathcal{E}|^{1.06}$. The model reveals interpretable geometry–relation mappings (hyperbolic for hierarchies, complex for asymmetry, Euclidean for symmetry) and provides an open-source implementation to support scalable, geometry-aware reasoning in open-world knowledge systems.

Abstract

Knowledge graphs have emerged as fundamental structures for representing complex relational data across scientific and enterprise domains. However, existing embedding methods face critical limitations when modeling diverse relationship types at scale: Euclidean models struggle with hierarchies, vector space models cannot capture asymmetry, and hyperbolic models fail on symmetric relations. We propose HyperComplEx, a hybrid embedding framework that adaptively combines hyperbolic, complex, and Euclidean spaces via learned attention mechanisms. A relation-specific space weighting strategy dynamically selects optimal geometries for each relation type, while a multi-space consistency loss ensures coherent predictions across spaces. We evaluate HyperComplEx on computer science research knowledge graphs ranging from 1K papers (~25K triples) to 10M papers (~45M triples), demonstrating consistent improvements over state-of-the-art baselines including TransE, RotatE, DistMult, ComplEx, SEPA, and UltraE. Additional tests on standard benchmarks confirm significantly higher results than all baselines. On the 10M-paper dataset, HyperComplEx achieves 0.612 MRR, a 4.8% relative gain over the best baseline, while maintaining efficient training, achieving 85 ms inference per triple. The model scales near-linearly with graph size through adaptive dimension allocation. We release our implementation and dataset family to facilitate reproducible research in scalable knowledge graph embeddings.

HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings

TL;DR

This work addresses the challenge of heterogeneous relational patterns in large-scale knowledge graphs by proposing HyperComplEx, an adaptive multi-space embedding framework that unifies hyperbolic, complex, and Euclidean geometries. It introduces a relation-specific attention mechanism and a multi-space consistency loss, along with adaptive dimension allocation and scalable architecture (sharded embeddings, mixed precision) to enable near-linear scalability. Empirically, HyperComplEx achieves state-of-the-art link prediction across eight datasets, including a MRR on the 10M-paper CS dataset, with a near-linear training time . The model reveals interpretable geometry–relation mappings (hyperbolic for hierarchies, complex for asymmetry, Euclidean for symmetry) and provides an open-source implementation to support scalable, geometry-aware reasoning in open-world knowledge systems.

Abstract

Knowledge graphs have emerged as fundamental structures for representing complex relational data across scientific and enterprise domains. However, existing embedding methods face critical limitations when modeling diverse relationship types at scale: Euclidean models struggle with hierarchies, vector space models cannot capture asymmetry, and hyperbolic models fail on symmetric relations. We propose HyperComplEx, a hybrid embedding framework that adaptively combines hyperbolic, complex, and Euclidean spaces via learned attention mechanisms. A relation-specific space weighting strategy dynamically selects optimal geometries for each relation type, while a multi-space consistency loss ensures coherent predictions across spaces. We evaluate HyperComplEx on computer science research knowledge graphs ranging from 1K papers (~25K triples) to 10M papers (~45M triples), demonstrating consistent improvements over state-of-the-art baselines including TransE, RotatE, DistMult, ComplEx, SEPA, and UltraE. Additional tests on standard benchmarks confirm significantly higher results than all baselines. On the 10M-paper dataset, HyperComplEx achieves 0.612 MRR, a 4.8% relative gain over the best baseline, while maintaining efficient training, achieving 85 ms inference per triple. The model scales near-linearly with graph size through adaptive dimension allocation. We release our implementation and dataset family to facilitate reproducible research in scalable knowledge graph embeddings.

Paper Structure

This paper contains 30 sections, 20 equations, 3 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Multi-Space Embedding Framework
  5. Hyperbolic Space Scoring
  6. Complex Space Scoring
  7. Euclidean Space Scoring
  8. Adaptive Space Attention
  9. Optimization Objective
  10. Self-Adversarial Ranking Loss
  11. Multi-Space Consistency Regularization
  12. Regularization
  13. Scalable Architecture Design
  14. Adaptive Dimension Allocation
  15. Sharded and Cached Embeddings
  16. ...and 15 more sections

Figures (3)

  • Figure 1: Training Time vs. Graph Size. Training follows a near-linear power law $T \propto |E|^{1.06}$, obtained from log–log OLS regression after overhead correction across CS-1K→CS-10M, confirming consistent scalability.
  • Figure 2: Inference Latency Distribution. Box plot showing inference latency quartiles, confirming HyperComplEx's competitive performance.
  • Figure 3: MRR Comparison on CS-1M Dataset. HyperComplEx achieves highest MRR among all baseline models.