HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings

TL;DR

HyperComplEx introduces an adaptive multi-space embedding framework combining hyperbolic, complex, and Euclidean spaces with learned attention to effectively model diverse relation types in large-scale knowledge graphs, outperforming existing methods.

Contribution

It proposes a novel hybrid embedding model with relation-specific space weighting and multi-space consistency, improving scalability and accuracy in knowledge graph embeddings.

Findings

Achieves 4.8% relative gain in MRR on large-scale datasets

Outperforms state-of-the-art baselines across multiple benchmarks

Maintains efficient training with near-linear scaling

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.