Abstract

Complex-valued knowledge graph embedding (KGE) models like ComplEx effectively capture asymmetric relations but are fundamentally constrained by integer-order transformations. This restriction limits their ability to model multi-scale interactions, hierarchical correlations, and non-local semantic dependencies inherent in heterogeneous graphs. To address these limitations, this paper introduces FracComplEx, a novel fractional-order extension that embeds fractional calculus into the complex latent space. By leveraging fractional operators, the framework introduces non-local dynamics and memory-aware mechanisms to continuously generalize standard linear transformations. The core architecture employs a fractional-order parameter α as a controllable scaling mechanism that balances local relational details with global topology, optimizing representation smoothness and flexibility. We provide rigorous theoretical findings demonstrating that fractional transformations enhance the embedding’s expressive capacity, spectral characteristics, and perturbation robustness beyond conventional integer-order benchmarks. Extensive experiments on FB15k-237, WN18RR, and CoDEx-M establish the empirical superiority of FracComplEx, yielding significant improvements in Mean Reciprocal Rank (MRR) and Hits@K metrics over classical baselines, particularly under severe structural data sparsity.

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