AdaGeM: Adaptive Geometric Learning on Manifolds for Hyper-Relational Knowledge Graphs

Abstract

Hyper-relational Knowledge Graphs (HKGs) extend traditional knowledge graphs by introducing high-order dependencies, where auxiliary qualifiers provide detailed information. However, modeling such intricate topologies (e.g., mixtures of hierarchies, cycles, and chains) is challenging. Existing methods suffer from structural distortion due to reliance on a single geometric space and overlook dynamic semantics across entity roles. To address these issues, we propose AdaGeM (Adaptive Geometric Learning on Manifolds), an innovative space-adaptive framework that integrates geometric learning with a role-aware Transformer. First, we propose an adaptive geometric hypergraph encoder that projects entities into a product manifold and design a topology-aware gating mechanism to dynamically select optimal geometric spaces for each entity. Second, we develop a role-aware Transformer equipped with role-specific projections and micro-structural bias injection to refine embeddings by distinguishing entity semantics across different roles and focusing on valid n-ary interactions, respectively. Extensive experiments on benchmark datasets demonstrate that AdaGeM outperforms state-of-the-art baselines in entity/relation prediction tasks, with ablation studies validating the necessity of multi-manifold modeling for heterogeneous HKG structures.