Lorentz equivariant model for knowledge-enhanced hyperbolic collaborative filtering

Abstract

Introducing prior auxiliary information from the knowledge graph (KG) to assist the user–item graph can improve the comprehensive performance of the recommender system. Many recent studies have shown that the ensemble properties of hyperbolic spaces fit the scale-free and hierarchical characteristics exhibited in the above two types of graphs well. Therefore, hyperbolic-based recommender systems have achieved a series of outstanding performances. However, in existing hyperbolic methods, equivariance is not considered. Thus, they cannot generalize symmetric features under given transformations, which seriously limits the capability of the model. Moreover, they cannot balance preserving the heterogeneity and mining the high-order entity information to users across two graphs. To fill these gaps, we propose a rigorous Lorentz group equivariant knowledge-enhanced collaborative filtering (LECF) model. Innovatively, we jointly update the attribute embeddings (containing the high-order entity signals from the KG) and hyperbolic embeddings (the distance between hyperbolic embeddings reveals the recommendation tendency) via the LECF layer with Lorentz Equivariant Transformation. Moreover, we propose Hyperbolic Sparse Attention Mechanism to sample the most informative neighboring nodes. Lorentz equivariance is strictly maintained throughout the entire model, and enforcing equivariance is proven necessary experimentally. Extensive experiments on three real-world datasets demonstrate that the proposed LECF remarkably outperforms state-of-the-art methods.