Lorentz Equivariant Model for Knowledge-Enhanced Hyperbolic Collaborative Filtering
This addresses the need for more effective and generalizable recommender systems by ensuring equivariance in hyperbolic collaborative filtering, though it appears incremental relative to existing hyperbolic methods.
The paper tackles the problem of improving recommender systems by incorporating knowledge graph information in hyperbolic spaces, proposing a Lorentz equivariant model (LECF) that achieves state-of-the-art performance on three real-world benchmarks.
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 show that the ensemble properties of hyperbolic spaces fit the scale-free and hierarchical characteristics exhibited in the above two types of graphs well. However, existing hyperbolic methods ignore the consideration of equivariance, 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 rigorously Lorentz group equivariant knowledge-enhanced collaborative filtering model (LECF). 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) by the LECF layer with Lorentz Equivariant Transformation. Moreover, we propose Hyperbolic Sparse Attention Mechanism to sample the most informative neighbor nodes. Lorentz equivariance is strictly maintained throughout the entire model, and enforcing equivariance is proven necessary experimentally. Extensive experiments on three real-world benchmarks demonstrate that LECF remarkably outperforms state-of-the-art methods.