  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.
