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.

翻译：引入知识图谱中的先验辅助信息来辅助用户-物品图，能够提升推荐系统的综合性能。近期研究表明，双曲空间的集成性质很好地契合了上述两类图中呈现的无标度与层次化特性。然而，现有双曲方法忽略了等变性的考量，因此无法在给定变换下泛化对称特征，严重限制了模型能力。此外，它们无法在保留异质性与挖掘跨两图的高阶实体信息之间取得平衡。为弥补这些不足，我们提出了一种严格的洛伦兹群等变知识增强协同过滤模型（LECF）。创新性地，我们通过具有洛伦兹等变变换的LECF层，联合更新属性嵌入（包含来自知识图谱的高阶实体信号）与双曲嵌入（双曲嵌入间的距离揭示推荐倾向）。此外，我们提出双曲稀疏注意力机制来采样最具信息量的邻居节点。整个模型中严格保持洛伦兹等变性，且实验证明强制等变性是必要的。在三个真实基准数据集上的大量实验表明，LECF显著优于现有最先进方法。