Lorentz Equivariant Model for Knowledge-Enhanced Hyperbolic Collaborative Filtering

TL;DR

This paper introduces a Lorentz group equivariant model for knowledge-enhanced hyperbolic collaborative filtering, improving recommendation accuracy by maintaining symmetry properties and effectively integrating high-order entity information from knowledge graphs.

Contribution

The paper proposes a novel Lorentz equivariant framework that jointly updates attribute and hyperbolic embeddings, enforcing strict equivariance and enhancing heterogeneity preservation in recommendations.

Findings

LECF outperforms state-of-the-art methods on three benchmarks.

Lorentz equivariance improves model generalization and robustness.

Hyperbolic Sparse Attention effectively samples informative neighbors.

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 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.