HVAE: Hyperbolic Variational Autoencoder For Flexible Knowledge Transfer Across Multiple Domains

Cross-domain recommendation (CDR) serves as a pivotal solution to data sparsity and cold-start problems by transferring knowledge across distinct domains. However, existing approaches predominately rely on Euclidean embedding spaces, which suffer from a fundamental geometry-distribution mismatch: real-world user-item interactions typically exhibit power-law distributions and latent hierarchical structures that flat Euclidean spaces cannot accurately represent without significant distortion. This geometric limitation not only compromises representation quality but, more critically, hinders the effective disentanglement of domain-invariant user preferences from domain-specific interests, limiting transferability in low-overlap scenarios. To bridge this gap, we introduce the Mixed-Curvature Hyperbolic Variational Auto-Encoder (HVAE), a principled framework that unifies knowledge extraction and transfer within a hyperbolic manifold. By leveraging the exponential expansion capacity of hyperbolic geometry, HVAE naturally accommodates hierarchical data structures, enabling precise disentanglement of user intents without the need for strict domain overlap constraints. Furthermore, we propose a rigorous hyperbolic Wasserstein barycenter mechanism to align invariant distributions across heterogeneous domains. Extensive experiments on large-scale industrial and public datasets demonstrate that HVAE achieves superior performance, particularly in challenging scenarios with long-tail distributions and minimal domain overlap.