HGKAN: Hyperbolic Graph-Based Kolmogorov–Arnold Network for Social Recommendation

Abstract

Social recommendation utilizes social relationships to alleviate data sparsity and improve recommendation quality. Nevertheless, existing approaches still encounter several limitations. First, user preference structures in social networks are often hierarchical and non-Euclidean, whereas most existing models rely on Euclidean embeddings that are insufficient for capturing such complex geometries. Second, noisy social connections may propagate unreliable information and degrade representation quality. Third, commonly used multi-view fusion strategies based on multilayer perceptrons (MLPs) often lack the expressive capability required to effectively integrate heterogeneous user signals. To address these challenges, this paper proposes HGKAN (Hyperbolic Graph-Based Kolmogorov–Arnold Network), a unified framework that combines hyperbolic representation learning, graph neural networks, and KAN-based nonlinear fusion for social recommendation. Specifically, a Hyperbolic Intent Attention module is introduced to learn fine-grained and hierarchical user intent representations in hyperbolic space. In addition, a Hyperbolic Attention GCN is designed to denoise and aggregate social information while preserving complex relational structures. Furthermore, a KAN-based Multi-View Fusion Layer is developed to replace conventional MLP-based fusion, enabling more expressive and interpretable integration of preference, social, and intent representations. Extensive experiments conducted on three public benchmark datasets, including Yelp, Ciao, and Douban, demonstrate that HGKAN consistently outperforms several state-of-the-art recommendation methods. Experimental results show that the proposed framework achieves substantial improvements in both Recall@5 and NDCG@5, with all performance gains being statistically significant (p < 0.05). These findings verify the effectiveness of integrating hyperbolic geometric learning with KAN-based multi-view fusion for robust and accurate social recommendation.