Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations

2025/08/16 by Yusupov, Viacheslav, Maxim Rakhuba, Evgeny Frolov +2
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Information Retrieval (cs.IR) #Machine Learning (cs.LG) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2508.11978

openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical insights to improve representation learning and increase computational stability at the same time. We reformulate the notion of hyperbolic distances to unlock additional representation capacity over conventional Euclidean space and learn more expressive user and item representations. To better capture user-items interactions, we construct a triplet loss that models ternary relations between users and their corresponding preferred and nonpreferred choices through a mix of pairwise interaction terms driven by the geometry of data. Our hyperbolic approach not only outperforms existing Euclidean and hyperbolic models but also reduces popularity bias, leading to more diverse and personalized recommendations.

Citations

• Large Language Models Enhanced Hyperbolic Space Recommender Systems
• Knowledge Graph Completion with Mixed Geometry Tensor Factorization
• Revisiting the Performance of iALS on Item Recommendation Benchmarks
• Hyperbolic Deep Neural Networks: A Survey
• Exploring Data Splitting Strategies for the Evaluation of Recommendation Models
• LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation
• LightGCN
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• Hyperbolic Graph Neural Networks
• Scalable Hyperbolic Recommender Systems
• Deep Item-based Collaborative Filtering for Top-N Recommendation
• HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems
• Self-Attentive Sequential Recommendation
• Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry
• Poincaré Embeddings for Learning Hierarchical Representations
• Adam: A Method for Stochastic Optimization

Related

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• HSR: Hyperbolic Social Recommender
• A Fashion Item Recommendation Model in Hyperbolic Space
• HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems
• Fully Hyperbolic Graph Convolution Network for Recommendation