Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations

2025-08-16

AI Summary

To address the limited expressiveness, computational instability, and popularity bias inherent in Euclidean-space modeling for recommender systems, this paper proposes a hyperbolic representation learning framework. Methodologically, it (1) reformulates the hyperbolic distance function to better capture user–item–context ternary relations; (2) introduces a Riemannian manifold-based triplet loss that incorporates pairwise interaction terms, jointly optimizing the geometric relationships among users, preferred items, and non-preferred items on the hyperbolic hypersphere; and (3) employs Riemannian optimization to ensure training stability. Extensive experiments on multiple benchmark datasets demonstrate that the proposed method significantly outperforms state-of-the-art Euclidean and hyperbolic baselines. It achieves consistent improvements in standard metrics (e.g., Recall@K) while effectively mitigating popularity bias—thereby enhancing recommendation diversity and personalization.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Data Mining & Knowledge Management: Recommender Systems
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems

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.

Problem

• Improving hyperbolic triplet loss with geometric insights for recommendations
• Enhancing representation learning and computational stability in hyperbolic space
• Reducing popularity bias for diverse and personalized recommendations

Innovation

• Hyperbolic geometry for complex pattern capture
• Reformulated hyperbolic distances enhance representation capacity
• Geometric triplet loss models ternary user-item relations