# Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations

arXiv: https://arxiv.org/abs/2508.11978 · HTML: https://mlsanity.com/paper/2508.11978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 16 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Exploring Data Splitting Strategies for the Evaluation of Recommendation Models](https://mlsanity.com/paper/2007.13237/) (2020)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [A Survey on Popularity Bias in Recommender Systems](https://mlsanity.com/paper/2308.01118/) (2023)
- [Revisiting the Performance of iALS on Item Recommendation Benchmarks](https://mlsanity.com/paper/2110.14037/) (2021)
- [Deep Item-based Collaborative Filtering for Top-N Recommendation](https://mlsanity.com/paper/1811.04392/) (2018)
- [Scalable Hyperbolic Recommender Systems](https://mlsanity.com/paper/1902.08648/) (2019)
- [Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks](https://mlsanity.com/paper/2008.06716/) (2020)
- [User Diverse Preference Modeling by Multimodal Attentive Metric Learning](https://mlsanity.com/paper/1908.07738/) (2019)
- [Learning Feature Interactions with Lorentzian Factorization Machine](https://mlsanity.com/paper/1911.09821/) (2019)
- [Knowledge Graph Completion with Mixed Geometry Tensor Factorization](https://mlsanity.com/paper/2504.02589/) (2025)
- [Large Language Models Enhanced Hyperbolic Space Recommender Systems](https://mlsanity.com/paper/2504.05694/) (2025)

## Abstract (arXiv)

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.