# Learning Feature Interactions with Lorentzian Factorization Machine

arXiv: https://arxiv.org/abs/1911.09821 · HTML: https://mlsanity.com/paper/1911.09821/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2019.

## Built on by (most cited first, 8 of 8)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [User Response Prediction in Online Advertising](https://mlsanity.com/paper/2101.02342/) (2021)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [MerRec: A Large-scale Multipurpose Mercari Dataset for Consumer-to-Consumer Recommendation Systems](https://mlsanity.com/paper/2402.14230/) (2024)
- [Knowledge Graph Completion with Mixed Geometry Tensor Factorization](https://mlsanity.com/paper/2504.02589/) (2025)
- [Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations](https://mlsanity.com/paper/2508.11978/) (2025)
- [Disentangled Interest Network for Out-of-Distribution CTR Prediction](https://mlsanity.com/paper/2602.00002/) (2025)

## Abstract (arXiv)

Learning representations for feature interactions to model user behaviors is critical for recommendation system and click-trough rate (CTR) predictions. Recent advances in this area are empowered by deep learning methods which could learn sophisticated feature interactions and achieve the state-of-the-art result in an end-to-end manner. These approaches require large number of training parameters integrated with the low-level representations, and thus are memory and computational inefficient. In this paper, we propose a new model named "LorentzFM" that can learn feature interactions embedded in a hyperbolic space in which the violation of triangle inequality for Lorentz distances is available. To this end, the learned representation is benefited by the peculiar geometric properties of hyperbolic triangles, and result in a significant reduction in the number of parameters (20% to 80%) because all the top deep learning layers are not required. With such a lightweight architecture, LorentzFM achieves comparable and even materially better results than the deep learning methods such as DeepFM, xDeepFM and Deep & Cross in both recommendation and CTR prediction tasks.