# tensorFM: Low-Rank Approximations of Cross-Order Feature Interactions

arXiv: https://arxiv.org/abs/2602.15229 · HTML: https://mlsanity.com/paper/2602.15229/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems](https://mlsanity.com/paper/1803.05170/) (2018)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [Attentional Factorization Machines: Learning the Weight of Feature Interactions via Attention Networks](https://mlsanity.com/paper/1708.04617/) (2017)
- [DeepLight: Learning Illumination for Unconstrained Mobile Mixed Reality](https://mlsanity.com/paper/1904.01175/) (2019)
- [Field-weighted Factorization Machines for Click-Through Rate Prediction in Display Advertising](https://mlsanity.com/paper/1806.03514/) (2018)
- [Higher-Order Factorization Machines](https://mlsanity.com/paper/1607.07195/) (2016)
- [FinalMLP: An Enhanced Two-Stream MLP Model for CTR Prediction](https://mlsanity.com/paper/2304.00902/) (2023)
- [FM2: Field-matrixed Factorization Machines for Recommender Systems](https://mlsanity.com/paper/2102.12994/) (2021)
- [Field-aware Factorization Machines in a Real-world Online Advertising System](https://mlsanity.com/paper/1701.04099/) (2017)
- [Unified Embedding: Battle-Tested Feature Representations for Web-Scale ML Systems](https://mlsanity.com/paper/2305.12102/) (2023)
- [Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms](https://mlsanity.com/paper/1607.08810/) (2016)
- [Function Basis Encoding of Numerical Features in Factorization Machines](https://mlsanity.com/paper/2305.14528/) (2023)
- [Scalable Higher-Order Tensor Product Spline Models](https://mlsanity.com/paper/2402.01090/) (2024)
- [Low Rank Field-Weighted Factorization Machines for Low Latency Item Recommendation](https://mlsanity.com/paper/2408.00801/) (2024)

## Abstract (arXiv)

We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical values as features. Such problems frequently arise in practical applications, including click-through rate prediction and social sciences. We introduce and analyze {tensorFM}, a new model that efficiently captures high-order interactions between attributes via a low-rank tensor approximation representing the strength of these interactions. Our model generalizes field-weighted factorization machines. Empirically, tensorFM demonstrates competitive performance with state-of-the-art methods. Additionally, its low latency makes it well-suited for time-sensitive applications, such as online advertising.