# Adaptive Factorization Network: Learning Adaptive-Order Feature Interactions

arXiv: https://arxiv.org/abs/1909.03276 · HTML: https://mlsanity.com/paper/1909.03276/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2019.

## Built on by (most cited first, 30 of 48)

- [Wukong: Towards a Scaling Law for Large-Scale Recommendation](https://mlsanity.com/paper/2403.02545/) (2024)
- [On the Embedding Collapse when Scaling up Recommendation Models](https://mlsanity.com/paper/2310.04400/) (2023)
- [ARM-Net: Adaptive Relation Modeling Network for Structured Data](https://mlsanity.com/paper/2107.01830/) (2021)
- [CL4CTR: A Contrastive Learning Framework for CTR Prediction](https://mlsanity.com/paper/2212.00522/) (2022)
- [GraphFM: Graph Factorization Machines for Feature Interaction Modeling](https://mlsanity.com/paper/2105.11866/) (2021)
- [PEAR: Personalized Re-ranking with Contextualized Transformer for Recommendation](https://mlsanity.com/paper/2203.12267/) (2022)
- [LiRank: Industrial Large Scale Ranking Models at LinkedIn](https://mlsanity.com/paper/2402.06859/) (2024)
- [FLIP: Fine-grained Alignment between ID-based Models and Pretrained Language Models for CTR Prediction](https://mlsanity.com/paper/2310.19453/) (2023)
- [Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactions](https://mlsanity.com/paper/2209.15409/) (2022)
- [Deep Feature Embedding for Tabular Data](https://mlsanity.com/paper/2408.17162/) (2024)
- [Detecting Arbitrary Order Beneficial Feature Interactions for Recommender Systems](https://mlsanity.com/paper/2206.13764/) (2022)
- [MerRec: A Large-scale Multipurpose Mercari Dataset for Consumer-to-Consumer Recommendation Systems](https://mlsanity.com/paper/2402.14230/) (2024)
- [DCAP: Deep Cross Attentional Product Network for User Response Prediction](https://mlsanity.com/paper/2105.08649/) (2021)
- [Powering In-Database Dynamic Model Slicing for Structured Data Analytics](https://mlsanity.com/paper/2405.00568/) (2024)
- [Field Matters: A Lightweight LLM-enhanced Method for CTR Prediction](https://mlsanity.com/paper/2505.14057/) (2025)
- [Exploring Recommender System Evaluation: A Multi-Modal User Agent Framework for A/B Testing](https://mlsanity.com/paper/2601.04554/) (2026)
- [Boosting Factorization Machines via Saliency-Guided Mixup](https://mlsanity.com/paper/2206.08661/) (2022)
- [Revisiting Feature Interactions from the Perspective of Quadratic Neural Networks for Click-through Rate Prediction](https://mlsanity.com/paper/2505.17999/) (2025)
- [TokenFormer: Unify the Multi-Field and Sequential Recommendation Worlds](https://mlsanity.com/paper/2604.13737/) (2026)
- [ReasonRec: A Reasoning-Augmented Multimodal Agent for Unified Recommendation](https://mlsanity.com/paper/2606.28357/) (2026)
- [Exploiting Field Dependencies for Learning on Categorical Data](https://mlsanity.com/paper/2307.09321/) (2023)
- [All-in-One: Heterogeneous Interaction Modeling for Cold-Start Rating Prediction](https://mlsanity.com/paper/2403.17740/) (2024)
- [Efficient Click-Through Rate Prediction for Developing Countries via Tabular Learning](https://mlsanity.com/paper/2104.07553/) (2021)
- [Dynamic Parameterized Network for CTR Prediction](https://mlsanity.com/paper/2111.04983/) (2021)
- [Human Pose Driven Object Effects Recommendation](https://mlsanity.com/paper/2209.08353/) (2022)
- [Weighted Multi-Level Feature Factorization for App ads CTR and installation prediction](https://mlsanity.com/paper/2308.02568/) (2023)
- [Beyond KAN: Introducing KarSein for Adaptive High-Order Feature Interaction Modeling in CTR Prediction](https://mlsanity.com/paper/2408.08713/) (2024)
- [AdaF^2M^2: Comprehensive Learning and Responsive Leveraging Features in Recommendation System](https://mlsanity.com/paper/2501.15816/) (2025)
- [Scaled Supervision is an Implicit Lipschitz Regularizer](https://mlsanity.com/paper/2503.14813/) (2025)
- [LoKA: Low-precision Kernel Applications for Recommendation Models At Scale](https://mlsanity.com/paper/2605.10886/) (2026)

## Abstract (arXiv)

Various factorization-based methods have been proposed to leverage second-order, or higher-order cross features for boosting the performance of predictive models. They generally enumerate all the cross features under a predefined maximum order, and then identify useful feature interactions through model training, which suffer from two drawbacks. First, they have to make a trade-off between the expressiveness of higher-order cross features and the computational cost, resulting in suboptimal predictions. Second, enumerating all the cross features, including irrelevant ones, may introduce noisy feature combinations that degrade model performance. In this work, we propose the Adaptive Factorization Network (AFN), a new model that learns arbitrary-order cross features adaptively from data. The core of AFN is a logarithmic transformation layer to convert the power of each feature in a feature combination into the coefficient to be learned. The experimental results on four real datasets demonstrate the superior predictive performance of AFN against the start-of-the-arts.