mlsanityData to 7 Oct 2026

FM2: Field-matrixed Factorization Machines for Recommender Systems

arXiv 2102.12994 ↗First posted 20 Feb 2021cs.IR cs.LGcited by 31

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Abstract (arXiv)

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or FM2). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 15 of its 30 references that are in the map. First posted on arXiv 20 Feb 2021.

Builds on

15 of 30 references.

References · 15

  1. 2016Wide & Deep Learning for Recommender Systemscited by 745
  2. 2017DeepFM: A Factorization-Machine based Neural Network for CTR Predictioncited by 673
  3. 2017Deep Interest Network for Click-Through Rate Predictioncited by 541
  4. 2017Deep & Cross Network for Ad Click Predictionscited by 392
  5. 2018AutoInt: Automatic Feature Interaction Learning via Self-Attentive Neural Networkscited by 319
  6. 2018xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systemscited by 277
  7. 2017Neural Factorization Machines for Sparse Predictive Analyticscited by 183
  8. 2016Product-based Neural Networks for User Response Predictioncited by 145
  9. 2016Deep Learning over Multi-field Categorical Data: A Case Study on User Response Predictioncited by 67
  10. 2018Field-weighted Factorization Machines for Click-Through Rate Prediction in Display Advertisingcited by 59
  11. 2017Rocket Launching: A Universal and Efficient Framework for Training Well-performing Light Netcited by 27
  12. 2017Field-aware Factorization Machines in a Real-world Online Advertising Systemcited by 21
3 more
  1. 2019Predicting Different Types of Conversions with Multi-Task Learning in Online Advertisingcited by 21
  2. 2013OFF-Set: One-pass Factorization of Feature Sets for Online Recommendation in Persistent Cold Start Settingscited by 8
  3. 2013Pricing Ad Slots with Consecutive Multi-unit Demandcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 4; 2024: 5; 2025: 8; 2026: 4.

31 papers.

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  1. 2022Click-Through Rate Prediction in Online Advertising: A Literature Reviewcited by 31
  2. 2023On the Embedding Collapse when Scaling up Recommendation Modelscited by 29
  3. 2021SAR-Net: A Scenario-Aware Ranking Network for Personalized Fair Recommendation in Hundreds of Travel Scenarioscited by 23
  4. 2022CausPref: Causal Preference Learning for Out-of-Distribution Recommendationcited by 17
  5. 2022CL4CTR: A Contrastive Learning Framework for CTR Predictioncited by 14
  6. 2023A Survey on Fairness-aware Recommender Systemscited by 14
  7. 2021GraphFM: Graph Factorization Machines for Feature Interaction Modelingcited by 13
  8. 2024Ads Recommendation in a Collapsed and Entangled Worldcited by 13
  9. 2025External Large Foundation Model: How to Efficiently Serve Trillions of Parameters for Online Ads Recommendationcited by 13
  10. 2021Memorize, Factorize, or be Na"ive: Learning Optimal Feature Interaction Methods for CTR Predictioncited by 12
  11. 2025Hierarchical LoRA MoE for Efficient CTR Model Scalingcited by 10
  12. 2023Temporal Interest Network for User Response Predictioncited by 9
19 more
  1. 2024InterFormer: Effective Heterogeneous Interaction Learning for Click-Through Rate Predictioncited by 8
  2. 2024MerRec: A Large-scale Multipurpose Mercari Dataset for Consumer-to-Consumer Recommendation Systemscited by 6
  3. 2025Field Matters: A Lightweight LLM-enhanced Method for CTR Predictioncited by 4
  4. 2022Boosting Factorization Machines via Saliency-Guided Mixupcited by 3
  5. 2023Hierarchically Fusing Long and Short-Term User Interests for Click-Through Rate Prediction in Product Searchcited by 3
  6. 2025Robust Uplift Modeling with Large-Scale Contexts for Real-time Marketingcited by 3
  7. 2025Revisiting Feature Interactions from the Perspective of Quadratic Neural Networks for Click-through Rate Predictioncited by 3
  8. 2026TokenFormer: Unify the Multi-Field and Sequential Recommendation Worldscited by 3
  9. 2022AutoAttention: Automatic Field Pair Selection for Attention in User Behavior Modelingcited by 2
  10. 2024Low Rank Field-Weighted Factorization Machines for Low Latency Item Recommendationcited by 2
  11. 2022PHN: Parallel heterogeneous network with soft gating for CTR predictioncited by 1
  12. 2022Directed Acyclic Graph Factorization Machines for CTR Prediction via Knowledge Distillationcited by 1
  13. 2025AdaF^2M^2: Comprehensive Learning and Responsive Leveraging Features in Recommendation Systemcited by 1
  14. 2024From Data to Decisions: The Transformational Power of Machine Learning in Business Recommendationscited by 0
  15. 2025Large Foundation Model for Ads Recommendationcited by 0
  16. 2025Toward a benchmark for CTR prediction in online advertising: datasets, evaluation protocols and perspectivescited by 0
  17. 2026tensorFM: Low-Rank Approximations of Cross-Order Feature Interactionscited by 0
  18. 2026Understanding DNNs in Feature Interaction Models: A Dimensional Collapse Perspectivecited by 0
  19. 2026SpecFormer: Mitigating Embedding and Attention Collapse via Spectral-Aware Transformer for Recommendationcited by 0