mlsanityData to 14 Oct 2026

Higher-Order Factorization Machines

arXiv 1607.07195 ↗First posted 25 Jul 2016stat.ML cs.LGcited by 45

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Abstract (arXiv)

Factorization machines (FMs) are a supervised learning approach that can use second-order feature combinations even when the data is very high-dimensional. Unfortunately, despite increasing interest in FMs, there exists to date no efficient training algorithm for higher-order FMs (HOFMs). In this paper, we present the first generic yet efficient algorithms for training arbitrary-order HOFMs. We also present new variants of HOFMs with shared parameters, which greatly reduce model size and prediction times while maintaining similar accuracy. We demonstrate the proposed approaches on four different link prediction tasks.

Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Jul 2016.

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Citing papers per year: 2021: 17; 2022: 8; 2023: 6; 2024: 4; 2025: 6; 2026: 4.

45 papers.

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  1. 2021Hyperbolic Deep Neural Networks: A Surveycited by 139
  2. 2024Wukong: Towards a Scaling Law for Large-Scale Recommendationcited by 74
  3. 2021A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendationcited by 59
  4. 2021Tensor Methods in Computer Vision and Deep Learningcited by 52
  5. 2021Deep Learning for Click-Through Rate Estimationcited by 33
  6. 2023A Survey on Vertical Federated Learning: From a Layered Perspectivecited by 30
  7. 2023Self-optimizing Feature Generation via Categorical Hashing Representation and Hierarchical Reinforcement Crossingcited by 30
  8. 2021ARM-Net: Adaptive Relation Modeling Network for Structured Datacited by 24
  9. 2021User Response Prediction in Online Advertisingcited by 15
  10. 2021Learning Graph Meta Embeddings for Cold-Start Ads in Click-Through Rate Predictioncited by 13
  11. 2021GraphFM: Graph Factorization Machines for Feature Interaction Modelingcited by 13
  12. 2022DHEN: A Deep and Hierarchical Ensemble Network for Large-Scale Click-Through Rate Predictioncited by 12
33 more
  1. 2023HyperFormer: Learning Expressive Sparse Feature Representations via Hypergraph Transformercited by 8
  2. 2022Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactionscited by 7
  3. 2021XCrossNet: Feature Structure-Oriented Learning for Click-Through Rate Predictioncited by 6
  4. 2023Quantized Fourier and Polynomial Features for more Expressive Tensor Network Modelscited by 6
  5. 2021DCAP: Deep Cross Attentional Product Network for User Response Predictioncited by 5
  6. 2021Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modellingcited by 4
  7. 2024Scalable Higher-Order Tensor Product Spline Modelscited by 4
  8. 2025Field Matters: A Lightweight LLM-enhanced Method for CTR Predictioncited by 4
  9. 2025MoE-MLoRA for Multi-Domain CTR Prediction: Efficient Adaptation with Expert Specializationcited by 4
  10. 2022Position: Tensor Networks are a Valuable Asset for Green AIcited by 3
  11. 2022Factorized Structured Regression for Large-Scale Varying Coefficient Modelscited by 3
  12. 2022Boosting Factorization Machines via Saliency-Guided Mixupcited by 3
  13. 2024GPRec: Bi-level User Modeling for Deep Recommenderscited by 3
  14. 2026PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decodingcited by 3
  15. 2021AEFE: Automatic Embedded Feature Engineering for Categorical Featurescited by 2
  16. 2023xDeepInt: a hybrid architecture for modeling the vector-wise and bit-wise feature interactionscited by 2
  17. 2023Exploiting Field Dependencies for Learning on Categorical Datacited by 2
  18. 2021DexDeepFM: Ensemble Diversity Enhanced Extreme Deep Factorization Machine Modelcited by 1
  19. 2021FINT: Field-aware INTeraction Neural Network For CTR Predictioncited by 1
  20. 2021Dynamic Parameterized Network for CTR Predictioncited by 1
  21. 2022Additive Higher-Order Factorization Machinescited by 1
  22. 2022Directed Acyclic Graph Factorization Machines for CTR Prediction via Knowledge Distillationcited by 1
  23. 2021DNN2LR: Automatic Feature Crossing for Credit Scoringcited by 0
  24. 2021SHORING: Design Provable Conditional High-Order Interaction Network via Symbolic Testingcited by 0
  25. 2022Variational Factorization Machines for Preference Elicitation in Large-Scale Recommender Systemscited by 0
  26. 2024On subdifferential chain rule of matrix factorization and beyondcited by 0
  27. 2025LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Modelscited by 0
  28. 2025DCN^2: Interplay of Implicit Collision Weights and Explicit Cross Layers for Large-Scale Recommendationcited by 0
  29. 2025Surrogate Modeling via Factorization Machine and Ising Model with Enhanced Higher-Order Interaction Learningcited by 0
  30. 2025LLM-Empowered Representation Learning for Emerging Item Recommendationcited by 0
  31. 2026Distribution-Aware End-to-End Embedding for Streaming Numerical Features in Click-Through Rate Predictioncited by 0
  32. 2026tensorFM: Low-Rank Approximations of Cross-Order Feature Interactionscited by 0
  33. 2026How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architecturalcited by 0