# GraphFM: Graph Factorization Machines for Feature Interaction Modeling

arXiv: https://arxiv.org/abs/2105.11866 · HTML: https://mlsanity.com/paper/2105.11866/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 75 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [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)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [AutoInt: Automatic Feature Interaction Learning via Self-Attentive Neural Networks](https://mlsanity.com/paper/1810.11921/) (2018)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems](https://mlsanity.com/paper/1803.05170/) (2018)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Neural Factorization Machines for Sparse Predictive Analytics](https://mlsanity.com/paper/1708.05027/) (2017)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Product-based Neural Networks for User Response Prediction](https://mlsanity.com/paper/1611.00144/) (2016)

## Built on by (most cited first, 13 of 13)

- [Click-Through Rate Prediction in Online Advertising: A Literature Review](https://mlsanity.com/paper/2202.10462/) (2022)
- [ClickPrompt: CTR Models are Strong Prompt Generators for Adapting Language Models to CTR Prediction](https://mlsanity.com/paper/2310.09234/) (2023)
- [Embedding in Recommender Systems: A Survey](https://mlsanity.com/paper/2310.18608/) (2023)
- [Causality-based CTR Prediction using Graph Neural Networks](https://mlsanity.com/paper/2301.12762/) (2023)
- [HyperFormer: Learning Expressive Sparse Feature Representations via Hypergraph Transformer](https://mlsanity.com/paper/2305.17386/) (2023)
- [FreshGNN: Reducing Memory Access via Stable Historical Embeddings for Graph Neural Network Training](https://mlsanity.com/paper/2301.07482/) (2023)
- [Explicit Feature Interaction-aware Graph Neural Networks](https://mlsanity.com/paper/2204.03225/) (2022)
- [Boosting Factorization Machines via Saliency-Guided Mixup](https://mlsanity.com/paper/2206.08661/) (2022)
- [Deep Evolutional Instant Interest Network for CTR Prediction in Trigger-Induced Recommendation](https://mlsanity.com/paper/2401.07769/) (2024)
- [Directed Acyclic Graph Factorization Machines for CTR Prediction via Knowledge Distillation](https://mlsanity.com/paper/2211.11159/) (2022)
- [From Features to Graphs: Exploring Graph Structures and Pairwise Interactions via GNNs](https://mlsanity.com/paper/2502.13471/) (2025)
- [DCN^2: Interplay of Implicit Collision Weights and Explicit Cross Layers for Large-Scale Recommendation](https://mlsanity.com/paper/2506.21624/) (2025)
- [CoT is Not the Chain of Truth: An Empirical Internal Analysis of Reasoning LLMs for Fake News Generation](https://mlsanity.com/paper/2602.04856/) (2026)

## Abstract (arXiv)

Factorization machine (FM) is a prevalent approach to modeling pairwise (second-order) feature interactions when dealing with high-dimensional sparse data. However, on the one hand, FM fails to capture higher-order feature interactions suffering from combinatorial expansion. On the other hand, taking into account interactions between every pair of features may introduce noise and degrade prediction accuracy. To solve the problems, we propose a novel approach, Graph Factorization Machine (GraphFM), by naturally representing features in the graph structure. In particular, we design a mechanism to select the beneficial feature interactions and formulate them as edges between features. Then the proposed model, which integrates the interaction function of FM into the feature aggregation strategy of Graph Neural Network (GNN), can model arbitrary-order feature interactions on the graph-structured features by stacking layers. Experimental results on several real-world datasets have demonstrated the rationality and effectiveness of our proposed approach. The code and data are available at https://github.com/CRIPAC-DIG/GraphCTR}{https://github.com/CRIPAC-DIG/GraphCTR