{"url":"/method/fefm","slug":"fefm","name":"FEFM","full_name":"Field Embedded Factorization Machine","full_name_withheld":false,"description_markdown":"**Field Embedded Factorization Machine**, or **FEFM**, is a factorization machine variant. For each field pair, FEFM introduces symmetric matrix embeddings along with the usual feature vector embeddings that are present in FM. Like FM, $v\\_{i}$ is the vector embedding of the $i^{t h}$ feature. However, unlike Field-Aware Factorization Machines (FFMs), FEFM doesn't explicitly learn field-specific feature embeddings. The learnable symmetric matrix $W\\_{F(i), F(j)}$ is the embedding for the field pair $F(i)$ and $F(j) .$ The interaction between the $i^{t h}$ feature and the $j^{t h}$ feature is mediated through $W_{F(i), F(j)} .$\r\n\r\n$$\r\n\\phi(\\theta, x)=\\phi\\_{F E F M}((w, v, W), x)=w\\_{0}+\\sum\\_{i=1}^{m} w_{i} x_{i}+\\sum\\_{i=1}^{m} \\sum\\_{j=i+1}^{m} v\\_{i}^{T} W\\_{F(i), F(j)} v\\_{j} x\\_{i} x\\_{j}\r\n$$\r\n\r\nwhere $W\\_{F(i), F(j)}$ is a $k \\times k$ symmetric matrix ( $k$ is the dimension of the feature vector embedding space containing feature vectors $v\\_{i}$ and $v\\_{j}$ ).\r\n\r\nThe symmetric property of the learnable matrix $W\\_{F(i), F(j)}$ is ensured by reparameterizing $W\\_{F(i), F(j)}$ as $U\\_{F(i), F(j)}+$ $U\\_{F(i), F(j)}^{T}$, where $U\\_{F(i), F(j)}^{T}$ is the transpose of the learnable matrix $U\\_{F(i), F(j)} .$ Note that $W_{F(i), F(j)}$ can also be interpreted as a vector transformation matrix which transforms a feature embedding when interacting with a specific field.","description_state":"present","introduced_year":null,"introduced_by":{"title":null,"paper":null,"first_author":null,"n_authors":0,"url_abs":null,"archive_paper_url":null},"source":{"url":"https://arxiv.org/abs/2009.09931v2","title":"Field-Embedded Factorization Machines for Click-through rate prediction","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Factorization Machines","url":"/methods/category/factorization-machines","pwc_aliases":[]}],"n_papers_tagged":2,"archive_num_papers":null,"papers_newest_first":[{"paper":null,"title":"Complementary Advantages: Exploiting Cross-Field Frequency Correlation for NIR-Assisted Image Denoising","date":"2024-12-21","arxiv_id":"2412.16645","n_code_links":0,"syntology":null},{"paper":"/paper/field-embedded-factorization-machines-for","title":"Field-Embedded Factorization Machines for Click-through rate prediction","date":"2020-09-13","arxiv_id":"2009.09931","n_code_links":4,"syntology":null}],"papers_shown":2,"tasks":[{"task":"/task/click-through-rate-prediction","name":"Click-Through Rate Prediction","papers":1},{"task":"/task/computational-efficiency","name":"Computational Efficiency","papers":1},{"task":"/task/denoising","name":"Denoising","papers":1},{"task":"/task/image-denoising","name":"Image Denoising","papers":1},{"task":"/task/prediction","name":"Prediction","papers":1},{"task":"/task/recommendation-systems","name":"Recommendation Systems","papers":1}],"tasks_shown":6,"n_tasks":6,"usage_by_year":[{"year":"2020","papers":1},{"year":"2024","papers":1}],"row_source":"embedded","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/fefm"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}