{"url":"/method/embedded-dot-product-affinity","slug":"embedded-dot-product-affinity","name":"Embedded Dot Product Affinity","full_name":"Embedded Dot Product Affinity","full_name_withheld":false,"description_markdown":"**Embedded Dot Product Affinity** is a type of affinity or self-similarity function between two points $\\mathbb{x\\_{i}}$ and $\\mathbb{x\\_{j}}$ that uses a dot product function in an embedding space:\r\n\r\n$$ f\\left(\\mathbb{x\\_{i}}, \\mathbb{x\\_{j}}\\right) = \\theta\\left(\\mathbb{x\\_{i}}\\right)^{T}\\phi\\left(\\mathbb{x\\_{j}}\\right) $$\r\n\r\nHere $\\theta\\left(x\\_{i}\\right) = W\\_{θ}x\\_{i}$ and $\\phi\\left(x\\_{j}\\right) = W\\_{φ}x\\_{j}$ are two embeddings.\r\n\r\nThe main difference between the dot product and [embedded Gaussian affinity](https://paperswithcode.com/method/embedded-gaussian-affinity) functions is the presence of [softmax](https://paperswithcode.com/method/softmax), which plays the role of an activation function.","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":"http://arxiv.org/abs/1711.07971v3","title":"Non-local Neural Networks","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/tea1528/Non-Local-NN-Pytorch/blob/986937674eb3b85d3d3fbaaa8f384c0a26624121/models/non_local.py#L99","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Affinity Functions","url":"/methods/category/affinity-functions","pwc_aliases":[]}],"n_papers_tagged":1,"archive_num_papers":null,"papers_newest_first":[{"paper":"/paper/non-local-neural-networks","title":"Non-local Neural Networks","date":"2017-11-21","arxiv_id":"1711.07971","n_code_links":32,"syntology":{"ran":3,"of":4,"unverified":1,"pointer_only":4}}],"papers_shown":1,"tasks":[{"task":"/task/action-classification","name":"Action Classification","papers":1},{"task":"/task/action-recognition-in-videos","name":"Action Recognition","papers":1},{"task":"/task/instance-segmentation","name":"Instance Segmentation","papers":1},{"task":"/task/keypoint-detection","name":"Keypoint Detection","papers":1},{"task":"/task/object-detection","name":"Object Detection","papers":1},{"task":"/task/pose-estimation","name":"Pose Estimation","papers":1},{"task":null,"name":"Position","papers":1},{"task":"/task/text-to-sql","name":"Text-To-SQL","papers":1},{"task":"/task/video-classification","name":"Video Classification","papers":1}],"tasks_shown":9,"n_tasks":9,"usage_by_year":[{"year":"2017","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/embedded-dot-product-affinity"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}