{"id":7599,"date":"2025-10-15T07:03:11","date_gmt":"2025-10-15T07:03:11","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/10\/15\/2510-11789\/"},"modified":"2025-10-15T07:03:11","modified_gmt":"2025-10-15T07:03:11","slug":"2510-11789","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/10\/15\/2510-11789\/","title":{"rendered":"Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models"},"content":{"rendered":"<p>    Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2510.11789v1 Announce Type: new<br \/>\nAbstract: We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a non-linear activation function. We prove that the minimax rate is $M^{-frac{2beta}{2beta+1}}$ with $M$ being the sample size, depending only on the smoothness $beta$ of the activation, and crucially independent of token count, ambient dimension, or rank of the weight matrix. These results highlight a fundamental dimension-free statistical efficiency of attention-style nonlocal models, even when the weight matrix and activation are not separately identifiable and provide a theoretical understanding of the attention mechanism and its training.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Shai Zucker, Xiong Wang, Fei Lu, Inbar Seroussi<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2510.11789\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dimension-Free Minimax Rates for Learning Pairwise Interactions in Attention-Style Models arXiv:2510.11789v1 Announce Type: new Abstract: We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a non-linear activation function. We prove that the minimax rate is $M^{-frac{2beta}{2beta+1}}$ with $M$ being the sample size, depending [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,420,190,112,191],"tags":[960,656,3578],"class_list":["post-7599","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-pr","category-math-st","category-stat-ml","category-stat-th","tag-attention","tag-dimension","tag-style"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7599"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=7599"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7599\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}