{"id":10556,"date":"2026-02-18T07:02:33","date_gmt":"2026-02-18T07:02:33","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/18\/2602-15538\/"},"modified":"2026-02-18T07:02:33","modified_gmt":"2026-02-18T07:02:33","slug":"2602-15538","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/18\/2602-15538\/","title":{"rendered":"Functional Central Limit Theorem for Stochastic Gradient Descent"},"content":{"rendered":"<p>    Functional Central Limit Theorem for Stochastic Gradient Descent<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2602.15538v1 Announce Type: new<br \/>\nAbstract: We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled trajectory. Our result characterizes the long-term fluctuations of the algorithm around the minimizer by providing a diffusion limit for the trajectory. In contrast with classical central limit theorems for the last iterate or Polyak-Ruppert averages, this functional result captures the temporal structure of the fluctuations and applies to non-smooth settings such as robust location estimation, including the geometric median.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Kessang Flamand, Victor-Emmanuel Brunel<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2602.15538\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Functional Central Limit Theorem for Stochastic Gradient Descent arXiv:2602.15538v1 Announce Type: new Abstract: We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled trajectory. Our result characterizes the long-term fluctuations [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[4795,188,4794],"class_list":["post-10556","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-central","tag-functional","tag-limit"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10556"}],"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=10556"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10556\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}