{"id":6109,"date":"2025-08-15T07:00:41","date_gmt":"2025-08-15T07:00:41","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/15\/2508-10782\/"},"modified":"2025-08-15T07:00:41","modified_gmt":"2025-08-15T07:00:41","slug":"2508-10782","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/15\/2508-10782\/","title":{"rendered":"Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling"},"content":{"rendered":"

Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling
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arXiv:2508.10782v1 Announce Type: new
\nAbstract: We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms — including gradient-based optimization methods and approximate message passing (AMP) — with Gaussian data matrices and full-memory, non-separable nonlinearities. The central result constructs an explicit coupling between the iterates of a generalized first-order method and a conditionally Gaussian process whose covariance evolves deterministically via a finite-dimensional state evolution recursion. This coupling yields tight, dimension-free bounds under mild Lipschitz and moment-matching conditions. Our analysis departs from classical inductive AMP proofs by employing a direct comparison between the generalized first-order method and the conditionally Gaussian comparison process. This approach provides a unified derivation of AMP theory for Gaussian matrices without relying on separability or asymptotics. A complementary lower bound on the Wasserstein distance demonstrates the sharpness of our upper bounds.<\/div>\n

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\n Galen Reeves
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Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling arXiv:2508.10782v1 Announce Type: new Abstract: We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms — including gradient-based optimization methods and approximate message passing (AMP) — with Gaussian data matrices and full-memory, non-separable nonlinearities. The central result constructs an explicit coupling between the […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,420,190,112,191],"tags":[1331,338,1152],"class_list":["post-6109","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-math-pr","category-math-st","category-stat-ml","category-stat-th","tag-bounds","tag-gaussian","tag-generalized"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6109"}],"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=6109"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6109\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=6109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=6109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=6109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}