{"id":5411,"date":"2025-07-18T07:02:26","date_gmt":"2025-07-18T07:02:26","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/18\/2507-12686\/"},"modified":"2025-07-18T07:02:26","modified_gmt":"2025-07-18T07:02:26","slug":"2507-12686","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/18\/2507-12686\/","title":{"rendered":"Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights"},"content":{"rendered":"<p>    Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2507.12686v1 Announce Type: new<br \/>\nAbstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation function and allowing the layer widths to grow to infinity at arbitrary relative rates. In the special case where all widths are proportional to a common scale parameter $n$ and there are $L-1$ hidden layers, we obtain convergence rates of order $n^{-({1}\/{6})^{L-1} + epsilon}$, for any $epsilon &gt; 0$.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Krishnakumar Balasubramanian, Nathan Ross<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2507.12686\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights arXiv:2507.12686v1 Announce Type: new Abstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation [&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":[487,486,338],"class_list":["post-5411","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-dimensional","tag-finite","tag-gaussian"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5411"}],"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=5411"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5411\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}