{"id":4851,"date":"2025-06-25T07:00:32","date_gmt":"2025-06-25T07:00:32","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/06\/25\/2506-19695\/"},"modified":"2025-06-25T07:00:32","modified_gmt":"2025-06-25T07:00:32","slug":"2506-19695","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/06\/25\/2506-19695\/","title":{"rendered":"Near-optimal estimates for the $ell^p$-Lipschitz constants of deep random ReLU neural networks"},"content":{"rendered":"

Near-optimal estimates for the $ell^p$-Lipschitz constants of deep random ReLU neural networks
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arXiv:2506.19695v1 Announce Type: new
\nAbstract: This paper studies the $ell^p$-Lipschitz constants of ReLU neural networks $Phi: mathbb{R}^d to mathbb{R}$ with random parameters for $p in [1,infty]$. The distribution of the weights follows a variant of the He initialization and the biases are drawn from symmetric distributions. We derive high probability upper and lower bounds for wide networks that differ at most by a factor that is logarithmic in the network’s width and linear in its depth. In the special case of shallow networks, we obtain matching bounds. Remarkably, the behavior of the $ell^p$-Lipschitz constant varies significantly between the regimes $ p in [1,2) $ and $ p in [2,infty] $. For $p in [2,infty]$, the $ell^p$-Lipschitz constant behaves similarly to $Vert gVert_{p’}$, where $g in mathbb{R}^d$ is a $d$-dimensional standard Gaussian vector and $1\/p + 1\/p’ = 1$. In contrast, for $p in [1,2)$, the $ell^p$-Lipschitz constant aligns more closely to $Vert g Vert_{2}$.<\/div>\n

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\n Sjoerd Dirksen, Patrick Finke, Paul Geuchen, Dominik St"oger, Felix Voigtlaender
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Near-optimal estimates for the $ell^p$-Lipschitz constants of deep random ReLU neural networks arXiv:2506.19695v1 Announce Type: new Abstract: This paper studies the $ell^p$-Lipschitz constants of ReLU neural networks $Phi: mathbb{R}^d to mathbb{R}$ with random parameters for $p in [1,infty]$. The distribution of the weights follows a variant of the He initialization and the biases are drawn […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,420,112],"tags":[3052,3053,491],"class_list":["post-4851","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-pr","category-stat-ml","tag-ell","tag-lipschitz","tag-networks"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4851"}],"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=4851"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4851\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}