{"id":4720,"date":"2025-06-19T07:02:33","date_gmt":"2025-06-19T07:02:33","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/06\/19\/2506-14899\/"},"modified":"2025-06-19T07:02:33","modified_gmt":"2025-06-19T07:02:33","slug":"2506-14899","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/06\/19\/2506-14899\/","title":{"rendered":"Optimal Convergence Rates of Deep Neural Network Classifiers"},"content":{"rendered":"

Optimal Convergence Rates of Deep Neural Network Classifiers
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arXiv:2506.14899v1 Announce Type: new
\nAbstract: In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s in [0,infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a H”{o}lder-$beta$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_*$ can be significantly smaller than the input dimension $d$. We prove that, under these conditions, the optimal convergence rate for the excess 0-1 risk of classifiers is $$ left( frac{1}{n} right)^{frac{betacdot(1wedgebeta)^q}{{frac{d_*}{s+1}+(1+frac{1}{s+1})cdotbetacdot(1wedgebeta)^q}}};;;, $$ which is independent of the input dimension $d$. Additionally, we demonstrate that ReLU deep neural networks (DNNs) trained with hinge loss can achieve this optimal convergence rate up to a logarithmic factor. This result provides theoretical justification for the excellent performance of ReLU DNNs in practical classification tasks, particularly in high-dimensional settings. The technique used to establish these results extends the oracle inequality presented in our previous work. The generalized approach is of independent interest.<\/div>\n

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\n Zihan Zhang, Lei Shi, Ding-Xuan Zhou
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Optimal Convergence Rates of Deep Neural Network Classifiers arXiv:2506.14899v1 Announce Type: new Abstract: In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s in [0,infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1274,1315,1486],"class_list":["post-4720","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-convergence","tag-function","tag-optimal"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4720"}],"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=4720"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4720\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4720"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4720"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}