{"id":1714,"date":"2025-02-07T07:02:26","date_gmt":"2025-02-07T07:02:26","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/07\/2502-03792\/"},"modified":"2025-02-07T07:02:26","modified_gmt":"2025-02-07T07:02:26","slug":"2502-03792","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/07\/2502-03792\/","title":{"rendered":"Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints"},"content":{"rendered":"

Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints
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arXiv:2502.03792v1 Announce Type: new
\nAbstract: We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures that the resulting network exhibits a high degree of Lipschitz regularity, that is, a small Lipschitz constant. Moreover, we show that this decay does not hinder the convergence rate of the empirical risk, now measured with the Huber loss, toward a critical point of the non-convex empirical risk. From these findings, we derive generalization bounds for two-layer neural networks trained with GD and a decaying LR with a sub-linear dependence on its number of trainable parameters, suggesting that the statistical behaviour of these networks is independent of overparameterization. We validate our theoretical results with a series of toy numerical experiments, where surprisingly, we observe that networks trained with constant step size GD exhibit similar learning and regularity properties to those trained with a decaying LR. This suggests that neural networks trained with standard GD may already be highly regular learners.<\/div>\n

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\n Kyle Sung, Anastasis Kratsios, Noah Forman
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Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints arXiv:2502.03792v1 Announce Type: new Abstract: We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures […]<\/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":[1671,118,1621],"class_list":["post-1714","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-layer","tag-neural","tag-two"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1714"}],"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=1714"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1714\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1714"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1714"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}