{"id":4184,"date":"2025-05-29T07:02:26","date_gmt":"2025-05-29T07:02:26","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/05\/29\/2505-21791\/"},"modified":"2025-05-29T07:02:26","modified_gmt":"2025-05-29T07:02:26","slug":"2505-21791","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/05\/29\/2505-21791\/","title":{"rendered":"Global Minimizers of $ell^p$-Regularized Objectives Yield the Sparsest ReLU Neural Networks"},"content":{"rendered":"

Global Minimizers of $ell^p$-Regularized Objectives Yield the Sparsest ReLU Neural Networks
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arXiv:2505.21791v1 Announce Type: new
\nAbstract: Overparameterized neural networks can interpolate a given dataset in many different ways, prompting the fundamental question: which among these solutions should we prefer, and what explicit regularization strategies will provably yield these solutions? This paper addresses the challenge of finding the sparsest interpolating ReLU network — i.e., the network with the fewest nonzero parameters or neurons — a goal with wide-ranging implications for efficiency, generalization, interpretability, theory, and model compression. Unlike post hoc pruning approaches, we propose a continuous, almost-everywhere differentiable training objective whose global minima are guaranteed to correspond to the sparsest single-hidden-layer ReLU networks that fit the data. This result marks a conceptual advance: it recasts the combinatorial problem of sparse interpolation as a smooth optimization task, potentially enabling the use of gradient-based training methods. Our objective is based on minimizing $ell^p$ quasinorms of the weights for $0 <\/div>\n

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\n Julia Nakhleh, Robert D. Nowak
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Global Minimizers of $ell^p$-Regularized Objectives Yield the Sparsest ReLU Neural Networks arXiv:2505.21791v1 Announce Type: new Abstract: Overparameterized neural networks can interpolate a given dataset in many different ways, prompting the fundamental question: which among these solutions should we prefer, and what explicit regularization strategies will provably yield these solutions? This paper addresses the challenge 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":[491,1046,2799],"class_list":["post-4184","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-networks","tag-relu","tag-sparsest"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4184"}],"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=4184"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4184\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}