{"id":2502,"date":"2025-03-19T07:02:25","date_gmt":"2025-03-19T07:02:25","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/19\/2503-13512\/"},"modified":"2025-03-19T07:02:25","modified_gmt":"2025-03-19T07:02:25","slug":"2503-13512","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/19\/2503-13512\/","title":{"rendered":"Positivity sets of hinge functions"},"content":{"rendered":"<p>    Positivity sets of hinge functions<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2503.13512v1 Announce Type: new<br \/>\nAbstract: In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give a necessary condition for any subset of $mathbb R^d$. We give various examples of such one-layer neural networks.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Josef Schicho, Ayush Kumar Tewari, Audie Warren<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2503.13512\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Positivity sets of hinge functions arXiv:2503.13512v1 Announce Type: new Abstract: In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,2062,113,2063,2064,1172,112],"tags":[2065,2066,884],"class_list":["post-2502","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-dm","category-cs-lg","category-cs-sc","category-math-co","category-math-fa","category-stat-ml","tag-give","tag-positivity","tag-sets"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2502"}],"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=2502"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2502\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}