{"id":7381,"date":"2025-10-06T07:02:49","date_gmt":"2025-10-06T07:02:49","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/10\/06\/2510-02420\/"},"modified":"2025-10-06T07:02:49","modified_gmt":"2025-10-06T07:02:49","slug":"2510-02420","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/10\/06\/2510-02420\/","title":{"rendered":"Higher-arity PAC learning, VC dimension and packing lemma"},"content":{"rendered":"<p>    Higher-arity PAC learning, VC dimension and packing lemma<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2510.02420v1 Announce Type: new<br \/>\nAbstract: The aim of this note is to overview some of our work in Chernikov, Towsner&#8217;20 (arXiv:2010.00726) developing higher arity VC theory (VC$_n$ dimension), including a generalization of Haussler packing lemma, and an associated tame (slice-wise) hypergraph regularity lemma; and to demonstrate that it characterizes higher arity PAC learning (PAC$_n$ learning) in $n$-fold product spaces with respect to product measures introduced by Kobayashi, Kuriyama and Takeuchi&#8217;15. We also point out how some of the recent results in arXiv:2402.14294, arXiv:2505.15688, arXiv:2509.20404 follow from our work in arXiv:2010.00726.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Artem Chernikov, Henry Towsner<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2510.02420\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Higher-arity PAC learning, VC dimension and packing lemma arXiv:2510.02420v1 Announce Type: new Abstract: The aim of this note is to overview some of our work in Chernikov, Towsner&#8217;20 (arXiv:2010.00726) developing higher arity VC theory (VC$_n$ dimension), including a generalization of Haussler packing lemma, and an associated tame (slice-wise) hypergraph regularity lemma; and to demonstrate that [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,2062,113,2064,3894,190,112,191],"tags":[3962,3960,3961],"class_list":["post-7381","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-dm","category-cs-lg","category-math-co","category-math-lo","category-math-st","category-stat-ml","category-stat-th","tag-arity","tag-arxiv","tag-higher"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7381"}],"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=7381"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7381\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}