{"id":10366,"date":"2026-02-10T07:02:22","date_gmt":"2026-02-10T07:02:22","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/10\/2602-07710\/"},"modified":"2026-02-10T07:02:22","modified_gmt":"2026-02-10T07:02:22","slug":"2602-07710","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/10\/2602-07710\/","title":{"rendered":"On Generation in Metric Spaces"},"content":{"rendered":"

On Generation in Metric Spaces
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arXiv:2602.07710v1 Announce Type: new
\nAbstract: We study generation in separable metric instance spaces. We extend the language generation framework from Kleinberg and Mullainathan [2024] beyond countable domains by defining novelty through metric separation and allowing asymmetric novelty parameters for the adversary and the generator. We introduce the $(varepsilon,varepsilon’)$-closure dimension, a scale-sensitive analogue of closure dimension, which yields characterizations of uniform and non-uniform generatability and a sufficient condition for generation in the limit. Along the way, we identify a sharp geometric contrast. Namely, in doubling spaces, including all finite-dimensional normed spaces, generatability is stable across novelty scales and invariant under equivalent metrics. In general metric spaces, however, generatability can be highly scale-sensitive and metric-dependent; even in the natural infinite-dimensional Hilbert space $ell^2$, all notions of generation may fail abruptly as the novelty parameters vary.<\/div>\n

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\n Jiaxun Li, Vinod Raman, Ambuj Tewari
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On Generation in Metric Spaces arXiv:2602.07710v1 Announce Type: new Abstract: We study generation in separable metric instance spaces. We extend the language generation framework from Kleinberg and Mullainathan [2024] beyond countable domains by defining novelty through metric separation and allowing asymmetric novelty parameters for the adversary and the generator. We introduce the $(varepsilon,varepsilon’)$-closure dimension, a […]<\/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":[979,769,1136],"class_list":["post-10366","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-generation","tag-metric","tag-spaces"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10366"}],"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=10366"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10366\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}