{"id":3242,"date":"2026-08-03T04:00:00","date_gmt":"2026-08-03T04:00:00","guid":{"rendered":"https:\/\/futurenews24.com\/index.php\/2026\/08\/03\/2605-06938\/"},"modified":"2026-08-03T17:59:13","modified_gmt":"2026-08-03T17:59:13","slug":"2605-06938","status":"publish","type":"post","link":"https:\/\/futurenews24.com\/index.php\/2026\/08\/03\/2605-06938\/","title":{"rendered":"[2605.06938] A Nonlinear Singular Worth Principle for Neural Networks"},"content":{"rendered":"<p><br \/>\n<\/p>\n<div id=\"content-inner\">\n<div id=\"abs\">\n<div class=\"dateline\">\n  [Submitted on 7 May 2026 (v1), last revised 30 Jul 2026 (this version, v2)]<\/div>\n<p>View a PDF of the paper titled A Nonlinear Singular Worth Principle for Neural Networks, by Brian Charles Brown and 4 different authors<\/p>\n<p>    View PDF<br \/>\n    HTML (experimental)<\/p>\n<blockquote class=\"abstract mathjax\"><p>\n            <span class=\"descriptor\">Summary:<\/span>Lately Brown et al. [2025] established a singular worth decomposition (SVD) for maps (particularly nonlinear) satisfying sure norm circumstances. We show that the majority fashionable neural architectures admit this nonlinear SVD (NLSVD) representation&#8212;with no change in input&#8211;output behavior&#8212;and enumerate the lessons lined. On this factorization the community is a left-invertible nonlinear map adopted by a remaining linear layer. Furthermore, the left-invertible issue is norm-preserving, so distances within the embedding (activations earlier than the ultimate linear layer) calibrate on to distances in enter area. We introduce a versatile structure that yields an specific decomposition at coaching time, a data-driven algorithm for estimating the illustration from educated fashions, and the mathematical foundations for nonlinear analogues of row and null areas in neural networks. Empirical case research illustrate makes use of of the idea for latent-space pullback (visualization and information technology), bias detection, and membership-inference robustness beneath coaching. Altogether, these foundations assist new approaches to core issues in neural-network evaluation.\n    <\/p><\/blockquote><\/div>\n<\/div>\n<div>\n<h2>Submission historical past<\/h2>\n<p> From: Robert Bridges [view email]                  [v1]<br \/>\n        Thu, 7 Could 2026 20:55:14 UTC (1,601 KB)<br \/>\n    [v2]<br \/>\n        Thu, 30 Jul 2026 19:29:56 UTC (1,979 KB)\n<\/p><\/div>\n<p><br \/>\n<br \/><a href=\"https:\/\/arxiv.org\/abs\/2605.06938\">Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Submitted on 7 May 2026 (v1), last revised 30 Jul 2026 (this version, v2)] View a PDF of the paper titled A Nonlinear Singular Worth Principle for Neural Networks, by Brian Charles Brown and 4 different authors View PDF HTML (experimental) Summary:Lately Brown et al. [2025] established a singular worth decomposition (SVD) for maps (particularly [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3244,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"http:\/\/arxiv.org\/static\/browse\/0.3.4\/images\/arxiv-logo-fb.png","fifu_image_alt":"","jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[],"jnews_override_bookmark_settings":[],"jnews_social_meta":[],"jnews_override_counter":[],"footnotes":""},"categories":[2],"tags":[2977,2359,3659,3660,2167],"class_list":["post-3242","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-research-breakthroughs","tag-networks","tag-neural","tag-nonlinear","tag-singular","tag-theory"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>[2605.06938] A Nonlinear Singular Worth Principle for Neural Networks - 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