{"id":271,"date":"2019-11-03T07:05:38","date_gmt":"2019-11-03T07:05:38","guid":{"rendered":"http:\/\/www.aix.web.tr\/?p=271"},"modified":"2024-06-26T13:41:28","modified_gmt":"2024-06-26T13:41:28","slug":"kolmogorov-karmasikligi","status":"publish","type":"post","link":"https:\/\/aix.web.tr\/en\/kolmogorov-karmasikligi\/","title":{"rendered":"Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"271\" class=\"elementor elementor-271\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b93cb7e elementor-section-stretched elementor-hidden-tablet elementor-hidden-phone elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b93cb7e\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container 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d=\"M473,67.3c-203.9,88.3-263.1-34-320.3,0C66,119.1,0,59.7,0,59.7V0h1000v59.7 c0,0-62.1,26.1-94.9,29.3c-32.8,3.3-62.8-12.3-75.8-22.1C806,49.6,745.3,8.7,694.9,4.7S492.4,59,473,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" opacity=\"0.66\" d=\"M734,67.3c-45.5,0-77.2-23.2-129.1-39.1c-28.6-8.7-150.3-10.1-254,39.1 s-91.7-34.4-149.2,0C115.7,118.3,0,39.8,0,39.8V0h1000v36.5c0,0-28.2-18.5-92.1-18.5C810.2,18.1,775.7,67.3,734,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M766.1,28.9c-200-57.5-266,65.5-395.1,19.5C242,1.8,242,5.4,184.8,20.6C128,35.8,132.3,44.9,89.9,52.5C28.6,63.7,0,0,0,0 h1000c0,0-9.9,40.9-83.6,48.1S829.6,47,766.1,28.9z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-58612f3a\" data-id=\"58612f3a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2e2491fa elementor-widget elementor-widget-heading\" data-id=\"2e2491fa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Makine \u00d6\u011frenimi, Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131\u200b<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-93cda62 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"93cda62\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-87f59bc\" data-id=\"87f59bc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-28499a7 elementor-widget elementor-widget-spacer\" data-id=\"28499a7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2635b41 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2635b41\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-47f1d36\" data-id=\"47f1d36\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-630ef7e elementor-widget elementor-widget-text-editor\" data-id=\"630ef7e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>A\u00e7\u0131klama<\/h2><p>Bu ara\u015ft\u0131rma yaz\u0131s\u0131nda <a href=\"https:\/\/aix.web.tr\/en\/makine-ogrenimi-farkli-makine-ogrenimi-turlerine-ve-nasil-calistiklarina-derinlemesine-bir-bakis\/\">Makine \u00d6\u011frenimi<\/a>, Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131 konular\u0131n\u0131 &#8220;<a href=\"https:\/\/aix.web.tr\/en\/sinir-agi-nedir-tanimi-avantajlari-ve-dezavantajlari-nelerdir\/\">Sinir A\u011f\u0131<\/a>&#8221; \u00e7\u00f6zmek i\u00e7in ara\u015ft\u0131r\u0131yoruz. Yaz\u0131 i\u00e7erisinde bu konular hakk\u0131nda detayl\u0131 ara\u015ft\u0131rmalar, sorunlar ve bu sorunlar\u0131n \u00e7\u00f6z\u00fcmleri yer almakta. T\u00fcm bunlar\u0131n \u0131\u015f\u0131\u011f\u0131nda sinir a\u011flar\u0131n i\u015flevi ve tatl\u0131 noktan\u0131n temel prensipleri hakk\u0131nda ayd\u0131nlanacaks\u0131n\u0131z.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3887617 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3887617\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5e04e15\" data-id=\"5e04e15\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2a01929 elementor-widget elementor-widget-text-editor\" data-id=\"2a01929\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>Makine \u00d6\u011frenimi<\/h2><p>Makine \u00d6\u011freniminin, geleneksel y\u00f6ntemlerle nas\u0131l \u00e7\u00f6z\u00fclece\u011fini bilmedi\u011fimiz karma\u015f\u0131k sorunlar\u0131n \u00fcstesinden gelmek i\u00e7in olduk\u00e7a g\u00fc\u00e7l\u00fc bir ara\u00e7 oldu\u011funu biliyoruz. G\u00f6r\u00fcnt\u00fc s\u0131n\u0131fland\u0131rma gibi problemler <a href=\"https:\/\/aix.web.tr\/en\/2023te-makine-ogrenmesi-neredeyiz-ve-nereye-gidiyoruz\/\">Makine \u00d6\u011frenmesi<\/a> ile etkili bir \u015fekilde \u00e7\u00f6z\u00fclebilir, \u00e7\u00fcnk\u00fc g\u00fcn\u00fcn sonunda, bu t\u00fcr bir g\u00f6rev i\u00e7in veri toplamak, bu kadar karma\u015f\u0131k ve zor bir problem i\u00e7in elle yaz\u0131lm\u0131\u015f kurallara uymaktan \u00e7ok daha kolayd\u0131r.<\/p><p>Fakat ne \u00e7\u00f6zece\u011fimizi zaten bildi\u011fimiz durumlarda ne olacak? Makine \u00d6\u011frenimini, halihaz\u0131rda bilmi\u015f oldu\u011fumuz \u00e7\u00f6z\u00fcmlere uygulamak i\u00e7in ne yapaca\u011f\u0131z? Fizik sim\u00fclasyonu gibi g\u00f6revler, g\u00f6revi y\u00f6neten kural ve denklemlerin zaten iyi biliniyor bu durumlarda ne olacak?<\/p><p>Pek \u00e7ok durumda, bunu yapmak i\u00e7in bilgisayar bilimlerindeki ezberleme ve hesaplama aras\u0131ndaki denge gibi ilgin\u00e7 kavramlar ve Kolmogorov karma\u015f\u0131kl\u0131\u011f\u0131 olarak adland\u0131r\u0131lan bir kavram iyi bir \u00e7\u00f6z\u00fcm gibi duruyor.<\/p><p>Bu konuda d\u00fc\u015f\u00fcnmeye ba\u015flaman\u0131n yolu \u015fudur: a\u00e7\u0131k olmasa da, ilgilendi\u011fimiz herhangi bir fenomen, problem veya matematiksel i\u015flev i\u00e7in (ilk etapta cevap bulmak i\u00e7in bir yol olmas\u0131 \u015fart\u0131yla) her zaman bir yol vard\u0131r. Yaln\u0131zca ne kadar hesaplama yapt\u0131\u011f\u0131m\u0131z ve ne kadar haf\u0131za kulland\u0131\u011f\u0131m\u0131z aras\u0131nda bir de\u011fi\u015fim yapmaktay\u0131z.<\/p><p>\u00d6rne\u011fin, <code>sin(x)'i<\/code> hesaplayan \u00e7ok basit bir Python program\u0131n\u0131 ele alal\u0131m:<\/p><pre><code class=\"rainbow\" data-language=\"python\"><span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>(x):\n    <span class=\"keyword\">return<\/span> np.<span class=\"function call\">sin<\/span>(x)\n<\/code><\/pre><p>Bu, <code> sin <\/code> i\u015flevinin &#8220;do\u011frudan&#8221; bir hesaplamas\u0131 olarak adland\u0131rd\u0131\u011f\u0131m\u0131z \u015feydir, ancak<br \/><code> sin <\/code> i\u015flevinin varsay\u0131msal olarak hesaplanmas\u0131 i\u00e7in pahal\u0131 bir i\u015flem oldu\u011funu varsay\u0131yoruz. Bu durumda farkl\u0131 bir yakla\u015f\u0131m almak isteyebiliriz.<br \/>\u00d6rne\u011fin, bir\u00e7ok farkl\u0131 <code> x <\/code> de\u011feri i\u00e7in <code> sin(x) <\/code> \u00f6n hesaplama de\u011ferleri<br \/>ve bunlar\u0131 a\u015fa\u011f\u0131daki gibi b\u00fcy\u00fck bir arama tablosunda dizeleyin:<\/p><pre><code class=\"rainbow\" data-language=\"python\"><span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>(x):\n    <span class=\"keyword\">return<\/span> {\n        <span class=\"constant numeric\">0.00<\/span>: <span class=\"constant numeric\">0.00<\/span>,\n        <span class=\"constant numeric\">0.34<\/span>: <span class=\"constant numeric\">0.34<\/span>,\n        <span class=\"constant numeric\">0.69<\/span>: <span class=\"constant numeric\">0.64<\/span>,\n        <span class=\"constant numeric\">1.04<\/span>: <span class=\"constant numeric\">0.86<\/span>,\n        <span class=\"constant numeric\">1.39<\/span>: <span class=\"constant numeric\">0.98<\/span>,\n        <span class=\"constant language\">...<\/span> :  <span class=\"constant language\">...<\/span>,\n        <span class=\"constant numeric\">1.74<\/span>: <span class=\"constant numeric\">0.98<\/span>,\n        <span class=\"constant numeric\">2.09<\/span>: <span class=\"constant numeric\">0.86<\/span>,\n        <span class=\"constant numeric\">2.44<\/span>: <span class=\"constant numeric\">0.64<\/span>,\n        <span class=\"constant numeric\">2.79<\/span>: <span class=\"constant numeric\">0.34<\/span>,\n        <span class=\"constant numeric\">3.14<\/span>: <span class=\"constant numeric\">0.00<\/span>,\n    }[x]\n<\/code><\/pre><p>\u015eimdi, baz\u0131 pahal\u0131 i\u015flemlerle sin(x) de\u011ferini \u201cdo\u011frudan\u201d hesaplamak yerine, arama tablosundaki giri\u015fimizin de\u011ferine bakarak an\u0131nda sin(x) de\u011ferini \u201chesaplayabiliriz\u201d. Dezavantaj\u0131 \u015fudur &#8211; \u015fimdi sin fonksiyonunu y\u00fcz binlerce kez \u00f6nceden hesaplamam\u0131z ve t\u00fcm \u00f6nceden hesaplanm\u0131\u015f sin(x) de\u011ferlerini bellekte tutmam\u0131z gerekir. Daha az hesaplama kar\u015f\u0131l\u0131\u011f\u0131nda daha fazla bellek kullan\u0131m\u0131 (ve \u00f6n hesaplama) yapt\u0131k. Her ne kadar arama tablosu a\u015f\u0131lmaz derecede b\u00fcy\u00fck olabilse de ve karma\u015f\u0131k fonksiyonlar i\u00e7in \u00f6nceden hesaplama zaman\u0131 delice b\u00fcy\u00fck olsa da, teoride bu ayn\u0131 numara, sin gibi sadece \u00e7ok basit fonksiyonlar i\u00e7in de\u011fil, ilgilendi\u011fimiz her fonksiyon i\u00e7in de ge\u00e7erlidir.<\/p><p>\u0130ki u\u00e7 veri noktas\u0131 gibi bu iki program\u0131 d\u00fc\u015f\u00fcnebiliriz &#8211; ayn\u0131 i\u015flevi \u00e7ok farkl\u0131 hesaplama ve bellek kullan\u0131mlar\u0131yla hesaplaman\u0131n iki farkl\u0131 yolu. E\u011fer onlar\u0131n haf\u0131za kullan\u0131mlar\u0131n\u0131 ve hesaplama zamanlar\u0131n\u0131 \u00f6l\u00e7mek ve bunlar\u0131 bir grafi\u011fe \u00e7izmek isteseydik, muhtemelen \u015f\u00f6yle bir \u015fey olurdu:<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/graph_programs.png\" alt=\"graph programs\" \/><\/p><p>Bundan sonra sorulacak do\u011fal soru, bu iki u\u00e7 aras\u0131nda bir yerde yer alan herhangi bir jenerik program olup olmad\u0131\u011f\u0131d\u0131r. Haf\u0131zay\u0131 ve hesaplamay\u0131, hesaplad\u0131klar\u0131 temel fonksiyona uygun bir \u015fekilde i\u015flemden ge\u00e7iren programlar. (Bu program asl\u0131nda var) \u00d6rne\u011fin, yeniden hesaplamay\u0131 \u00f6nlemek i\u00e7in hesaplamalar\u0131 \u00f6nbelle\u011fe alan genel bir program yazabiliriz. Bu, baz\u0131 ek bellek kullan\u0131mlar\u0131n\u0131n maliyeti kar\u015f\u0131l\u0131\u011f\u0131nda \u00e7\u0131kt\u0131y\u0131 zaten hesaplad\u0131\u011f\u0131m\u0131z bir girdi elde edersek, baz\u0131 performans tasarrufu sa\u011flar:<\/p><pre><code class=\"rainbow\" data-language=\"python\">cache <span class=\"keyword operator\">=<\/span> {}\n\n<span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>(x):\n    <span class=\"keyword\">if<\/span> x <span class=\"keyword\">in<\/span> cache:\n        <span class=\"keyword\">return<\/span> cache[x]\n    <span class=\"keyword\">else<\/span>:\n        y <span class=\"keyword operator\">=<\/span> np.<span class=\"function call\">sin<\/span>(x)\n        cache[x] <span class=\"keyword operator\">=<\/span> y\n        <span class=\"keyword\">return<\/span> y\n<\/code><\/pre><p>Daha \u00f6nce oldu\u011fu gibi, hesaplama i\u00e7in belle\u011fi takas etmenin &#8220;genel&#8221; bir yolunu bulduk.<br \/>Hangi fonksiyonla ilgilenirsek ilgilenelim (en az\u0131ndan teoride) \u00e7al\u0131\u015fabilir.<\/p><p>Ayr\u0131ca, fonksiyonumuza <em>yakla\u015ft\u0131\u011f\u0131m\u0131z<\/em> programlar\u0131 da bulabilirsiniz. Daha h\u0131zl\u0131 ve daha az do\u011fru hesaplama kar\u015f\u0131l\u0131\u011f\u0131nda biraz daha fazla bellek kullanarak bilgi i\u015flem yapmakta m\u00fcmk\u00fcn. \u0130\u015fte <code>sin<\/code> i\u015flevi i\u00e7in bir yakla\u015f\u0131m:<\/p><pre><code class=\"rainbow\" data-language=\"python\"><span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>(x):\n    x <span class=\"keyword operator\">=<\/span> x % (<span class=\"constant numeric\">2<\/span><span class=\"keyword operator\">*<\/span>np.pi)\n    <span class=\"keyword\">return<\/span> (\n        (<span class=\"constant numeric\">16<\/span><span class=\"keyword operator\">*<\/span>x<span class=\"keyword operator\">*<\/span>(np.pi <span class=\"keyword operator\">-<\/span> x)) \/ \n        (<span class=\"constant numeric\">5<\/span><span class=\"keyword operator\">*<\/span>np.pi<span class=\"keyword operator\">*<\/span>np.pi <span class=\"keyword operator\">-<\/span> <span class=\"constant numeric\">4<\/span><span class=\"keyword operator\">*<\/span>x<span class=\"keyword operator\">*<\/span>(np.pi <span class=\"keyword operator\">-<\/span> x)))\n<\/code><\/pre><p>\u0130lk \u00f6nce bu i\u015flevlerde ek bellek kullan\u0131m\u0131n\u0131n nerede oldu\u011fu a\u00e7\u0131k olmayabilir, ancak bu durumda <code>2<\/code>, <code>16<\/code>, <code>5<\/code>, <code>4<\/code>, ve<br \/><code>pi<\/code> t\u0131pk\u0131 arama tablosundaki gibi ek &#8220;\u00f6zel&#8221; de\u011ferlerdir &#8211; bunlar &#8220;bellek&#8221; dir. Ve bu belirli yakla\u015f\u0131m<code>sin<\/code>, ile s\u0131n\u0131rl\u0131 olsa da, bu program\u0131n benzer g\u00f6r\u00fcnen ancak herhangi bir i\u015flevi basit\u00e7e farkl\u0131 uygun sabit de\u011ferler bularak bulabilen genel bir versiyonunu bulmak o kadar zor de\u011fildir.<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/graph_programs_full.png\" alt=\"graph programs full\" \/><\/p><p>Bu iki ekleme g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda sorulacak ba\u015fka bir soru \u015fudur: \u015eimdiye kadar sundu\u011fumuz gibi, grafi\u011fin sol alt k\u0131sm\u0131ndaki noktada yatan &#8211; \u00e7ok fazla bellek kullanmamak &#8211; kullanmamay\u0131 sa\u011flayacak genel bir program var m\u0131? Sorusunu \u00f6n\u00fcm\u00fcze getiriyor.<\/p><p>Bize yol g\u00f6sterecek y\u00f6n Makine \u00d6\u011frenimidir- \u00e7\u00fcnk\u00fc i\u015flevi \u00e7evrimd\u0131\u015f\u0131 olarak de\u011ferlendirmekle ilgilenirsek, e\u011fitim verilerini toplayabilir ve daha sonra i\u015flevi yakla\u015ft\u0131rmak i\u00e7in genel Makine \u00d6\u011frenimi algoritmas\u0131yla e\u011fitebiliriz. Makine \u00d6\u011frenimi&#8217;nde, performanslar\u0131n\u0131 g\u00f6rmek i\u00e7in grafi\u011fimize ekleyebilece\u011fimiz farkl\u0131 bir genel algoritma s\u0131n\u0131f\u0131m\u0131z var.<\/p><p>\u00d6rnek olarak, Sinir A\u011flar\u0131&#8217;na bir g\u00f6z atal\u0131m &#8211; Sinir A\u011flar\u0131n\u0131n hesaplama \u00f6zelliklerini incelersek, muhtemelen denemek zorunda kalmadan bu grafik \u00fczerinde nerede durabileceklerini tahmin edebiliriz.<\/p><p>Her \u015feyden \u00f6nce, hesaplama zaman\u0131na bakal\u0131m. \u015eimdi, bir Sinir A\u011f\u0131n\u0131n hesaplama s\u00fcresi temel olarak sahip oldu\u011fu a\u011f\u0131rl\u0131klar\u0131n say\u0131s\u0131yla orant\u0131l\u0131d\u0131r ve sahip oldu\u011fu a\u011f\u0131rl\u0131klar\u0131n say\u0131s\u0131 da bellek kullan\u0131m\u0131n\u0131 belirler. Bu y\u00fczden hesaplama s\u00fcresi ve bellek kullan\u0131m\u0131 standart bir Sinir A\u011f\u0131nda birle\u015ftirilmi\u015ftir &#8211; g\u00f6rsel olarak Sinir A\u011flar\u0131 her zaman grafi\u011fin k\u00f6\u015fesinde bir yerde bulunur.<\/p><p>Di\u011fer soru ise &#8220;Sinir A\u011f\u0131nda&#8221; ka\u00e7 tane a\u011f\u0131rl\u0131\u011fa ihtiyac\u0131m\u0131z oldu\u011funu ne belirler? Kabaca, bu iki \u015fey taraf\u0131ndan belirlenir &#8211; Sinir A\u011f\u0131n\u0131n ne kadar do\u011fru olmas\u0131n\u0131 istedi\u011fimiz ve uydurdu\u011fumuz fonksiyonun ne kadar karma\u015f\u0131k oldu\u011fu. E\u011fer b\u00fct\u00fcn bu \u00f6zelliklere birlikte bakarsak, bunun gibi bir \u015fey g\u00f6r\u00fcr\u00fcz.<\/p><pre><code>            Computation Time     is proportional to     Memory Usage\n            Memory Usage         is proportional to     Accuracy\n            Accuracy   is inversely proportional to     Complexity\n<\/code><\/pre><p>Bu nedenle, Sinir A\u011f\u0131m\u0131z\u0131n k\u00f6\u015fegeninin ne kadar uza\u011fa gidece\u011fi, nihayetinde istedi\u011fimiz do\u011fruluk ve uydurmak istedi\u011fimiz fonksiyonun karma\u015f\u0131kl\u0131\u011f\u0131 ile y\u00f6netilir. Bu hem iyi hem de k\u00f6t\u00fc bir haberdir &#8211; iyi, \u00e7\u00fcnk\u00fc yakla\u015ft\u0131rmak istedi\u011fimiz i\u015flev karma\u015f\u0131k de\u011filse, o zaman kendimize g\u00fcvenece\u011fimizden emin olabiliriz &#8211; d\u00fc\u015f\u00fck hesaplama s\u00fcresi ve d\u00fc\u015f\u00fck bellek kullan\u0131m\u0131 &#8211; ve \u00e7\u00fcnk\u00fc k\u00f6t\u00fc yan\u0131 ise pahal\u0131 ve \u00e7ok fazla bellek kullan\u0131m\u0131na sebep oluyor.<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/graph_programs_sweet_spot.png\" alt=\"graph programs full\" \/><\/p><p>Fakat bir fonksiyonun karma\u015f\u0131kl\u0131\u011f\u0131 ile tam olarak ne kastediyoruz? Bunu daha iyi sezgisel bir \u015fekilde anlayabilseydik, Sinir A\u011flar\u0131&#8217;n\u0131n tatl\u0131 noktaya ne zaman vurabilece\u011fini daha do\u011fru tahmin edebiliyor olurduk. Bir i\u015flevin ne kadar karma\u015f\u0131k oldu\u011funa karar vermek i\u015fte Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131&#8217;n\u0131n devreye girdi\u011fi yer buras\u0131d\u0131r.<\/p><hr \/><h2>Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131<\/h2><p>Basit\u00e7e s\u00f6ylemek gerekirse, baz\u0131 fonksiyonlar\u0131n Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131, verilen t\u00fcm girdiler i\u00e7in fonksiyonla tamamen ayn\u0131 \u00e7\u0131kt\u0131lar\u0131 \u00fcretebilen m\u00fcmk\u00fcn olan en k\u0131sa program\u0131n uzunlu\u011fudur. Ayr\u0131ca, Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131 kurallar\u0131na g\u00f6re, programlar\u0131n herhangi bir \u015fekilde dosya a\u00e7mas\u0131na veya d\u0131\u015f d\u00fcnyayla ileti\u015fim kurmas\u0131na izin verilmez &#8211; t\u00fcm veriler kaynak kodunda saklanmal\u0131d\u0131r.<\/p><p>\u00d6rne\u011fin, hi\u00e7bir girdi almayan ve dizgiyi \u00e7\u0131karan i\u015flev:<\/p><pre><code>abababababababababababababababab<\/code><\/pre><p>basit\u00e7e k\u00fc\u00e7\u00fck program taraf\u0131ndan \u00fcretilebilir:<\/p><pre><code class=\"rainbow\" data-language=\"python\"><span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>():\n    <span class=\"keyword\">print<\/span> <span class=\"string\">\"ab\"<\/span> <span class=\"keyword operator\">*<\/span> <span class=\"constant numeric\">16<\/span>\n<\/code><\/pre><p>Bu, tekrarlayan <code>ab<\/code>\u00a0 bu i\u015flevi ifade eden \u00e7\u0131kt\u0131, \u00f6zellikle karma\u015f\u0131k bir i\u015flev de\u011fildir. \u00d6te yandan, girdi ve dizgeyi \u00fcreten i\u015flev:<\/p><pre><code>4c1j5b2p0cv4w1x8rx2y39umgw5q85s7<\/code><\/pre><p>nispeten daha karma\u015f\u0131kt\u0131r &#8211; temelde verbatim dizesini basmak i\u00e7in bir program gerektirir:<\/p><pre><code class=\"rainbow\" data-language=\"python\"><span class=\"storage function\">def<\/span> <span class=\"entity name function\">f<\/span>():\n    <span class=\"keyword\">print<\/span> <span class=\"string\">\"4c1j5b2p0cv4w1x8rx2y39umgw5q85s7\"<\/span>\n<\/code><\/pre><p>Bu dizginin saklanmas\u0131 program\u0131 \u00e7ok daha b\u00fcy\u00fck yapar, bu da onu \u00fcreten i\u015flevin karma\u015f\u0131k olmas\u0131 gerekti\u011fi anlam\u0131na gelir.<\/p><p>Burada dikkat edilmesi gereken ilgin\u00e7 bir \u015fey var &#8211; ilk program (* operat\u00f6r\u00fcn\u00fc kullanarak) bir \u015fey hesaplar, ikincisi ise sadece dizgiyi ezberler. Bu hemen bize iyi bir y\u00f6nlemdirme verir: ezberlemesi gereken i\u015flevler genellikle daha karma\u015f\u0131kt\u0131r.<\/p><p>Ve Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131, dizeleri \u00e7\u0131karan i\u015flevlerle s\u0131n\u0131rl\u0131 de\u011fildir. Resimler, fizik sim\u00fclasyonlar\u0131 veya ba\u015fka herhangi bir \u015fey \u00fcreten fonksiyonlar i\u00e7in ayn\u0131 analizi kullanabiliriz. A\u015fa\u011f\u0131daki g\u00f6r\u00fcnt\u00fcleri g\u00f6z \u00f6n\u00fcne al\u0131n, ikisinin de karma\u015f\u0131k i\u015flevlerden \u00fcretildi\u011fini d\u00fc\u015f\u00fcn\u00fcyor muyuz?<\/p><p style=\"text-align: center;\"><img decoding=\"async\" style=\"margin-right: 30px;\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/image_simple0.png\" alt=\"simple 0\" \/><img decoding=\"async\" style=\"margin-left: 30px;\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/image_simple1.png\" alt=\"simple 1\" \/><\/p><p>Asl\u0131nda pek de\u011fil &#8211; muhtemelen her iki resmi de olu\u015fturabilecek basit bir program var &#8211; olu\u015fturmak i\u00e7in basit kurallar alm\u0131\u015f gibi g\u00f6r\u00fcn\u00fcyorlar. Peki ya bu g\u00f6r\u00fcnt\u00fcler?<\/p><p style=\"text-align: center;\"><img decoding=\"async\" style=\"margin-right: 30px;\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/image_complex0.png\" alt=\"complex 0\" \/><a href=\"https:\/\/www.atc-anadolu.com\/Weather.htm\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"alignnone size-medium wp-image-1215\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2020\/05\/climatetur02-300x163.gif\" alt=\"\" width=\"300\" height=\"163\" \/><\/a><\/p><p>\u015eimdi bunlar \u00e7ok daha karma\u015f\u0131k. Program i\u00e7inde \u00e7ok fazla ham veri depolamaks\u0131z\u0131n bu g\u00f6r\u00fcnt\u00fclerden herhangi birini \u00fcretebilecek bir program d\u00fc\u015f\u00fcnmek zor g\u00f6r\u00fcn\u00fcyor. Burada ba\u015fka bir sezgi kazan\u0131yoruz: bu do\u011fal veriler genellikle karma\u015f\u0131k ve ezber gerektiriyor. Peki ya bu iki resim?<\/p><p style=\"text-align: center;\"><img decoding=\"async\" style=\"margin-right: 30px;\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/image_fractal.png\" alt=\"fractal\" \/><img decoding=\"async\" style=\"margin-left: 30px;\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/image_random.gif\" alt=\"random\" \/><\/p><p>Aha &#8211; bu sefer hileli bir soru. \u0130lk g\u00f6r\u00fcnt\u00fc elbette bir fraktald\u0131r &#8211; karma\u015f\u0131k g\u00f6r\u00fcnen ama asl\u0131nda bizim bildi\u011fimiz gibi bir g\u00f6r\u00fcnt\u00fcy\u00fc olu\u015fturmak i\u00e7in kullan\u0131labilecek basit bir program vard\u0131.<\/p><p>\u0130kincisi rasgele g\u00fcr\u00fclt\u00fcd\u00fcr &#8211; ve iki cevab\u0131 olabilir. E\u011fer bu g\u00fcr\u00fclt\u00fc s\u00f6zde rasgele say\u0131 \u00fcretecinden geliyorsa veya sadece bu kesin g\u00fcr\u00fclt\u00fcy\u00fc de\u011fil, g\u00fcr\u00fclt\u00fc \u00fcretmek istiyorsak, s\u00f6zde rastgele say\u0131 \u00fcrete\u00e7lerinin g\u00f6receli olarak basit programlar oldu\u011funu bildi\u011fimiz i\u00e7in teknik olarak karma\u015f\u0131k de\u011fildir &#8211; ancak &#8211; e\u011fer bu ger\u00e7ek rastgele g\u00fcr\u00fclt\u00fc ise ve tam olarak \u00e7o\u011faltmak istiyoruz, o zaman maksimum derecede karma\u015f\u0131kt\u0131r &#8211; basit\u00e7e saklamak ve yazmadan olu\u015fturmak i\u00e7in m\u00fcmk\u00fcn bir program yoktur. Bu bize ba\u015fka bir sezgiyi verir: sadece giri\u015f ve \u00e7\u0131k\u0131\u015flar\u0131n\u0131 g\u00f6zlemleyerek bir fonksiyonun karma\u015f\u0131kl\u0131\u011f\u0131n\u0131 bilmek son derece zordur.<\/p><p>Peki ya fizik sim\u00fclasyonu gibi bir \u015fey? Kenar kasalar\u0131 unutun ve \u015fu an i\u00e7in sorular\u0131 kand\u0131r\u0131n ve topun hareketi g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda bu videodaki kuma\u015f\u0131n hareketini \u00fcretmek i\u00e7in bir program yazman\u0131z gerekti\u011fini hayal edin. Peki bu karma\u015f\u0131k m\u0131?<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/ClothSwingCut.gif\" alt=\"simple swing\" \/><\/p><p>Kesinlikle di\u011fer \u00f6rneklerimizle k\u0131yasland\u0131\u011f\u0131nda \u00f6yle duruyor, belki de ilk bak\u0131\u015fta d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcn\u00fcz kadar karma\u015f\u0131k de\u011fildir &#8211; bence kuma\u015f\u0131n hareketini sadece hareketin a\u015famas\u0131n\u0131 bilerek olduk\u00e7a do\u011fru bir \u015fekilde tahmin etmenin m\u00fcmk\u00fcn olaca\u011f\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcyorum. Topun \u0130\u00e7imdeki duygu, zekice bir \u015fey yaparsan\u0131z, sadece bir parametreyi al\u0131p cevaben kuma\u015f\u0131n durumunu iyi bir \u015fekilde tahmin edebilecek basit bir program\u0131n olabilece\u011fidir. Peki ya bu?<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/FineFolds.gif\" alt=\"fine folds\" \/><\/p><p>Tamam, \u015fimdi bu karma\u015f\u0131k &#8211; devam eden her t\u00fcr k\u00fc\u00e7\u00fck k\u0131vr\u0131mlar ve kaotik hareketler var ve bu kesin davran\u0131\u015f\u0131 \u00fcretmek i\u00e7in b\u00fcy\u00fck bir karma\u015f\u0131k program yazman\u0131z gerekecek gibi g\u00f6r\u00fcn\u00fcyor.<\/p><p>Ancak, karma\u015f\u0131kl\u0131\u011f\u0131 do\u011frudan sezgimizle hissetmek yerine do\u011frudan hesaplayabilmemizin bir yolu var m\u0131? Genel durumda bunun imkans\u0131z oldu\u011fu g\u00f6sterilmi\u015ftir &#8211; ancak buna <a href=\"https:\/\/en.wikipedia.org\/wiki\/Principal_component_analysis\" target=\"_blank\" rel=\"noopener\">Temel Bir Bile\u015fen Analizi<\/a> (PCA) ad\u0131 verilen bir algoritma ile yakla\u015f\u0131k bir hesaplama yapabiliriz. PCA&#8217;y\u0131 baz\u0131 verilere uygulad\u0131\u011f\u0131n\u0131zda, geri ald\u0131\u011f\u0131n\u0131z \u015fey, belirli bir hata e\u015fi\u011fi i\u00e7in ne kadar say\u0131ya ihtiya\u00e7 duyulabilece\u011fine dair tahmin veren basit bir algoritmad\u0131r.<\/p><p>Bunu bir fizik sim\u00fclasyondan toplanan baz\u0131 verilere uygulamay\u0131 deneyelim. \u0130lgin\u00e7tir ki, fiziksel sim\u00fclasyon verilerine uyguland\u0131\u011f\u0131nda, PCA \u00f6zel bir davran\u0131\u015f sergiler &#8211; bize sim\u00fclasyonun &#8220;karma\u015f\u0131kl\u0131\u011f\u0131n\u0131&#8221; s\u00f6ylemenin yan\u0131 s\u0131ra, ilgilendi\u011fimiz fiziksel olarak sim\u00fcle edilen nesne i\u00e7in ana deformasyon eksenlerini de \u00e7\u0131kar\u0131r:<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/DeepClothSheetPCA.gif\" alt=\"PCA\" \/><\/p><p>Karma\u015f\u0131kl\u0131\u011f\u0131, orijinal hareketi yeniden yap\u0131land\u0131rmak i\u00e7in bu deformasyon eksenlerinin ne kadar\u0131n\u0131n gerekli oldu\u011funu inceleyerek \u00f6l\u00e7ebiliriz. \u0130leri geri sallanan kuma\u015f tabakam\u0131z gibi basit bir hareket i\u00e7in hareketi neredeyse tamamen yeniden yap\u0131land\u0131rabilmek i\u00e7in sadece bir veya iki eksene ihtiya\u00e7 duyar\u0131z, karma\u015f\u0131k ince k\u0131vr\u0131ml\u0131 kuma\u015flar\u0131m\u0131z i\u00e7in y\u00fczlerce hatta binlerce ekseneihtiyac\u0131m\u0131z vard\u0131r.<\/p><p>A\u015fa\u011f\u0131da, bir karaktere ba\u011fl\u0131 bir pelerin hareketini yeniden yap\u0131land\u0131rmak i\u00e7in farkl\u0131 say\u0131da eksen se\u00e7ersek neler oldu\u011funun bir kar\u015f\u0131la\u015ft\u0131rmas\u0131n\u0131 g\u00f6rebilirsiniz. Daha az eksenle daha az ayr\u0131nt\u0131 elde edersiniz &#8211; karma\u015f\u0131kl\u0131k etkili bir \u015fekilde azalt\u0131l\u0131r. Bu durumda, orijinal kuma\u015f\u0131n yakla\u015f\u0131k 3000 k\u00f6\u015fesi olmas\u0131na ra\u011fmen, kuma\u015f\u0131n durumunu, kalite, detay ve karma\u015f\u0131kl\u0131k a\u00e7\u0131s\u0131ndan \u00e7ok fazla kay\u0131p olmadan temsil etmek i\u00e7in sadece 256 eksene (bazen Temel olarak da adland\u0131r\u0131l\u0131r) ihtiyac\u0131m\u0131z vard\u0131r.<\/p><p style=\"text-align: center;\"><img decoding=\"async\" src=\"http:\/\/www.aix.web.tr\/wp-content\/uploads\/2019\/12\/pca_comparison.png\" alt=\"PCA comparison\" \/><\/p><p>Bu bize fizik sim\u00fclasyonlar\u0131n\u0131n neredeyse her zaman ilk bak\u0131\u015fta g\u00f6r\u00fcnd\u00fcklerinden daha az karma\u015f\u0131k oldu\u011fu g\u00f6steriyor.(bunun da k\u0131s\u0131tlama teorisine dayanarak iyi bir nedeni var). T\u00fcm bunlarda bize, Sinir A\u011f\u0131 ile olduk\u00e7a basit bir fizik sim\u00fclasyonu yakla\u015ft\u0131rmaya \u00e7al\u0131\u015f\u0131rsak, hesaplama ve ezberleme aras\u0131ndaki tatl\u0131 noktaya ula\u015fma \u015fans\u0131m\u0131z\u0131n y\u00fcksek oldu\u011funu g\u00f6steriyor!<\/p><hr \/><h2>Sonu\u00e7<\/h2><p>Sinir A\u011flar\u0131 sadece nas\u0131l \u00e7\u00f6zece\u011fimizi bilmedi\u011fimiz \u015feyler i\u00e7in iyi de\u011fildir, nas\u0131l \u00e7\u00f6zece\u011fimizi bildi\u011fimiz problemlerde b\u00fcy\u00fck performans kazan\u0131mlar\u0131 sa\u011flayabilirler. Asl\u0131nda, Sinir A\u011flar\u0131&#8217;n\u0131n bir g\u00f6revde ne kadar iyi bir performans g\u00f6stermesini bekledi\u011fimizi anlamak ve bir \u00e7e\u015fit sezgi elde etmek i\u00e7in Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131 kavram\u0131n\u0131 kullanabiliriz (ve hatta PCA&#8217;y\u0131 basit bir \u00f6nlem i\u00e7in kullanabiliriz).<\/p><p>Ancak gelece\u011fe bakt\u0131\u011f\u0131m\u0131zda, t\u00fcm bunlarla ilgili hala garip bir \u015fey var &#8211; ki asl\u0131nda yapmak istedi\u011fimiz \u015feyi yapmad\u0131k &#8211; bellek kullan\u0131m\u0131 i\u00e7in kolayca i\u015flem yapman\u0131n bir yolunu bulduk &#8211; Standart Sinir A\u011flar\u0131&#8217;nda ikisi birle\u015ftiler ve hesaplama zaman\u0131 her zaman a\u011f\u0131rl\u0131k say\u0131s\u0131yla orant\u0131l\u0131yd\u0131. T\u00fcm bunlar\u0131n \u0131\u015f\u0131\u011f\u0131nda, karma\u015f\u0131kl\u0131k azsa tatl\u0131 noktaya varabilece\u011fimiz sonucuna var\u0131yoruz.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d816fdf elementor-widget elementor-widget-html\" data-id=\"d816fdf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:block; text-align:center;\"\r\n     data-ad-layout=\"in-article\"\r\n     data-ad-format=\"fluid\"\r\n     data-ad-client=\"ca-pub-6077638139121629\"\r\n     data-ad-slot=\"4633720670\"><\/ins>\r\n<script>\r\n     (adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-32aee2a9 elementor-section-height-min-height elementor-section-content-middle elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"32aee2a9\" data-element_type=\"section\" data-e-type=\"section\" 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opacity=\"0.33\" d=\"M473,67.3c-203.9,88.3-263.1-34-320.3,0C66,119.1,0,59.7,0,59.7V0h1000v59.7 c0,0-62.1,26.1-94.9,29.3c-32.8,3.3-62.8-12.3-75.8-22.1C806,49.6,745.3,8.7,694.9,4.7S492.4,59,473,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" opacity=\"0.66\" d=\"M734,67.3c-45.5,0-77.2-23.2-129.1-39.1c-28.6-8.7-150.3-10.1-254,39.1 s-91.7-34.4-149.2,0C115.7,118.3,0,39.8,0,39.8V0h1000v36.5c0,0-28.2-18.5-92.1-18.5C810.2,18.1,775.7,67.3,734,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M766.1,28.9c-200-57.5-266,65.5-395.1,19.5C242,1.8,242,5.4,184.8,20.6C128,35.8,132.3,44.9,89.9,52.5C28.6,63.7,0,0,0,0 h1000c0,0-9.9,40.9-83.6,48.1S829.6,47,766.1,28.9z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 1000 100\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" opacity=\"0.33\" d=\"M473,67.3c-203.9,88.3-263.1-34-320.3,0C66,119.1,0,59.7,0,59.7V0h1000v59.7 c0,0-62.1,26.1-94.9,29.3c-32.8,3.3-62.8-12.3-75.8-22.1C806,49.6,745.3,8.7,694.9,4.7S492.4,59,473,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" opacity=\"0.66\" d=\"M734,67.3c-45.5,0-77.2-23.2-129.1-39.1c-28.6-8.7-150.3-10.1-254,39.1 s-91.7-34.4-149.2,0C115.7,118.3,0,39.8,0,39.8V0h1000v36.5c0,0-28.2-18.5-92.1-18.5C810.2,18.1,775.7,67.3,734,67.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M766.1,28.9c-200-57.5-266,65.5-395.1,19.5C242,1.8,242,5.4,184.8,20.6C128,35.8,132.3,44.9,89.9,52.5C28.6,63.7,0,0,0,0 h1000c0,0-9.9,40.9-83.6,48.1S829.6,47,766.1,28.9z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-43d4fdce\" data-id=\"43d4fdce\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4dcd9db9 elementor-widget elementor-widget-heading\" data-id=\"4dcd9db9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-large\">Unutmay\u0131n her geri bildirim bizi daha ileriye ta\u015f\u0131yacakt\u0131r!<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-27e37e55\" data-id=\"27e37e55\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5204be6c elementor-align-center elementor-widget elementor-widget-button\" data-id=\"5204be6c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-lg\" href=\"http:\/\/www.aix.web.tr\/basvuru\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">\u0130leti\u015fim<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Makine \u00d6\u011frenimi, Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131\u200b A\u00e7\u0131klama Bu ara\u015ft\u0131rma yaz\u0131s\u0131nda Makine \u00d6\u011frenimi, Kolmogorov Karma\u015f\u0131kl\u0131\u011f\u0131 konular\u0131n\u0131 &#8220;Sinir A\u011f\u0131&#8221; \u00e7\u00f6zmek i\u00e7in ara\u015ft\u0131r\u0131yoruz. Yaz\u0131 i\u00e7erisinde bu konular hakk\u0131nda detayl\u0131 ara\u015ft\u0131rmalar,&hellip;<\/p>","protected":false},"author":1,"featured_media":735,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[28,27,17,7],"class_list":["post-271","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-projects","tag-kolmogorov","tag-kolmogorov-karmasikligi","tag-yapay-zeka","tag-yapay-zeka-arastirma"],"_links":{"self":[{"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/posts\/271","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/comments?post=271"}],"version-history":[{"count":0,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/posts\/271\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/media\/735"}],"wp:attachment":[{"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/media?parent=271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/categories?post=271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aix.web.tr\/en\/wp-json\/wp\/v2\/tags?post=271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}