{"id":346753,"date":"2023-03-15T03:00:59","date_gmt":"2023-03-15T03:00:59","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=346753"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=346753","title":{"rendered":"<span>\u041f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0434\u043b\u044f \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438. \u0427\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440<\/span>"},"content":{"rendered":"<div><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<p>\u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0432 \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f. \u0412 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0432\u0435\u0441\u044c \u043d\u0430\u0431\u043e\u0440 \u0444\u043e\u0440\u043c\u0443\u043b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0445 \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u043e\u0439 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438. \u0412 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u0441\u0442\u0430\u0442\u044c\u0438 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440.  <\/p>\n<p>\u00ab\u041f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f\u00bb (<em>fully connected<\/em>) \u2014 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043a\u0430\u0436\u0434\u044b\u0439 \u043d\u0435\u0439\u0440\u043e\u043d \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0441\u043b\u043e\u044f \u0441\u043e\u0435\u0434\u0438\u043d\u0451\u043d \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0441\u043b\u043e\u044f. \u00ab\u041f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f\u00bb (<em>feedforward<\/em>) \u2014 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u0438\u0433\u043d\u0430\u043b \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c \u0432 \u043e\u0434\u043d\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043e\u0442 \u0432\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u043a \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c\u0443 \u0441\u043b\u043e\u044e.<\/p>\n<p>\u041f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f (\u00ab<a href=\"https:\/\/en.wikipedia.org\/wiki\/Perceptron\" rel=\"noopener noreferrer nofollow\">\u043f\u0435\u0440\u0446\u0435\u043f\u0442\u0440\u043e\u043d<\/a>\u00bb) \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0438\u0439 \u0438 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0442\u0438\u043f\u0438\u0447\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0438\u0441\u043a\u0443\u0441\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438.<\/p>\n<h2>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/h2>\n<ol>\n<li>\n<p>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_2\" rel=\"noopener noreferrer nofollow\">\u0414\u0438\u0437\u0430\u0439\u043d \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_3\" rel=\"noopener noreferrer nofollow\">\u041f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_4\" rel=\"noopener noreferrer nofollow\">\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435<\/a><\/p>\n<p>4.1. <a href=\"https:\/\/anchor_4_1\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0432\u0435\u0441\u043e\u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u044b W^3<\/a><\/p>\n<p>4.2. <a href=\"https:\/\/anchor_4_2\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 b^3<\/a><\/p>\n<p>4.3. <a href=\"https:\/\/anchor_4_3\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0432\u0435\u0441\u043e\u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u044b W^2<\/a><\/p>\n<p>4.4. <a href=\"https:\/\/anchor_4_4\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 b^2<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_5\" rel=\"noopener noreferrer nofollow\">\u0427\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_6\" rel=\"noopener noreferrer nofollow\">\u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0441\u043b\u043e\u0451\u0432<\/a><\/p>\n<\/li>\n<\/ol>\n<h2>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/h2>\n<p>\u0418\u0441\u043a\u0443\u0441\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u0430 \u0442\u043e\u0447\u043d\u0435\u0435 \u2014 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Function_composition\" rel=\"noopener noreferrer nofollow\">\u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0435\u0439<\/a> (\u0441\u0443\u043f\u0435\u0440\u043f\u043e\u0437\u0438\u0446\u0438\u0435\u0439) \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/p>\n<p>\u0411\u044b\u043b\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043e (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Universal_approximation_theorem\" rel=\"noopener noreferrer nofollow\">George Cybenko, 1989<\/a>), \u0447\u0442\u043e \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u0441 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u043d\u0438\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u043c \u0441\u043b\u043e\u0435\u043c \u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u044b\u043c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e \u043c\u043e\u0436\u0435\u0442 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Approximation\" rel=\"noopener noreferrer nofollow\">\u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c <\/a>\u043b\u044e\u0431\u0443\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0442.\u0435. \u043f\u043e \u0441\u0432\u043e\u0435\u0439 \u0441\u0443\u0442\u0438 \u043e\u043d\u0430 \u2014 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0442\u043e\u0440.<\/p>\n<blockquote>\n<p>\u00ab\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0447\u0430\u0449\u0435, \u0447\u0435\u043c \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u0431\u044b \u043e\u0436\u0438\u0434\u0430\u0442\u044c. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u2014 \u0421\u0442\u043e\u0443\u043d\u0430 \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e \u043b\u044e\u0431\u0430\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u0415\u0441\u043b\u0438 \u043e\u0441\u043b\u0430\u0431\u0438\u0442\u044c \u043d\u0430\u0448\u0438 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0438 \u0434\u0430\u043b\u0435\u0435, \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0440\u044f\u0434\u044b \u0422\u0435\u0439\u043b\u043e\u0440\u0430 \u0438 \u0440\u044f\u0434\u044b \u0424\u0443\u0440\u044c\u0435, \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u044e\u0449\u0438\u0435 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 (\u0432 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u0445 \u0438\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u0435\u0439 \u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f). \u0422\u043e\u0442 \u0444\u0430\u043a\u0442, \u0447\u0442\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c \u2014 \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u044f\u0432\u043b\u0435\u043d\u0438\u0435 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u0434\u0430\u0435\u0442 \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u0435 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u044d\u043c\u043f\u0438\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u043d\u043e\u0433\u043e \u043c\u0430\u043b\u044b\u0445 \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432 \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u044b\u0445 \u0441\u0435\u0442\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435, \u0441\u0443\u0434\u044f \u043f\u043e \u0432\u0441\u0435\u043c\u0443, \u0434\u0430\u044e\u0442 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438\u00bb.<\/p>\n<p>\u2014 \u0420\u0430\u043c\u0441\u0443\u043d\u0434\u0430\u0440 \u0411., \u0417\u0430\u0434\u0435 \u0420.\u0411. TensorFlow \u0434\u043b\u044f \u0433\u043b\u0443\u0431\u043e\u043a\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f. \u0421\u043f\u0431., 2019. \u0421. 101.   <\/p>\n<\/blockquote>\n<p>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435, \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{a}^3=\\mathbf{a}^3(\\mathbf{x}^3),\\\\\\mathbf{x}^3=\\mathbf{W}^3\\times\\mathbf{a}^2(\\mathbf{x}^2)+\\mathbf{b}^3,\\\\\\mathbf{x}^2=\\mathbf{W}^2\\times\\mathbf{x}^1+\\mathbf{b}^2,\" alt=\"\\mathbf{a}^3=\\mathbf{a}^3(\\mathbf{x}^3),\\\\\\mathbf{x}^3=\\mathbf{W}^3\\times\\mathbf{a}^2(\\mathbf{x}^2)+\\mathbf{b}^3,\\\\\\mathbf{x}^2=\\mathbf{W}^2\\times\\mathbf{x}^1+\\mathbf{b}^2,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3a2\/efe\/fd5\/3a2efefd59d17feffbf6b80aaa8e7346.svg\" width=\"697\" height=\"85\"\/><\/p>\n<p>\u0433\u0434\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}^1\" alt=\"\\mathbf{x}^1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/046\/a40\/b64\/046a40b6467160c5d0ab7ad3550161c3.svg\" width=\"21\" height=\"21\"\/>\u2014 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u2014 \u043f\u0435\u0440\u0432\u044b\u0439 \u0441\u043b\u043e\u0439, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}^2\" alt=\"\\mathbf{x}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0b1\/ea5\/90a\/0b1ea590ad48cc18b9b517e04363b714.svg\" width=\"21\" height=\"21\"\/>\u2014 \u0432\u0442\u043e\u0440\u043e\u0439, \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}^3\" alt=\"\\mathbf{x}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b7a\/51b\/914\/b7a51b91426bf9934a49f48ae267ad2d.svg\" width=\"21\" height=\"21\"\/>\u2014 \u0442\u0440\u0435\u0442\u0438\u0439 \u0441\u043b\u043e\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{b}^2\" alt=\"\\mathbf{b}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8ed\/bc8\/14f\/8edbc814fd8457249b6b85f2b20f1e9a.svg\" width=\"21\" height=\"21\"\/>, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{b}^3\" alt=\"\\mathbf{b}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/017\/494\/089\/01749408903429fc8278d2b51ca33ada.svg\" width=\"21\" height=\"21\"\/> \u2014 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^2\" alt=\"\\mathbf{W}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d70\/6c3\/15b\/d706c315be6ccdfb31f2f5b99176d1a9.svg\" width=\"32\" height=\"21\"\/>, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^3\" alt=\"\\mathbf{W}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/38e\/fb3\/7c3\/38efb37c3b45dc8dbd42bf14f5e1af19.svg\" width=\"32\" height=\"21\"\/> \u2014 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0438 \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e \u0441\u043b\u043e\u0451\u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{a}^2\" alt=\"\\mathbf{a}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/589\/42e\/3dc\/58942e3dcbdb421835c4fde40393940a.svg\" width=\"20\" height=\"21\"\/> \u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0441\u043b\u043e\u044f, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{a}^3\" alt=\"\\mathbf{a}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/02f\/8ac\/b26\/02f8acb26b0c131a51ff1b55c203b54a.svg\" width=\"20\" height=\"21\"\/>\u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e, \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0441\u043b\u043e\u044f \u0438, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438.<\/p>\n<p>\u041c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0438\u043d\u044f\u0442\u0443\u044e \u0432 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 \u043f\u043e \u043d\u0435\u0439\u0440\u043e\u043d\u0430\u043c \u0441\u0435\u0442\u044f\u043c \u0437\u0430\u043f\u0438\u0441\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"{\\mathbf{W}}\\times{\\mathbf{x}}\" alt=\"{\\mathbf{W}}\\times{\\mathbf{x}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7a5\/67c\/2b3\/7a567c2b3f1319529bebd50a14bcb496.svg\" width=\"58\" height=\"17\"\/>, \u0433\u0434\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}\" alt=\"\\mathbf{x}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/95a\/be9\/4a4\/95abe94a41446f8aacf2d0ff8364a678.svg\" width=\"12\" height=\"12\"\/> \u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0441\u0442\u043e\u043b\u0431\u0435\u0446 (\u0432 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u0434 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e (\u043f\u043e \u0443\u043c\u043e\u043b\u0447\u0430\u043d\u0438\u044e) \u043f\u043e\u043d\u0438\u043c\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440-\u0441\u0442\u043e\u043b\u0431\u0435\u0446). \u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"{\\mathbf{A}}\\times{\\mathbf{B}}\" alt=\"{\\mathbf{A}}\\times{\\mathbf{B}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d54\/af7\/76f\/d54af776f94b9645791521f80e5ee2f2.svg\" width=\"56\" height=\"17\"\/> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043e, \u0435\u0441\u043b\u0438 \u0447\u0438\u0441\u043b\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{A}\" alt=\"\\mathbf{A}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/791\/d6c\/503\/791d6c5036213e57aa063e0352abbd32.svg\" width=\"17\" height=\"17\"\/> \u0440\u0430\u0432\u043d\u043e \u0447\u0438\u0441\u043b\u0443 \u0441\u0442\u0440\u043e\u043a <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{B}\" alt=\"\\mathbf{B}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dcb\/062\/028\/dcb062028f738dda24962c616a15ab99.svg\" width=\"16\" height=\"17\"\/>. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0447\u0438\u0441\u043b\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"j\" alt=\"j\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/96d\/1de\/517\/96d1de517ef33f57c6516ec78b437f96.svg\" width=\"8\" height=\"19\"\/> \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}_{ij}\" alt=\"\\mathbf{W}_{ij}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/1fa\/40d\/50d\/1fa40d50d5d266c2978a871d0e276a09.svg\" width=\"35\" height=\"22\"\/>\u0440\u0430\u0432\u043d\u043e \u0447\u0438\u0441\u043b\u0443 \u0441\u0442\u0440\u043e\u043a <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"i\" alt=\"i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/5ca\/f0e\/700\/5caf0e70084a631955a3648f0146b23c.svg\" width=\"7\" height=\"16\"\/> \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}\" alt=\"\\mathbf{x}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ddf\/bc6\/44e\/ddfbc644e369fb9d384ba8e095a27c7c.svg\" width=\"12\" height=\"12\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{a}\" alt=\"\\mathbf{a}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/1c3\/3b8\/7d2\/1c33b87d2e7fdb392acd65dc2ebfcda8.svg\" width=\"11\" height=\"12\"\/>.<\/p>\n<p><em>\u0414\u043b\u044f \u043a\u043e\u043c\u0444\u043e\u0440\u0442\u043d\u043e\u0433\u043e \u0447\u0442\u0435\u043d\u0438\u044f \u0441\u0442\u0430\u0442\u044c\u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u0431\u043b\u0430\u0434\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u043c \u0437\u043d\u0430\u043d\u0438\u0435\u043c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b (\u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u2014 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u043d\u0430\u0434 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438), \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445.<\/em><\/p>\n<h2>\u0414\u0438\u0437\u0430\u0439\u043d \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/h2>\n<p><a class=\"anchor\" name=\"anchor_2\" id=\"anchor_2\"><\/a><\/p>\n<p>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u0438\u043c\u0435\u0435\u0442 \u0442\u0440\u0438 \u0441\u043b\u043e\u044f \u0441 \u0442\u0440\u0435\u043c\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u0430\u043c\u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u0437 \u043d\u0438\u0445. \u041d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0433\u043e \u0447\u0435\u0440\u0435\u0437 \u0441\u0435\u0442\u044c \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0438\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sigmoid_function\" rel=\"noopener noreferrer nofollow\">\u0441\u0438\u0433\u043c\u043e\u0438\u0434<\/a> (<em>sigmoid<\/em>) \u043d\u0430 \u0441\u043a\u0440\u044b\u0442\u043e\u043c \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c \u0441\u043b\u043e\u044f\u0445:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"f(x)=\\frac{1}{1+e^{-x}}.\" alt=\"f(x)=\\frac{1}{1+e^{-x}}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8f8\/9b5\/722\/8f89b5722226aece4209dd2caca300ba.svg\" width=\"140\" height=\"45\"\/><\/p>\n<p>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u043d\u0441\u0442\u0432\u043e \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438\u043c\u0435\u044e\u0442 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0439 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u0438\u0437\u0432\u043b\u0435\u043a\u0430\u0442\u044c \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u0432 \u0434\u0430\u043d\u043d\u044b\u0445.<\/p>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/3fd\/3f5\/97a\/3fd3f597a08430108ba2ede840d5bd8e.png\" alt=\"\u0410\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438\" title=\"\u0410\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438\" width=\"780\" height=\"410\" data-src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3fd\/3f5\/97a\/3fd3f597a08430108ba2ede840d5bd8e.png\"\/><\/p>\n<div><figcaption>\u0410\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/figcaption><\/div>\n<\/figure>\n<p>\u041f\u0435\u0440\u0435\u043f\u0438\u0448\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c\u043e\u0439 \u0441\u0435\u0442\u0438 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u043d\u043d\u044b\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{a}^3=\\mathbf{f}(\\mathbf{x}^3)=\\mathbf{f}\\left(\\left[\\begin{matrix}w_{11}^3&amp;w_{12}^3&amp;w_{13}^3\\\\w_{21}^3&amp;w_{22}^3&amp;w_{23}^3\\\\w_{31}^3&amp;w_{32}^3&amp;w_{33}^3\\\\\\end{matrix}\\right]\\times\\mathbf{a}^2+\\left[\\begin{matrix}b_1^3\\\\b_2^3\\\\b_3^3\\\\\\end{matrix}\\right]\\right),\" alt=\"\\mathbf{a}^3=\\mathbf{f}(\\mathbf{x}^3)=\\mathbf{f}\\left(\\left[\\begin{matrix}w_{11}^3&amp;w_{12}^3&amp;w_{13}^3\\\\w_{21}^3&amp;w_{22}^3&amp;w_{23}^3\\\\w_{31}^3&amp;w_{32}^3&amp;w_{33}^3\\\\\\end{matrix}\\right]\\times\\mathbf{a}^2+\\left[\\begin{matrix}b_1^3\\\\b_2^3\\\\b_3^3\\\\\\end{matrix}\\right]\\right),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7d9\/387\/8ac\/7d93878ac1d30bbfde445535d7e3e7f3.svg\" width=\"444\" height=\"85\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{a}^2=\\mathbf{f}(\\mathbf{x}^2)=\\mathbf{f}\\left(\\left[\\begin{matrix}w_{11}^2&amp;w_{12}^2&amp;w_{13}^2\\\\w_{21}^2&amp;w_{22}^2&amp;w_{23}^2\\\\w_{31}^2&amp;w_{32}^2&amp;w_{33}^2\\\\\\end{matrix}\\right]\\times\\left[\\begin{matrix}x_1^1\\\\x_2^1\\\\x_3^1\\\\\\end{matrix}\\right]+\\left[\\begin{matrix}b_1^2\\\\b_2^2\\\\b_3^2\\\\\\end{matrix}\\right]\\right).\" alt=\"\\mathbf{a}^2=\\mathbf{f}(\\mathbf{x}^2)=\\mathbf{f}\\left(\\left[\\begin{matrix}w_{11}^2&amp;w_{12}^2&amp;w_{13}^2\\\\w_{21}^2&amp;w_{22}^2&amp;w_{23}^2\\\\w_{31}^2&amp;w_{32}^2&amp;w_{33}^2\\\\\\end{matrix}\\right]\\times\\left[\\begin{matrix}x_1^1\\\\x_2^1\\\\x_3^1\\\\\\end{matrix}\\right]+\\left[\\begin{matrix}b_1^2\\\\b_2^2\\\\b_3^2\\\\\\end{matrix}\\right]\\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c07\/997\/3d8\/c079973d8b3650c30d2c5bd87c39ba7d.svg\" width=\"476\" height=\"84\"\/><\/p>\n<p>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u043f\u043e\u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043a \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0443 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}\" alt=\"\\mathbf{x}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b10\/664\/02f\/b1066402f969bdbd2463e199e67789ad.svg\" width=\"12\" height=\"12\"\/>.<\/p>\n<h2>\u041f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430<\/h2>\n<p><a class=\"anchor\" name=\"anchor_3\" id=\"anchor_3\"><\/a><\/p>\n<p>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u043f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"a_1^2=\\ f(x_1^2)\\ =\\ f(w_{11}^2x_1^1+w_{12}^2x_2^1+w_{13}^2x_3^1+b_1^2),\\\\a_2^2=\\ f(x_2^2)\\ =f(w_{21}^2x_1^1+w_{22}^2x_2^1+w_{23}^2x_3^1+b_2^2),\\\\a_3^2=\\ \\ f(x_3^2)\\ =f(w_{31}^2x_1^1+w_{32}^2x_2^1+w_{33}^2x_3^1+b_3^2);\\\\a_1^3=\\ f(x_1^3)\\ =\\ f(w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3),\\\\a_2^3=\\ f(x_2^3)\\ =f(w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3),\\\\a_3^3=\\ \\ f(x_3^3)\\ =f(w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3);\" alt=\"a_1^2=\\ f(x_1^2)\\ =\\ f(w_{11}^2x_1^1+w_{12}^2x_2^1+w_{13}^2x_3^1+b_1^2),\\\\a_2^2=\\ f(x_2^2)\\ =f(w_{21}^2x_1^1+w_{22}^2x_2^1+w_{23}^2x_3^1+b_2^2),\\\\a_3^2=\\ \\ f(x_3^2)\\ =f(w_{31}^2x_1^1+w_{32}^2x_2^1+w_{33}^2x_3^1+b_3^2);\\\\a_1^3=\\ f(x_1^3)\\ =\\ f(w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3),\\\\a_2^3=\\ f(x_2^3)\\ =f(w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3),\\\\a_3^3=\\ \\ f(x_3^3)\\ =f(w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3);\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/152\/b52\/11f\/152b5211ffd3838aa4128b5b24e03567.svg\" width=\"697\" height=\"177\"\/><\/p>\n<p>\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Loss_function\" rel=\"noopener noreferrer nofollow\">\u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438<\/a> (<em>cost function<\/em>)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"Cost=\\frac{1}{n}\\sum_{i=1}^{n}{\\left(y_i-a_i^3\\right)^2{\\rightarrow}min},\" alt=\"Cost=\\frac{1}{n}\\sum_{i=1}^{n}{\\left(y_i-a_i^3\\right)^2{\\rightarrow}min},\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/218\/442\/635\/218442635d1d1de445ced92e0d0406b7.svg\" width=\"263\" height=\"57\"\/><\/p>\n<p>\u0433\u0434\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"i\" alt=\"i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a8b\/a7a\/470\/a8ba7a4706196d8b13f0f1fb39d231f3.svg\" width=\"7\" height=\"16\"\/>\u2014 \u043d\u043e\u043c\u0435\u0440 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0433\u043e \u0446\u0435\u043b\u0435\u0432\u043e\u0433\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"y_i\" alt=\"y_i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/355\/049\/504\/3550495048f5dd38f6c0fed16f3a56b3.svg\" width=\"16\" height=\"15\"\/>(\u0432\u0435\u043a\u0442\u043e\u0440\u0430 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{y}\" alt=\"\\mathbf{y}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dbf\/dbd\/5ea\/dbfdbd5eaed49eaa127291a5d09a45b2.svg\" width=\"12\" height=\"15\"\/>) \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"a_i^3\" alt=\"a_i^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b8c\/09b\/2d1\/b8c09b2d1b2f56969272d79ceca0ac5b.svg\" width=\"19\" height=\"26\"\/>\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"n\" alt=\"n\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/caf\/b91\/614\/cafb9161448bfe7aeba2fb201fdb3101.svg\" width=\"12\" height=\"12\"\/> \u2014 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0432 \u0440\u0430\u0437\u0432\u0451\u0440\u043d\u0443\u0442\u043e\u043c \u0432\u0438\u0434\u0435:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"C=\\frac{1}{3}(\\left(y_1-a_1^3\\right)^2+\\left(y_2-a_2^3\\right)^2+\\left(y_3-a_3^3\\right)^2).\" alt=\"C=\\frac{1}{3}(\\left(y_1-a_1^3\\right)^2+\\left(y_2-a_2^3\\right)^2+\\left(y_3-a_3^3\\right)^2).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d1b\/937\/1dd\/d1b9371dd9a0eb515ee70f4c766f64a1.svg\" width=\"386\" height=\"42\"\/><\/p>\n<p>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430\u043c \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0438\u043b\u044c\u043d\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u0442\u0435\u043a\u0443\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043e\u0442 \u0446\u0435\u043b\u0435\u0432\u044b\u0445.<\/p>\n<h2>\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435<\/h2>\n<p><a class=\"anchor\" name=\"anchor_4\" id=\"anchor_4\"><\/a><\/p>\n<p>\u0412 \u0441\u0443\u0449\u043d\u043e\u0441\u0442\u0438, \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Backpropagation\" rel=\"noopener noreferrer nofollow\">\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u043e\u0448\u0438\u0431\u043a\u0438<\/a> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u0430\u044f \u0438\u0434\u0435\u044f.<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Gradient\" rel=\"noopener noreferrer nofollow\">\u0413\u0440\u0430\u0434\u0438\u0435\u043d\u0442<\/a> (\u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435) \u2014 \u0432\u0435\u043a\u0442\u043e\u0440, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0438\u0439 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430\u0438\u0441\u043a\u043e\u0440\u0435\u0439\u0448\u0435\u0433\u043e \u0440\u043e\u0441\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445. \u0412\u044b\u0447\u0438\u0442\u0430\u044f \u0438\u0437 \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0432\u0435\u0441\u043e\u0432 \u0438 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u0430\u043a \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\nabla{C}\" alt=\"\\nabla{C}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f17\/6f5\/90c\/f176f590c8af3ba8aa68bf60b2606671.svg\" width=\"31\" height=\"17\"\/>, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0443 \u0438\u0437 \u0431\u043b\u0438\u0436\u0430\u0439\u0448\u0438\u0445 (\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438) \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u0438, \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u043e\u0448\u0438\u0431\u043a\u0438. \u0421\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u043c\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430, \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0435\u0451 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\nabla{C}=0\" alt=\"\\nabla{C}=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8a7\/b7f\/d48\/8a7b7fd48b46eaa3d9870af5d820d129.svg\" width=\"66\" height=\"17\"\/>.<\/p>\n<p>\u042d\u0442\u043e\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gradient_descent\" rel=\"noopener noreferrer nofollow\">\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0441\u043f\u0443\u0441\u043a\u0430<\/a>. \u0418\u043d\u043e\u0433\u0434\u0430 \u043c\u043e\u0436\u0435\u0442 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0442\u044c \u043f\u0443\u0442\u0430\u043d\u0438\u0446\u0430 \u0438\u043b\u0438 \u043e\u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043b\u0435\u043d\u0438\u0435 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u0432, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u0442\u0435\u0441\u043d\u043e \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0438 \u043e\u0434\u0438\u043d \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u0440\u0443\u0433\u043e\u0433\u043e.<\/p>\n<p>\u041d\u0435\u0441\u043c\u043e\u0442\u0440\u044f \u043d\u0430 \u043f\u0440\u043e\u0441\u0442\u043e\u0442\u0443 \u0438 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c, \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0441\u043f\u0443\u0441\u043a\u0430 \u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0438\u043c\u0435\u0435\u0442 \u0441\u0432\u043e\u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Saddle_point\" rel=\"noopener noreferrer nofollow\">\u0441\u0435\u0434\u043b\u043e\u0432\u0430\u044f \u0442\u043e\u0447\u043a\u0430<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Maximum_and_minimum\" rel=\"noopener noreferrer nofollow\">\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c<\/a>, \u043f\u0435\u0440\u0435\u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u043a\u0430 (<em>overtraining<\/em>) (\u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0435 \u0432 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c).<\/p>\n<p><strong>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^3\" alt=\"\\mathbf{W}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c6e\/53b\/822\/c6e53b822cab00a7c4f7d78f1c236b1b.svg\" width=\"32\" height=\"21\"\/>:<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_1\" id=\"anchor_4_1\"><\/a><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{1}{3}\\sum_{i=1}^{3}\\frac{\\partial\\left(y_i-a_i^3\\right)^2}{\\partial\\mathbf{W}^3},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial\\left(y_i-a_i^3\\right)}{\\partial\\mathbf{W}^3}},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{2}{3}\\sum_{i=1}^{3}\\left(y_i-a_i^3\\right)\\left(\\frac{\\partial y_i}{\\partial\\mathbf{W}^3}-\\frac{\\partial a_i^3}{\\partial\\mathbf{W}^3}\\right),\" alt=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{1}{3}\\sum_{i=1}^{3}\\frac{\\partial\\left(y_i-a_i^3\\right)^2}{\\partial\\mathbf{W}^3},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial\\left(y_i-a_i^3\\right)}{\\partial\\mathbf{W}^3}},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=\\frac{2}{3}\\sum_{i=1}^{3}\\left(y_i-a_i^3\\right)\\left(\\frac{\\partial y_i}{\\partial\\mathbf{W}^3}-\\frac{\\partial a_i^3}{\\partial\\mathbf{W}^3}\\right),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/31d\/2ad\/f8b\/31d2adf8b873d429806f25ae9a50cfda.svg\" width=\"697\" height=\"193\"\/><\/p>\n<p>\u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"y_i\" alt=\"y_i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/284\/346\/908\/28434690845a3e4bba6e5127166cdb95.svg\" width=\"16\" height=\"15\"\/> \u2014 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430, \u0442\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial y_i}{\\partial\\mathbf{W}^3}=0\" alt=\"\\frac{\\partial y_i}{\\partial\\mathbf{W}^3}=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ed2\/783\/709\/ed27837090c2ad675afbf25edadf5747.svg\" width=\"85\" height=\"46\"\/>,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial a_i^3}{\\partial\\mathbf{W}^3}},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial a_i^3}{\\partial x_i^3}}\\frac{\\partial x_i^3}{\\partial\\mathbf{W}^3}.\" alt=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial a_i^3}{\\partial\\mathbf{W}^3}},\\\\\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{\\partial a_i^3}{\\partial x_i^3}}\\frac{\\partial x_i^3}{\\partial\\mathbf{W}^3}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f13\/f36\/c97\/f13f36c9756d7c5688bac66269a137b9.svg\" width=\"697\" height=\"124\"\/><\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043d\u0430\u0439\u0434\u0451\u043c \u0435\u0451 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial\\mathbf{W}^3}.\" alt=\"\\frac{\\partial C}{\\partial\\mathbf{W}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial\\mathbf{W}^3}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/653\/c0e\/60f\/653c0e60f67718d953e3e653010a5c4f.svg\" width=\"367\" height=\"64\"\/><\/p>\n<p>\u0412 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0438\u0437 \u0435\u0451 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432.<\/p>\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^3\" alt=\"w_{11}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/73d\/c41\/d81\/73dc41d8185ed5ede2233f5ca580742f.svg\" width=\"29\" height=\"25\"\/> \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^3\" alt=\"\\mathbf{W}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8f1\/511\/f8a\/8f1511f8a22868110120ec1ca4259907.svg\" width=\"32\" height=\"21\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{11}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{11}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{11}^3}).\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{11}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{11}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{11}^3}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bd8\/7ec\/7d1\/bd87ec7d1983a31d4db48d04de860054.svg\" width=\"583\" height=\"46\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^3\" alt=\"w_{11}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/daa\/c9a\/bd6\/daac9abd61bf8d09af5991da6ac2b2c3.svg\" width=\"29\" height=\"25\"\/>. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"x_1^3=w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3,\\\\x_2^3=w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3,\\\\x_3^3=w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3,\" alt=\"x_1^3=w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3,\\\\x_2^3=w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3,\\\\x_3^3=w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b5c\/ca3\/6f3\/b5cca36f31da7c9d7ca9cc263390428b.svg\" width=\"697\" height=\"87\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\u0442\u043e\u0433\u0434\u0430 \\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}a_1^2+0+0).\" alt=\"\u0442\u043e\u0433\u0434\u0430 \\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}a_1^2+0+0).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/9c4\/b63\/591\/9c4b6359138157306b84e1cb8025d8cd.svg\" width=\"425\" height=\"62\"\/><\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial C}{\\partial w_{11}^3}\" alt=\"\\frac{\\partial C}{\\partial w_{11}^3}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/385\/ad0\/ef4\/385ad0ef47954d8d6bea5501682fcecd.svg\" width=\"47\" height=\"51\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)}{\\left(1-\\frac{e^{x_1^3}}{1+e^{x_1^3}}\\right)}a_1^2\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_1^2.\" alt=\"\\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)}{\\left(1-\\frac{e^{x_1^3}}{1+e^{x_1^3}}\\right)}a_1^2\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{11}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_1^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/37f\/691\/ca2\/37f691ca2214af78409294e958a3ee55.svg\" width=\"697\" height=\"117\"\/><\/p>\n<p>\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0430\u0441\u0442\u043d\u044b\u043c \u0441\u043b\u0443\u0447\u0430\u0435\u043c <a href=\"https:\/\/en.wikipedia.org\/wiki\/Automatic_differentiation\" rel=\"noopener noreferrer nofollow\">\u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/a>, \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0430\u043c \u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u043e\u043c\u0443 \u0432\u0438\u0434\u0443.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{12}^3\" alt=\"w_{12}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/232\/e33\/280\/232e33280b6ae0d37a4377183cd140de.svg\" width=\"29\" height=\"25\"\/>\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{13}^3\" alt=\"w_{13}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/497\/daa\/23e\/497daa23e5397ce04c0d2b7cdc16d5bc.svg\" width=\"29\" height=\"26\"\/> \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{12}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{13}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_3^2.\" alt=\"\\frac{\\partial C}{\\partial w_{12}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{13}^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_3^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/2a6\/db9\/e7e\/2a6db9e7e488aaf0ed9190dc57d35d08.svg\" width=\"697\" height=\"108\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^3\" alt=\"w_{11}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/367\/2a4\/276\/3672a4276d423c8fe284ea249945b346.svg\" width=\"29\" height=\"25\"\/>, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{12}^3\" alt=\"w_{12}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8b3\/d4b\/700\/8b3d4b700a191a76dac78fee238c4c96.svg\" width=\"29\" height=\"25\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{13}^3\" alt=\"w_{13}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/78b\/06c\/201\/78b06c20107f0d2a6e3c16931b87529d.svg\" width=\"29\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{11}^3=\\ w_{11}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_1^2),\\\\^*w_{12}^3=\\ w_{12}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_2^2),\\\\^*w_{13}^3=\\ w_{13}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_3^2),\" alt=\"^*w_{11}^3=\\ w_{11}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_1^2),\\\\^*w_{12}^3=\\ w_{12}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_2^2),\\\\^*w_{13}^3=\\ w_{13}^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)a_3^2),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/65a\/dad\/e2e\/65adade2e0eaeb0851edfccdadc59629.svg\" width=\"697\" height=\"138\"\/><\/p>\n<p>\u0433\u0434\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\eta\" alt=\"\\eta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b39\/486\/fc9\/b39486fc9082fcc741fb1afd8c800eaa.svg\" width=\"10\" height=\"16\"\/> (\u0438\u0301\u0442\u0430) \u2014 \u0431\u0443\u043a\u0432\u0430 \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u043b\u0444\u0430\u0432\u0438\u0442\u0430, \u043e\u0431\u044b\u0447\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0430\u044f \u0434\u043b\u044f \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <a href=\"https:\/\/en.wikipedia.org\/wiki\/Learning_rate\" rel=\"noopener noreferrer nofollow\">\u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/a> (<em>learning rate<\/em>), \u0435\u0451 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043e \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \u043e\u0442 0 \u0434\u043e 1; * \u2014 \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439.<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^3\" alt=\"\\mathbf{W}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/4a2\/817\/db8\/4a2817db810cd5126ce17fcbbd127e37.svg\" width=\"32\" height=\"21\"\/>. \u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{21}^3\" alt=\"w_{21}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/998\/cd8\/73d\/998cd873d32d054855725fdcc77a8025.svg\" width=\"29\" height=\"25\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{21}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{21}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{21}^3}).\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{21}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{21}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{21}^3}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/de5\/479\/61a\/de547961aa0a26e31ca832c0ce0473ac.svg\" width=\"583\" height=\"46\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{21}^3\" alt=\"w_{21}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/95e\/5ad\/3a8\/95e5ad3a87cdc7b8f9af77c548b791ce.svg\" width=\"29\" height=\"25\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}(0+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}a_1^2+0).\" alt=\"\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}(0+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}a_1^2+0).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ac8\/80f\/bf9\/ac880fbf9a7d4619c03737bdb113b04a.svg\" width=\"383\" height=\"62\"\/><\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial C}{\\partial w_{21}^3}\" alt=\"\\frac{\\partial C}{\\partial w_{21}^3}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7d2\/94e\/ed6\/7d294eed6cc4f55a7119bc4d8b323c7f.svg\" width=\"47\" height=\"51\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)}{\\left(1-\\frac{e^{x_2^3}}{1+e^{x_2^3}}\\right)a_1^2}\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_1^2.\" alt=\"\\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)}{\\left(1-\\frac{e^{x_2^3}}{1+e^{x_2^3}}\\right)a_1^2}\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{21}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_1^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/81a\/3a0\/ec4\/81a3a0ec4c13abaf974060efb0860cc0.svg\" width=\"697\" height=\"117\"\/><\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{22}^3\" alt=\"w_{22}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c6b\/c9c\/99e\/c6bc9c99e64fb03047e378cf37ac7bab.svg\" width=\"29\" height=\"25\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{23}^3\" alt=\"w_{23}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/06a\/8d9\/62e\/06a8d962e461cbff6d2e07f62b61b03d.svg\" width=\"29\" height=\"26\"\/> \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{22}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{23}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_3^2.\" alt=\"\\frac{\\partial C}{\\partial w_{22}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{23}^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_3^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7e8\/38d\/f3d\/7e838df3d0aa893b9f48d1a51d828248.svg\" width=\"697\" height=\"108\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{21}^3\" alt=\"w_{21}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/8a2\/5de\/6b9\/8a25de6b9be0cea9867012692f55d4f9.svg\" width=\"29\" height=\"25\"\/>, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{22}^3\" alt=\"w_{22}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/e34\/97d\/2c4\/e3497d2c44d208772727bd297194017f.svg\" width=\"29\" height=\"25\"\/> \u0438<img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{23}^3\" alt=\"w_{23}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ff5\/851\/b7c\/ff5851b7cc6985115530db3fc8db72fa.svg\" width=\"29\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{21}^3=\\ w_{21}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_1^2),\\\\^*w_{22}^3=\\ w_{22}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_2^2),\\\\^*w_{23}^3=\\ w_{23}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_3^2).\" alt=\"^*w_{21}^3=\\ w_{21}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_1^2),\\\\^*w_{22}^3=\\ w_{22}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_2^2),\\\\^*w_{23}^3=\\ w_{23}^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)a_3^2).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/437\/cc1\/93b\/437cc193b673c7e219e85e2f348d690f.svg\" width=\"697\" height=\"138\"\/><\/p>\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{31}^3\" alt=\"w_{31}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/531\/77d\/e36\/53177de3684c901b2e55043c381f2d9a.svg\" width=\"29\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{31}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{31}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{31}^3}).\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial w_{31}^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial w_{31}^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial w_{31}^3}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b78\/1ae\/45e\/b781ae45eb30fc9f8dded7713c8a3897.svg\" width=\"583\" height=\"46\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{31}^3\" alt=\"w_{31}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/112\/614\/e06\/112614e06917f7e545e77d4edb38619f.svg\" width=\"29\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}(0+0+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}a_1^2).\" alt=\"\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}(0+0+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}a_1^2).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/367\/9ee\/532\/3679ee532b67d674b43dbb4ed093e398.svg\" width=\"389\" height=\"72\"\/><\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial C}{\\partial w_{31}^3}\" alt=\"\\frac{\\partial C}{\\partial w_{31}^3}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/754\/a08\/d57\/754a08d5727e4bb8f8824c4dc1b3eba1.svg\" width=\"47\" height=\"51\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)}{\\left(1-\\frac{e^{x_3^3}}{1+e^{x_3^3}}\\right)a_1^2}\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_1^2.\" alt=\"\\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)}{\\left(1-\\frac{e^{x_3^3}}{1+e^{x_3^3}}\\right)a_1^2}\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial w_{31}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_1^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b6e\/35a\/107\/b6e35a1070dfd48f688ef845db3bf637.svg\" width=\"697\" height=\"127\"\/><\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{32}^3\" alt=\"w_{32}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/11a\/fd7\/2c4\/11afd72c454b04cf9f2ef1d40f26a9af.svg\" width=\"29\" height=\"26\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{33}^3\" alt=\"w_{33}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/01a\/cef\/d91\/01acefd9124564c7c6d71b93cb472a65.svg\" width=\"29\" height=\"26\"\/> \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{32}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{33}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_3^2.\" alt=\"\\frac{\\partial C}{\\partial w_{32}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_2^2,\\\\\\frac{\\partial C}{\\partial w_{33}^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_3^2.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6b4\/ba8\/b7f\/6b4ba8b7f86c9208b92673a69c3816c8.svg\" width=\"697\" height=\"108\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{31}^3\" alt=\"w_{31}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/896\/d2d\/02e\/896d2d02e2968261abafe3df335c0d32.svg\" width=\"29\" height=\"26\"\/>, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{32}^3\" alt=\"w_{32}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/5a1\/be8\/293\/5a1be8293dbb18934ce241abd01bee41.svg\" width=\"29\" height=\"26\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{33}^3\" alt=\"w_{33}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/cc2\/c1d\/060\/cc2c1d060218d5b291ea2569db1cf3bf.svg\" width=\"29\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{31}^3=\\ w_{31}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_1^2),\\\\^*w_{32}^3=\\ w_{32}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_2^2),\\\\^*w_{33}^3=\\ w_{33}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_3^2).\" alt=\"^*w_{31}^3=\\ w_{31}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_1^2),\\\\^*w_{32}^3=\\ w_{32}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_2^2),\\\\^*w_{33}^3=\\ w_{33}^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)a_3^2).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f67\/083\/e98\/f67083e988ee29fa99b37cbab7cbea6e.svg\" width=\"697\" height=\"138\"\/><\/p>\n<p><strong>\u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{b}^3\" alt=\"\\mathbf{b}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bf8\/d0d\/796\/bf8d0d796601c4e68bd854b64d5b7595.svg\" width=\"21\" height=\"21\"\/>:<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_2\" id=\"anchor_4_2\"><\/a><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial\\mathbf{b}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial\\mathbf{b}^3}.\" alt=\"\\frac{\\partial C}{\\partial\\mathbf{b}^3}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial\\mathbf{b}^3}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7c2\/c5a\/afb\/7c2c5aafb8e8e0b91b2e4f15012bc353.svg\" width=\"346\" height=\"64\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_1^3\" alt=\"b_1^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7cb\/dcc\/6c0\/7cbdcc6c099805f6fb6a25966bdfee17.svg\" width=\"17\" height=\"25\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_1^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_1^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_1^3}),\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_1^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_1^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_1^3}),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3eb\/ad8\/373\/3ebad83736076ed7ddb9c8215952624d.svg\" width=\"554\" height=\"46\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}1+0+0).\" alt=\"\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}1+0+0).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/361\/563\/621\/36156362146764186141eb5cd6189b07.svg\" width=\"362\" height=\"62\"\/><\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\frac{\\partial C}{\\partial b_1^3}\" alt=\"\\frac{\\partial C}{\\partial b_1^3}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f31\/577\/ce0\/f31577ce0934a68d97e33430579ae8ca.svg\" width=\"35\" height=\"51\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)}\\left(1-\\frac{e^{x_1^3}}{1+e^{x_1^3}}\\right)\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right).\" alt=\"\\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)}\\left(1-\\frac{e^{x_1^3}}{1+e^{x_1^3}}\\right)\\\\\u0438\u043b\u0438 \\frac{\\partial C}{\\partial b_1^3}=-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0ad\/25b\/6de\/0ad25b6dec3a517ec07c5ecc1e2a9b4a.svg\" width=\"697\" height=\"117\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_1^3\" alt=\"b_1^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7d3\/6e7\/0b2\/7d36e70b2fce4130a4afa8b53f4a475d.svg\" width=\"17\" height=\"25\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*b_1^3=\\ b_1^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)).\" alt=\"^*b_1^3=\\ b_1^3-\\eta(-\\frac{2}{3}\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/45b\/f73\/586\/45bf735867d21edeec02cc5dd444a633.svg\" width=\"413\" height=\"42\"\/><\/p>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_2^3\" alt=\"b_2^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/201\/f31\/44d\/201f3144d8dcca4179863e2466090101.svg\" width=\"17\" height=\"25\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_3^3\" alt=\"b_3^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c83\/4e4\/25c\/c834e425c9f0d0fcf4a9a361bc258364.svg\" width=\"17\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_2^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_2^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_2^3}),\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_2^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_2^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_2^3}),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/75c\/c6d\/3cd\/75cc6d3cd529ac0963654b86001a87f4.svg\" width=\"554\" height=\"46\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}(0+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_2^2}+0),\\\\\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right).\" alt=\"\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}(0+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_2^2}+0),\\\\\\frac{\\partial C}{\\partial b_2^3}=-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/9a0\/e06\/664\/9a0e066643aba490926e7a02e00d63ca.svg\" width=\"697\" height=\"119\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_3^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_3^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_3^3}),\" alt=\"\\scriptsize\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial b_3^3}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial b_3^3}+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_3^3}),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3bb\/88b\/7aa\/3bb88b7aa921dd484fd262e0a720b60c.svg\" width=\"554\" height=\"46\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}(0+0+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_3^2}),\\\\\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right).\" alt=\"\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}(0+0+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial b_3^2}),\\\\\\frac{\\partial C}{\\partial b_3^3}=-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3d1\/f57\/b34\/3d1f57b34053f60480bb85d89d764058.svg\" width=\"697\" height=\"129\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_2^3\" alt=\"b_2^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/80b\/b7c\/c01\/80bb7cc01c8e2f08894a30ce24026d82.svg\" width=\"17\" height=\"25\"\/> \u0438<img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_3^3\" alt=\"b_3^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/104\/4eb\/269\/1044eb26987ff13ba5badf0d1064509b.svg\" width=\"17\" height=\"26\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*b_2^3=\\ b_2^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)),\\\\^*b_3^3=\\ b_3^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)).\" alt=\"^*b_2^3=\\ b_2^3-\\eta(-\\frac{2}{3}\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)),\\\\^*b_3^3=\\ b_3^3-\\eta(-\\frac{2}{3}\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ba0\/809\/feb\/ba0809feb439fb1f30d3304776251118.svg\" width=\"697\" height=\"90\"\/><\/p>\n<p><strong>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^2\" alt=\"\\mathbf{W}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/980\/173\/d15\/980173d15dc504f3cad1ec1c55371622.svg\" width=\"32\" height=\"21\"\/>. \u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^2\" alt=\"w_{11}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6ac\/892\/6bf\/6ac8926bfa4ab8864c01e1c46b81c976.svg\" width=\"29\" height=\"24\"\/> \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^2\" alt=\"\\mathbf{W}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/df1\/d52\/3aa\/df1d523aa1d13172cdaa7293a4030c57.svg\" width=\"32\" height=\"21\"\/>. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_3\" id=\"anchor_4_3\"><\/a><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"x_1^3=w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3,\\\\x_2^3=w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3,\\\\x_3^3=w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3,\" alt=\"x_1^3=w_{11}^3a_1^2+w_{12}^3a_2^2+w_{13}^3a_3^2+b_1^3,\\\\x_2^3=w_{21}^3a_1^2+w_{22}^3a_2^2+w_{23}^3a_3^2+b_2^3,\\\\x_3^3=w_{31}^3a_1^2+w_{32}^3a_2^2+w_{33}^3a_3^2+b_3^3,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/298\/e44\/885\/298e44885acff24956d84058b1a1389e.svg\" width=\"697\" height=\"87\"\/><\/p>\n<p>\u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"a_1^2=\\ f(x_1^2)\\ =\\ f(w_{11}^2x_1^1+w_{12}^2x_2^1+w_{13}^2x_3^1+b_1^2),\\\\a_2^2=\\ f(x_2^2)\\ =f(w_{21}^2x_1^1+w_{22}^2x_2^1+w_{23}^2x_3^1+b_2^2),\\\\a_3^2=\\ \\ f(x_3^2)\\ =f(w_{31}^2x_1^1+w_{32}^2x_2^1+w_{33}^2x_3^1+b_3^2),\" alt=\"a_1^2=\\ f(x_1^2)\\ =\\ f(w_{11}^2x_1^1+w_{12}^2x_2^1+w_{13}^2x_3^1+b_1^2),\\\\a_2^2=\\ f(x_2^2)\\ =f(w_{21}^2x_1^1+w_{22}^2x_2^1+w_{23}^2x_3^1+b_2^2),\\\\a_3^2=\\ \\ f(x_3^2)\\ =f(w_{31}^2x_1^1+w_{32}^2x_2^1+w_{33}^2x_3^1+b_3^2),\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/2ec\/b67\/a98\/2ecb67a981ca3112579e7daa7f62ce73.svg\" width=\"697\" height=\"85\"\/><\/p>\n<p>\u0442\u043e\u0433\u0434\u0430 \u0441\u0443\u043c\u043c\u0430 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^2\" alt=\"w_{11}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/32f\/e65\/1cf\/32fe651cffdc632d9c2d268e7611d24d.svg\" width=\"29\" height=\"24\"\/> \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^2\" alt=\"\\mathbf{W}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/e77\/587\/f15\/e77587f157ea41856b4245bcc417efce.svg\" width=\"32\" height=\"21\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2},\" alt=\"\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2},\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ae7\/a07\/02c\/ae7a0702cf80acee8beda105596604e5.svg\" width=\"438\" height=\"64\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}),\\\\\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}w_{11}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}w_{21}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}w_{31}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1),\\\\\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial w_{11}^2}),\\\\\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}w_{11}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}w_{21}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}w_{31}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)x_1^1),\\\\\\frac{\\partial C}{\\partial w_{11}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_1^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6eb\/55a\/039\/6eb55a039f5af44eaa7e0b6cb05aae97.svg\" width=\"515\" height=\"327\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0439 \u0432\u0435\u0441) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^2\" alt=\"w_{11}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/cc2\/1b1\/e51\/cc21b1e519e4a0008599bba5b13056e8.svg\" width=\"29\" height=\"24\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{11}^2=\\ w_{11}^2-\\eta\\frac{\\partial C}{\\partial w_{11}^2}.\" alt=\"^*w_{11}^2=\\ w_{11}^2-\\eta\\frac{\\partial C}{\\partial w_{11}^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/633\/56e\/aca\/63356eacab3b4b2bb3038993337c89ab.svg\" width=\"184\" height=\"51\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0438 \u0438\u0445 \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{W}^2\" alt=\"\\mathbf{W}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dc3\/de0\/fa0\/dc3de0fa07aa34e17ef1533b6ad64d70.svg\" width=\"32\" height=\"21\"\/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{12}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{12}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_2^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/1e6\/5ca\/cea\/1e65cacea076d20fec5a1237db6e82b2.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{13}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{13}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)x_3^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a48\/d91\/c7d\/a48d91c7dbbff78e60bfc6fe2a7a9e87.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{12}^2=\\ w_{12}^2-\\eta\\frac{\\partial C}{\\partial w_{12}^2}, ^*w_{13}^2=\\ w_{13}^2-\\eta\\frac{\\partial C}{\\partial w_{13}^2}.\" alt=\"^*w_{12}^2=\\ w_{12}^2-\\eta\\frac{\\partial C}{\\partial w_{12}^2}, ^*w_{13}^2=\\ w_{13}^2-\\eta\\frac{\\partial C}{\\partial w_{13}^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ed8\/c71\/88e\/ed8c7188e71a4c3becb934006e7692cb.svg\" width=\"371\" height=\"51\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{21}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{21}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_1^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b5d\/774\/381\/b5d7743819c6abc1e2cf6a6f2f494c25.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather} \\frac{\\partial C}{\\partial w_{22}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather} \\frac{\\partial C}{\\partial w_{22}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_2^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0e1\/328\/e53\/0e1328e534cf717b826576e4cdd3b250.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{23}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{23}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)x_3^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a87\/8b7\/2da\/a878b72da12bc5077e034c023369e475.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{21}^2=\\ w_{21}^2-\\eta\\frac{\\partial C}{\\partial w_{21}^2}, ^*w_{22}^2=\\ w_{22}^2-\\eta\\frac{\\partial C}{\\partial w_{22}^2},\\\\^*w_{23}^2=\\ w_{23}^2-\\eta\\frac{\\partial C}{\\partial w_{23}^2}.\" alt=\"^*w_{21}^2=\\ w_{21}^2-\\eta\\frac{\\partial C}{\\partial w_{21}^2}, ^*w_{22}^2=\\ w_{22}^2-\\eta\\frac{\\partial C}{\\partial w_{22}^2},\\\\^*w_{23}^2=\\ w_{23}^2-\\eta\\frac{\\partial C}{\\partial w_{23}^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/eb8\/f7e\/88e\/eb8f7e88e1aa32396e7922d6e4c275b9.svg\" width=\"697\" height=\"107\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{31}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{31}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_1^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/542\/f5d\/fda\/542f5dfdab48d588ddaa1c8075b55f51.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{32}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{32}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_2^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dc6\/5b0\/502\/dc65b05024cceae69999d68fd8ea6985.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{33}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial w_{33}^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)x_3^1).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b08\/a62\/705\/b08a62705d4612bb30d9f55fcfa652e5.svg\" width=\"423\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*w_{31}^2=\\ w_{31}^2-\\eta\\frac{\\partial C}{\\partial w_{31}^2}, ^*w_{32}^2=\\ w_{32}^2-\\eta\\frac{\\partial C}{\\partial w_{32}^2},\\\\^*w_{33}^2=\\ w_{33}^2-\\eta\\frac{\\partial C}{\\partial w_{33}^2}.\" alt=\"^*w_{31}^2=\\ w_{31}^2-\\eta\\frac{\\partial C}{\\partial w_{31}^2}, ^*w_{32}^2=\\ w_{32}^2-\\eta\\frac{\\partial C}{\\partial w_{32}^2},\\\\^*w_{33}^2=\\ w_{33}^2-\\eta\\frac{\\partial C}{\\partial w_{33}^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d05\/8b2\/285\/d058b228532a684003ea2d2af9ccc6e6.svg\" width=\"697\" height=\"107\"\/><\/p>\n<p><strong>\u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{b}^2\" alt=\"\\mathbf{b}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3e0\/aad\/203\/3e0aad203828151370001ab14adbaded.svg\" width=\"21\" height=\"21\"\/>. \u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_1^2\" alt=\"b_1^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/41d\/dd0\/cfd\/41ddd0cfd1d02a0fca10d0886b4d072c.svg\" width=\"17\" height=\"24\"\/>:<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_4\" id=\"anchor_4_4\"><\/a><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2},\" alt=\"\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}\\sum_{i=1}^{3}{\\left(y_i-a_i^3\\right)\\frac{e^{x_i^3}}{\\left(1+e^{x_i^3}\\right)^2}}\\frac{\\partial x_i^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2},\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/382\/e8d\/842\/382e8d8420027df5073e278ffceb6d9f.svg\" width=\"416\" height=\"64\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}),\\\\\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}w_{11}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)\\\\+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}w_{21}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}w_{31}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)),\\\\\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}\\frac{\\partial x_1^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}\\frac{\\partial x_2^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}\\frac{\\partial x_3^3}{\\partial a_1^2}\\frac{\\partial a_1^2}{\\partial x_1^2}\\frac{\\partial x_1^2}{\\partial b_1^2}),\\\\\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)\\frac{e^{x_1^3}}{\\left(1+e^{x_1^3}\\right)^2}w_{11}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)\\\\+\\left(y_2-a_2^3\\right)\\frac{e^{x_2^3}}{\\left(1+e^{x_2^3}\\right)^2}w_{21}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)\\\\+\\left(y_3-a_3^3\\right)\\frac{e^{x_3^3}}{\\left(1+e^{x_3^3}\\right)^2}w_{31}^3\\frac{e^{x_1^2}}{\\left(1+e^{x_1^2}\\right)}\\left(1-\\frac{e^{x_1^2}}{1+e^{x_1^2}}\\right)),\\\\\\frac{\\partial C}{\\partial b_1^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{11}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{21}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{31}^3a_1^2\\left(x_1^2\\right)\\left(1-a_1^2\\left(x_1^2\\right)\\right)).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/64b\/701\/3fc\/64b7013fcaf6a1be25d2766ed66d98ce.svg\" width=\"493\" height=\"327\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043b\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_1^2\" alt=\"b_1^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d5b\/ef9\/3b8\/d5bef93b863b80714d5dc3c4c9637454.svg\" width=\"17\" height=\"24\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*b_1^2=\\ b_1^2-\\eta\\frac{\\partial C}{\\partial b_1^2}.\" alt=\"^*b_1^2=\\ b_1^2-\\eta\\frac{\\partial C}{\\partial b_1^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/aca\/661\/4b3\/aca6614b37d76d94de8fc68b4ef3ed0e.svg\" width=\"147\" height=\"51\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{b}^2\" alt=\"\\mathbf{b}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f44\/f1f\/f4b\/f44f1ff4bb4523f5b3688ad6347046c7.svg\" width=\"21\" height=\"21\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_2^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_2^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{12}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{22}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{32}^3a_2^2\\left(x_2^2\\right)\\left(1-a_2^2\\left(x_2^2\\right)\\right)).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a77\/866\/e0f\/a77866e0f97f6977085c9ae4d16e732b.svg\" width=\"399\" height=\"81\"\/><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_3^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)).\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}\\frac{\\partial C}{\\partial b_3^2}=-\\frac{2}{3}(\\left(y_1-a_1^3\\right)a_1^3\\left(x_1^3\\right)\\left(1-a_1^3\\left(x_1^3\\right)\\right)w_{13}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)\\\\+\\left(y_2-a_2^3\\right)a_2^3\\left(x_2^3\\right)\\left(1-a_2^3\\left(x_2^3\\right)\\right)w_{23}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)\\\\+\\left(y_3-a_3^3\\right)a_3^3\\left(x_3^3\\right)\\left(1-a_3^3\\left(x_3^3\\right)\\right)w_{33}^3a_3^2\\left(x_3^2\\right)\\left(1-a_3^2\\left(x_3^2\\right)\\right)).\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0c0\/f0f\/588\/0c0f0f5883e268f6ed78f1cc99c793c1.svg\" width=\"399\" height=\"81\"\/><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_2^2\" alt=\"b_2^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c8a\/f21\/8a9\/c8af218a97299ebe8f115fbc1f51da76.svg\" width=\"17\" height=\"24\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"b_3^2\" alt=\"b_3^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/029\/17e\/bed\/02917ebed2baeb564a017f004bcd5202.svg\" width=\"17\" height=\"25\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"^*b_2^2=\\ b_2^2-\\eta\\frac{\\partial C}{\\partial b_2^2}, ^*b_3^2=\\ b_3^2-\\eta\\frac{\\partial C}{\\partial b_3^2}.\" alt=\"^*b_2^2=\\ b_2^2-\\eta\\frac{\\partial C}{\\partial b_2^2}, ^*b_3^2=\\ b_3^2-\\eta\\frac{\\partial C}{\\partial b_3^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/57f\/7a8\/666\/57f7a86668401b81b12b7b4ea7e43997.svg\" width=\"297\" height=\"51\"\/><\/p>\n<h2>\u0427\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440<\/h2>\n<p><a class=\"anchor\" name=\"anchor_5\" id=\"anchor_5\"><\/a><\/p>\n<p>\u0417\u0430\u0434\u0430\u0447\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0430\u0435\u0442 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}^1\" alt=\"\\mathbf{x}^1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0a5\/5d6\/681\/0a55d66815afc0cff95510b34a16e52b.svg\" width=\"20\" height=\"21\"\/>\u0432 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{y}\" alt=\"\\mathbf{y}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ae8\/884\/93a\/ae888493ab40546156434b2f7f8c0e3b.svg\" width=\"12\" height=\"15\"\/>.<\/p>\n<p>\u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f \u043d\u0430\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044f <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{y}=\\mathbf{f}(\\mathbf{x}^1)\" alt=\"\\mathbf{y}=\\mathbf{f}(\\mathbf{x}^1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a99\/02c\/0e5\/a9902c0e5f1e96d9f82f4c8365f48433.svg\" width=\"82\" height=\"25\"\/>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0434\u043b\u044f \u043d\u0430\u0431\u043e\u0440\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x_i^1\" alt=\"x_i^1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/4cd\/61d\/a6e\/4cd61da6e771ee52d7c43a2af78b3c81.svg\" width=\"20\" height=\"25\"\/> \u0432\u044b\u0434\u0430\u0451\u0442 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0439 \u043d\u0430\u0431\u043e\u0440\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"y_i\" alt=\"y_i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c46\/993\/b5b\/c46993b5b0a285a3057ab7c8951a6a46.svg\" width=\"16\" height=\"15\"\/>. \u0417\u0430\u0434\u0430\u0447\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u00ab\u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c\u00bb, \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c, \u0442.\u0435. \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{y}=\\mathbf{f}(\\mathbf{x}^1)\" alt=\"\\mathbf{y}=\\mathbf{f}(\\mathbf{x}^1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/140\/820\/630\/14082063046db9f4d6413fa8bcc0d148.svg\" width=\"82\" height=\"25\"\/>. \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u0443\u0441\u043f\u0435\u0448\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043d\u0430 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c \u0441\u043b\u043e\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{a}^3\" alt=\"\\mathbf{a}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/52b\/349\/1fb\/52b3491fbedbb59db258b5d9c76450af.svg\" width=\"20\" height=\"21\"\/> \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0440\u0430\u0432\u043d\u044b \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{y}\" alt=\"\\mathbf{y}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/2ca\/d02\/909\/2cad029099391196475e26a1dca09544.svg\" width=\"12\" height=\"15\"\/> \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u0443\u0435\u043c\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p>\u0412\u044b\u0431\u0435\u0440\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{W}^2=\\left[\\begin{matrix}0.88&amp;0.39&amp;0.9\\\\0.37&amp;0.14&amp;0.41\\\\0.96&amp;0.5&amp;0.6\\\\\\end{matrix}\\right],\\mathbf{W}^3=\\left[\\begin{matrix}0.29&amp;0.57&amp;0.36\\\\0.73&amp;0.53&amp;0.68\\\\0.01&amp;0.02&amp;0.58\\\\\\end{matrix}\\right],\\\\\\mathbf{b}^2=\\left[\\begin{matrix}0.23\\\\0.89\\\\0.08\\\\\\end{matrix}\\right], \\mathbf{b}^3=\\left[\\begin{matrix}0.78\\\\0.83\\\\0.8\\\\\\end{matrix}\\right].\" alt=\"\\mathbf{W}^2=\\left[\\begin{matrix}0.88&amp;0.39&amp;0.9\\\\0.37&amp;0.14&amp;0.41\\\\0.96&amp;0.5&amp;0.6\\\\\\end{matrix}\\right],\\mathbf{W}^3=\\left[\\begin{matrix}0.29&amp;0.57&amp;0.36\\\\0.73&amp;0.53&amp;0.68\\\\0.01&amp;0.02&amp;0.58\\\\\\end{matrix}\\right],\\\\\\mathbf{b}^2=\\left[\\begin{matrix}0.23\\\\0.89\\\\0.08\\\\\\end{matrix}\\right], \\mathbf{b}^3=\\left[\\begin{matrix}0.78\\\\0.83\\\\0.8\\\\\\end{matrix}\\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/900\/997\/a15\/900997a1533912461462a1ec0e063655.svg\" width=\"697\" height=\"158\"\/><\/p>\n<p>\u0410 \u0442\u0430\u043a\u0436\u0435 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0438 \u0446\u0435\u043b\u0435\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f: <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf{x}^1=\\left[\\begin{matrix}0.03\\\\0.72\\\\0.49\\\\\\end{matrix}\\right], \\mathbf{y}=\\left[\\begin{matrix}0.93\\\\0.74\\\\0.17\\\\\\end{matrix}\\right].\" alt=\"\\mathbf{x}^1=\\left[\\begin{matrix}0.03\\\\0.72\\\\0.49\\\\\\end{matrix}\\right], \\mathbf{y}=\\left[\\begin{matrix}0.93\\\\0.74\\\\0.17\\\\\\end{matrix}\\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c3f\/7e1\/935\/c3f7e1935fb14118bd8fb6a33caa669b.svg\" width=\"236\" height=\"76\"\/><\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u043f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0451\u0432:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{a}^2=\\left[\\begin{matrix}0.726750911\\\\0.769022513\\\\0.681961335\\\\\\end{matrix}\\right], \\mathbf{a}^3=\\left[\\begin{matrix}0.842189045\\\\0.903072871\\\\0.771744079\\\\\\end{matrix}\\right].\" alt=\"\\mathbf{a}^2=\\left[\\begin{matrix}0.726750911\\\\0.769022513\\\\0.681961335\\\\\\end{matrix}\\right], \\mathbf{a}^3=\\left[\\begin{matrix}0.842189045\\\\0.903072871\\\\0.771744079\\\\\\end{matrix}\\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/9f8\/50f\/e7d\/9f850fe7dac1549ad7429c4b3fc72506.svg\" width=\"385\" height=\"78\"\/><\/p>\n<p>\u0414\u043b\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\eta=0.01\" alt=\"\\eta=0.01\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d79\/905\/6db\/d799056dbf5fc898f29252c3651943c0.svg\" width=\"71\" height=\"21\"\/>.<\/p>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0432\u043e\u0439 <a href=\"https:\/\/machine-learning.paperspace.com\/wiki\/epoch\" rel=\"noopener noreferrer nofollow\">\u044d\u043f\u043e\u0445\u0438<\/a> (<em>epoch<\/em>) \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0432\u0435\u0441\u043e\u0432 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^3\" alt=\"w_{11}^3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/53b\/4a1\/7f1\/53b4a17f1d6e9c16d3230d14880756c1.svg\" width=\"29\" height=\"25\"\/>\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"w_{11}^2\" alt=\"w_{11}^2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/678\/435\/045\/6784350452c3e3b965c43ff1c3d85a24.svg\" width=\"29\" height=\"24\"\/>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\scriptsize{\\begin{gather}^*w_{11}^3=0.29+0.01\\cdot \\frac{2}{3}\\cdot (0.93-0.842189045)\\cdot 0.842189045\\cdot (1-0.842189045)\\cdot 0.726750911=0.290056544,\\\\^*w_{11}^2=0.88+0.01\\cdot \\frac{2}{3}\\cdot (\\left(0.93-0.842189045\\right)\\cdot 0.842189045\\cdot \\left(1-0.842189045\\right)\\cdot 0.29\\cdot 0.726750911\\cdot\\\\ \\left(1-0.726750911\\right)\\cdot 0.03+\\left(0.74-0.903072871\\right)\\cdot \\:0.903072871\\cdot \\left(1-0.903072871\\right)\\cdot \\:0.73\\cdot \\:0.769022513\\cdot\\\\ \\left(1-0.769022513\\right)\\cdot \\:0.03+\\left(0.17-0.771744079\\right)\\cdot \\:0.771744079\\cdot \\left(1-0.771744079\\right)\\cdot \\:0.01\\cdot \\:0.681961335\\cdot\\\\ \\left(1-0.681961335\\right)\\cdot \\:0.03)=0.879999678.\\end{gather}}\" alt=\"\\scriptsize{\\begin{gather}^*w_{11}^3=0.29+0.01\\cdot \\frac{2}{3}\\cdot (0.93-0.842189045)\\cdot 0.842189045\\cdot (1-0.842189045)\\cdot 0.726750911=0.290056544,\\\\^*w_{11}^2=0.88+0.01\\cdot \\frac{2}{3}\\cdot (\\left(0.93-0.842189045\\right)\\cdot 0.842189045\\cdot \\left(1-0.842189045\\right)\\cdot 0.29\\cdot 0.726750911\\cdot\\\\ \\left(1-0.726750911\\right)\\cdot 0.03+\\left(0.74-0.903072871\\right)\\cdot \\:0.903072871\\cdot \\left(1-0.903072871\\right)\\cdot \\:0.73\\cdot \\:0.769022513\\cdot\\\\ \\left(1-0.769022513\\right)\\cdot \\:0.03+\\left(0.17-0.771744079\\right)\\cdot \\:0.771744079\\cdot \\left(1-0.771744079\\right)\\cdot \\:0.01\\cdot \\:0.681961335\\cdot\\\\ \\left(1-0.681961335\\right)\\cdot \\:0.03)=0.879999678.\\end{gather}}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/e2b\/2e4\/407\/e2b2e4407c7ff0aa014ecbb08f11961a.svg\" width=\"639\" height=\"124\"\/><\/p>\n<p>\u041d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u0441\u043e\u0432 \u0438 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0438 \u0441 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u043c\u0438 \u0440\u0430\u043d\u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438.<\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 10 000 \u044d\u043f\u043e\u0445 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432 \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0439 \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\mathbf{W}^2=\\left[\\begin{matrix}0.881449843&amp;0.424796239&amp;0.923680774\\\\0.372218081&amp;0.193233937&amp;0.446228651\\\\0.957567842&amp;0.441628217&amp;0.560274759\\\\\\end{matrix}\\right],\\\\\\mathbf{W}^3=\\left[\\begin{matrix}0.480573892&amp;0.772236752&amp;0.529654336\\\\0.394700365&amp;0.174298746&amp;0.381672097\\\\-0.771753134&amp;-0.808346904&amp;-0.127425218\\\\\\end{matrix}\\right],\\\\\\mathbf{a}^3=\\left[\\begin{matrix}0.913047169\\\\0.741592957\\\\0.173072228\\\\\\end{matrix}\\right].\" alt=\"\\mathbf{W}^2=\\left[\\begin{matrix}0.881449843&amp;0.424796239&amp;0.923680774\\\\0.372218081&amp;0.193233937&amp;0.446228651\\\\0.957567842&amp;0.441628217&amp;0.560274759\\\\\\end{matrix}\\right],\\\\\\mathbf{W}^3=\\left[\\begin{matrix}0.480573892&amp;0.772236752&amp;0.529654336\\\\0.394700365&amp;0.174298746&amp;0.381672097\\\\-0.771753134&amp;-0.808346904&amp;-0.127425218\\\\\\end{matrix}\\right],\\\\\\mathbf{a}^3=\\left[\\begin{matrix}0.913047169\\\\0.741592957\\\\0.173072228\\\\\\end{matrix}\\right].\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/9f6\/a7a\/63a\/9f6a7a63a8130c245b77fffa8ad573bf.svg\" width=\"697\" height=\"239\"\/><\/p>\n<h2>\u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0441\u043b\u043e\u0451\u0432<\/h2>\n<p><a class=\"anchor\" name=\"anchor_6\" id=\"anchor_6\"><\/a><\/p>\n<p>\u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0447\u0430\u0441\u0442\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u043e\u0448\u0438\u0431\u043a\u0438 \u0434\u043b\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0441 \u043e\u0434\u043d\u0438\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u043c \u0441\u043b\u043e\u0435\u043c. \u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0441 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u0445 \u0441\u043b\u043e\u0451\u0432.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\delta_i^L=\\left(y_i-a_i^L\\right)a_i^L\\left(x_i^L\\right)\\left(1-a_i^L\\left(x_i^L\\right)\\right),\\\\\\delta_i^l=\\sum_{k=1}^{n}{\\delta_k^{l+1}w_{ki}^{l+1}\\frac{\\partial a_i^l}{\\partial x_i^l}},\\\\\\frac{\\partial C}{\\partial w_{ij}^l}=\\frac{1}{n}\\delta_i^l\\frac{\\partial x_i^l}{\\partial w_{ij}^l},\\\\\\frac{\\partial C}{\\partial b_i^l}=\\delta_i^l,\" alt=\"\\delta_i^L=\\left(y_i-a_i^L\\right)a_i^L\\left(x_i^L\\right)\\left(1-a_i^L\\left(x_i^L\\right)\\right),\\\\\\delta_i^l=\\sum_{k=1}^{n}{\\delta_k^{l+1}w_{ki}^{l+1}\\frac{\\partial a_i^l}{\\partial x_i^l}},\\\\\\frac{\\partial C}{\\partial w_{ij}^l}=\\frac{1}{n}\\delta_i^l\\frac{\\partial x_i^l}{\\partial w_{ij}^l},\\\\\\frac{\\partial C}{\\partial b_i^l}=\\delta_i^l,\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/837\/88d\/e78\/83788de78c013c4ac0421cce623e3c5b.svg\" width=\"697\" height=\"210\"\/><\/p>\n<p>\u0433\u0434\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"L\" alt=\"L\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ac4\/654\/fdf\/ac4654fdfd48b9587a6221654b9c7fb3.svg\" width=\"13\" height=\"17\"\/>\u2014 \u043d\u043e\u043c\u0435\u0440 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u044f, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"i\" alt=\"i\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/cb4\/7c3\/299\/cb47c329910db67c66c135f29c816bc4.svg\" width=\"7\" height=\"16\"\/>\u2014 \u0438\u043d\u0434\u0435\u043a\u0441 \u0441\u0442\u0440\u043e\u043a\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432, <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"n\" alt=\"n\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ee1\/513\/ba6\/ee1513ba602bb07f9571835f5273bf75.svg\" width=\"12\" height=\"12\"\/>\u2014 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\delta\" alt=\"\\delta\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/871\/cf5\/223\/871cf5223b2a0433ff02ca2ae38bee73.svg\" width=\"9\" height=\"17\"\/>\u2014 \u043e\u0431\u043e\u0431\u0449\u0451\u043d\u043d\u043e\u0435 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Delta_rule\" rel=\"noopener noreferrer nofollow\">\u0434\u0435\u043b\u044c\u0442\u0430-\u043f\u0440\u0430\u0432\u0438\u043b\u043e<\/a> (<em>delta rule<\/em>).<\/p>\n<p>\u041d\u0430\u0434\u0435\u0435\u043c\u0441\u044f, \u0447\u0442\u043e \u0441\u0442\u0430\u0442\u044c\u044f \u0431\u0443\u0434\u0435\u0442 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u0439 \u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u043e\u0439 \u0434\u043b\u044f \u0432\u0441\u0435\u0445, \u043a\u0442\u043e \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0430\u0435\u0442 \u043a \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044e \u0433\u043b\u0443\u0431\u0438\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u044b\u0445 \u0441\u0435\u0442\u0435\u0439!<\/p>\n<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p> <!----> <!----><\/div>\n<p> <!----> <!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/post\/722422\/\"> https:\/\/habr.com\/ru\/post\/722422\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<div><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<p>\u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0432 \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f. \u0412 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0432\u0435\u0441\u044c \u043d\u0430\u0431\u043e\u0440 \u0444\u043e\u0440\u043c\u0443\u043b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0445 \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u043e\u0439 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438. \u0412 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u0441\u0442\u0430\u0442\u044c\u0438 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440.  <\/p>\n<p>\u00ab\u041f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f\u00bb (<em>fully connected<\/em>) \u2014 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043a\u0430\u0436\u0434\u044b\u0439 \u043d\u0435\u0439\u0440\u043e\u043d \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0441\u043b\u043e\u044f \u0441\u043e\u0435\u0434\u0438\u043d\u0451\u043d \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0441\u043b\u043e\u044f. \u00ab\u041f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f\u00bb (<em>feedforward<\/em>) \u2014 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u0438\u0433\u043d\u0430\u043b \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c \u0432 \u043e\u0434\u043d\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043e\u0442 \u0432\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u043a \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c\u0443 \u0441\u043b\u043e\u044e.<\/p>\n<p>\u041f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f (\u00ab<a href=\"https:\/\/en.wikipedia.org\/wiki\/Perceptron\" rel=\"noopener noreferrer nofollow\">\u043f\u0435\u0440\u0446\u0435\u043f\u0442\u0440\u043e\u043d<\/a>\u00bb) \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0438\u0439 \u0438 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0442\u0438\u043f\u0438\u0447\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0438\u0441\u043a\u0443\u0441\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438.<\/p>\n<h2>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/h2>\n<ol>\n<li>\n<p>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_2\" rel=\"noopener noreferrer nofollow\">\u0414\u0438\u0437\u0430\u0439\u043d \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_3\" rel=\"noopener noreferrer nofollow\">\u041f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_4\" rel=\"noopener noreferrer nofollow\">\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435<\/a><\/p>\n<p>4.1. <a href=\"https:\/\/anchor_4_1\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0432\u0435\u0441\u043e\u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u044b W^3<\/a><\/p>\n<p>4.2. <a href=\"https:\/\/anchor_4_2\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 b^3<\/a><\/p>\n<p>4.3. <a href=\"https:\/\/anchor_4_3\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0432\u0435\u0441\u043e\u0432 \u043c\u0430\u0442\u0440\u0438\u0446\u044b W^2<\/a><\/p>\n<p>4.4. <a href=\"https:\/\/anchor_4_4\" rel=\"noopener noreferrer nofollow\">\u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043d\u043e\u0432\u044b\u0445 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 b^2<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_5\" rel=\"noopener noreferrer nofollow\">\u0427\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440<\/a><\/p>\n<\/li>\n<li>\n<p><a href=\"https:\/\/anchor_6\" rel=\"noopener noreferrer nofollow\">\u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0441\u043b\u043e\u0451\u0432<\/a><\/p>\n<\/li>\n<\/ol>\n<h2>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/h2>\n<p>\u0418\u0441\u043a\u0443\u0441\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u0430 \u0442\u043e\u0447\u043d\u0435\u0435 \u2014 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Function_composition\" rel=\"noopener noreferrer nofollow\">\u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0435\u0439<\/a> (\u0441\u0443\u043f\u0435\u0440\u043f\u043e\u0437\u0438\u0446\u0438\u0435\u0439) \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/p>\n<p>\u0411\u044b\u043b\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043e (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Universal_approximation_theorem\" rel=\"noopener noreferrer nofollow\">George Cybenko, 1989<\/a>), \u0447\u0442\u043e \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u0430\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u0441 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u043d\u0438\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u043c \u0441\u043b\u043e\u0435\u043c \u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u044b\u043c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e \u043c\u043e\u0436\u0435\u0442 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Approximation\" rel=\"noopener noreferrer nofollow\">\u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c <\/a>\u043b\u044e\u0431\u0443\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0442.\u0435. \u043f\u043e \u0441\u0432\u043e\u0435\u0439 \u0441\u0443\u0442\u0438 \u043e\u043d\u0430 \u2014 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u044b\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0442\u043e\u0440.<\/p>\n<blockquote>\n<p>\u00ab\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0447\u0430\u0449\u0435, \u0447\u0435\u043c \u043c\u043e\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u0431\u044b \u043e\u0436\u0438\u0434\u0430\u0442\u044c. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430 \u2014 \u0421\u0442\u043e\u0443\u043d\u0430 \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e \u043b\u044e\u0431\u0430\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430 \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u0415\u0441\u043b\u0438 \u043e\u0441\u043b\u0430\u0431\u0438\u0442\u044c \u043d\u0430\u0448\u0438 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0438 \u0434\u0430\u043b\u0435\u0435, \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0440\u044f\u0434\u044b \u0422\u0435\u0439\u043b\u043e\u0440\u0430 \u0438 \u0440\u044f\u0434\u044b \u0424\u0443\u0440\u044c\u0435, \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u044e\u0449\u0438\u0435 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 (\u0432 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u0445 \u0438\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u0435\u0439 \u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f). \u0422\u043e\u0442 \u0444\u0430\u043a\u0442, \u0447\u0442\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c \u2014 \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u043e\u0431\u044b\u0447\u043d\u043e\u0435 \u044f\u0432\u043b\u0435\u043d\u0438\u0435 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u0434\u0430\u0435\u0442 \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u0435 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u044d\u043c\u043f\u0438\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u043d\u043e\u0433\u043e \u043c\u0430\u043b\u044b\u0445 \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432 \u043f\u043e\u043b\u043d\u043e\u0441\u0432\u044f\u0437\u043d\u044b\u0445 \u0441\u0435\u0442\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435, \u0441\u0443\u0434\u044f \u043f\u043e \u0432\u0441\u0435\u043c\u0443, \u0434\u0430\u044e\u0442 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438\u00bb.<\/p>\n<p>\u2014 \u0420\u0430\u043c\u0441\u0443\u043d\u0434\u0430\u0440 \u0411., \u0417\u0430\u0434\u0435 \u0420.\u0411. TensorFlow \u0434\u043b\u044f \u0433\u043b\u0443\u0431\u043e\u043a\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f. \u0421\u043f\u0431., 2019. \u0421. 101.   <\/p>\n<\/blockquote>\n<p>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435, \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<p>\u0433\u0434\u0435 \u2014 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u2014 \u043f\u0435\u0440\u0432\u044b\u0439 \u0441\u043b\u043e\u0439, \u2014 \u0432\u0442\u043e\u0440\u043e\u0439, \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0438 \u2014 \u0442\u0440\u0435\u0442\u0438\u0439 \u0441\u043b\u043e\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438, ,  \u2014 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0438 ,  \u2014 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0438 \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e \u0441\u043b\u043e\u0451\u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e,  \u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0441\u043b\u043e\u044f, \u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e, \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0441\u043b\u043e\u044f \u0438, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438.<\/p>\n<p>\u041c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0438\u043d\u044f\u0442\u0443\u044e \u0432 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 \u043f\u043e \u043d\u0435\u0439\u0440\u043e\u043d\u0430\u043c \u0441\u0435\u0442\u044f\u043c \u0437\u0430\u043f\u0438\u0441\u044c , \u0433\u0434\u0435  \u2014 \u0432\u0435\u043a\u0442\u043e\u0440-\u0441\u0442\u043e\u043b\u0431\u0435\u0446 (\u0432 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u0434 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e (\u043f\u043e \u0443\u043c\u043e\u043b\u0447\u0430\u043d\u0438\u044e) \u043f\u043e\u043d\u0438\u043c\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440-\u0441\u0442\u043e\u043b\u0431\u0435\u0446). \u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446  \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043e, \u0435\u0441\u043b\u0438 \u0447\u0438\u0441\u043b\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432  \u0440\u0430\u0432\u043d\u043e \u0447\u0438\u0441\u043b\u0443 \u0441\u0442\u0440\u043e\u043a . \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0447\u0438\u0441\u043b\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432  \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0440\u0430\u0432\u043d\u043e \u0447\u0438\u0441\u043b\u0443 \u0441\u0442\u0440\u043e\u043a  \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432  \u0438 .<\/p>\n<p><em>\u0414\u043b\u044f \u043a\u043e\u043c\u0444\u043e\u0440\u0442\u043d\u043e\u0433\u043e \u0447\u0442\u0435\u043d\u0438\u044f \u0441\u0442\u0430\u0442\u044c\u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043e\u0431\u043b\u0430\u0434\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u043c \u0437\u043d\u0430\u043d\u0438\u0435\u043c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b (\u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u2014 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u043d\u0430\u0434 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438), \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445.<\/em><\/p>\n<h2>\u0414\u0438\u0437\u0430\u0439\u043d \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/h2>\n<p><a class=\"anchor\" name=\"anchor_2\" id=\"anchor_2\"><\/a><\/p>\n<p>\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u0430\u044f \u0441\u0435\u0442\u044c \u0438\u043c\u0435\u0435\u0442 \u0442\u0440\u0438 \u0441\u043b\u043e\u044f \u0441 \u0442\u0440\u0435\u043c\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u0430\u043c\u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u0437 \u043d\u0438\u0445. \u041d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0433\u043e \u0447\u0435\u0440\u0435\u0437 \u0441\u0435\u0442\u044c \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0438\u0432\u0430\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sigmoid_function\" rel=\"noopener noreferrer nofollow\">\u0441\u0438\u0433\u043c\u043e\u0438\u0434<\/a> (<em>sigmoid<\/em>) \u043d\u0430 \u0441\u043a\u0440\u044b\u0442\u043e\u043c \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c \u0441\u043b\u043e\u044f\u0445:<\/p>\n<p>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u043d\u0441\u0442\u0432\u043e \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438\u043c\u0435\u044e\u0442 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0439 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u0438\u0437\u0432\u043b\u0435\u043a\u0430\u0442\u044c \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u0432 \u0434\u0430\u043d\u043d\u044b\u0445.<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0410\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438<\/figcaption><\/div>\n<\/figure>\n<p>\u041f\u0435\u0440\u0435\u043f\u0438\u0448\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c\u043e\u0439 \u0441\u0435\u0442\u0438 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u043d\u043d\u044b\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432:<\/p>\n<p>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u043f\u043e\u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043a \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0443 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 .<\/p>\n<h2>\u041f\u0440\u044f\u043c\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0441\u0438\u0433\u043d\u0430\u043b\u0430<\/h2>\n<p><a class=\"anchor\" name=\"anchor_3\" id=\"anchor_3\"><\/a><\/p>\n<p>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u043f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0447\u0435\u0440\u0435\u0437 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u0443\u044e \u0441\u0435\u0442\u044c:<\/p>\n<p>\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Loss_function\" rel=\"noopener noreferrer nofollow\">\u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438<\/a> (<em>cost function<\/em>)<\/p>\n<p>\u0433\u0434\u0435 \u2014 \u043d\u043e\u043c\u0435\u0440 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0433\u043e \u0446\u0435\u043b\u0435\u0432\u043e\u0433\u043e (\u0432\u0435\u043a\u0442\u043e\u0440\u0430 ) \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439,  \u2014 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0432 \u0440\u0430\u0437\u0432\u0451\u0440\u043d\u0443\u0442\u043e\u043c \u0432\u0438\u0434\u0435:<\/p>\n<p>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430\u043c \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0438\u043b\u044c\u043d\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u0442\u0435\u043a\u0443\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043e\u0442 \u0446\u0435\u043b\u0435\u0432\u044b\u0445.<\/p>\n<h2>\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435<\/h2>\n<p><a class=\"anchor\" name=\"anchor_4\" id=\"anchor_4\"><\/a><\/p>\n<p>\u0412 \u0441\u0443\u0449\u043d\u043e\u0441\u0442\u0438, \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Backpropagation\" rel=\"noopener noreferrer nofollow\">\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u043e\u0448\u0438\u0431\u043a\u0438<\/a> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u0430\u044f \u0438\u0434\u0435\u044f.<\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Gradient\" rel=\"noopener noreferrer nofollow\">\u0413\u0440\u0430\u0434\u0438\u0435\u043d\u0442<\/a> (\u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435) \u2014 \u0432\u0435\u043a\u0442\u043e\u0440, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0438\u0439 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430\u0438\u0441\u043a\u043e\u0440\u0435\u0439\u0448\u0435\u0433\u043e \u0440\u043e\u0441\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445. \u0412\u044b\u0447\u0438\u0442\u0430\u044f \u0438\u0437 \u0442\u0435\u043a\u0443\u0449\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0432\u0435\u0441\u043e\u0432 \u0438 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u0430\u043a \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 , \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0443 \u0438\u0437 \u0431\u043b\u0438\u0436\u0430\u0439\u0448\u0438\u0445 (\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438) \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u0438 \u0438, \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u043e\u0448\u0438\u0431\u043a\u0438. \u0421\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u043c\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430, \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0435\u0451 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, .<\/p>\n<p>\u042d\u0442\u043e\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gradient_descent\" rel=\"noopener noreferrer nofollow\">\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0441\u043f\u0443\u0441\u043a\u0430<\/a>. \u0418\u043d\u043e\u0433\u0434\u0430 \u043c\u043e\u0436\u0435\u0442 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0442\u044c \u043f\u0443\u0442\u0430\u043d\u0438\u0446\u0430 \u0438\u043b\u0438 \u043e\u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043b\u0435\u043d\u0438\u0435 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u0432, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u0442\u0435\u0441\u043d\u043e \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0438 \u043e\u0434\u0438\u043d \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u0440\u0443\u0433\u043e\u0433\u043e.<\/p>\n<p>\u041d\u0435\u0441\u043c\u043e\u0442\u0440\u044f \u043d\u0430 \u043f\u0440\u043e\u0441\u0442\u043e\u0442\u0443 \u0438 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c, \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0441\u043f\u0443\u0441\u043a\u0430 \u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0438\u043c\u0435\u0435\u0442 \u0441\u0432\u043e\u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Saddle_point\" rel=\"noopener noreferrer nofollow\">\u0441\u0435\u0434\u043b\u043e\u0432\u0430\u044f \u0442\u043e\u0447\u043a\u0430<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Maximum_and_minimum\" rel=\"noopener noreferrer nofollow\">\u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c<\/a>, \u043f\u0435\u0440\u0435\u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u043a\u0430 (<em>overtraining<\/em>) (\u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0435 \u0432 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c).<\/p>\n<p><strong>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b<\/strong> :<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_1\" id=\"anchor_4_1\"><\/a><\/p>\n<p>\u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443  \u2014 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430, \u0442\u043e ,<\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043d\u0430\u0439\u0434\u0451\u043c \u0435\u0451 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e:<\/p>\n<p>\u0412 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0438\u0437 \u0435\u0451 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432.<\/p>\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439  \u043c\u0430\u0442\u0440\u0438\u0446\u044b :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 . \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f :<\/p>\n<p>\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0448\u0438\u0431\u043a\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0430\u0441\u0442\u043d\u044b\u043c \u0441\u043b\u0443\u0447\u0430\u0435\u043c <a href=\"https:\/\/en.wikipedia.org\/wiki\/Automatic_differentiation\" rel=\"noopener noreferrer nofollow\">\u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/a>, \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0430\u043c \u0438 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u043e\u043c\u0443 \u0432\u0438\u0434\u0443.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0438  \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 ,  \u0438 :<\/p>\n<p>\u0433\u0434\u0435  (\u0438\u0301\u0442\u0430) \u2014 \u0431\u0443\u043a\u0432\u0430 \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0430\u043b\u0444\u0430\u0432\u0438\u0442\u0430, \u043e\u0431\u044b\u0447\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0430\u044f \u0434\u043b\u044f \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <a href=\"https:\/\/en.wikipedia.org\/wiki\/Learning_rate\" rel=\"noopener noreferrer nofollow\">\u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/a> (<em>learning rate<\/em>), \u0435\u0451 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043e \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \u043e\u0442 0 \u0434\u043e 1; * \u2014 \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439.<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b . \u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 :<\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f :<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445  \u0438  \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 ,  \u0438:<\/p>\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 :<\/p>\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u0438\u0433\u043c\u043e\u0438\u0434 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f :<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445  \u0438  \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f (\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0432\u0435\u0441\u0430) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 ,  \u0438 :<\/p>\n<p><strong>\u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> :<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_2\" id=\"anchor_4_2\"><\/a><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e 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(\u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0439 \u0432\u0435\u0441) \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0438 \u0438\u0445 \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b .<\/p>\n<p><strong>\u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0439\u0434\u0451\u043c \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u043e \u0432\u0441\u0435\u043c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/strong> . \u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 :<\/p>\n<p><a class=\"anchor\" name=\"anchor_4_4\" id=\"anchor_4_4\"><\/a><\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043b\u044f :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430 :<\/p>\n<p>\u041d\u0430\u0439\u0434\u0451\u043c \u043d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445  \u0438 :<\/p>\n<h2>\u0427\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440<\/h2>\n<p><a class=\"anchor\" name=\"anchor_5\" id=\"anchor_5\"><\/a><\/p>\n<p>\u0417\u0430\u0434\u0430\u0447\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0430\u0435\u0442 \u0432 .<\/p>\n<p>\u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f \u043d\u0430\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044f , \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0434\u043b\u044f \u043d\u0430\u0431\u043e\u0440\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445  \u0432\u044b\u0434\u0430\u0451\u0442 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0439 \u043d\u0430\u0431\u043e\u0440\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 . \u0417\u0430\u0434\u0430\u0447\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u00ab\u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c\u00bb, \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c, \u0442.\u0435. \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e . \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u0443\u0441\u043f\u0435\u0448\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043d\u0430 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u043c \u0441\u043b\u043e\u0435  \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0440\u0430\u0432\u043d\u044b \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430  \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0438\u0440\u0443\u0435\u043c\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p>\u0412\u044b\u0431\u0435\u0440\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0439 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438:<\/p>\n<p>\u0410 \u0442\u0430\u043a\u0436\u0435 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0438 \u0446\u0435\u043b\u0435\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f: <\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u0440\u044f\u043c\u043e\u0433\u043e \u043f\u0440\u043e\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0441\u0438\u0433\u043d\u0430\u043b\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0451\u0432:<\/p>\n<p>\u0414\u043b\u044f \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 .<\/p>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0434\u043b\u044f \u043f\u0435\u0440\u0432\u043e\u0439 <a href=\"https:\/\/machine-learning.paperspace.com\/wiki\/epoch\" rel=\"noopener noreferrer nofollow\">\u044d\u043f\u043e\u0445\u0438<\/a> (<em>epoch<\/em>) \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u043e\u0431\u043d\u043e\u0432\u043b\u0451\u043d\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0432\u0435\u0441\u043e\u0432 \u0438 :<\/p>\n<p>\u041d\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u0441\u043e\u0432 \u0438 \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0439 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0438 \u0441 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u043c\u0438 \u0440\u0430\u043d\u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438.<\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 10 000 \u044d\u043f\u043e\u0445 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432 \u0438 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0439 \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 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\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u043e\u0439 \u0441\u0435\u0442\u0438 \u0441 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u0445 \u0441\u043b\u043e\u0451\u0432.<\/p>\n<p>\u0433\u0434\u0435 \u2014 \u043d\u043e\u043c\u0435\u0440 \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u044f, \u2014 \u0438\u043d\u0434\u0435\u043a\u0441 \u0441\u0442\u0440\u043e\u043a\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0435\u0441\u043e\u0432, \u2014 \u0447\u0438\u0441\u043b\u043e \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n<p>\u2014 \u043e\u0431\u043e\u0431\u0449\u0451\u043d\u043d\u043e\u0435 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Delta_rule\" rel=\"noopener noreferrer nofollow\">\u0434\u0435\u043b\u044c\u0442\u0430-\u043f\u0440\u0430\u0432\u0438\u043b\u043e<\/a> (<em>delta rule<\/em>).<\/p>\n<p>\u041d\u0430\u0434\u0435\u0435\u043c\u0441\u044f, \u0447\u0442\u043e \u0441\u0442\u0430\u0442\u044c\u044f \u0431\u0443\u0434\u0435\u0442 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u0439 \u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u043e\u0439 \u0434\u043b\u044f \u0432\u0441\u0435\u0445, \u043a\u0442\u043e \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0430\u0435\u0442 \u043a \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044e \u0433\u043b\u0443\u0431\u0438\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043d\u044b\u0445 \u0441\u0435\u0442\u0435\u0439!<\/p>\n<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p> <!----> <!----><\/div>\n<p> <!----> <!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/post\/722422\/\"> https:\/\/habr.com\/ru\/post\/722422\/<\/a><br \/><\/br><\/br><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-346753","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/346753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=346753"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/346753\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=346753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=346753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=346753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}