{"id":821,"date":"2026-09-15T08:30:34","date_gmt":"2026-09-15T08:30:34","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=821"},"modified":"2026-09-15T08:30:35","modified_gmt":"2026-09-15T08:30:35","slug":"kak-sozdat-nejroset","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/kak-sozdat-nejroset\/","title":{"rendered":"\u041a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c \u0441 \u043d\u0443\u043b\u044f: \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 Python"},"content":{"rendered":"<p><strong>\u041d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c (\u0438\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)<\/strong> &#8212; \u044d\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u0432 \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u043e\u0438 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432-\u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432, \u0430 \u043d\u0443\u0436\u043d\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u0443\u044e\u0442 \u0432\u0440\u0443\u0447\u043d\u0443\u044e, \u0430 \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u044e\u0442 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445. \u041d\u0438\u0436\u0435 \u044f \u043f\u043e\u043a\u0430\u0436\u0443, \u043a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u0442\u0430\u043a\u0443\u044e \u0441\u0435\u0442\u044c \u0441 \u043d\u0443\u043b\u044f \u043d\u0430 Python \u0438 numpy: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0446\u0435\u043b\u0438\u043a\u043e\u043c \u0434\u0430\u043c \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0443 XOR, \u0430 \u043f\u043e\u0442\u043e\u043c \u0440\u0430\u0437\u0431\u0435\u0440\u0443 \u0435\u0433\u043e \u043f\u043e \u0448\u0430\u0433\u0430\u043c &#8212; forward-\u043f\u0440\u043e\u0445\u043e\u0434, \u043e\u0448\u0438\u0431\u043a\u0443 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435.<\/p>\n<div class=\"oj-toc\" style=\"background:#f6f6f6;border-radius:8px;padding:14px 20px;margin:20px 0\">\n<p><strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/strong><\/p>\n<ol>\n<li><a href=\"#s1\">\u0418\u0437 \u0447\u0435\u0433\u043e \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c: \u043d\u0435\u0439\u0440\u043e\u043d, \u0441\u043b\u043e\u0439, \u0432\u0435\u0441\u0430, \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u044f<\/a><\/li>\n<li><a href=\"#s2\">\u041c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 Python<\/a><\/li>\n<li><a href=\"#s3\">\u0420\u0430\u0437\u0431\u043e\u0440 \u043f\u043e \u0448\u0430\u0433\u0430\u043c<\/a><\/li>\n<li><a href=\"#s4\">\u0427\u0442\u043e \u0434\u0430\u043b\u044c\u0448\u0435: \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0438 \u0432\u043c\u0435\u0441\u0442\u043e \u0440\u0443\u0447\u043d\u043e\u0433\u043e backprop<\/a><\/li>\n<li><a href=\"#s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/a><\/li>\n<li><a href=\"#s6\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/a><\/li>\n<li><a href=\"#s7\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<p>\u0421\u0435\u0442\u044c \u0432 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0443\u0447\u0435\u0431\u043d\u0430\u044f: \u0434\u0432\u0430 \u0441\u043b\u043e\u044f, \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u043c \u0441\u043f\u0443\u0441\u043a\u043e\u043c, \u0431\u0435\u0437 \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0430 &#8212; \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0443 \u0438\u0437\u043d\u0443\u0442\u0440\u0438, \u0430 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043f\u0440\u043e\u043c\u044b\u0448\u043b\u0435\u043d\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c. \u0412 \u043a\u043e\u043d\u0446\u0435 \u043f\u043e\u043a\u0430\u0436\u0443, \u0447\u0435\u043c \u044d\u0442\u0443 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0443 \u0437\u0430\u043c\u0435\u043d\u044f\u044e\u0442 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0432 2026 \u0433\u043e\u0434\u0443.<\/p>\n<h2 id=\"s1\">\u0418\u0437 \u0447\u0435\u0433\u043e \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c: \u043d\u0435\u0439\u0440\u043e\u043d, \u0441\u043b\u043e\u0439, \u0432\u0435\u0441\u0430, \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u044f<\/h2>\n<p>\u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043f\u0438\u0441\u0430\u0442\u044c \u043a\u043e\u0434, \u0440\u0430\u0437\u0432\u0435\u0434\u0443 \u043f\u044f\u0442\u044c \u0442\u0435\u0440\u043c\u0438\u043d\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u043e\u0432\u0438\u0447\u043a\u0438 \u0447\u0430\u0441\u0442\u043e \u043f\u0443\u0442\u0430\u044e\u0442. \u0414\u0430\u043b\u044c\u0448\u0435 \u0432 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043a\u0430\u0436\u0434\u044b\u0439 \u0438\u0437 \u043d\u0438\u0445 &#8212; \u044d\u0442\u043e \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0430\u044f \u0441\u0442\u0440\u043e\u043a\u0430 \u043a\u043e\u0434\u0430.<\/p>\n<ul>\n<li><strong>\u041d\u0435\u0439\u0440\u043e\u043d<\/strong> &#8212; \u043e\u0434\u0438\u043d \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442: \u043e\u043d \u0431\u0435\u0440\u0435\u0442 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u0442 \u043a\u0430\u0436\u0434\u043e\u0435 \u043d\u0430 \u0441\u0432\u043e\u0439 \u0432\u0435\u0441, \u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u0435\u0442 \u0438 \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u0442 \u0441\u0443\u043c\u043c\u0443 \u0447\u0435\u0440\u0435\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438.<\/li>\n<li><strong>\u0412\u0435\u0441\u0430<\/strong> &#8212; \u0447\u0438\u0441\u043b\u0430-\u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0443 \u0432\u0445\u043e\u0434\u043e\u0432 \u043d\u0435\u0439\u0440\u043e\u043d\u0430. \u0418\u043c\u0435\u043d\u043d\u043e \u0438\u0445 \u0441\u0435\u0442\u044c \u043c\u0435\u043d\u044f\u0435\u0442 \u043f\u0440\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438; \u0432 \u043a\u043e\u0434\u0435 \u044d\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u044b <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">W1<\/code> \u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">W2<\/code>.<\/li>\n<li><strong>\u0421\u043b\u043e\u0439<\/strong> &#8212; \u0433\u0440\u0443\u043f\u043f\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432, \u0440\u0430\u0431\u043e\u0442\u0430\u044e\u0449\u0438\u0445 \u043d\u0430\u0434 \u043e\u0434\u043d\u0438\u043c \u0432\u0445\u043e\u0434\u043e\u043c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e. \u041e\u0434\u0438\u043d \u0441\u043b\u043e\u0439 &#8212; \u044d\u0442\u043e \u043e\u0434\u043d\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0432\u0435\u0441\u043e\u0432 \u0438 \u043e\u0434\u043d\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440.<\/li>\n<li><strong>\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438<\/strong> &#8212; \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u0443\u043c\u043c\u044b (\u0443 \u043d\u0430\u0441 \u0441\u0438\u0433\u043c\u043e\u0438\u0434\u0430). \u0411\u0435\u0437 \u043d\u0435\u0435 \u0441\u0435\u0442\u044c \u0438\u0437 \u043b\u044e\u0431\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0441\u043b\u043e\u0435\u0432 \u043e\u0441\u0442\u0430\u043b\u0430\u0441\u044c \u0431\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0438 XOR \u0431\u044b \u043d\u0435 \u0440\u0435\u0448\u0438\u043b\u0430.<\/li>\n<li><strong>\u042d\u043f\u043e\u0445\u0430<\/strong> &#8212; \u043e\u0434\u0438\u043d \u043f\u043e\u043b\u043d\u044b\u0439 \u043f\u0440\u043e\u0445\u043e\u0434 \u043f\u043e \u0432\u0441\u0435\u043c \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c \u0441 \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u0432\u0435\u0441\u043e\u0432. \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 &#8212; \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e \u044d\u043f\u043e\u0445 \u043f\u043e\u0434\u0440\u044f\u0434.<\/li>\n<\/ul>\n<table>\n<thead>\n<tr>\n<th>\u0422\u0435\u0440\u043c\u0438\u043d<\/th>\n<th>\u0427\u0442\u043e \u044d\u0442\u043e<\/th>\n<th>\u0412 \u043a\u043e\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u041d\u0435\u0439\u0440\u043e\u043d<\/td>\n<td>\u0432\u0437\u0432\u0435\u0448\u0435\u043d\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u0430 \u0432\u0445\u043e\u0434\u043e\u0432 + \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u044f<\/td>\n<td>\u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u0441\u0442\u0440\u043e\u043a\u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">X @ W1<\/code><\/td>\n<\/tr>\n<tr>\n<td>\u0412\u0435\u0441\u0430<\/td>\n<td>\u043f\u043e\u0434\u0431\u0438\u0440\u0430\u0435\u043c\u044b\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b<\/td>\n<td><code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">W1<\/code>, <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">W2<\/code><\/td>\n<\/tr>\n<tr>\n<td>\u0421\u043b\u043e\u0439<\/td>\n<td>\u043d\u0430\u0431\u043e\u0440 \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432, \u043e\u0434\u043d\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446<\/td>\n<td><code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">sigmoid(X @ W1 + b1)<\/code><\/td>\n<\/tr>\n<tr>\n<td>\u0410\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u044f<\/td>\n<td>\u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c (\u0441\u0438\u0433\u043c\u043e\u0438\u0434\u0430)<\/td>\n<td>\u0444\u0443\u043d\u043a\u0446\u0438\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">sigmoid<\/code><\/td>\n<\/tr>\n<tr>\n<td>\u042d\u043f\u043e\u0445\u0430<\/td>\n<td>\u043f\u0440\u043e\u0445\u043e\u0434 \u043f\u043e \u0432\u0441\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c<\/td>\n<td>\u043e\u0434\u043d\u0430 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u044f \u0446\u0438\u043a\u043b\u0430 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">for<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0421\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 (feed-forward) &#8212; \u044d\u0442\u043e \u043a\u043e\u0433\u0434\u0430 \u0441\u0438\u0433\u043d\u0430\u043b \u0438\u0434\u0435\u0442 \u0441\u0442\u0440\u043e\u0433\u043e \u0432 \u043e\u0434\u043d\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0443: \u0432\u0445\u043e\u0434 -&gt; \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0441\u043b\u043e\u0439 -&gt; \u0432\u044b\u0445\u043e\u0434, \u0431\u0435\u0437 \u0446\u0438\u043a\u043b\u043e\u0432 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0445 \u0441\u0432\u044f\u0437\u0435\u0439. \u041d\u0430\u0448 \u043f\u0440\u0438\u043c\u0435\u0440 &#8212; \u0438\u043c\u0435\u043d\u043d\u043e \u0442\u0430\u043a\u0430\u044f \u0441\u0435\u0442\u044c \u0441 \u043e\u0434\u043d\u0438\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u043c \u0441\u043b\u043e\u0435\u043c.<\/p>\n<h2 id=\"s2\">\u041c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 Python<\/h2>\n<p>\u041d\u0438\u0436\u0435 &#8212; \u043f\u043e\u043b\u043d\u044b\u0439 \u0441\u043a\u0440\u0438\u043f\u0442. \u041e\u043d \u043a\u043e\u043f\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0446\u0435\u043b\u0438\u043a\u043e\u043c \u0438 \u0437\u0430\u043f\u0443\u0441\u043a\u0430\u0435\u0442\u0441\u044f \u043d\u0430 Python 3 \u0441 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043d\u044b\u043c numpy (<code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">pip install numpy<\/code>). \u0417\u0430\u0434\u0430\u0447\u0430 &#8212; \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u0438\u0439 XOR: \u0441\u0435\u0442\u044c \u0434\u043e\u043b\u0436\u043d\u0430 \u0432\u044b\u0434\u0430\u0432\u0430\u0442\u044c 1, \u043a\u043e\u0433\u0434\u0430 \u0432\u0445\u043e\u0434\u044b \u0440\u0430\u0437\u043d\u044b\u0435, \u0438 0, \u043a\u043e\u0433\u0434\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435. \u041e\u0434\u043d\u0438\u043c \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u043c XOR \u043d\u0435 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0431\u0435\u0440\u0435\u043c \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0441\u043b\u043e\u0439.<\/p>\n<p>\u0410\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u0430 &#8212; 2-2-1: \u0434\u0432\u0430 \u0432\u0445\u043e\u0434\u0430, \u0434\u0432\u0430 \u043d\u0435\u0439\u0440\u043e\u043d\u0430 \u0432 \u0441\u043a\u0440\u044b\u0442\u043e\u043c \u0441\u043b\u043e\u0435, \u043e\u0434\u0438\u043d \u0432\u044b\u0445\u043e\u0434. <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">np.random.seed(1)<\/code> \u0444\u0438\u043a\u0441\u0438\u0440\u0443\u0435\u0442 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0435 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u0435\u0441\u0430, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0432\u043e\u0441\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043b\u0441\u044f \u043e\u0434\u0438\u043d \u0432 \u043e\u0434\u0438\u043d.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">numpy<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">as<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">np<\/span>\n\n<span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">seed<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #7F848E\"># \u0418\u0433\u0440\u0443\u0448\u0435\u0447\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 XOR: 4 \u043f\u0440\u0438\u043c\u0435\u0440\u0430, 2 \u0432\u0445\u043e\u0434\u0430 -&gt; 1 \u0432\u044b\u0445\u043e\u0434<\/span>\n<span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">array<\/span><span style=\"color: #ABB2BF\">([[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">]])<\/span>\n<span style=\"color: #E06C75\">Y<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">array<\/span><span style=\"color: #ABB2BF\">([[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">],<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">]])<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">z<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #D19A66\">1<\/span> <span style=\"color: #56B6C2\">\/<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">exp<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #E06C75\">z<\/span><span style=\"color: #ABB2BF\">))<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">sigmoid_deriv<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">):<\/span>        <span style=\"color: #7F848E\"># a = sigmoid(z)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">a<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">a<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #7F848E\"># \u0412\u0435\u0441\u0430 \u0434\u0432\u0443\u0445 \u0441\u043b\u043e\u0435\u0432: 2-&gt;2 (\u0441\u043a\u0440\u044b\u0442\u044b\u0439) \u0438 2-&gt;1 (\u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0439)<\/span>\n<span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">uniform<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E06C75\">b1<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">zeros<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">uniform<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E06C75\">b2<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">zeros<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">))<\/span>\n\n<span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0.5<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">epoch<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">20001<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #7F848E\"># forward: \u043f\u0440\u044f\u043c\u043e\u0439 \u043f\u0440\u043e\u0445\u043e\u0434<\/span>\n    <span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b1<\/span><span style=\"color: #ABB2BF\">)<\/span>      <span style=\"color: #7F848E\"># \u0432\u044b\u0445\u043e\u0434 \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0441\u043b\u043e\u044f<\/span>\n    <span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b2<\/span><span style=\"color: #ABB2BF\">)<\/span>    <span style=\"color: #7F848E\"># \u0432\u044b\u0445\u043e\u0434 \u0441\u0435\u0442\u0438<\/span>\n\n    <span style=\"color: #7F848E\"># loss: \u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430<\/span>\n    <span style=\"color: #E06C75\">loss<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">mean<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #E06C75\">Y<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">**<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n    <span style=\"color: #7F848E\"># backprop: \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<\/span>\n    <span style=\"color: #E06C75\">d_out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">Y<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">sigmoid_deriv<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">d_h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">d_out<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">sigmoid_deriv<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n    <span style=\"color: #7F848E\"># \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0441\u043e\u0432 (\u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u0439 \u0441\u043f\u0443\u0441\u043a)<\/span>\n    <span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">d_out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">b2<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">d_out<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sum<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">axis<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">keepdims<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #E5C07B\">True<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">d_h<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #E06C75\">b1<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">d_h<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sum<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">axis<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">keepdims<\/span><span style=\"color: #56B6C2\">=<\/span><span style=\"color: #E5C07B\">True<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">epoch<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #D19A66\">1<\/span> <span style=\"color: #56B6C2\">or<\/span> <span style=\"color: #E06C75\">epoch<\/span> <span style=\"color: #56B6C2\">%<\/span> <span style=\"color: #D19A66\">2000<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"epoch {<\/span><span style=\"color: #E06C75\">epoch<\/span><span style=\"color: #98C379\">:5d}  loss {<\/span><span style=\"color: #E06C75\">loss<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\\n\u041f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0441\u0435\u0442\u0438:\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">x<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">p<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">zip<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"{<\/span><span style=\"color: #E06C75\">x<\/span><span style=\"color: #98C379\">} -&gt; {<\/span><span style=\"color: #E06C75\">p<\/span><span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">]<\/span><span style=\"color: #98C379\">:.3f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u041e\u0436\u0438\u0434\u0430\u0435\u043c\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442: \u043e\u0448\u0438\u0431\u043a\u0430 \u043f\u0430\u0434\u0430\u0435\u0442 \u043e\u0442 \u044d\u043f\u043e\u0445\u0438 \u043a \u044d\u043f\u043e\u0445\u0435 \u043f\u043e\u0447\u0442\u0438 \u0434\u043e \u043d\u0443\u043b\u044f, \u0430 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0441\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043a \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u043c (\u043e\u043a\u043e\u043b\u043e 0 \u0434\u043b\u044f \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0432\u0445\u043e\u0434\u043e\u0432 \u0438 \u043e\u043a\u043e\u043b\u043e 1 \u0434\u043b\u044f \u0440\u0430\u0437\u043d\u044b\u0445). \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0432\u044b\u0432\u043e\u0434 \u043f\u0440\u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">seed(1)<\/code>:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">epoch     1  loss 0.2761\nepoch  2000  loss 0.0029\nepoch  4000  loss 0.0009\nepoch  6000  loss 0.0006\nepoch  8000  loss 0.0004\nepoch 10000  loss 0.0003\nepoch 12000  loss 0.0002\nepoch 14000  loss 0.0002\nepoch 16000  loss 0.0002\nepoch 18000  loss 0.0002\nepoch 20000  loss 0.0001\n\n\u041f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0441\u0435\u0442\u0438:\n[0 0] -&gt; 0.011\n[0 1] -&gt; 0.988\n[1 0] -&gt; 0.988\n[1 1] -&gt; 0.012\n<\/code><\/pre>\n<p>\u041e\u0448\u0438\u0431\u043a\u0430 \u0443\u043f\u0430\u043b\u0430 \u0441 0.2761 \u0434\u043e 0.0001 &#8212; \u0441\u0435\u0442\u044c \u043e\u0431\u0443\u0447\u0438\u043b\u0430\u0441\u044c. \u0414\u0430\u043b\u044c\u0448\u0435 \u0440\u0430\u0437\u0431\u0435\u0440\u0443, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0432\u043d\u0443\u0442\u0440\u0438 \u0446\u0438\u043a\u043b\u0430.<\/p>\n<h2 id=\"s3\">\u0420\u0430\u0437\u0431\u043e\u0440 \u043f\u043e \u0448\u0430\u0433\u0430\u043c<\/h2>\n<h3>1. Forward: \u043f\u0440\u044f\u043c\u043e\u0439 \u043f\u0440\u043e\u0445\u043e\u0434<\/h3>\n<p>\u041d\u0430 \u043f\u0440\u044f\u043c\u043e\u043c \u043f\u0440\u043e\u0445\u043e\u0434\u0435 \u0441\u0435\u0442\u044c \u0441\u0447\u0438\u0442\u0430\u0435\u0442 \u0441\u0432\u043e\u0439 \u043e\u0442\u0432\u0435\u0442. \u0414\u0430\u043d\u043d\u044b\u0435 \u0438\u0434\u0443\u0442 \u0447\u0435\u0440\u0435\u0437 \u0434\u0432\u0430 \u0441\u043b\u043e\u044f:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b1<\/span><span style=\"color: #ABB2BF\">)<\/span>      <span style=\"color: #7F848E\"># \u0432\u044b\u0445\u043e\u0434 \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0441\u043b\u043e\u044f<\/span>\n<span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b2<\/span><span style=\"color: #ABB2BF\">)<\/span>    <span style=\"color: #7F848E\"># \u0432\u044b\u0445\u043e\u0434 \u0441\u0435\u0442\u0438<\/span><\/code><\/pre>\n<p><code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">X @ W1<\/code> &#8212; \u044d\u0442\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0432\u0445\u043e\u0434\u043e\u0432 \u043d\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u0432\u0435\u0441\u043e\u0432, \u0442\u043e \u0441\u0430\u043c\u043e\u0435 \u00ab\u043d\u0435\u0439\u0440\u043e\u043d = \u0432\u0437\u0432\u0435\u0448\u0435\u043d\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u0430\u00bb, \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0435 \u0441\u0440\u0430\u0437\u0443 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0447\u0435\u0442\u044b\u0440\u0435\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432. \u041f\u0440\u0438\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0441\u043c\u0435\u0449\u0435\u043d\u0438\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">b1<\/code> \u0438 \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u043c \u0447\u0435\u0440\u0435\u0437 \u0441\u0438\u0433\u043c\u043e\u0438\u0434\u0443 &#8212; \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0432\u044b\u0445\u043e\u0434 \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0441\u043b\u043e\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">h<\/code>. \u0422\u043e\u0442 \u0436\u0435 \u043f\u0440\u0438\u0435\u043c \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u043c \u0434\u043b\u044f \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0441\u043b\u043e\u044f \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043e\u0442\u0432\u0435\u0442 \u0441\u0435\u0442\u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">out<\/code> (\u0447\u0438\u0441\u043b\u0430 \u043e\u0442 0 \u0434\u043e 1).<\/p>\n<h3>2. Loss: \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0435\u0442\u044c \u043e\u0448\u0438\u0431\u043b\u0430\u0441\u044c<\/h3>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">loss<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">np<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">mean<\/span><span style=\"color: #ABB2BF\">((<\/span><span style=\"color: #E06C75\">Y<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">**<\/span> <span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u042d\u0442\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430 (MSE): \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 \u043e\u0436\u0438\u0434\u0430\u0435\u043c\u044b\u043c <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">Y<\/code> \u0438 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u043c <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">out<\/code>, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0438 \u0443\u0441\u0440\u0435\u0434\u043d\u0435\u043d\u043d\u0430\u044f. \u0427\u0435\u043c \u043c\u0435\u043d\u044c\u0448\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">loss<\/code>, \u0442\u0435\u043c \u0431\u043b\u0438\u0436\u0435 \u043e\u0442\u0432\u0435\u0442\u044b \u0441\u0435\u0442\u0438 \u043a \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u043c. \u0418\u043c\u0435\u043d\u043d\u043e \u044d\u0442\u0443 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u0442\u044c.<\/p>\n<h3>3. Backprop: \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<\/h3>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">d_out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">Y<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">sigmoid_deriv<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">d_h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">d_out<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W2<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">sigmoid_deriv<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>Backpropagation \u043e\u0442\u0432\u0435\u0447\u0430\u0435\u0442 \u043d\u0430 \u0432\u043e\u043f\u0440\u043e\u0441: \u043a\u0430\u043a \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u0441 \u043f\u043e\u0432\u043b\u0438\u044f\u043b \u043d\u0430 \u043e\u0448\u0438\u0431\u043a\u0443. \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u00ab\u0434\u0435\u043b\u044c\u0442\u0443\u00bb \u0432\u044b\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">d_out<\/code> &#8212; \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0438 \u0432 \u043a\u0430\u043a\u0443\u044e \u0441\u0442\u043e\u0440\u043e\u043d\u0443 \u043e\u0448\u0438\u0431\u0441\u044f \u0432\u044b\u0445\u043e\u0434, \u0441 \u043f\u043e\u043f\u0440\u0430\u0432\u043a\u043e\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438. \u0417\u0430\u0442\u0435\u043c \u043f\u0440\u043e\u0431\u0440\u0430\u0441\u044b\u0432\u0430\u0435\u043c \u044d\u0442\u0443 \u0434\u0435\u043b\u044c\u0442\u0443 \u043d\u0430\u0437\u0430\u0434 \u0447\u0435\u0440\u0435\u0437 \u0432\u0435\u0441\u0430 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">W2<\/code> \u043d\u0430 \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0441\u043b\u043e\u0439 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0435\u0433\u043e \u0434\u0435\u043b\u044c\u0442\u0443 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">d_h<\/code>. \u0422\u0430\u043a \u043e\u0448\u0438\u0431\u043a\u0430 \u00ab\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f\u00bb \u043f\u043e \u0441\u043b\u043e\u044f\u043c \u043e\u0442 \u0432\u044b\u0445\u043e\u0434\u0430 \u043a\u043e \u0432\u0445\u043e\u0434\u0443.<\/p>\n<h3>4. \u041e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0441\u043e\u0432: \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u044b\u0439 \u0441\u043f\u0443\u0441\u043a<\/h3>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">d_out<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">-=<\/span> <span style=\"color: #E06C75\">lr<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">X<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">T<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">d_h<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0414\u0435\u043b\u044c\u0442\u044b \u0438 \u0432\u0445\u043e\u0434\u044b \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u043b\u043e\u044f \u0434\u0430\u044e\u0442 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 &#8212; \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043e\u0448\u0438\u0431\u043a\u0430 \u0440\u0430\u0441\u0442\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u0435\u0435 \u0432\u0441\u0435\u0433\u043e. \u0427\u0442\u043e\u0431\u044b \u043e\u0448\u0438\u0431\u043a\u0443 \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u0442\u044c, \u0434\u0435\u043b\u0430\u0435\u043c \u0448\u0430\u0433 \u0432 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u0443\u044e \u0441\u0442\u043e\u0440\u043e\u043d\u0443: \u0432\u044b\u0447\u0438\u0442\u0430\u0435\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">lr<\/code>. \u0421\u043c\u0435\u0449\u0435\u043d\u0438\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">b1<\/code> \u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">b2<\/code> \u043e\u0431\u043d\u043e\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0442\u0430\u043a \u0436\u0435. \u041f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u043c \u044d\u0442\u043e 20000 \u044d\u043f\u043e\u0445 &#8212; \u0438 \u0432\u0435\u0441\u0430 \u043f\u043e\u0434\u0441\u0442\u0440\u0430\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0442\u0430\u043a, \u0447\u0442\u043e \u0441\u0435\u0442\u044c \u0440\u0435\u0448\u0430\u0435\u0442 XOR.<\/p>\n<p>\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">lr<\/code> &#8212; \u044d\u0442\u043e \u0440\u0430\u0437\u043c\u0435\u0440 \u0448\u0430\u0433\u0430. \u0421\u043b\u0438\u0448\u043a\u043e\u043c \u0431\u043e\u043b\u044c\u0448\u043e\u0439 &#8212; \u043e\u0448\u0438\u0431\u043a\u0430 \u0441\u043a\u0430\u0447\u0435\u0442, \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0439 &#8212; \u0441\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043c\u0435\u0434\u043b\u0435\u043d\u043d\u043e. \u0417\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">0.5<\/code> \u0434\u043b\u044f \u044d\u0442\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0430\u0435\u0442 \u0443\u0441\u0442\u043e\u0439\u0447\u0438\u0432\u0443\u044e \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c.<\/p>\n<h3>\u0427\u0430\u0441\u0442\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430: \u0437\u0430\u0431\u044b\u0442\u044c \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c<\/h3>\n<p>\u041f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043f\u0440\u043e\u043c\u0430\u0445 &#8212; \u0443\u0431\u0440\u0430\u0442\u044c \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u044e \u0438\u0437 \u0441\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u0441\u043b\u043e\u044f, \u0434\u0443\u043c\u0430\u044f, \u0447\u0442\u043e \u00ab\u0441\u0443\u043c\u043c\u0430 \u0438 \u0442\u0430\u043a \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f\u00bb:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">X<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W1<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b1<\/span>          <span style=\"color: #7F848E\"># \u0431\u0435\u0437 sigmoid<\/span>\n<span style=\"color: #E06C75\">out<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">sigmoid<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">h<\/span> <span style=\"color: #56B6C2\">@<\/span> <span style=\"color: #E06C75\">W2<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">b2<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<p>\u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043f\u0440\u0438 <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">seed(1)<\/code>: \u043e\u0448\u0438\u0431\u043a\u0430 \u0437\u0430\u0441\u0442\u0440\u0435\u0432\u0430\u0435\u0442 \u043e\u043a\u043e\u043b\u043e <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">loss 0.5<\/code> \u0438 \u043d\u0435 \u043f\u0430\u0434\u0430\u0435\u0442, \u0430 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0432\u044b\u0440\u043e\u0436\u0434\u0430\u044e\u0442\u0441\u044f &#8212; \u0432\u0441\u0435 \u0441\u0442\u0440\u0435\u043c\u044f\u0442\u0441\u044f \u043a <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">1.0<\/code> \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0432\u0445\u043e\u0434\u0430, \u0438 XOR \u043d\u0435 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f. \u041f\u0440\u0438\u0447\u0438\u043d\u0430: \u0431\u0435\u0437 \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u0441\u043a\u0440\u044b\u0442\u044b\u0439 \u0441\u043b\u043e\u0439 \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0443 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u043c\u0443 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044e \u043f\u0435\u0440\u0435\u0434 \u0441\u0438\u0433\u043c\u043e\u0438\u0434\u043e\u0439, \u0430 XOR \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043c. \u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 &#8212; \u0432\u0435\u0440\u043d\u0443\u0442\u044c \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0441\u0442\u044c: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">h = sigmoid(X @ W1 + b1)<\/code>.<\/p>\n<h2 id=\"s4\">\u0427\u0442\u043e \u0434\u0430\u043b\u044c\u0448\u0435: \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0438 \u0432\u043c\u0435\u0441\u0442\u043e \u0440\u0443\u0447\u043d\u043e\u0433\u043e backprop<\/h2>\n<p>\u0420\u0443\u0447\u043d\u043e\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0448\u0435 \u043d\u0443\u0436\u0435\u043d, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0443. \u0412 \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u044b \u043d\u0435 \u0432\u044b\u0432\u043e\u0434\u044f\u0442 \u0440\u0443\u043a\u0430\u043c\u0438: \u0438\u0445 \u0441\u0447\u0438\u0442\u0430\u0435\u0442 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0432\u043d\u0443\u0442\u0440\u0438 \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0430. \u041d\u0430 2026 \u0433\u043e\u0434 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0435 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u044b &#8212; <strong>PyTorch<\/strong> \u0438 <strong>TensorFlow<\/strong> (\u0447\u0430\u0441\u0442\u043e \u0447\u0435\u0440\u0435\u0437 \u0443\u0434\u043e\u0431\u043d\u0443\u044e \u043d\u0430\u0434\u0441\u0442\u0440\u043e\u0439\u043a\u0443 Keras).<\/p>\n<p>\u0422\u0430 \u0436\u0435 \u0441\u0435\u0442\u044c \u043d\u0430 \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0435 &#8212; \u044d\u0442\u043e \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0442\u0440\u043e\u043a: \u0441\u043b\u043e\u0438 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0434\u0435\u043a\u043b\u0430\u0440\u0430\u0442\u0438\u0432\u043d\u043e, \u0430 forward, loss \u0438 backprop \u0431\u0435\u0440\u0435\u0442 \u043d\u0430 \u0441\u0435\u0431\u044f \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0430. \u041f\u043b\u044e\u0441 \u0440\u0430\u0431\u043e\u0442\u0430 \u043d\u0430 GPU, \u0433\u043e\u0442\u043e\u0432\u044b\u0435 \u0441\u043b\u043e\u0438 \u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440\u044b &#8212; \u0432\u0441\u0435 \u0442\u043e, \u0447\u0442\u043e \u0432 \u0443\u0447\u0435\u0431\u043d\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043f\u0438\u0448\u0435\u0448\u044c \u0441\u0430\u043c.<\/p>\n<p>\u0412\u0430\u0436\u043d\u0430\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430: \u043d\u0430\u0448 \u043f\u0440\u0438\u043c\u0435\u0440 &#8212; \u044d\u0442\u043e \u043f\u0440\u0438\u043d\u0446\u0438\u043f, \u0430 \u043d\u0435 \u0437\u0430\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u0434\u043b\u044f \u043f\u0440\u043e\u0434\u0430\u043a\u0448\u0435\u043d\u0430. \u041e\u043d \u043e\u0431\u0443\u0447\u0435\u043d \u043d\u0430 \u0447\u0435\u0442\u044b\u0440\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 XOR, \u0431\u0435\u0437 \u0440\u0430\u0437\u0431\u0438\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0443\u044e \u0438 \u0442\u0435\u0441\u0442\u043e\u0432\u0443\u044e \u0432\u044b\u0431\u043e\u0440\u043a\u0438, \u0431\u0435\u0437 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0438 \u043a\u043e\u043d\u0442\u0440\u043e\u043b\u044f \u043f\u0435\u0440\u0435\u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f. \u041e\u043d \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u0441\u0435\u0442\u044c \u0443\u0447\u0438\u0442\u0441\u044f, \u043d\u043e \u043d\u0435 \u0433\u043e\u0434\u0438\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u0442\u0435\u043c \u0431\u043e\u043b\u0435\u0435 \u0434\u043b\u044f \u00ab\u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0440\u044b\u043d\u043a\u0430\u00bb.<\/p>\n<h2 id=\"s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u041d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c &#8212; \u044d\u0442\u043e \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u0435\u0442 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0432\u0445\u043e\u0434\u0430 \u0432 \u0432\u044b\u0445\u043e\u0434 \u043d\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043f\u0440\u0430\u0432\u0438\u043b, \u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u043c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445 \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u043e\u0438 \u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432.<\/li>\n<li>\u041c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u0440\u0430\u0431\u043e\u0447\u0443\u044e \u0441\u0435\u0442\u044c \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u043d\u0430 Python \u0438 numpy \u0432 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0434\u0435\u0441\u044f\u0442\u043a\u043e\u0432 \u0441\u0442\u0440\u043e\u043a: \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0448\u0435 \u0440\u0435\u0448\u0430\u0435\u0442 XOR \u0438 \u0441\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0441 \u043e\u0448\u0438\u0431\u043a\u0438 0.2761 \u0434\u043e 0.0001.<\/li>\n<li>\u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 &#8212; \u044d\u0442\u043e \u0446\u0438\u043a\u043b \u0438\u0437 \u0447\u0435\u0442\u044b\u0440\u0435\u0445 \u0448\u0430\u0433\u043e\u0432: forward (\u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043e\u0442\u0432\u0435\u0442), loss (\u0438\u0437\u043c\u0435\u0440\u0438\u0442\u044c \u043e\u0448\u0438\u0431\u043a\u0443), backprop (\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0448\u0438\u0431\u043a\u0443 \u043f\u043e \u0441\u043b\u043e\u044f\u043c), \u043e\u0431\u043d\u043e\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0441\u043e\u0432 (\u0448\u0430\u0433 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043d\u043e\u0433\u043e \u0441\u043f\u0443\u0441\u043a\u0430).<\/li>\n<li>\u041d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0430\u043a\u0442\u0438\u0432\u0430\u0446\u0438\u0438 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u0430: \u0431\u0435\u0437 \u043d\u0435\u0435 \u0441\u043b\u043e\u0438 \u0441\u0445\u043b\u043e\u043f\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c, \u0438 XOR \u043d\u0435 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f.<\/li>\n<li>\u0423\u0447\u0435\u0431\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0431\u0435\u0437 \u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a\u0430 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0443, \u043d\u043e \u043d\u0435 \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u0442 \u0440\u0435\u0430\u043b\u044c\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c: \u0432 2026 \u0433\u043e\u0434\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0431\u0435\u0440\u0443\u0442 PyTorch \u0438\u043b\u0438 TensorFlow.<\/li>\n<\/ul>\n<h2 id=\"s6\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/h2>\n<p>\u0422\u043e\u0442 \u0436\u0435 \u0446\u0438\u043a\u043b forward &#8212; loss &#8212; backprop \u043b\u0435\u0436\u0438\u0442 \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u044b\u0445 \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u0435\u0439: \u0440\u0430\u0441\u043f\u043e\u0437\u043d\u0430\u0432\u0430\u043d\u0438\u044f \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438 \u0442\u0435\u043a\u0441\u0442\u0430, \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0430\u0446\u0438\u0439, \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u043e\u0432 \u043f\u043e \u0442\u0430\u0431\u043b\u0438\u0447\u043d\u044b\u043c \u0434\u0430\u043d\u043d\u044b\u043c. \u0420\u0430\u0437\u043d\u0438\u0446\u0430 \u0441 \u0443\u0447\u0435\u0431\u043d\u044b\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u043c &#8212; \u0432 \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0435, \u043e\u0431\u044a\u0435\u043c\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u0430\u0445 (\u0444\u0440\u0435\u0439\u043c\u0432\u043e\u0440\u043a \u0438 GPU \u0432\u043c\u0435\u0441\u0442\u043e \u0440\u0443\u0447\u043d\u043e\u0433\u043e numpy), \u043d\u043e \u043f\u0440\u0438\u043d\u0446\u0438\u043f \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0442\u043e\u0442 \u0436\u0435.<\/p>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p style=\"margin:0 0 8px\"><strong>\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0442\u0435\u043c\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/strong><\/p>\n<p>\u0415\u0441\u043b\u0438 \u0445\u043e\u0447\u0435\u0442\u0441\u044f \u0434\u043e\u0439\u0442\u0438 \u043e\u0442 \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0434\u043e \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0441\u0438\u0441\u0442\u0435\u043c\u043d\u043e, \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043a\u0443\u0440\u0441 <a href=\"https:\/\/otus.ru\/lessons\/ml-basic\/?utm_source=oj&amp;utm_medium=article&amp;utm_campaign=kak-sozdat-nejroset&amp;utm_content=course\">Machine Learning. Basic<\/a> \u0432 Otus &#8212; \u0442\u0430\u043c \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u044e\u0442, \u043a\u0430\u043a \u0433\u043e\u0442\u043e\u0432\u0438\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u0435, \u043e\u0431\u0443\u0447\u0430\u0442\u044c \u0438 \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435. \u041f\u043e\u043d\u044f\u0442\u044c \u0444\u043e\u0440\u043c\u0430\u0442 \u0437\u0430\u043d\u044f\u0442\u0438\u0439 \u0438 \u0443\u0440\u043e\u0432\u0435\u043d\u044c \u043f\u043e\u0433\u0440\u0443\u0436\u0435\u043d\u0438\u044f \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 <a href=\"https:\/\/otus.ru\/events\/?utm_source=oj&amp;utm_medium=article&amp;utm_campaign=kak-sozdat-nejroset&amp;utm_content=events\">\u0431\u0435\u0441\u043f\u043b\u0430\u0442\u043d\u044b\u0435 \u0432\u0435\u0431\u0438\u043d\u0430\u0440\u044b<\/a>: \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u043b\u0443\u0448\u0430\u0442\u044c \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u044f \u0438 \u0437\u0430\u0434\u0430\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u0434\u043e \u0441\u0442\u0430\u0440\u0442\u0430.<\/p>\n<\/div>\n<p>\u0421\u043c\u0435\u0436\u043d\u044b\u0435 \u0442\u0435\u043c\u044b: <a href=\"https:\/\/otus.ru\/journal\/nejronnye-seti-opisanie-osobennosti-vidy\/\">\u041d\u0435\u0439\u0440\u043e\u043d\u043d\u044b\u0435 \u0441\u0435\u0442\u0438: \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438, \u0432\u0438\u0434\u044b<\/a>, <a href=\"https:\/\/otus.ru\/journal\/keras-opisanie-i-osobennosti\/\">Keras: \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u0438 \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438<\/a>, <a href=\"https:\/\/otus.ru\/journal\/iskusstvennyj-intellekt-opisanie-harakteristika-sozdanie\/\">\u0418\u0441\u043a\u0443\u0441\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0438\u043d\u0442\u0435\u043b\u043b\u0435\u043a\u0442: \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435, \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0430, \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435<\/a>.<\/p>\n<h2 id=\"s7\">FAQ<\/h2>\n<p><strong>\u041d\u0443\u0436\u043d\u0430 \u043b\u0438 \u0432\u0438\u0434\u0435\u043e\u043a\u0430\u0440\u0442\u0430, \u0447\u0442\u043e\u0431\u044b \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u043d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c \u0441 \u043d\u0443\u043b\u044f?<\/strong><br \/>\n\u0414\u043b\u044f \u0443\u0447\u0435\u0431\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043d\u0430 XOR &#8212; \u043d\u0435\u0442: \u043e\u043d \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0440\u0435 \u043c\u0433\u043d\u043e\u0432\u0435\u043d\u043d\u043e. GPU \u043d\u0443\u0436\u0435\u043d, \u043a\u043e\u0433\u0434\u0430 \u0434\u0430\u043d\u043d\u044b\u0445 \u0438 \u0432\u0435\u0441\u043e\u0432 \u043c\u043d\u043e\u0433\u043e (\u0431\u043e\u043b\u044c\u0448\u0438\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0442\u0435\u043a\u0441\u0442\u044b), \u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0440\u0435 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u0434\u043e\u043b\u0433\u0438\u043c.<\/p>\n<p><strong>\u0421\u043a\u043e\u043b\u044c\u043a\u043e \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u0443\u0436\u043d\u043e \u0434\u043b\u044f \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f?<\/strong><br \/>\n\u0414\u043b\u044f XOR \u0445\u0432\u0430\u0442\u0430\u0435\u0442 \u0447\u0435\u0442\u044b\u0440\u0435\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0430 \u0438\u0441\u0447\u0435\u0440\u043f\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u043c\u0438 \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e. \u0414\u043b\u044f \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043d\u0443\u0436\u043d\u044b \u0441\u043e\u0442\u043d\u0438 \u0438 \u0442\u044b\u0441\u044f\u0447\u0438 \u0440\u0430\u0437\u043c\u0435\u0447\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432, \u0430 \u0435\u0449\u0435 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u0441\u0442\u043e\u0432\u0430\u044f \u0432\u044b\u0431\u043e\u0440\u043a\u0430, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u0441\u0435\u0442\u044c \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0437\u0430\u0443\u0447\u0438\u043b\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0435 \u0434\u0430\u043d\u043d\u044b\u0435.<\/p>\n<p><strong>\u041f\u043e\u0447\u0435\u043c\u0443 \u0443 \u043c\u0435\u043d\u044f \u0432\u044b\u0445\u043e\u0434\u044f\u0442 \u0434\u0440\u0443\u0433\u0438\u0435 \u0447\u0438\u0441\u043b\u0430, \u0447\u0435\u043c \u0432 \u043f\u0440\u0438\u043c\u0435\u0440\u0435?<\/strong><br \/>\n\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0445 \u0432\u0435\u0441\u043e\u0432. \u0415\u0441\u043b\u0438 \u0443\u0431\u0440\u0430\u0442\u044c \u0438\u043b\u0438 \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">np.random.seed(1)<\/code>, \u0441\u0442\u0430\u0440\u0442\u043e\u0432\u044b\u0435 \u0432\u0435\u0441\u0430 \u0431\u0443\u0434\u0443\u0442 \u0434\u0440\u0443\u0433\u0438\u043c\u0438, \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043e\u0448\u0438\u0431\u043a\u0438 \u0438 \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043d\u0438\u0439 \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043e\u0439\u0434\u0443\u0442\u0441\u044f, \u0445\u043e\u0442\u044f \u0441\u0435\u0442\u044c \u0432\u0441\u0435 \u0440\u0430\u0432\u043d\u043e \u0434\u043e\u043b\u0436\u043d\u0430 \u0441\u043e\u0439\u0442\u0438\u0441\u044c \u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044e XOR.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c (\u0438\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) &#8212; \u044d\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u0432 \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u043e\u0438 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432-\u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432, \u0430 \u043d\u0443\u0436\u043d\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u0443\u044e\u0442 \u0432\u0440\u0443\u0447\u043d\u0443\u044e, \u0430 \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u044e\u0442 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445. \u041d\u0438\u0436\u0435 \u044f \u043f\u043e\u043a\u0430\u0436\u0443, \u043a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u0442\u0430\u043a\u0443\u044e \u0441\u0435\u0442\u044c \u0441 \u043d\u0443\u043b\u044f \u043d\u0430 Python \u0438 numpy: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0446\u0435\u043b\u0438\u043a\u043e\u043c \u0434\u0430\u043c \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0443 XOR, [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":880,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[60],"class_list":["post-821","post","type-post","status-publish","format-standard","has-post-thumbnail","","category-polza","tag-nejronnye-seti"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u041d\u0435\u0439\u0440\u043e\u0441\u0435\u0442\u044c (\u0438\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) - \u044d\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u0432 \u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0435 \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u043e\u0438 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432-\u043d\u0435\u0439\u0440\u043e\u043d\u043e\u0432, \u0430 \u043d\u0443\u0436\u043d\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u0443\u044e\u0442 \u0432\u0440\u0443\u0447\u043d\u0443\u044e, \u0430 \u043f\u043e\u0434\u0431\u0438\u0440\u0430\u044e\u0442 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445. \u041d\u0438\u0436\u0435 \u044f \u043f\u043e\u043a\u0430\u0436\u0443, \u043a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u0442\u0430\u043a\u0443\u044e \u0441\u0435\u0442\u044c \u0441 \u043d\u0443\u043b\u044f \u043d\u0430 Python \u0438 numpy: \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0446\u0435\u043b\u0438\u043a\u043e\u043c \u0434\u0430\u043c \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0431\u043e\u0447\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u0431\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0443 XOR,\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"A. 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