{"id":16548,"date":"2024-01-26T19:44:07","date_gmt":"2024-01-26T16:14:07","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/"},"modified":"2024-01-26T19:44:07","modified_gmt":"2024-01-26T16:14:07","slug":"%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/","title":{"rendered":"\u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646: \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_87 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\" >\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d8%b4%d8%a8%da%a9%d9%87_%d8%b9%d8%b5%d8%a8%db%8c_%d8%a8%d8%a7_%da%a9%d9%84%d8%a7%d8%b3_%d9%87%d8%a7%db%8c_%d8%ae%d8%b1%d9%88%d8%ac%db%8c_%da%86%d9%86%d8%af%da%af%d8%a7%d9%86%d9%87\" >\u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0627 \u06a9\u0644\u0627\u0633 \u0647\u0627\u06cc \u062e\u0631\u0648\u062c\u06cc \u0686\u0646\u062f\u06af\u0627\u0646\u0647<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_softmax_%d9%88_cross-entropy\" >\u062a\u0648\u0627\u0628\u0639 Softmax \u0648 Cross-Entropy<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d9%81%db%8c%d8%af_%d9%81%d9%88%d8%b1%d9%88%d8%a7%d8%b1%d8%af\" >\u0641\u06cc\u062f \u0641\u0648\u0631\u0648\u0627\u0631\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d9%be%d8%b3_%d8%a7%d9%86%d8%aa%d8%b4%d8%a7%d8%b1\" >\u067e\u0633 \u0627\u0646\u062a\u0634\u0627\u0631<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%da%a9%d8%af_%d8%b4%d8%a8%da%a9%d9%87_%d9%87%d8%a7%db%8c_%d8%b9%d8%b5%d8%a8%db%8c_%d8%a8%d8%b1%d8%a7%db%8c_%d8%b7%d8%a8%d9%82%d9%87_%d8%a8%d9%86%d8%af%db%8c_%da%86%d9%86%d8%af_%da%a9%d9%84%d8%a7%d8%b3%d9%87\" >\u06a9\u062f \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0628\u0631\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%db%8c%d8%ac%d8%a7%d8%af-%db%8c%da%a9-%d8%b4%d8%a8%da%a9%d9%87-%d8%b9%d8%b5%d8%a8%db%8c-%d8%a7%d8%b2-%d8%a7%d8%a8%d8%aa%d8%af%d8%a7-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86-%d8%b7\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 12<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<p>\u0627\u06cc\u0646 \u0633\u0648\u0645\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u0642\u0627\u0644\u0627\u062a \u0627\u0633\u062a \u0631\u0648\u06cc &#8220;\u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646&#8221;.<\/p>\n<p>\u0627\u06af\u0631 \u062a\u062c\u0631\u0628\u0647 \u0642\u0628\u0644\u06cc \u0628\u0627 \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0646\u062f\u0627\u0631\u06cc\u062f\u060c \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc \u06a9\u0646\u0645 \u0627\u0628\u062a\u062f\u0627 \u0642\u0633\u0645\u062a 1 \u0648 \u0642\u0633\u0645\u062a 2 \u0627\u06cc\u0646 \u0645\u062c\u0645\u0648\u0639\u0647 \u0631\u0627 \u0628\u062e\u0648\u0627\u0646\u06cc\u062f (\u0644\u06cc\u0646\u06a9 \u0628\u0627\u0644\u0627).  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0627 \u0645\u0641\u0627\u0647\u06cc\u0645 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0622\u0646 \u0645\u0642\u0627\u0644\u0627\u062a \u0627\u062d\u0633\u0627\u0633 \u0631\u0627\u062d\u062a\u06cc \u06a9\u0631\u062f\u06cc\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0631\u06af\u0631\u062f\u06cc\u062f \u0648 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0631\u0627 \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u06cc\u062f.<\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u06cc \u062f\u06cc\u062f\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0642\u0627\u062f\u0631 \u0628\u0647 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u062f\u0631 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\u062a\u0639\u0644\u0642 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u06cc\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0633\u0627\u062f\u0647 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0642\u0627\u062f\u0631 \u0628\u0647 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647 \u0627\u0633\u062a.<\/p>\n<h2 id=\"dataset\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\"><\/span>\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0646\u06af\u0627\u0647\u06cc \u06a9\u0648\u062a\u0627\u0647 \u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062e\u0648\u062f \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.  \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0645\u0627 \u062f\u0648 \u0648\u06cc\u0698\u06af\u06cc \u0648\u0631\u0648\u062f\u06cc \u0648 \u06cc\u06a9\u06cc \u0627\u0632 \u0633\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0645\u06a9\u0646 \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.  \u0645\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0633\u062a\u06cc \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n\nnp.random.seed(<span class=\"hljs-number\">42<\/span>)\n\ncat_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((<span class=\"hljs-number\">0<\/span>, -<span class=\"hljs-number\">3<\/span>))\nmouse_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">3<\/span>))\ndog_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((-<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">3<\/span>))\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627\u060c \u0645\u0627 \u0628\u0627 \u0648\u0627\u0631\u062f \u06a9\u0631\u062f\u0646 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647\u200c\u0647\u0627\u06cc \u062e\u0648\u062f \u0634\u0631\u0648\u0639 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0633\u0647 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 700 x 2 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0647\u0631 \u0639\u0646\u0635\u0631 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0635\u0648\u06cc\u0631\u06cc \u0627\u0632 \u06cc\u06a9 \u062d\u06cc\u0648\u0627\u0646 \u062e\u0627\u0635 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f.  \u0647\u0631 \u0639\u0646\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0633\u0647 \u06a9\u0644\u0627\u0633 \u062e\u0631\u0648\u062c\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u0646\u06a9\u062a\u0647 \u0645\u0647\u0645\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0622\u0646 \u062a\u0648\u062c\u0647 \u06a9\u0631\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0639\u0646\u0627\u0635\u0631 the \u0631\u0627 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645 <code>cat_images<\/code> \u0622\u0631\u0627\u06cc\u0647 \u0631\u0648\u06cc \u06cc\u06a9 \u0635\u0641\u062d\u0647 \u062f\u0648 \u0628\u0639\u062f\u06cc\u060c \u0622\u0646\u0647\u0627 \u062f\u0631 \u0645\u0631\u06a9\u0632 x=0 \u0648 y=-3 \u062e\u0648\u0627\u0647\u0646\u062f \u0628\u0648\u062f.  \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u0639\u0646\u0627\u0635\u0631 \u0627\u0632 <code>mouse_images<\/code> \u0622\u0631\u0627\u06cc\u0647 \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 x=3 \u0648 y=3 \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0639\u0646\u0627\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>dog_images<\/code> \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 x=-3 \u0648 y=3 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062e\u0648\u062f \u0631\u0627 \u0631\u0633\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0627\u06cc\u0646 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f.<\/p>\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u0628\u0627\u06cc\u062f \u0628\u0647 \u0635\u0648\u0631\u062a \u0639\u0645\u0648\u062f\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627 \u0628\u067e\u06cc\u0648\u0646\u062f\u06cc\u0645 \u062a\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0646\u0647\u0627\u06cc\u06cc \u062e\u0648\u062f \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">feature_set = np.vstack((cat_images, mouse_images, dog_images))\n<\/code><\/pre>\n<p>\u0645\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645 \u0648 \u0627\u06a9\u0646\u0648\u0646 \u0628\u0627\u06cc\u062f \u0628\u0631\u0686\u0633\u0628 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u06a9\u0648\u0631\u062f \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062e\u0648\u062f \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645.  \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\">labels = np.array((<span class=\"hljs-number\">0<\/span>)*<span class=\"hljs-number\">700<\/span> + (<span class=\"hljs-number\">1<\/span>)*<span class=\"hljs-number\">700<\/span> + (<span class=\"hljs-number\">2<\/span>)*<span class=\"hljs-number\">700<\/span>)\n<\/code><\/pre>\n<p>\u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0641\u0648\u0642 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u062a\u06a9 \u0628\u0639\u062f\u06cc \u0627\u0632 2100 \u0639\u0646\u0635\u0631 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u062f.  700 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 0 \u0628\u0631\u0686\u0633\u0628 \u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u0627\u0646\u062f\u060c 700 \u0639\u0646\u0635\u0631 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0639\u0646\u0648\u0627\u0646 1 \u0628\u0631\u0686\u0633\u0628 \u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u0627\u0646\u062f \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 700 \u0639\u0646\u0635\u0631 \u0622\u062e\u0631 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 2 \u0628\u0631\u0686\u0633\u0628 \u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u0627\u0646\u062f. \u0627\u06cc\u0646 \u062a\u0646\u0647\u0627 \u0631\u0627\u0647 \u0645\u06cc\u0627\u0646\u0628\u0631 \u0645\u0627 \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u0633\u0631\u06cc\u0639 \u0628\u0631\u0686\u0633\u0628 \u0647\u0627 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u0628\u0631\u0686\u0633\u0628 \u062e\u0631\u0648\u062c\u06cc \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0645\u0632\u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u06cc\u06a9 \u062f\u0627\u063a \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 \u0632\u06cc\u0631\u0627 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0627 \u062f\u0627\u0631\u0627\u06cc \u0633\u0647 \u06af\u0631\u0647 \u0648 \u0647\u0631 \u06af\u0631\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. node \u0628\u0627 \u06cc\u06a9 \u06a9\u0644\u0627\u0633 \u062e\u0631\u0648\u062c\u06cc \u0645\u0637\u0627\u0628\u0642\u062a \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.  \u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0647 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u06cc\u06a9 \u062e\u0631\u0648\u062c\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0645\u06cc \u0634\u0648\u062f\u060c \u0645\u0642\u062f\u0627\u0631 \u0645\u0631\u0628\u0648\u0637\u0647 \u0628\u0627\u0634\u062f node \u0628\u0627\u06cc\u062f 1 \u0628\u0627\u0634\u062f \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 \u0628\u0627\u06cc\u062f \u0645\u0642\u062f\u0627\u0631 0 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f. \u0628\u0631\u0627\u06cc \u0622\u0646\u060c \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u06a9\u0648\u0631\u062f \u0628\u0647 \u0633\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u0631\u0627\u06cc \u0628\u0631\u0686\u0633\u0628 \u062e\u0631\u0648\u062c\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.  \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u06a9\u062f\u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u06cc\u06a9 \u062f\u0627\u063a \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u0622\u0631\u0627\u06cc\u0647 \u0628\u0631\u062f\u0627\u0631\u06cc \u0631\u0645\u0632\u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u06cc\u06a9 \u062f\u0627\u063a \u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0645\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">one_hot_labels = np.zeros((<span class=\"hljs-number\">2100<\/span>, <span class=\"hljs-number\">3<\/span>))\n\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">2100<\/span>):\n    one_hot_labels(i, labels(i)) = <span class=\"hljs-number\">1<\/span>\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627 \u0645\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>one_hot_labels<\/code> \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 2100 x 3 \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0631 \u0631\u062f\u06cc\u0641 \u062d\u0627\u0648\u06cc \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0645\u0632\u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u06cc\u06a9 \u062f\u0627\u063a \u0628\u0631\u0627\u06cc \u0631\u06a9\u0648\u0631\u062f \u0645\u0631\u0628\u0648\u0637\u0647 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0648\u06cc\u0698\u06af\u06cc \u0627\u0633\u062a.  \u0633\u067e\u0633 1 \u0631\u0627 \u062f\u0631 \u0633\u062a\u0648\u0646 \u0645\u0631\u0628\u0648\u0637\u0647 \u062f\u0631\u062c \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u06af\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f\u060c \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f \u06a9\u0647 <code>one_hot_labels<\/code> \u0622\u0631\u0627\u06cc\u0647 1 \u062f\u0631 \u0634\u0627\u062e\u0635 0 \u0628\u0631\u0627\u06cc 700 \u0631\u06a9\u0648\u0631\u062f \u0627\u0648\u0644\u060c 1 \u062f\u0631 \u0634\u0627\u062e\u0635 1 \u0628\u0631\u0627\u06cc 700 \u0631\u06a9\u0648\u0631\u062f \u0628\u0639\u062f\u06cc \u0648 1 \u062f\u0631 \u0634\u0627\u062e\u0635 2 \u0628\u0631\u0627\u06cc 700 \u0631\u06a9\u0648\u0631\u062f \u0622\u062e\u0631 \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0627\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0647 \u062a\u0627\u0632\u06af\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0631\u0633\u0645 \u06a9\u0646\u06cc\u0645.  \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">plt.scatter(feature_set(:,<span class=\"hljs-number\">0<\/span>), feature_set(:,<span class=\"hljs-number\">1<\/span>), c=labels, cmap=<span class=\"hljs-string\">'plasma'<\/span>, s=<span class=\"hljs-number\">100<\/span>, alpha=<span class=\"hljs-number\">0.5<\/span>)\nplt.show()\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627\u060c \u0628\u0627\u06cc\u062f \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u0645\u0634\u0627\u0647\u062f\u0647 \u06a9\u0646\u06cc\u062f:<\/p>\n<p><img decoding=\"async\" class=\"img-responsive\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/creating-neural-network-scratch-python-multi-class-classification-1.png\" alt=\"\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062a\u0648\u0644\u06cc\u062f \u0634\u062f\u0647\" title=\"\"><\/p>\n<p>\u0634\u0645\u0627 \u0628\u0647 \u0648\u0636\u0648\u062d \u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u0645\u0627 \u0639\u0646\u0627\u0635\u0631 \u0645\u062a\u0639\u0644\u0642 \u0628\u0647 \u0633\u0647 \u06a9\u0644\u0627\u0633 \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u062f\u0627\u0631\u06cc\u0645.  \u0648\u0638\u06cc\u0641\u0647 \u0645\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0627 \u0642\u0627\u0628\u0644\u06cc\u062a \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u062f\u0631 \u06a9\u0644\u0627\u0633 \u0647\u0627\u06cc \u0641\u0648\u0642 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n<h2 id=\"neuralnetworkwithmultipleoutputclasses\"><span class=\"ez-toc-section\" id=\"%d8%b4%d8%a8%da%a9%d9%87_%d8%b9%d8%b5%d8%a8%db%8c_%d8%a8%d8%a7_%da%a9%d9%84%d8%a7%d8%b3_%d9%87%d8%a7%db%8c_%d8%ae%d8%b1%d9%88%d8%ac%db%8c_%da%86%d9%86%d8%af%da%af%d8%a7%d9%86%d9%87\"><\/span>\u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0627 \u06a9\u0644\u0627\u0633 \u0647\u0627\u06cc \u062e\u0631\u0648\u062c\u06cc \u0686\u0646\u062f\u06af\u0627\u0646\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u06a9\u0647 \u0642\u0635\u062f \u0637\u0631\u0627\u062d\u06cc \u0622\u0646 \u0631\u0627 \u062f\u0627\u0631\u06cc\u0645 \u062f\u0627\u0631\u0627\u06cc \u0645\u0639\u0645\u0627\u0631\u06cc \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" class=\"img-responsive\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/creating-neural-network-scratch-python-multi-class-classification-2.png\" alt=\"\u0633\u0627\u062e\u062a\u0627\u0631 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc\" title=\"\"><\/p>\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0645\u0627 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0634\u0628\u06cc\u0647 \u0628\u0647 \u0634\u0628\u06a9\u0647\u200c\u0627\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a 2 \u0645\u062c\u0645\u0648\u0639\u0647 \u062a\u0648\u0633\u0639\u0647 \u062f\u0627\u062f\u06cc\u0645.  \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0644\u0627\u06cc\u0647 \u0648\u0631\u0648\u062f\u06cc \u0628\u0627 2 \u0648\u06cc\u0698\u06af\u06cc \u0648\u0631\u0648\u062f\u06cc \u0648 \u06cc\u06a9 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0628\u0627 4 \u06af\u0631\u0647 \u0627\u0633\u062a.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0633\u0647 \u06af\u0631\u0647 \u062f\u0627\u0631\u06cc\u0645.  \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0645\u0627 \u0642\u0627\u062f\u0631 \u0628\u0647 \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u062a\u0639\u062f\u0627\u062f \u062e\u0631\u0648\u062c\u06cc \u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 3 \u0627\u0633\u062a.<\/p>\n<h3 id=\"softmaxandcrossentropyfunctions\"><span class=\"ez-toc-section\" id=\"%d8%aa%d9%88%d8%a7%d8%a8%d8%b9_softmax_%d9%88_cross-entropy\"><\/span>\u062a\u0648\u0627\u0628\u0639 Softmax \u0648 Cross-Entropy<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u062d\u0631\u06a9\u062a \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u0628\u0647 \u0628\u062e\u0634 \u06a9\u062f\u060c \u0627\u062c\u0627\u0632\u0647 \u062f\u0647\u06cc\u062f \u0628\u0647 \u0637\u0648\u0631 \u062e\u0644\u0627\u0635\u0647 \u0628\u0647 \u0628\u0631\u0631\u0633\u06cc \u0622\u0646 \u0628\u067e\u0631\u062f\u0627\u0632\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Softmax_function\">\u0633\u0627\u0641\u062a \u0645\u06a9\u0633<\/a> \u0648 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cross_entropy\">\u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0628\u0644<\/a> \u062a\u0648\u0627\u0628\u0639\u060c \u06a9\u0647 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0648 \u0627\u0632 \u062f\u0633\u062a \u062f\u0627\u062f\u0646 \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0631\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<h4 id=\"softmaxfunction\">\u0639\u0645\u0644\u06a9\u0631\u062f \u0633\u0627\u0641\u062a \u0645\u06a9\u0633<\/h4>\n<p>\u0627\u0632 \u0645\u0639\u0645\u0627\u0631\u06cc \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0645\u0627\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u0633\u0647 \u06af\u0631\u0647 \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u062f\u0627\u0631\u06cc\u0645.  \u0645\u0627 \u0686\u0646\u062f\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u062f\u0627\u0631\u06cc\u0645.  \u06cc\u06a9\u06cc \u0627\u0632 \u06af\u0632\u06cc\u0646\u0647 \u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 sigmoid \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u06cc\u0645.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644\u200c\u0633\u0627\u0632\u06cc \u0631\u0627\u062d\u062a\u200c\u062a\u0631 \u0628\u0647 \u0634\u06a9\u0644 softmax \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f \u0648 \u0628\u0631\u062f\u0627\u0631 \u062f\u06cc\u06af\u0631\u06cc \u0628\u0627 \u0647\u0645\u0627\u0646 \u0637\u0648\u0644 \u062e\u0631\u0648\u062c\u06cc \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0627 \u0634\u0627\u0645\u0644 \u0633\u0647 \u06af\u0631\u0647 \u0627\u0633\u062a\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062e\u0631\u0648\u062c\u06cc \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645 node \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u0628\u0631\u062f\u0627\u0631 \u0648\u0631\u0648\u062f\u06cc.  \u062e\u0631\u0648\u062c\u06cc \u0637\u0648\u0644\u06cc \u0627\u0632 \u0647\u0645\u0627\u0646 \u0628\u0631\u062f\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0647\u0645\u0647 \u0639\u0646\u0627\u0635\u0631 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 1 \u0627\u0633\u062a. \u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc\u060c \u062a\u0627\u0628\u0639 softmax \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0634\u0648\u062f:<\/p>\n<p>$$ y_i(z_i) = \\frac{e^{z_i}}{ \\sum\\nlimits_{k=1}^{k}{e^{z_k}} } $$\n<\/p>\n<p>\u062a\u0627\u0628\u0639 softmax \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u062a\u0648\u0627\u0646 \u0647\u0631 \u0639\u0646\u0635\u0631 \u0648\u0631\u0648\u062f\u06cc \u0631\u0627 \u0628\u0631 \u0645\u062c\u0645\u0648\u0639 \u0646\u0645\u0627\u0647\u0627\u06cc \u0647\u0645\u0647 \u0639\u0646\u0627\u0635\u0631 \u0648\u0631\u0648\u062f\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0633\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">softmax<\/span>(<span class=\"hljs-params\">A<\/span>):<\/span>\n    expA = np.exp(A)\n    <span class=\"hljs-keyword\">return<\/span> expA \/ expA.<span class=\"hljs-built_in\">sum<\/span>()\n\nnums = np.array((<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>))\n<span class=\"hljs-built_in\">print<\/span>(softmax(nums))\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627 \u0645\u0627 \u06cc\u06a9 \u062a\u0627\u0628\u0639 softmax \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f\u060c \u0646\u0645\u0627\u0647\u0627\u06cc \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f \u0648 \u0633\u067e\u0633 \u0627\u0639\u062f\u0627\u062f \u062d\u0627\u0635\u0644 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0628\u0631 \u0645\u062c\u0645\u0648\u0639 \u062a\u0648\u0627\u0646\u200c\u0647\u0627\u06cc \u0647\u0645\u0647 \u0627\u0639\u062f\u0627\u062f \u062f\u0631 \u0628\u0631\u062f\u0627\u0631 \u0648\u0631\u0648\u062f\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<p>\u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631 \u0648\u0631\u0648\u062f\u06cc \u0634\u0627\u0645\u0644 \u0639\u0646\u0627\u0635\u0631 4\u060c 5 \u0648 6 \u0627\u0633\u062a. \u062f\u0631 \u062e\u0631\u0648\u062c\u06cc\u060c \u0633\u0647 \u0639\u062f\u062f \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f \u06a9\u0647 \u0628\u06cc\u0646 0 \u0648 1 \u0644\u0647 \u0634\u062f\u0647 \u0627\u0646\u062f \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639 \u0627\u0639\u062f\u0627\u062f \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 1 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u062e\u0631\u0648\u062c\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">(0.09003057 0.24472847 0.66524096)\n<\/code><\/pre>\n<p>\u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0633\u0627\u0641\u062a \u0645\u06a9\u0633 \u062f\u0648 \u0645\u0632\u06cc\u062a \u0639\u0645\u062f\u0647 \u0646\u0633\u0628\u062a \u0628\u0647 \u0633\u0627\u06cc\u0631 \u062a\u0648\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u062f\u0627\u0631\u062f\u060c \u0628\u0647 \u062e\u0635\u0648\u0635 \u0628\u0631\u0627\u06cc \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647: \u0645\u0632\u06cc\u062a \u0627\u0648\u0644 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0627\u0628\u0639 \u0633\u0627\u0641\u062a \u0645\u06a9\u0633 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u0645\u06cc \u06af\u06cc\u0631\u062f \u0648 \u0645\u0632\u06cc\u062a \u062f\u0648\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062e\u0631\u0648\u062c\u06cc \u0628\u06cc\u0646 0 \u0648 1 \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc \u06a9\u0646\u062f. \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0645\u0627\u060c \u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627\u06cc \u062e\u0631\u0648\u062c\u06cc \u06a9\u062f\u06af\u0630\u0627\u0631\u06cc \u0634\u062f\u0647 \u06cc\u06a9\u200c\u0637\u0631\u0641\u0647 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631\u06cc \u0628\u06cc\u0646 0 \u0648 1 \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a. \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u062e\u0631\u0648\u062c\u06cc \u0641\u06cc\u062f \u0641\u0648\u0631\u0648\u0627\u0631\u062f process \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 1 \u0628\u0627\u0634\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 softmax \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u062f\u0647 \u0622\u0644\u06cc \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u062e\u0631\u0648\u062c\u06cc \u0631\u0627 \u0628\u06cc\u0646 0 \u0648 1 \u0644\u0647 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h4 id=\"crossentropyfunction\">\u062a\u0627\u0628\u0639 \u0645\u062a\u0642\u0627\u0628\u0644 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc<\/h4>\n<p>\u0628\u0627 \u0639\u0645\u0644\u06a9\u0631\u062f \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc softmax \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mean_squared_error\">\u062e\u0637\u0627\u06cc \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0645\u0631\u0628\u0639\u0627\u062a<\/a> \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u06cc\u0645 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u062a\u0627\u0628\u0639 cost \u0628\u0631\u0627\u06cc \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u0647\u0632\u06cc\u0646\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0631\u0627\u06cc \u062a\u0627\u0628\u0639 softmax\u060c \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627\u062d\u062a\u200c\u062a\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n<p>\u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc\u060c \u062a\u0627\u0628\u0639 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0628\u0644 \u0628\u0647 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p>$$ H(y,\\hat{y}) = -\\sum_i y_i \\log \\hat{y_i} $$\n<\/p>\n<p>\u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0645\u062c\u0645\u0648\u0639 \u062d\u0627\u0635\u0644 \u0627\u0632 \u0647\u0645\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u0648\u0627\u0642\u0639\u06cc \u0628\u0627 \u0648\u0631\u0648\u062f \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0646\u0641\u06cc \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a.  \u0628\u0631\u0627\u06cc \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u0637\u0628\u0642\u0647\u060c \u062a\u0627\u0628\u0639 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647\u062a\u0631\u06cc \u0627\u0632 \u062a\u0627\u0628\u0639 \u0646\u0632\u0648\u0644 \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u0627 \u062f\u0627\u0646\u0634 \u06a9\u0627\u0641\u06cc \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647 \u0631\u0627 \u062d\u0644 \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0645\u0627 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/p>\n<p>\u0645\u062b\u0644 \u0647\u0645\u06cc\u0634\u0647\u060c \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u062f\u0631 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647 \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u0634\u0648\u062f: \u067e\u06cc\u0634\u200c\u062e\u0648\u0631 \u0648 \u0627\u0646\u062a\u0634\u0627\u0631 \u067e\u0633.<\/p>\n<h3 id=\"feedforward\"><span class=\"ez-toc-section\" id=\"%d9%81%db%8c%d8%af_%d9%81%d9%88%d8%b1%d9%88%d8%a7%d8%b1%d8%af\"><\/span>\u0641\u06cc\u062f \u0641\u0648\u0631\u0648\u0627\u0631\u062f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0641\u0627\u0632 \u0641\u06cc\u062f \u0641\u0648\u0631\u0648\u0627\u0631\u062f \u06a9\u0645\u0627\u0628\u06cc\u0634 \u0645\u0634\u0627\u0628\u0647 \u0622\u0646\u0686\u0647 \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u06cc \u062f\u06cc\u062f\u06cc\u0645 \u0628\u0627\u0642\u06cc \u062e\u0648\u0627\u0647\u062f \u0645\u0627\u0646\u062f.  \u062a\u0646\u0647\u0627 \u062a\u0641\u0627\u0648\u062a \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06a9\u0646\u0648\u0646 \u0645\u0627 \u0627\u0632 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc softmax \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0628\u0647 \u062c\u0627\u06cc \u062a\u0627\u0628\u0639 sigmoid \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u0628\u0647 \u06cc\u0627\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f\u060c \u0628\u0631\u0627\u06cc \u062e\u0631\u0648\u062c\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0647\u0645\u0686\u0646\u0627\u0646 \u0627\u0632 \u062a\u0627\u0628\u0639 sigmoid \u0645\u0627\u0646\u0646\u062f \u0642\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u062a\u0627\u0628\u0639 softmax \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u062f \u0634\u062f.<\/p>\n<h4 id=\"phase1\">\u0641\u0627\u0632 1<\/h4>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 \u0627\u0632 \u062f\u0648 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0648 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u0641\u0627\u0632 \u067e\u06cc\u0634\u062e\u0648\u0631 \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0641\u0627\u0632 \u0641\u0631\u0639\u06cc \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f\u0645.<\/p>\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0627\u0648\u0644 \u0631\u0648\u0634 \u0645\u062d\u0627\u0633\u0628\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u0632 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u06cc\u062f.  \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u06a9\u0648\u0631\u062f \u0648\u0631\u0648\u062f\u06cc\u060c \u062f\u0648 \u0648\u06cc\u0698\u06af\u06cc &#8220;x1&#8221; \u0648 &#8220;x2&#8221; \u062f\u0627\u0631\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u06a9\u062f\u0627\u0645 node \u062f\u0631 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646\u060c \u0628\u0627\u06cc\u062f \u0648\u0631\u0648\u062f\u06cc \u0631\u0627 \u0628\u0627 \u0648\u0632\u0646 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0636\u0631\u0628 \u06a9\u0646\u06cc\u0645. node \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0645\u0642\u062f\u0627\u0631 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f\u060c \u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u0627\u0635\u0637\u0644\u0627\u062d \u062a\u0639\u0635\u0628 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0633\u067e\u0633 \u0645\u062d\u0635\u0648\u0644 \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u0631\u0627 \u0627\u0632 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644\u200c\u0633\u0627\u0632\u06cc \u0633\u06cc\u06af\u0645\u0648\u0626\u06cc\u062f \u0639\u0628\u0648\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u062a\u0627 \u0645\u0642\u062f\u0627\u0631 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645.<\/p>\n<p>\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u062f\u0627\u0631 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0627\u0648\u0644\u06cc\u0646 node \u062f\u0631 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u06a9\u0647 \u0628\u0627 &#8220;ah1&#8221; \u0645\u0634\u062e\u0635 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0627\u06cc\u062f \u0645\u062d\u0627\u0633\u0628\u0647 \u0632\u06cc\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f:<\/p>\n<p>$$<br \/>zh1 = x1w1 + x2w2 + b<br \/>$$<\/p>\n<p>$$<br \/>ah1 = \\frac{\\mathrm{1} }{\\mathrm{1} + e^{-zh1} }<br \/>$$<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0631\u0627\u06cc \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0628\u06cc\u0634\u062a\u0631\u06cc\u0646 \u0627\u0633\u062a node \u062f\u0631 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646  \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc 2\u060c 3 \u0648 4 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<h4 id=\"phase2\">\u0641\u0627\u0632 2<\/h4>\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f.  \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0631\u0627 \u0628\u0627 \u0648\u0632\u0646 \u0645\u062a\u0646\u0627\u0638\u0631 \u0622\u0646\u0647\u0627 \u0636\u0631\u0628 \u06a9\u0646\u06cc\u062f \u0648 \u0646\u062a\u06cc\u062c\u0647 \u0631\u0627 \u0627\u0632 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0639\u0628\u0648\u0631 \u062f\u0647\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a softmax \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0631\u06cc\u0627\u0636\u06cc \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 \u0632\u06cc\u0631 \u0628\u06cc\u0627\u0646 \u06a9\u0631\u062f:<\/p>\n<p>$$<br \/>zo1 = ah1w9 + ah2w10 + ah3w11 + ah4w12<br \/>$$<\/p>\n<p>$$<br \/>zo2 = ah1w13 + ah2w14 + ah3w15 + ah4w16<br \/>$$<\/p>\n<p>$$<br \/>zo3 = ah1w17 + ah2w18 + ah3w19 + ah4w20<br \/>$$<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 zo1\u060c zo2 \u0648 zo3 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u062f\u0647\u0646\u062f \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0648\u0631\u0648\u062f\u06cc \u062a\u0627\u0628\u0639 \u0633\u06cc\u06af\u0645\u0648\u0626\u06cc\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u0627\u0645 \u0627\u06cc\u0646 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 &#8220;\u0632\u0648&#8221; \u0628\u06af\u0630\u0627\u0631\u06cc\u0645.<\/p>\n<pre><code class=\"hljs\">zo = (zo1, zo2, zo3)\n<\/code><\/pre>\n<p>\u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc a01 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u062a\u0627\u0628\u0639 softmax \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p>$$<br \/>ao1(zo) = \\frac{e^{zo1}}{ \\sum\\nlimits_{k=1}^{k}{e^{zok}} }<br \/>$$<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 &#8220;a01&#8221; \u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0627\u06cc \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0647\u0627 \u0627\u0633\u062a node \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc  \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u062a\u0627\u0628\u0639 softmax \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 ao2 \u0648 ao3 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u06af\u0627\u0645 \u067e\u06cc\u0634\u200c\u062e\u0648\u0631 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0627 \u062e\u0631\u0648\u062c\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0634\u0628\u06cc\u0647 \u0628\u0647 \u0645\u0631\u062d\u0644\u0647 \u067e\u06cc\u0634\u200c\u062e\u0648\u0631 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0631\u0627\u06cc \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0628\u0627\u06cc\u0646\u0631\u06cc \u0627\u0633\u062a.  \u062a\u0646\u0647\u0627 \u062a\u0641\u0627\u0648\u062a \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0627 \u0627\u0632 \u062a\u0627\u0628\u0639 softmax \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0628\u0647 \u062c\u0627\u06cc \u062a\u0627\u0628\u0639 sigmoid \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<h3 id=\"backpropagation\"><span class=\"ez-toc-section\" id=\"%d9%be%d8%b3_%d8%a7%d9%86%d8%aa%d8%b4%d8%a7%d8%b1\"><\/span>\u067e\u0633 \u0627\u0646\u062a\u0634\u0627\u0631<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u06cc\u062f\u0647 \u0627\u0635\u0644\u06cc \u062f\u0631 \u067e\u0633 \u0627\u0646\u062a\u0634\u0627\u0631 \u0645\u062c\u062f\u062f \u06cc\u06a9\u0633\u0627\u0646 \u0627\u0633\u062a.  \u0645\u0627 \u0628\u0627\u06cc\u062f \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u0622\u0646 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u0628\u0627 \u0628\u0647 \u0631\u0648\u0632 \u0631\u0633\u0627\u0646\u06cc \u0648\u0632\u0646 \u0647\u0627 \u0628\u0647 \u06af\u0648\u0646\u0647 \u0627\u06cc \u0628\u0647\u06cc\u0646\u0647 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0632\u06cc\u0646\u0647 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0633\u062f.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0631 \u062e\u0644\u0627\u0641 \u0645\u0642\u0627\u0644\u0627\u062a \u0642\u0628\u0644\u06cc \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mean_squared_error\">\u062e\u0637\u0627\u06cc \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0645\u0631\u0628\u0639\u0627\u062a<\/a> \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647\u060c \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u062c\u0627\u06cc \u0622\u0646 \u0627\u0632 \u062a\u0627\u0628\u0639 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u067e\u0633 \u0627\u0646\u062a\u0634\u0627\u0631 \u06cc\u06a9 \u0627\u0633\u062a <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Optimization_problem\">\u0645\u0634\u06a9\u0644 \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc<\/a> \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Maxima_and_minima\">\u062d\u062f\u0627\u0642\u0644 \u0639\u0645\u0644\u06a9\u0631\u062f<\/a> \u0628\u0631\u0627\u06cc \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0645\u0627<\/p>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u06cc\u0646\u06cc\u0645\u0645 \u06cc\u06a9 \u062a\u0627\u0628\u0639\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0639\u0628\u0627\u0631\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Optimization_problem\">\u0634\u06cc\u0628 \u0645\u0646\u0627\u0633\u0628<\/a> \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0646\u0632\u0648\u0644 \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0631\u06cc\u0627\u0636\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f:<\/p>\n<p>$$ \u062a\u06a9\u0631\u0627\u0631 \\ \u062a\u0627 \\ \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc: \\begin{Bmatrix} w_j := w_j &#8211; \\alpha \\frac{\\partial }{\\partial w_j} J(w_0,w_1 &#8230;&#8230;. w_n) \\end{Bmatrix} &#8230;&#8230;&#8230;&#8230;. (1) $$\n<\/p>\n<p>\u062c\u0632\u0626\u06cc\u0627\u062a \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u06cc\u0646\u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u062a\u0627\u0628\u0639 \u0646\u0632\u0648\u0644\u06cc \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0645\u06cc \u0631\u0633\u0627\u0646\u062f \u0642\u0628\u0644\u0627\u064b \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u06cc \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0627 \u0641\u0642\u0637 \u0639\u0645\u0644\u06cc\u0627\u062a \u0631\u06cc\u0627\u0636\u06cc \u0631\u0627 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.<\/p>\n<p>\u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0645\u0627 \u0627\u06cc\u0646 \u0627\u0633\u062a:<\/p>\n<p>$$ H(y,\\hat{y}) = -\\sum_i y_i \\log \\hat{y_i} $$\n<\/p>\n<p>\u062f\u0631 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0645\u0627 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0631 \u0639\u0646\u0635\u0631 \u0628\u0631\u062f\u0627\u0631 \u0628\u0627 \u062e\u0631\u0648\u062c\u06cc \u06cc\u06a9\u06cc \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f node \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc  \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 softmax \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06af\u0631 &#8220;ao&#8221; \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u0647\u0627\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0627\u0632 \u062a\u0645\u0627\u0645 \u06af\u0631\u0647 \u0647\u0627\u06cc \u062e\u0631\u0648\u062c\u06cc \u0648 &#8220;y&#8221; \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u0647\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u06af\u0631\u0647 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u062f\u0631 \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u0628\u0627\u0634\u062f\u060c \u0627\u0633\u0627\u0633\u0627\u064b \u0628\u0627\u06cc\u062f \u0627\u06cc\u0646 \u062a\u0627\u0628\u0639 \u0631\u0627 \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0628\u0631\u0633\u0627\u0646\u06cc\u0645:<\/p>\n<p>$$ \u0647\u0632\u06cc\u0646\u0647(y, {ao}) = -\\sum_i y_i \\log {ao_i} $$\n<\/p>\n<h4 id=\"phase1\">\u0641\u0627\u0632 1<\/h4>\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0627\u0648\u0644 \u0628\u0627\u06cc\u062f \u0648\u0632\u0646 \u0647\u0627\u06cc w9 \u062a\u0627 w20 \u0631\u0627 \u0628\u0647 \u0631\u0648\u0632 \u06a9\u0646\u06cc\u0645.  \u0627\u06cc\u0646\u0647\u0627 \u0648\u0632\u0646 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0627\u0632 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u060c \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0628\u0647 \u062d\u062f\u0627\u0642\u0644 \u0631\u0633\u0627\u0646\u062f\u0646 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647\u060c \u0628\u0627\u06cc\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u0631\u0627 \u0637\u0648\u0631\u06cc \u0628\u0647 \u0631\u0648\u0632 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0647\u0632\u06cc\u0646\u0647 \u06a9\u0627\u0647\u0634 \u06cc\u0627\u0628\u062f.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0628\u0627\u06cc\u062f \u0645\u0634\u062a\u0642 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0647\u0631 \u0648\u0632\u0646 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645.  \u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0647\u06cc\u0645:<\/p>\n<p>$$<br \/>\\frac {dcost}{dwo} = \\frac {dcost}{dao} *, \\frac {dao}{dzo} * \\frac {dzo}{dwo} &#8230;.. (1)<br \/>$$<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 &#8220;wo&#8221; \u0628\u0647 \u0648\u0632\u0646 \u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u0634\u0627\u0631\u0647 \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0628\u062e\u0634 \u0627\u0648\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f:<\/p>\n<p>$$<br \/>\\frac {dcost}{dao} *\\ \\frac {dao}{dzo} &#8230;&#8230; (2)<br \/>$$<\/p>\n<p>\u0645\u0634\u062a\u0642 \u062f\u0642\u06cc\u0642 \u062a\u0627\u0628\u0639 \u0627\u0632 \u062f\u0633\u062a \u062f\u0627\u062f\u0646 \u0622\u0646\u062a\u0631\u0648\u067e\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u0628\u0627 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc softmax \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u0627\u0641\u062a <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/deepnotes.io\/softmax-crossentropy\">\u0627\u06cc\u0646 \u0644\u06cc\u0646\u06a9<\/a>.<\/p>\n<p>\u0645\u0634\u062a\u0642 \u0645\u0639\u0627\u062f\u0644\u0647 (2) \u0639\u0628\u0627\u0631\u062a \u0627\u0633\u062a \u0627\u0632:<\/p>\n<p>$$<br \/>\\frac {dcost}{dao} *\\ \\frac {dao}{dzo} = ao &#8211; y &#8230;&#8230;. (3)<br \/>$$<\/p>\n<p>\u062c\u0627\u06cc\u06cc \u06a9\u0647 &#8220;ao&#8221; \u062e\u0631\u0648\u062c\u06cc \u067e\u06cc\u0634 \u0628\u06cc\u0646\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 &#8220;y&#8221; \u062e\u0631\u0648\u062c\u06cc \u0648\u0627\u0642\u0639\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f &#8220;dzo&#8221; \u0631\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 &#8220;dwo&#8221; \u0627\u0632 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em>.  \u0645\u0634\u062a\u0642 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u062e\u0631\u0648\u062c\u06cc \u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0645\u06cc \u0622\u06cc\u0646\u062f\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>\\frac {dzo}{dwo} = \u0622\u0647<br \/>$$<\/p>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0648\u0633\u0637 <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em> \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0627 \u0646\u0631\u062e \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0636\u0631\u0628 \u06a9\u0631\u062f \u0648 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u0641\u0639\u0644\u06cc \u06a9\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627\u06cc\u062f \u0628\u0627\u06cc\u0627\u0633 &#8220;bo&#8221; \u0631\u0627 \u0628\u0631\u0627\u06cc \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0628\u0647 \u0631\u0648\u0632 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0628\u0627\u06cc\u062f \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u062e\u0648\u062f \u0631\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0633\u0648\u06af\u06cc\u0631\u06cc \u0645\u062a\u0645\u0627\u06cc\u0632 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0627\u0631\u0632\u0634 \u0633\u0648\u06af\u06cc\u0631\u06cc \u062c\u062f\u06cc\u062f \u0631\u0627 \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645:<\/p>\n<p>$$<br \/>\\frac {dcost}{dbo} = \\frac {dcost}{dao} *\\ \\frac {dao}{dzo} * \\frac {dzo}{dbo} &#8230;.. (4)<br \/>$$<\/p>\n<p>\u0642\u0633\u0645\u062a \u0627\u0648\u0644 \u0627\u0632 <em>\u0645\u0639\u0627\u062f\u0644\u0647 4<\/em> \u0642\u0628\u0644\u0627 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a <em>\u0645\u0639\u0627\u062f\u0644\u0647 3<\/em>.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0641\u0642\u0637 \u0628\u0627\u06cc\u062f &#8220;dzo&#8221; \u0631\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 &#8220;bo&#8221; \u06a9\u0647 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc 1 \u0627\u0633\u062a \u0628\u0647 \u0631\u0648\u0632 \u06a9\u0646\u06cc\u0645. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646:<\/p>\n<p>$$<br \/>\\frac {dcost}{dbo} = ao &#8211; y &#8230;&#8230;&#8230;.. (5)<br \/>$$<\/p>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0627\u06cc\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0648\u0633\u0637 <em>\u0645\u0639\u0627\u062f\u0644\u0647 5<\/em> \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0627 \u0646\u0631\u062e \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0636\u0631\u0628 \u06a9\u0631\u062f \u0648 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u062a\u0639\u0635\u0628 \u0641\u0639\u0644\u06cc \u06a9\u0645 \u06a9\u0631\u062f.<\/p>\n<h4 id=\"phase2\">\u0641\u0627\u0632 2<\/h4>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0628\u062e\u0634\u060c \u062e\u0637\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u0644\u0627\u06cc\u0647 \u0642\u0628\u0644\u06cc \u0628\u0627\u0632 \u0645\u06cc\u200c\u06af\u0631\u062f\u0627\u0646\u06cc\u0645 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u06cc\u0639\u0646\u06cc \u0648\u0632\u0646\u200c\u0647\u0627\u06cc w1 \u062a\u0627 w8 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u062c\u0645\u0648\u0639\u0627\u064b \u0648\u0632\u0646 \u0644\u0627\u06cc\u0647 \u0647\u0627\u06cc \u067e\u0646\u0647\u0627\u0646 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 &#8220;wh&#8221; \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645.  \u0645\u0627 \u0627\u0633\u0627\u0633\u0627\u064b \u0628\u0627\u06cc\u062f \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0631\u0627 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 &#8220;wh&#8221; \u0645\u062a\u0645\u0627\u06cc\u0632 \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u0632 \u0646\u0638\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u0647 \u062a\u0645\u0627\u06cc\u0632 \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0622\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p>$$<br \/>\\frac {dcost}{dwh} = \\frac {dcost}{dah} *, \\frac {dah}{dzh} * \\frac {dzh}{dwh} &#8230;&#8230; (6)<br \/>$$<\/p>\n<p>\u0627\u06cc\u0646\u062c\u0627 \u0628\u0627\u0632 \u0647\u0645 \u0645\u06cc\u0634\u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0647 6<\/em> \u0628\u0647 \u0634\u0631\u0627\u06cc\u0637 \u0641\u0631\u062f\u06cc<\/p>\n<p>\u0627\u0648\u0644\u06cc\u0646 \u0639\u0628\u0627\u0631\u062a &#8220;dcost&#8221; \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 &#8220;dah&#8221; \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u0647 \u0627\u06cc \u062a\u0645\u0627\u06cc\u0632 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062a\u0645\u0627\u06cc\u0632 \u06a9\u0631\u062f:<\/p>\n<p>$$<br \/>\\frac {dcost}{dah} = \\frac {dcost}{dzo} *\\ \\frac {dzo}{dah} &#8230;&#8230; (7)<br \/>$$<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062f\u0648\u0628\u0627\u0631\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0634\u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0647 7<\/em> \u0628\u0647 \u0634\u0631\u0627\u06cc\u0637 \u0641\u0631\u062f\u06cc  \u0627\u0632 <em>\u0645\u0639\u0627\u062f\u0644\u0647 3<\/em>\u060c \u0645\u0627 \u0622\u0646 \u0631\u0627 \u0645\u06cc\u062f\u0627\u0646\u06cc\u0645:<\/p>\n<p>$$<br \/>\\frac {dcost}{dao} *\\ \\frac {dao}{dzo} =\\frac {dcost}{dzo} = = ao &#8211; y &#8230;&#8230;.. (8)<br \/>$$<\/p>\n<p>\u062d\u0627\u0644\u0627 \u0628\u0627\u06cc\u062f dzo\/dah \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0647 7<\/em>\u06a9\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0648\u0632\u0646 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0637\u0627\u0628\u0642 \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>\\frac {dzo}{dah} = wo &#8230;&#8230; (9)<br \/>$$<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0642\u062f\u0627\u0631 dcost\/dah \u0631\u0627 \u0628\u0627 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u06a9\u0631\u062f\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0632 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0627\u062a 8<\/em> \u0648 <em>9<\/em> \u06a9\u0647 \u062f\u0631 <em>\u0645\u0639\u0627\u062f\u0644\u0647 7<\/em>.<\/p>\n<p>\u0628\u0631\u06af\u0634\u062a\u0646 \u0628\u0647 <em>\u0645\u0639\u0627\u062f\u0644\u0647 6<\/em>\u060c \u0645\u0627 \u0647\u0646\u0648\u0632 dah\/dzh \u0648 dzh\/dwh \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0646\u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645.<\/p>\n<p>\u0627\u0648\u0644\u06cc\u0646 \u062a\u0631\u0645 dah\/dzh \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0631\u062f:<\/p>\n<p>$$<br \/>\\frac {dah}{dzh} = sigmoid(zh) * (1-sigmoid(zh)) &#8230;&#8230;.. (10)<br \/>$$<\/p>\n<p>\u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c dzh\/dwh \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0631\u0648\u062f\u06cc \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>\\frac {dzh}{dwh} = \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc &#8230;&#8230;.. (11)<br \/>$$<\/p>\n<p>\u0627\u06af\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0632 \u0631\u0627 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0627\u062a 7<\/em>\u060c <em>10<\/em> \u0648 <em>11<\/em> \u06a9\u0647 \u062f\u0631 <em>\u0645\u0639\u0627\u062f\u0644\u0647 6<\/em>\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0631\u0648\u0632 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0648\u0632\u0646 \u0644\u0627\u06cc\u0647 \u0647\u0627\u06cc \u067e\u0646\u0647\u0627\u0646 \u0631\u0627 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0646\u06cc\u0645.  \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0648\u0632\u0646\u200c\u0647\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 &#8220;wh&#8221;\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0631\u06af\u0631\u062f\u0627\u0646\u062f\u0647 \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 <em>\u0645\u0639\u0627\u062f\u0644\u0647 6<\/em> \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0627 \u0646\u0631\u062e \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0636\u0631\u0628 \u06a9\u0631\u062f \u0648 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u0632\u0646 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0641\u0639\u0644\u06cc \u06a9\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u0645\u0634\u062a\u0642 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0628\u0627\u06cc\u0627\u0633 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 &#8220;bh&#8221; \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u0648\u062f:<\/p>\n<p>$$<br \/>\\frac {dcost}{dbh} = \\frac {dcost}{dah} *, \\frac {dah}{dzh} * \\frac {dzh}{dbh} &#8230;&#8230; (12)<br \/>$$<\/p>\n<p>\u06a9\u0647 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u0628\u0627:<\/p>\n<p>$$<br \/>\\frac {dcost}{dbh} = \\frac {dcost}{dah} *, \\frac {dah}{dzh} &#8230;&#8230; (13)<br \/>$$<\/p>\n<p>\u0632\u06cc\u0631\u0627\u060c<\/p>\n<p>$$<br \/>\\frac {dzh}{dbh} = 1<br \/>$$<\/p>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0627\u06cc\u0627\u0633 \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0648\u0633\u0637 <em>\u0645\u0639\u0627\u062f\u0644\u0647 13<\/em> \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0627 \u0646\u0631\u062e \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0636\u0631\u0628 \u06a9\u0631\u062f \u0648 \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u0627\u06cc\u0627\u0633 \u0644\u0627\u06cc\u0647 \u067e\u0646\u0647\u0627\u0646 \u0641\u0639\u0644\u06cc \u06a9\u0645 \u06a9\u0631\u062f \u0648 \u0627\u06cc\u0646 \u0628\u0631\u0627\u06cc \u0627\u0646\u062a\u0634\u0627\u0631 \u0628\u0647 \u0639\u0642\u0628 \u0627\u0633\u062a.<\/p>\n<p>\u0634\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u0634\u0627\u0647\u062f\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0628\u0647 \u062c\u0644\u0648 \u0648 \u0639\u0642\u0628 \u0627\u0646\u062a\u0634\u0627\u0631 process \u06a9\u0627\u0645\u0644\u0627\u064b \u0634\u0628\u06cc\u0647 \u0686\u06cc\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u062e\u0631\u06cc\u0646 \u0645\u0642\u0627\u0644\u0627\u062a \u062e\u0648\u062f \u062f\u06cc\u062f\u06cc\u0645.  \u062a\u0646\u0647\u0627 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0645\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0627\u062f\u06cc\u0645 \u062a\u0627\u0628\u0639 \u0641\u0639\u0627\u0644 \u0633\u0627\u0632\u06cc \u0648 \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0627\u0633\u062a.<\/p>\n<h2 id=\"codeforneuralnetworksformulticlassclassification\"><span class=\"ez-toc-section\" id=\"%da%a9%d8%af_%d8%b4%d8%a8%da%a9%d9%87_%d9%87%d8%a7%db%8c_%d8%b9%d8%b5%d8%a8%db%8c_%d8%a8%d8%b1%d8%a7%db%8c_%d8%b7%d8%a8%d9%82%d9%87_%d8%a8%d9%86%d8%af%db%8c_%da%86%d9%86%d8%af_%da%a9%d9%84%d8%a7%d8%b3%d9%87\"><\/span>\u06a9\u062f \u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u0628\u0631\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u06a9\u0644\u0627\u0633\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0645\u0627 \u062a\u0626\u0648\u0631\u06cc \u067e\u0634\u062a \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u0637\u0628\u0642\u0647 \u067e\u0648\u0634\u0634 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc\u0645 \u0648 \u0627\u06a9\u0646\u0648\u0646 \u0632\u0645\u0627\u0646 \u0622\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u0646\u0638\u0631\u06cc\u0647 \u0631\u0627 \u0639\u0645\u0644\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u0647 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u062f\u0642\u062a \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n\nnp.random.seed(<span class=\"hljs-number\">42<\/span>)\n\ncat_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((<span class=\"hljs-number\">0<\/span>, -<span class=\"hljs-number\">3<\/span>))\nmouse_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">3<\/span>))\ndog_images = np.random.randn(<span class=\"hljs-number\">700<\/span>, <span class=\"hljs-number\">2<\/span>) + np.array((-<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">3<\/span>))\n\nfeature_set = np.vstack((cat_images, mouse_images, dog_images))\n\nlabels = np.array((<span class=\"hljs-number\">0<\/span>)*<span class=\"hljs-number\">700<\/span> + (<span class=\"hljs-number\">1<\/span>)*<span class=\"hljs-number\">700<\/span> + (<span class=\"hljs-number\">2<\/span>)*<span class=\"hljs-number\">700<\/span>)\n\none_hot_labels = np.zeros((<span class=\"hljs-number\">2100<\/span>, <span class=\"hljs-number\">3<\/span>))\n\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">2100<\/span>):\n    one_hot_labels(i, labels(i)) = <span class=\"hljs-number\">1<\/span>\n\nplt.figure(figsize=(<span class=\"hljs-number\">10<\/span>,<span class=\"hljs-number\">7<\/span>))\nplt.scatter(feature_set(:,<span class=\"hljs-number\">0<\/span>), feature_set(:,<span class=\"hljs-number\">1<\/span>), c=labels, cmap=<span class=\"hljs-string\">'plasma'<\/span>, s=<span class=\"hljs-number\">100<\/span>, alpha=<span class=\"hljs-number\">0.5<\/span>)\nplt.show()\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">sigmoid<\/span>(<span class=\"hljs-params\">x<\/span>):<\/span>\n    <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-number\">1<\/span>\/(<span class=\"hljs-number\">1<\/span>+np.exp(-x))\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">sigmoid_der<\/span>(<span class=\"hljs-params\">x<\/span>):<\/span>\n    <span class=\"hljs-keyword\">return<\/span> sigmoid(x) *(<span class=\"hljs-number\">1<\/span>-sigmoid (x))\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">softmax<\/span>(<span class=\"hljs-params\">A<\/span>):<\/span>\n    expA = np.exp(A)\n    <span class=\"hljs-keyword\">return<\/span> expA \/ expA.<span class=\"hljs-built_in\">sum<\/span>(axis=<span class=\"hljs-number\">1<\/span>, keepdims=<span class=\"hljs-literal\">True<\/span>)\n\ninstances = feature_set.shape(<span class=\"hljs-number\">0<\/span>)\nattributes = feature_set.shape(<span class=\"hljs-number\">1<\/span>)\nhidden_nodes = <span class=\"hljs-number\">4<\/span>\noutput_labels = <span class=\"hljs-number\">3<\/span>\n\nwh = np.random.rand(attributes,hidden_nodes)\nbh = np.random.randn(hidden_nodes)\n\nwo = np.random.rand(hidden_nodes,output_labels)\nbo = np.random.randn(output_labels)\nlr = <span class=\"hljs-number\">10e-4<\/span>\n\nerror_cost = ()\n\n<span class=\"hljs-keyword\">for<\/span> epoch <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(<span class=\"hljs-number\">50000<\/span>):\n\n\n    \n    zh = np.dot(feature_set, wh) + bh\n    ah = sigmoid(zh)\n\n    \n    zo = np.dot(ah, wo) + bo\n    ao = softmax(zo)\n\n\n\n\n\n    dcost_dzo = ao - one_hot_labels\n    dzo_dwo = ah\n\n    dcost_wo = np.dot(dzo_dwo.T, dcost_dzo)\n\n    dcost_bo = dcost_dzo\n\n\n\n    dzo_dah = wo\n    dcost_dah = np.dot(dcost_dzo , dzo_dah.T)\n    dah_dzh = sigmoid_der(zh)\n    dzh_dwh = feature_set\n    dcost_wh = np.dot(dzh_dwh.T, dah_dzh * dcost_dah)\n\n    dcost_bh = dcost_dah * dah_dzh\n\n    \n\n    wh -= lr * dcost_wh\n    bh -= lr * dcost_bh.<span class=\"hljs-built_in\">sum<\/span>(axis=<span class=\"hljs-number\">0<\/span>)\n\n    wo -= lr * dcost_wo\n    bo -= lr * dcost_bo.<span class=\"hljs-built_in\">sum<\/span>(axis=<span class=\"hljs-number\">0<\/span>)\n\n    <span class=\"hljs-keyword\">if<\/span> epoch % <span class=\"hljs-number\">200<\/span> == <span class=\"hljs-number\">0<\/span>:\n        loss = np.<span class=\"hljs-built_in\">sum<\/span>(-one_hot_labels * np.log(ao))\n        <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Loss function value: '<\/span>, loss)\n        error_cost.append(loss)\n<\/code><\/pre>\n<p>\u06a9\u062f \u0628\u0633\u06cc\u0627\u0631 \u0634\u0628\u06cc\u0647 \u0628\u0647 \u06a9\u062f\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0642\u0628\u0644\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645.  \u062f\u0631 \u0628\u062e\u0634 \u0641\u06cc\u062f \u0641\u0648\u0631\u0648\u0627\u0631\u062f\u060c \u062a\u0646\u0647\u0627 \u062a\u0641\u0627\u0648\u062a \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 &#8220;ao&#8221; \u06a9\u0647 \u062e\u0631\u0648\u062c\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a\u060c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <code>softmax<\/code> \u062a\u0627\u0628\u0639.<\/p>\n<p>\u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u062f\u0631 \u0628\u062e\u0634 \u067e\u0633 \u0627\u0646\u062a\u0634\u0627\u0631\u060c \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0648\u0632\u0646 \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc\u060c \u062a\u0627\u0628\u0639 \u0647\u0632\u06cc\u0646\u0647 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 <code>softmax<\/code> \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647 \u062c\u0627\u06cc <code>sigmoid<\/code> \u062a\u0627\u0628\u0639.<\/p>\n<p>\u0627\u06af\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f\u060c \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f \u06a9\u0647 \u0647\u0632\u06cc\u0646\u0647 \u062e\u0637\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc 0.5 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.  \u0634\u06a9\u0644 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0647\u0632\u06cc\u0646\u0647 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u062f\u0648\u0631\u0647 \u0647\u0627 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f.<\/p>\n<p><img decoding=\"async\" class=\"img-responsive\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/creating-neural-network-scratch-python-multi-class-classification-3.png\" alt=\"\u0647\u0632\u06cc\u0646\u0647 \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 \u062f\u0648\u0631\u0647 \u0647\u0627\" title=\"\"><\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f\u060c \u062f\u0648\u0631\u0647 \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0647\u0632\u06cc\u0646\u0647 \u062e\u0637\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0645\u0627 \u0644\u0627\u0632\u0645 \u0646\u06cc\u0633\u062a.<\/p>\n<p>\u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647\u060c \u0627\u06af\u0631 \u0647\u0645\u0627\u0646 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0631\u0627 \u0628\u0627 \u062a\u0627\u0628\u0639 sigmoid \u062f\u0631 \u0644\u0627\u06cc\u0647 \u062e\u0631\u0648\u062c\u06cc \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f\u060c \u062d\u062f\u0627\u0642\u0644 \u0647\u0632\u06cc\u0646\u0647 \u062e\u0637\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0639\u062f \u0627\u0632 50000 \u062f\u0648\u0631\u0647 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u0648\u0631\u06cc\u062f \u062d\u062f\u0648\u062f 1.5 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u06a9\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 0.5 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 softmax \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f.<\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0639\u0635\u0628\u06cc \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0642\u0627\u062f\u0631 \u0628\u0647 \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0686\u0646\u062f \u0637\u0628\u0642\u0647 \u0647\u0633\u062a\u0646\u062f.  \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u06cc\u062f\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc 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data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;16548&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0634\u0628\u06a9\u0647 \u0639\u0635\u0628\u06cc \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646: \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc 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