{"id":2582,"date":"2025-06-13T01:09:34","date_gmt":"2025-06-12T16:09:34","guid":{"rendered":"https:\/\/www.dogrow.net\/nnet\/?p=2582"},"modified":"2025-06-16T01:49:42","modified_gmt":"2025-06-15T16:49:42","slug":"blog57-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86sigmoidx%e3%81%ae%e5%be%ae%e5%88%86","status":"publish","type":"post","link":"https:\/\/www.dogrow.net\/nnet\/blog57-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86sigmoidx%e3%81%ae%e5%be%ae%e5%88%86\/","title":{"rendered":"(57) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 sigmoid(x)\u306e\u5fae\u5206"},"content":{"rendered":"<h1 class=\"my_h\">\u30101\u3011\u3084\u308a\u305f\u3044\u3053\u3068<\/h1>\n<p>PyTorch\u3084 TensorFlow\u306a\u3069\u306e\u6a5f\u68b0\u5b66\u7fd2\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u308f\u306a\u3044\u5834\u5408\u3001\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u63d0\u4f9b\u3057\u3066\u304f\u308c\u3066\u3044\u308b\u6a5f\u80fd\u3092\u81ea\u529b\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n<p>\u524d\u56de\u306e\u6295\u7a3f\u3067\u306f\u3001\u6d3b\u6027\u5316\u95a2\u6570 tanh(x) \u306e\u5fae\u5206\u3092\u898b\u305f\u3002<br \/>\n\u300c\u9006\u4f1d\u64ad\u3067\u4f7f\u3046\u5fae\u5206\u300d\u30b7\u30ea\u30fc\u30ba\u306e\u6295\u7a3f\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/blog56-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86tanhx%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\">(56) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 tanh(x)\u306e\u5fae\u5206<\/a><br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/blog57-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86sigmoidx%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\">(57) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 sigmoid(x)\u306e\u5fae\u5206<\/a> <span class='my_fw_bold'>\u2190\u4eca\u56de<\/span><br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/58-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86-relux%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\">(58) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 ReLU(x)\u306e\u5fae\u5206<\/a><br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/blog59-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86-mse%ef%bc%88%e5%b9%b3%e5%9d%87%e4%ba%8c%e4%b9%97%e8%aa%a4%e5%b7%ae%ef%bc%89%e3%81%ae%e5%be%ae%e5%88%86\/\" target=\"_blank\">(59) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 MSE\uff08\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee\uff09\u306e\u5fae\u5206<\/a><br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/blog60-%e4%bb%96%e3%82%af%e3%83%a9%e3%82%b9%e5%88%86%e9%a1%9e%e3%81%a7%e4%bd%bf%e3%81%86softmax\/\" target=\"_blank\">(60) \u4ed6\u30af\u30e9\u30b9\u5206\u985e\u3067\u4f7f\u3046 Softmax<\/a><br \/>\n<a href=\"https:\/\/www.dogrow.net\/nnet\/blog61-%e3%83%8d%e3%82%a4%e3%83%94%e3%82%a2%e6%95%b0e%e3%81%af%e5%be%ae%e5%88%86%e3%81%97%e3%81%a6%e3%82%82e%e3%81%ab%e3%81%aa%e3%82%8b%e3%80%82\/\" target=\"_blank\">(61) \u6a5f\u68b0\u5b66\u7fd2\u3067\u591a\u7528\u3055\u308c\u308b\u30cd\u30a4\u30d4\u30a2\u6570\u3068\u306f\uff1f<\/a><\/p>\n<p>\u4eca\u56de\u306f\u3001\u540c\u3058\u304f\u6d3b\u6027\u5316\u95a2\u6570\u3068\u3057\u3066\u4f7f\u308f\u308c\u308b sigmoid\u306e\u5fae\u5206\u306b\u3064\u3044\u3066\u898b\u3066\u307f\u308b\u3002<\/p>\n<h1 class=\"my_h\">\u30102\u3011\u3084\u3063\u3066\u307f\u308b<\/h1>\n<h2 class=\"my_h\">1) sigmoid\u3068\u306f\uff1f<\/h2>\n<p>sigmoid(x), sigmoid'(x) \u3092\u307e\u3068\u3081\u3066\u56f3\u793a\u3059\u308b\u3002<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/i4.jpg\" alt=\"\"  \/><\/p>\n<p>sigmoid\u95a2\u6570\u306f S\u5b57\u66f2\u7dda\u306a\u306e\u3067\u3001\u5fae\u5206\u5024\u306f x=0\u3067\u6700\u5927\u5024\u3092\u53d6\u308a\u3001S\u5b57\u306e\u7aef\u3078\u5411\u304b\u3063\u3066 0\u3078\u53ce\u675f\u3057\u3066\u3044\u304f\u3002<br \/>\n\u3053\u308c\u306f tanh(x)\u306e\u3068\u304d\u3068\u540c\u3058\u3060\u3002<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nimport numpy as np\r\nimport matplotlib.pyplot as plt\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\ndef sigmoid(x):                   # \u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\r\n    return 1 \/ (1 + np.exp(-x))\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\ndef sigmoid_derivative(x):        # \u5fae\u5206\uff08sigmoid(x) * (1 - sigmoid(x))\uff09\r\n    s = sigmoid(x)\r\n    return s * (1 - s)\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\nx = np.linspace(-10, 10, 500)     # x \u306e\u7bc4\u56f2\r\ny_sigmoid = sigmoid(x)\r\ny_deriv = sigmoid_derivative(x)\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\nplt.figure(figsize=(10, 6))       # \u30b0\u30e9\u30d5\u8868\u793a\r\nplt.plot(x, y_sigmoid, label=&quot;sigmoid(x)&quot;, linewidth=2)\r\nplt.plot(x, y_deriv, label=&quot;sigmoid&#039;(x)&quot;, linestyle=&#039;--&#039;, linewidth=2)\r\nplt.title(&quot;sigmoid Function and Its Derivative&quot;)\r\nplt.xlabel(&quot;x&quot;)\r\nplt.ylabel(&quot;value&quot;)\r\nplt.grid(True)\r\nplt.legend()\r\nplt.show()\r\n<\/pre>\n<h2 class=\"my_h\">2) S\u5b57\u95a2\u6570\u3092\u4f7f\u3046\u7406\u7531\u306f\uff1f<\/h2>\n<p><span class='my_fc_blueBBig'>\u25a0\u9577\u6240<\/span><br \/>\n\u975e\u7dda\u5f62\u306a\u306e\u3067\u3001\u8907\u96d1\u306a\u95a2\u6570\u3084\u30d1\u30bf\u30fc\u30f3\u304c\u5b66\u3079\u308b\u3002<br \/>\n\u51fa\u529b\u304c\u4e00\u5b9a\u7bc4\u56f2\u306b\u53ce\u307e\u308b\u305f\u3081\u3001\u5b89\u5b9a\u6027\u304c\u3042\u308b\u3002<br \/>\n\u306a\u3081\u3089\u304b\u3067\u5fae\u5206\u53ef\u80fd\uff08\uff1d\u9023\u7d9a\u7684\uff09\u306a\u305f\u3081\u3001\u52fe\u914d\u964d\u4e0b\u6cd5\u304c\u4f7f\u3048\u308b\u3002<\/p>\n<p><span class='my_fc_redBBig'>\u25a0\u77ed\u6240<\/span><br \/>\nx\u306e\u7d76\u5bfe\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u5fae\u5206\u304c\u307b\u307c 0\u306b\u306a\u308b\u3002\u2192 <span class='my_fc_redBBig'>\u52fe\u914d\u6d88\u5931<\/span><\/p>\n<h2 class=\"my_h\">3) sigmoid'(x)\u306e\u8a08\u7b97\u5f0f<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image1-2.jpg\" alt=\"\" \/><\/p>\n<p><span class='my_fs_big2B'>\u25a0\u8a3c\u660e<\/span><br \/>\n\u4ee5\u4e0b\u3001\u611a\u76f4\u306b\u3053\u308c\u3092\u8a3c\u660e\u3057\u3066\u307f\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image4-1.jpg\" alt=\"\" \/><\/p>\n<p>\u3053\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e8c\u3064\u306e\u95a2\u6570\u306b\u5206\u3051\u3001\u5408\u6210\u95a2\u6570\u306e\u5fae\u5206\u306b\u3059\u308b\u3002<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image5-1.jpg\" alt=\"\" \/><\/p>\n<p>\u3053\u3046\u3059\u308b\u3068\u3001\u5408\u6210\u95a2\u6570\u306e\u5fae\u5206\u306e\u9023\u9396\u5f8b\uff08chain rule\uff09\u306b\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5c55\u958b\u3067\u304d\u308b\u3002<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image6-1.jpg\" alt=\"\" \/>\u30fb\u30fb\u30fb(1)<\/p>\n<p>\u3053\u3053\u3067\u3001<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image8.jpg\" alt=\"\" \/><\/p>\n<p>\u3053\u308c\u3089\u3092 (1) \u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<br \/>\n<img decoding=\"async\" src=\"https:\/\/www.dogrow.net\/nnet\/wp-content\/uploads\/2025\/06\/Image13.jpg\" alt=\"\" \/><\/p>\n<p><span class='my_fc_blueBBig'>OK\u3060\uff01<\/span><\/p>\n<h2 class=\"my_h\">4) sigmoid\u306e\u5fae\u5206\u3092 Python\u3067\u5b9f\u88c5\u3059\u308b\u3002<\/h2>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\ndef sigmoid(x):\r\n    return 1 \/ (1 + np.exp(-x))\r\n\r\ndef sigmoid_derivative(x):\r\n    s = sigmoid(x)\r\n    return s * (1 - s)\r\n<\/pre>\n<p>\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\u306b\u898b\u3048\u308b\u304c\u3001\u3053\u3053\u306b\u306f Python + Numpy\u306e\u5e95\u529b\u304c\u96a0\u308c\u3066\u3044\u308b\u3002<br \/>\n<span class='my_fc_blueBBig'>numpy\u306e\u30d9\u30af\u30c8\u30eb\u5316\u95a2\u6570\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u5165\u529b\u5024 x\u306f\u591a\u6b21\u5143\u914d\u5217\uff08ndarray\uff09\u3092\u4f7f\u3048\u308b\u3002<br \/>\n \u2192 \u30df\u30cb\u30d0\u30c3\u30c1\u30c7\u30fc\u30bf\u7b49\u3001\u8907\u6570\u30c7\u30fc\u30bf\u3092\u307e\u3068\u3081\u3066\u51e6\u7406\u3067\u304d\u308b\u3002<\/span><br \/>\n<span class='my_fc_deeppinkBBig'>\u203b\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u4e26\u5217\u51e6\u7406\u306f\u30e9\u30a4\u30d6\u30e9\u30ea\u5185\u90e8\u306b\u96a0\u853d\u3055\u308c\u3066\u3044\u308b\u3002<\/span><\/p>\n<hr class=\"my_hr_bottom\">\n","protected":false},"excerpt":{"rendered":"<p>\u30101\u3011\u3084\u308a\u305f\u3044\u3053\u3068 PyTorch\u3084 TensorFlow\u306a\u3069\u306e\u6a5f\u68b0\u5b66\u7fd2\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u308f\u306a\u3044\u5834\u5408\u3001\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u63d0\u4f9b\u3057\u3066\u304f\u308c\u3066\u3044\u308b\u6a5f\u80fd\u3092\u81ea\u529b\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002 \u524d\u56de\u306e\u6295\u7a3f\u3067\u306f\u3001\u6d3b\u6027\u5316\u95a2\u6570 tanh(x) \u306e\u5fae\u5206\u3092\u898b\u305f\u3002 \u2026 <span class=\"read-more\"><a href=\"https:\/\/www.dogrow.net\/nnet\/blog57-%e9%80%86%e4%bc%9d%e6%92%ad%e3%81%a7%e4%bd%bf%e3%81%86sigmoidx%e3%81%ae%e5%be%ae%e5%88%86\/\">\u7d9a\u304d\u3092\u8aad\u3080 &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34,23,32],"tags":[],"class_list":["post-2582","post","type-post","status-publish","format-standard","hentry","category-34","category-23","category-32"],"views":671,"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/comments?post=2582"}],"version-history":[{"count":25,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2582\/revisions"}],"predecessor-version":[{"id":2929,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2582\/revisions\/2929"}],"wp:attachment":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/media?parent=2582"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/categories?post=2582"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/tags?post=2582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}