{"id":2675,"date":"2025-06-14T01:33:50","date_gmt":"2025-06-13T16:33:50","guid":{"rendered":"https:\/\/www.dogrow.net\/nnet\/?p=2675"},"modified":"2025-06-16T01:50:01","modified_gmt":"2025-06-15T16:50:01","slug":"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","status":"publish","type":"post","link":"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\/","title":{"rendered":"(58) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 ReLU(x)\u306e\u5fae\u5206"},"content":{"rendered":"

\u30101\u3011\u3084\u308a\u305f\u3044\u3053\u3068<\/h1>\n

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

\u524d\u56de\u3001\u524d\u3005\u56de\u306e\u6295\u7a3f\u3067\u306f\u3001\u6d3b\u6027\u5316\u95a2\u6570 tanh(x) \u3068 sigmoid(x) \u306e\u5fae\u5206\u3092\u898b\u305f\u3002
\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
\n(56) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 tanh(x)\u306e\u5fae\u5206<\/a>
\n(57) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 sigmoid(x)\u306e\u5fae\u5206<\/a>
\n(58) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 ReLU(x)\u306e\u5fae\u5206<\/a> \u2190\u4eca\u56de<\/span>
\n(59) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 MSE\uff08\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee\uff09\u306e\u5fae\u5206<\/a>
\n(60) \u4ed6\u30af\u30e9\u30b9\u5206\u985e\u3067\u4f7f\u3046 Softmax<\/a>
\n(61) \u6a5f\u68b0\u5b66\u7fd2\u3067\u591a\u7528\u3055\u308c\u308b\u30cd\u30a4\u30d4\u30a2\u6570\u3068\u306f\uff1f<\/a><\/p>\n

\u4eca\u56de\u306f\u3001\u540c\u3058\u304f\u6d3b\u6027\u5316\u95a2\u6570\u3068\u3057\u3066\u4f7f\u308f\u308c\u308b ReLU\u306e\u5fae\u5206\u306b\u3064\u3044\u3066\u898b\u3066\u307f\u308b\u3002
\n\u6539\u3081\u3066\u898b\u76f4\u3059\u3088\u3046\u306a\u3053\u3068\u306f\u7121\u3044\u306e\u3060\u304c\u5099\u5fd8\u9332\u30fb\u30fb\u30fb<\/p>\n

\u30102\u3011\u3084\u3063\u3066\u307f\u308b<\/h1>\n

1) ReLU\u3068\u306f\uff1f<\/h2>\n

ReLU(x), ReLU'(x) \u3092\u307e\u3068\u3081\u3066\u56f3\u793a\u3059\u308b\u3002
\n\"\"<\/p>\n

\u5165\u529b\u5024 x\u306e\u6b63\u8ca0\u3067\u51fa\u529b\u5024 y\u306e\u7b97\u51fa\u5f0f\u304c\u5909\u308f\u308b\u3002
\n\u3068\u3063\u3066\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u4ed5\u69d8\u3067\u3001\u8a08\u7b97\u6642\u306e\u30de\u30b7\u30f3\u8ca0\u8377\u304c\u975e\u5e38\u306b\u4f4e\u3044\u3002
\n\n
\u5165\u529b\u5024x<\/th>\u51fa\u529b\u5024y<\/th>\u5fae\u5206\u5024<\/th><\/tr>
x \uff1e 0<\/td>y = x<\/td>1<\/td><\/tr>
x \u2266 0<\/td>y = 0<\/td>0<\/td><\/tr>\n<\/table><\/p>\n
\r\nimport numpy as np\r\nimport matplotlib.pyplot as plt\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\ndef relu(x):                      # ReLU\u95a2\u6570\r\n    return np.maximum(0, x)\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\ndef relu_derivative(x):           # ReLU\u306e\u5c0e\u95a2\u6570\r\n    return np.where(x > 0, 1, 0)\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\nx = np.linspace(-10, 10, 400)     # x\u8ef8\u306e\u5024\r\ny_relu = relu(x)\r\ny_relu_prime = relu_derivative(x)\r\n\r\n#\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\nplt.figure(figsize=(10, 6))       # \u30b0\u30e9\u30d5\u306e\u63cf\u753b\r\nplt.plot(x, y_relu, label="ReLU(x)", linewidth=2)\r\nplt.plot(x, y_relu_prime, label="ReLU'(x)", linestyle='--', linewidth=2)\r\nplt.title("Graphs of ReLU(x) and ReLU'(x)")\r\nplt.xlabel("x")\r\nplt.ylabel("y")\r\nplt.xlim(-10, 10)\r\nplt.ylim(-1, 11)\r\nplt.yticks(np.arange(-1, 11, 1))  # Y\u8ef8\u30921\u523b\u307f\u306b\u8a2d\u5b9a\r\nplt.grid(True, which='major', axis='y', linestyle='--')  # Y\u8ef8\u30b0\u30ea\u30c3\u30c9\r\nplt.axhline(0, color='black', linewidth=0.5)\r\nplt.axvline(0, color='black', linewidth=0.5)\r\nplt.legend()\r\nplt.show()\r\n<\/pre>\n
2) S\u5b57\u95a2\u6570\u3067\u306f\u306a\u304f ReLU\u304c\u4f7f\u308f\u308c\u308b\u7406\u7531\u306f\uff1f<\/h2>\n
\u25a0\u9577\u6240<\/span>
\n\u30fb\u52fe\u914d\u6d88\u5931\uff08vanishing gradient\uff09\u3092\u8d77\u3053\u3057\u306b\u304f\u3044\u3002
\n\u3000\u203bS\u5b57\u578b\u95a2\u6570\uff08\u4f8b\uff1asigmoid, tanh\uff09\u306f\u3001\u5165\u529b\u306e\u7d76\u5bfe\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u52fe\u914d\uff08\u5c0e\u95a2\u6570\u306e\u5024\uff09\u304c 0 \u306b\u8fd1\u3065\u304f\uff08\u98fd\u548c\u3059\u308b\uff09\u7279\u6027\u304c\u3042\u308b\u3002
\n\u30fb\u8a08\u7b97\u304c\u9ad8\u901f
\n\u30fb\u30b9\u30d1\u30fc\u30b9\u306a\u6d3b\u6027\u5316\u3092\u751f\u3080\u3002
\n\u3000\u5165\u529b\u304c\u8ca0\u306e\u5834\u5408\u306b\u51fa\u529b\u304c 0 \u306b\u306a\u308b\u305f\u3081\u3001\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u4e00\u90e8\u304c\u81ea\u7136\u306b\u975e\u6d3b\u6027\uff08=0\uff09\u3068\u306a\u308a\u3001\u30b9\u30d1\u30fc\u30b9\u6027\u304c\u5f97\u3089\u308c\u308b\u3002
\n\u3000\u2192 \u904e\u5b66\u7fd2\u6291\u5236\u3084\u30e2\u30c7\u30eb\u306e\u52b9\u7387\u5316\u306b\u5bc4\u4e0e\u3002
\n\u30fb\u52fe\u914d\u304c\u5927\u304d\u304f\u6b8b\u308b\u30fb\u8a08\u7b97\u304c\u8efd\u3044\u30fb\u30b9\u30d1\u30fc\u30b9\u6027\u7b49\u306b\u3088\u308a\u3001\u5b66\u7fd2\u304c\u65e9\u304f\u5b89\u5b9a\u3057\u3084\u3059\u3044\u3002<\/p>\n
\u30b9\u30d1\u30fc\u30b9\u6027\uff1a<\/span>
\n\u300c\u307e\u3070\u3089\u300d\u300c\u5c11\u306a\u3044\u300d\u300c\u5bc6\u5ea6\u304c\u4f4e\u3044\u300d\u300c\u304e\u3063\u3057\u308a\u8a70\u307e\u3063\u3066\u3044\u306a\u3044\u3001\u3068\u3053\u308d\u3069\u3053\u308d\u3057\u304b\u5b58\u5728\u3057\u306a\u3044\u300d
\n\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3067\u3001\u51fa\u529b\u304c0\u306b\u306a\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u304c\u591a\u3044\u72b6\u614b\u306e\u3053\u3068\u3002<\/p>\n
\u53c2\u8003\uff1a <\/span>
\n\u30fb\u30b9\u30d1\u30fc\u30b9\u306a\u884c\u5217\uff08sparse matrix\uff09\uff1a \u8981\u7d20\u306e\u307b\u3068\u3093\u3069\u304c 0 \u306e\u884c\u5217
\n\u30fb\u30b9\u30d1\u30fc\u30b9\uff08sparse\uff09\u306a\u30c7\u30fc\u30bf\uff1a \u591a\u304f\u306e\u8981\u7d20\u304c\u300c0\u300d\u307e\u305f\u306f\u300c\u7a7a\u300d\u3067\u3042\u308b\u30c7\u30fc\u30bf
\n\u3000\u4f8b\uff1a[0, 0, 0, 1, 0, 0, 2, 0] \u306e\u3088\u3046\u306b\u3001\u5024\u304c\u3042\u308b\u7b87\u6240\u304c\u5c11\u306a\u3044<\/p>\n
\u25a0\u77ed\u6240<\/span>
\n\u30fbDead Neuron\u554f\u984c
\n\u3000\u5165\u529b\u304c\u5e38\u306b\u8ca0\u306e\u5024\u3070\u304b\u308a\u306b\u306a\u308b\u3068\u3001\u305d\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u51fa\u529b\u304c\u5e38\u306b0\u306b\u306a\u308a\u3001\u5b66\u7fd2\u3055\u308c\u306a\u304f\u306a\u308b\uff08dead neuron\uff09\u3002
\n\u3000\u5bfe\u7b56\u3068\u3057\u3066 Leaky ReLU, ELU, He\u521d\u671f\u5316\u3001\u9069\u5207\u306a\u5b66\u7fd2\u7387\uff08learning rate\uff09\u306e\u8a2d\u5b9a\u3001Dropout\u7b49\u3005\u3092\u5de5\u592b\u3059\u308b\u3002<\/p>\n
3) \u500b\u4eba\u7684\u306a ReLU\u3068\u306e\u51fa\u4f1a\u3044<\/h2>\n
\u521d\u3081\u3066 ReLU\u3092\u77e5\u3063\u305f\u306e\u306f 2014\u5e74\u306e\u3053\u3068\u3002
\n\u5f53\u6642\u3001\u753b\u50cf\u8a8d\u8b58\u30b7\u30b9\u30c6\u30e0\u958b\u767a\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u306b\u5f93\u4e8b\u3057\u3066\u3044\u305f\u6642\u306b\u3001\u30c1\u30fc\u30e0\u306e\u982d\u8133\u3060\u3063\u305f\u8ce2\u3044\u65b9\u304b\u3089\u306e\u6307\u793a\u3067 matlab\u5b9f\u88c5\u3057\u305f\u306e\u304c\u521d\u3081\u3060\u3063\u305f\u306f\u305a\u3002
\n\uff08\u305d\u306e 3\u5e74\u5f8c\u3001\u6211\u304c\u5b50\u306b\u540d\u524d\u3092\u3064\u3051\u308b\u3068\u304d\u306b\u3001\u305d\u306e\u65b9\u306e\u540d\u524d\u306e\u4e00\u6587\u5b57\u3092\u3044\u305f\u3060\u304d\u307e\u3057\u305f\u3002\uff09<\/p>\n
\u6d3b\u6027\u5316\u95a2\u6570\u3068\u8a00\u3048\u3070 sigmoid or tanh \u3068\u6c7a\u3081\u3064\u3051\u3066\u4f7f\u3063\u3066\u3044\u305f\u81ea\u5206\u306b\u306f\u885d\u6483\u7684\u3060\u3063\u305f\u3002
\n\"\"
\n\u3048\u3063\uff1f
\n\u3053\u3093\u306a\u5358\u7d14\u306a\u30ed\u30b8\u30c3\u30af\u3067\u3088\u3044\u306e\uff1f
\n\u5165\u529b\u5024\u304c\u5927\u304d\u304f\u306a\u3063\u305f\u3089\u7206\u767a\u3059\u308b\u3067\u3057\u3087\uff1f
\n\u5165\u529b\u5024\u304c\u8ca0\u306e\u6642\u306b\u52fe\u914d\u304c\u6d88\u3048\u308b\u3093\u3067\u3059\u3051\u3069\uff1f<\/span><\/p>\n
\u3057\u304b\u3057\u30fb\u30fb\u30fb
\n\u305d\u306e\u5fc3\u914d\u306f\u3059\u3050\u306b\u671f\u5f85\u3078\u3068\u5909\u308f\u3063\u305f\u3002
\n\u901f\u3044\uff01
\n\u30a8\u30e9\u30fc\u5024\u304c\u4e0b\u304c\u308b\u4e0b\u304c\u308b\uff01 \u5b66\u7fd2\u304c\u9032\u3080\u9032\u3080\uff01<\/span><\/p>\n
\u305d\u308c\u4ee5\u6765\u3001Neural Network\u3092\u4f5c\u308b\u3068\u304d\u306b\u306f\u5fc5\u305a\u7d44\u307f\u8fbc\u307f\u3001\u6709\u52b9\u6027\u3092\u8a66\u3057\u3066\u3044\u308b\u3002<\/p>\n
4) ReLU'(x)\u306e\u8a08\u7b97\u5f0f<\/h2>\n
\u5b9a\u7fa9\uff1a<\/span>
\n\"\"<\/p>\n
\u5c0e\u95a2\u6570\uff1a<\/span>
\n<\/p>\n
\u30de\u30b7\u30f3\u8ca0\u8377\u304c\u4f4e\u3044\u3001\u3053\u306e\u30b7\u30f3\u30d7\u30eb\u3055\u304c ReLU\u306e\u7279\u5fb4\u3060\u3002<\/span><\/p>\n
5) ReLU\u306e\u5fae\u5206\u3092 Python\u3067\u5b9f\u88c5\u3059\u308b\u3002<\/h2>\n
\r\ndef relu(x):\r\n    return np.maximum(0, x)\r\n\r\ndef relu_derivative(x):\r\n    return np.where(x > 0, 1, 0)\r\n<\/pre>\n
\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
\nnumpy\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
\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>
\n\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
\n","protected":false},"excerpt":{"rendered":"
\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\u3001\u524d\u3005\u56de\u306e\u6295\u7a3f\u3067\u306f\u3001\u6d3b\u6027\u5316\u95a2\u6570 tanh(x) \u3068 si\u2026 \u7d9a\u304d\u3092\u8aad\u3080 »<\/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":[23,32],"tags":[],"class_list":["post-2675","post","type-post","status-publish","format-standard","hentry","category-23","category-32"],"views":853,"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2675","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=2675"}],"version-history":[{"count":41,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2675\/revisions"}],"predecessor-version":[{"id":2930,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/posts\/2675\/revisions\/2930"}],"wp:attachment":[{"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/media?parent=2675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/categories?post=2675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dogrow.net\/nnet\/wp-json\/wp\/v2\/tags?post=2675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}