{"id":9224,"date":"2024-03-20T15:10:25","date_gmt":"2024-03-20T07:10:25","guid":{"rendered":"\/?p=9224"},"modified":"2024-03-20T15:10:25","modified_gmt":"2024-03-20T07:10:25","slug":"%e6%bf%80%e6%b4%bb%e5%87%bd%e6%95%b0%e5%92%8c%e5%a4%9a%e5%88%86%e7%b1%bbsoftmax%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"\/?p=9224","title":{"rendered":"\u6fc0\u6d3b\u51fd\u6570\u548c\u591a\u5206\u7c7b(softmax\u56de\u5f52)"},"content":{"rendered":"<h2>\u6fc0\u6d3b\u51fd\u6570<\/h2>\n<p>\u6fc0\u6d3b\u51fd\u6570\u65e8\u5728\u5e2e\u52a9\u7f51\u7edc\u5b66\u4e60\u6570\u636e\u4e2d\u7684\u590d\u6742\u6a21\u5f0f\uff0c\u7c7b\u4f3c\u4e8e\u4eba\u7c7b\u5927\u8111\u4e2d\u7684\u795e\u7ecf\u5143\u6a21\u578b\uff0c\u6fc0\u6d3b\u51fd\u6570\u51b3\u5b9a\u4e86\u5411\u50cf\u4e00\u4e2a\u4f20\u7ecf\u5143\u4f20\u9012\u7684\u6570\u503c\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240320135642760.png\" alt=\"image-20240320135642760\" \/><\/p>\n<p>\u6fc0\u6d3b\u51fd\u6570\uff08Activation Function\uff09\u662f\u4e00\u79cd\u6dfb\u52a0\u5230\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u51fd\u6570\uff0c\u65e8\u5728\u5e2e\u52a9\u7f51\u7edc\u5b66\u4e60\u6570\u636e\u4e2d\u7684\u590d\u6742\u6a21\u5f0f\u3002\u7c7b\u4f3c\u4e8e\u4eba\u7c7b\u5927\u8111\u4e2d\u57fa\u4e8e\u795e\u7ecf\u5143\u7684\u6a21\u578b\uff0c\u6fc0\u6d3b\u51fd\u6570\u6700\u7ec8\u51b3\u5b9a\u4e86\u8981\u53d1\u5c04\u7ed9\u4e0b\u4e00\u4e2a\u795e\u7ecf\u5143\u7684\u5185\u5bb9\u3002<\/p>\n<p>\u5728\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u4e00\u4e2a\u8282\u70b9\u7684\u6fc0\u6d3b\u51fd\u6570\u5b9a\u4e49\u4e86\u8be5\u8282\u70b9\u5728\u7ed9\u5b9a\u7684\u8f93\u5165\u6216\u8f93\u5165\u96c6\u5408\u4e0b\u7684\u8f93\u51fa\u3002\u6807\u51c6\u7684\u8ba1\u7b97\u673a\u82af\u7247\u7535\u8def\u53ef\u4ee5\u770b\u4f5c\u662f\u6839\u636e\u8f93\u5165\u5f97\u5230\u5f00\uff081\uff09\u6216\u5173\uff080\uff09\u8f93\u51fa\u7684\u6570\u5b57\u7535\u8def\u6fc0\u6d3b\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u6fc0\u6d3b\u51fd\u6570\u662f\u786e\u5b9a\u795e\u7ecf\u7f51\u7edc\u8f93\u51fa\u7684\u6570\u5b66\u65b9\u7a0b\u5f0f\uff0c\u672c\u6587\u6982\u8ff0\u4e86\u6df1\u5ea6\u5b66\u4e60\u4e2d\u5e38\u89c1\u7684\u5341\u79cd\u6fc0\u6d3b\u51fd\u6570\u53ca\u5176\u4f18\u7f3a\u70b9\u3002<\/p>\n<p>\u9996\u5148\u6211\u4eec\u6765\u4e86\u89e3\u4e00\u4e0b\u4eba\u5de5\u795e\u7ecf\u5143\u7684\u5de5\u4f5c\u539f\u7406\uff0c\u5927\u81f4\u5982\u4e0b\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240320150246246.png\" alt=\"image-20240320150246246\" \/><\/p>\n<p>\u5c06\u5176\u8fc7\u7a0b\u53ef\u89c6\u5316\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240320135854709.png\" alt=\"image-20240320135854709\" \/><\/p>\n<h3><strong>1. Sigmoid \u6fc0\u6d3b\u51fd\u6570<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/2afc1f657b624e12b13305d55c2f8d4a.png\" alt=\"img\" \/><\/p>\n<p>Sigmoid \u51fd\u6570\u7684\u56fe\u50cf\u770b\u8d77\u6765\u50cf\u4e00\u4e2a S \u5f62\u66f2\u7ebf\u3002<\/p>\n<p>\u51fd\u6570\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/36902fbbfcb24f88a7a106f142478db8.png\" alt=\"img\" \/><\/p>\n<p>\u5728\u4ec0\u4e48\u60c5\u51b5\u4e0b\u9002\u5408\u4f7f\u7528 Sigmoid \u6fc0\u6d3b\u51fd\u6570\u5462\uff1f<\/p>\n<ul>\n<li>Sigmoid \u51fd\u6570\u7684\u8f93\u51fa\u8303\u56f4\u662f 0 \u5230 1\u3002\u7531\u4e8e\u8f93\u51fa\u503c\u9650\u5b9a\u5728 0 \u5230 1\uff0c\u56e0\u6b64\u5b83\u5bf9\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u8fdb\u884c\u4e86\u5f52\u4e00\u5316\uff1b<\/li>\n<li>\u7528\u4e8e\u5c06\u9884\u6d4b\u6982\u7387\u4f5c\u4e3a\u8f93\u51fa\u7684\u6a21\u578b\u3002\u7531\u4e8e\u6982\u7387\u7684\u53d6\u503c\u8303\u56f4\u662f 0 \u5230 1\uff0c\u56e0\u6b64 Sigmoid \u51fd\u6570\u975e\u5e38\u5408\u9002\uff1b<\/li>\n<li>\u68af\u5ea6\u5e73\u6ed1\uff0c\u907f\u514d\u300c\u8df3\u8dc3\u300d\u7684\u8f93\u51fa\u503c\uff1b<\/li>\n<li>\u51fd\u6570\u662f\u53ef\u5fae\u7684\u3002\u8fd9\u610f\u5473\u7740\u53ef\u4ee5\u627e\u5230\u4efb\u610f\u4e24\u4e2a\u70b9\u7684 sigmoid \u66f2\u7ebf\u7684\u659c\u7387\uff1b<\/li>\n<li>\u660e\u786e\u7684\u9884\u6d4b\uff0c\u5373\u975e\u5e38\u63a5\u8fd1 1 \u6216 0\u3002<\/li>\n<\/ul>\n<p>Sigmoid \u6fc0\u6d3b\u51fd\u6570\u6709\u54ea\u4e9b\u7f3a\u70b9\uff1f<\/p>\n<ul>\n<li>\u503e\u5411\u4e8e\u68af\u5ea6\u6d88\u5931\uff1b<\/li>\n<li>\u51fd\u6570\u8f93\u51fa\u4e0d\u662f\u4ee5 0 \u4e3a\u4e2d\u5fc3\u7684\uff0c\u8fd9\u4f1a\u964d\u4f4e\u6743\u91cd\u66f4\u65b0\u7684\u6548\u7387\uff1b<\/li>\n<li>Sigmoid \u51fd\u6570\u6267\u884c\u6307\u6570\u8fd0\u7b97\uff0c\u8ba1\u7b97\u673a\u8fd0\u884c\u5f97\u8f83\u6162\u3002<\/li>\n<\/ul>\n<h3><strong>2. Tanh \/ \u53cc\u66f2\u6b63\u5207\u6fc0\u6d3b\u51fd\u6570<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/fe5d3e703f63486fa092e72cfa1ee61c.png\" alt=\"img\" \/><\/p>\n<p>tanh \u6fc0\u6d3b\u51fd\u6570\u7684\u56fe\u50cf\u4e5f\u662f S \u5f62\uff0c\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/6db0c4c909f347ac8f375ae8b5d70b6c.png\" alt=\"img\" \/><\/p>\n<p>tanh \u662f\u4e00\u4e2a\u53cc\u66f2\u6b63\u5207\u51fd\u6570\u3002tanh \u51fd\u6570\u548c sigmoid \u51fd\u6570\u7684\u66f2\u7ebf\u76f8\u5bf9\u76f8\u4f3c\u3002\u4f46\u662f\u5b83\u6bd4 sigmoid \u51fd\u6570\u66f4\u6709\u4e00\u4e9b\u4f18\u52bf\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/25bb23f551a74eee926e1c69f261af19.png\" alt=\"img\" \/><\/p>\n<ul>\n<li>\u9996\u5148\uff0c\u5f53\u8f93\u5165\u8f83\u5927\u6216\u8f83\u5c0f\u65f6\uff0c\u8f93\u51fa\u51e0\u4e4e\u662f\u5e73\u6ed1\u7684\u5e76\u4e14\u68af\u5ea6\u8f83\u5c0f\uff0c\u8fd9\u4e0d\u5229\u4e8e\u6743\u91cd\u66f4\u65b0\u3002\u4e8c\u8005\u7684\u533a\u522b\u5728\u4e8e\u8f93\u51fa\u95f4\u9694\uff0ctanh \u7684\u8f93\u51fa\u95f4\u9694\u4e3a 1\uff0c\u5e76\u4e14\u6574\u4e2a\u51fd\u6570\u4ee5 0 \u4e3a\u4e2d\u5fc3\uff0c\u6bd4 sigmoid \u51fd\u6570\u66f4\u597d\uff1b<\/li>\n<li>\u5728 tanh \u56fe\u4e2d\uff0c\u8d1f\u8f93\u5165\u5c06\u88ab\u5f3a\u6620\u5c04\u4e3a\u8d1f\uff0c\u800c\u96f6\u8f93\u5165\u88ab\u6620\u5c04\u4e3a\u63a5\u8fd1\u96f6\u3002<\/li>\n<\/ul>\n<p>\u6ce8\u610f\uff1a\u5728\u4e00\u822c\u7684\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\u4e2d\uff0ctanh \u51fd\u6570\u7528\u4e8e\u9690\u85cf\u5c42\uff0c\u800c sigmoid \u51fd\u6570\u7528\u4e8e\u8f93\u51fa\u5c42\uff0c\u4f46\u8fd9\u5e76\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u9700\u8981\u6839\u636e\u7279\u5b9a\u95ee\u9898\u8fdb\u884c\u8c03\u6574\u3002<\/p>\n<h3><strong>3. ReLU \u6fc0\u6d3b\u51fd\u6570<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/ee2721d9712346fc9ae7e80e03520ff6.png\" alt=\"img\" \/><\/p>\n<p>ReLU \u6fc0\u6d3b\u51fd\u6570\u56fe\u50cf\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u51fd\u6570\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/53c3f4cdfdb3455d97693b1b69a5fdb7.png\" alt=\"img\" \/><\/p>\n<p>ReLU \u51fd\u6570\u662f\u6df1\u5ea6\u5b66\u4e60\u4e2d\u8f83\u4e3a\u6d41\u884c\u7684\u4e00\u79cd\u6fc0\u6d3b\u51fd\u6570\uff0c\u76f8\u6bd4\u4e8e sigmoid \u51fd\u6570\u548c tanh \u51fd\u6570\uff0c\u5b83\u5177\u6709\u5982\u4e0b\u4f18\u70b9\uff1a<\/p>\n<ul>\n<li>\u5f53\u8f93\u5165\u4e3a\u6b63\u65f6\uff0c\u4e0d\u5b58\u5728\u68af\u5ea6\u9971\u548c\u95ee\u9898\u3002<\/li>\n<li>\u8ba1\u7b97\u901f\u5ea6\u5feb\u5f97\u591a\u3002ReLU \u51fd\u6570\u4e2d\u53ea\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff0c\u56e0\u6b64\u5b83\u7684\u8ba1\u7b97\u901f\u5ea6\u6bd4 sigmoid \u548c tanh \u66f4\u5feb\u3002<\/li>\n<\/ul>\n<p>\u5f53\u7136\uff0c\u5b83\u4e5f\u6709\u7f3a\u70b9\uff1a<\/p>\n<ol>\n<li>Dead ReLU \u95ee\u9898\u3002\u5f53\u8f93\u5165\u4e3a\u8d1f\u65f6\uff0cReLU \u5b8c\u5168\u5931\u6548\uff0c\u5728\u6b63\u5411\u4f20\u64ad\u8fc7\u7a0b\u4e2d\uff0c\u8fd9\u4e0d\u662f\u95ee\u9898\u3002\u6709\u4e9b\u533a\u57df\u5f88\u654f\u611f\uff0c\u6709\u4e9b\u5219\u4e0d\u654f\u611f\u3002\u4f46\u662f\u5728\u53cd\u5411\u4f20\u64ad\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u8f93\u5165\u8d1f\u6570\uff0c\u5219\u68af\u5ea6\u5c06\u5b8c\u5168\u4e3a\u96f6\uff0csigmoid \u51fd\u6570\u548c tanh \u51fd\u6570\u4e5f\u5177\u6709\u76f8\u540c\u7684\u95ee\u9898\uff1b<\/li>\n<li>\u6211\u4eec\u53d1\u73b0 ReLU \u51fd\u6570\u7684\u8f93\u51fa\u4e3a 0 \u6216\u6b63\u6570\uff0c\u8fd9\u610f\u5473\u7740 ReLU \u51fd\u6570\u4e0d\u662f\u4ee5 0 \u4e3a\u4e2d\u5fc3\u7684\u51fd\u6570\u3002<\/li>\n<\/ol>\n<h3><strong>4. Leaky ReLU<\/strong><\/h3>\n<p>\u5b83\u662f\u4e00\u79cd\u4e13\u95e8\u8bbe\u8ba1\u7528\u4e8e\u89e3\u51b3 Dead ReLU \u95ee\u9898\u7684\u6fc0\u6d3b\u51fd\u6570\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/21290590b8f245d8a43f3833940cbf54.png\" alt=\"img\" \/><\/p>\n<p>ReLU vs Leaky ReLU<\/p>\n<p>\u4e3a\u4ec0\u4e48 Leaky ReLU \u6bd4 ReLU \u66f4\u597d\uff1f<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/4ca97e9808644b9eb3957e71d177287a.png\" alt=\"img\" \/><\/p>\n<ol>\n<li>Leaky ReLU \u901a\u8fc7\u628a x \u7684\u975e\u5e38\u5c0f\u7684\u7ebf\u6027\u5206\u91cf\u7ed9\u4e88\u8d1f\u8f93\u5165\uff080.01x\uff09\u6765\u8c03\u6574\u8d1f\u503c\u7684\u96f6\u68af\u5ea6\uff08zero gradients\uff09\u95ee\u9898\uff1b<\/li>\n<li>leak \u6709\u52a9\u4e8e\u6269\u5927 ReLU \u51fd\u6570\u7684\u8303\u56f4\uff0c\u901a\u5e38 a \u7684\u503c\u4e3a 0.01 \u5de6\u53f3\uff1b<\/li>\n<li>Leaky ReLU \u7684\u51fd\u6570\u8303\u56f4\u662f\uff08\u8d1f\u65e0\u7a77\u5230\u6b63\u65e0\u7a77\uff09\u3002<\/li>\n<\/ol>\n<p><strong>\u6ce8\u610f\uff1a<\/strong>\u4ece\u7406\u8bba\u4e0a\u8bb2\uff0cLeaky ReLU \u5177\u6709 ReLU \u7684\u6240\u6709\u4f18\u70b9\uff0c\u800c\u4e14 Dead ReLU \u4e0d\u4f1a\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u4f46\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u5c1a\u672a\u5b8c\u5168\u8bc1\u660e Leaky ReLU \u603b\u662f\u6bd4 ReLU \u66f4\u597d\u3002<\/p>\n<h3><strong>5. ELU<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/ae214e9687204a15931f5a58bc4b2f4c.png\" alt=\"img\" \/><\/p>\n<p>ELU vs Leaky ReLU vs ReLU<\/p>\n<p>ELU \u7684\u63d0\u51fa\u4e5f\u89e3\u51b3\u4e86 ReLU \u7684\u95ee\u9898\u3002\u4e0e ReLU \u76f8\u6bd4\uff0cELU \u6709\u8d1f\u503c\uff0c\u8fd9\u4f1a\u4f7f\u6fc0\u6d3b\u7684\u5e73\u5747\u503c\u63a5\u8fd1\u96f6\u3002\u5747\u503c\u6fc0\u6d3b\u63a5\u8fd1\u4e8e\u96f6\u53ef\u4ee5\u4f7f\u5b66\u4e60\u66f4\u5feb\uff0c\u56e0\u4e3a\u5b83\u4eec\u4f7f\u68af\u5ea6\u66f4\u63a5\u8fd1\u81ea\u7136\u68af\u5ea6\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f84f7299fb1a49a2b3584cde80e23ef6.png\" alt=\"img\" \/><\/p>\n<p>\u663e\u7136\uff0cELU \u5177\u6709 ReLU \u7684\u6240\u6709\u4f18\u70b9\uff0c\u5e76\u4e14\uff1a<\/p>\n<ul>\n<li>\u6ca1\u6709 Dead ReLU \u95ee\u9898\uff0c\u8f93\u51fa\u7684\u5e73\u5747\u503c\u63a5\u8fd1 0\uff0c\u4ee5 0 \u4e3a\u4e2d\u5fc3\uff1b<\/li>\n<li>ELU \u901a\u8fc7\u51cf\u5c11\u504f\u7f6e\u504f\u79fb\u7684\u5f71\u54cd\uff0c\u4f7f\u6b63\u5e38\u68af\u5ea6\u66f4\u63a5\u8fd1\u4e8e\u5355\u4f4d\u81ea\u7136\u68af\u5ea6\uff0c\u4ece\u800c\u4f7f\u5747\u503c\u5411\u96f6\u52a0\u901f\u5b66\u4e60\uff1b<\/li>\n<li>ELU \u5728\u8f83\u5c0f\u7684\u8f93\u5165\u4e0b\u4f1a\u9971\u548c\u81f3\u8d1f\u503c\uff0c\u4ece\u800c\u51cf\u5c11\u524d\u5411\u4f20\u64ad\u7684\u53d8\u5f02\u548c\u4fe1\u606f\u3002<\/li>\n<\/ul>\n<p>\u4e00\u4e2a\u5c0f\u95ee\u9898\u662f\u5b83\u7684\u8ba1\u7b97\u5f3a\u5ea6\u66f4\u9ad8\u3002\u4e0e Leaky ReLU \u7c7b\u4f3c\uff0c\u5c3d\u7ba1\u7406\u8bba\u4e0a\u6bd4 ReLU \u8981\u597d\uff0c\u4f46\u76ee\u524d\u5728\u5b9e\u8df5\u4e2d\u6ca1\u6709\u5145\u5206\u7684\u8bc1\u636e\u8868\u660e ELU \u603b\u662f\u6bd4 ReLU \u597d\u3002<\/p>\n<h3><strong>6. PReLU\uff08Parametric ReLU\uff09<\/strong><\/h3>\n<p><strong><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f0dfb0437c6442718445dc4d42dd6ebf.png\" alt=\"img\" \/><\/strong><\/p>\n<p>PReLU \u4e5f\u662f ReLU \u7684\u6539\u8fdb\u7248\u672c\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/9fb720b640744c3b93f8f827bb5b9a5f.png\" alt=\"img\" \/><\/p>\n<p>\u770b\u4e00\u4e0b PReLU \u7684\u516c\u5f0f\uff1a\u53c2\u6570\u03b1\u901a\u5e38\u4e3a 0 \u5230 1 \u4e4b\u95f4\u7684\u6570\u5b57\uff0c\u5e76\u4e14\u901a\u5e38\u76f8\u5bf9\u8f83\u5c0f\u3002<\/p>\n<ul>\n<li>\u5982\u679c a_i= 0\uff0c\u5219 f \u53d8\u4e3a ReLU<\/li>\n<li>\u5982\u679c a_i&gt; 0\uff0c\u5219 f \u53d8\u4e3a leaky ReLU<\/li>\n<li>\u5982\u679c a_i \u662f\u53ef\u5b66\u4e60\u7684\u53c2\u6570\uff0c\u5219 f \u53d8\u4e3a PReLU<\/li>\n<\/ul>\n<p>PReLU \u7684\u4f18\u70b9\u5982\u4e0b\uff1a<\/p>\n<ol>\n<li>\u5728\u8d1f\u503c\u57df\uff0cPReLU \u7684\u659c\u7387\u8f83\u5c0f\uff0c\u8fd9\u4e5f\u53ef\u4ee5\u907f\u514d Dead ReLU \u95ee\u9898\u3002<\/li>\n<li>\u4e0e ELU \u76f8\u6bd4\uff0cPReLU \u5728\u8d1f\u503c\u57df\u662f\u7ebf\u6027\u8fd0\u7b97\u3002\u5c3d\u7ba1\u659c\u7387\u5f88\u5c0f\uff0c\u4f46\u4e0d\u4f1a\u8d8b\u4e8e 0\u3002<\/li>\n<\/ol>\n<h3><strong>7. Softmax<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f283c68ffbd042db9724b70318377fb9.png\" alt=\"img\" \/><\/p>\n<p>Softmax \u662f\u7528\u4e8e\u591a\u7c7b\u5206\u7c7b\u95ee\u9898\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u5728\u591a\u7c7b\u5206\u7c7b\u95ee\u9898\u4e2d\uff0c\u8d85\u8fc7\u4e24\u4e2a\u7c7b\u6807\u7b7e\u5219\u9700\u8981\u7c7b\u6210\u5458\u5173\u7cfb\u3002\u5bf9\u4e8e\u957f\u5ea6\u4e3a K \u7684\u4efb\u610f\u5b9e\u5411\u91cf\uff0cSoftmax \u53ef\u4ee5\u5c06\u5176\u538b\u7f29\u4e3a\u957f\u5ea6\u4e3a K\uff0c\u503c\u5728\uff080\uff0c1\uff09\u8303\u56f4\u5185\uff0c\u5e76\u4e14\u5411\u91cf\u4e2d\u5143\u7d20\u7684\u603b\u548c\u4e3a 1 \u7684\u5b9e\u5411\u91cf\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/1da4d966c827486ab20402f2ce218b8d.png\" alt=\"img\" \/><\/p>\n<p>Softmax \u4e0e\u6b63\u5e38\u7684 max \u51fd\u6570\u4e0d\u540c\uff1amax \u51fd\u6570\u4ec5\u8f93\u51fa\u6700\u5927\u503c\uff0c\u4f46 Softmax \u786e\u4fdd\u8f83\u5c0f\u7684\u503c\u5177\u6709\u8f83\u5c0f\u7684\u6982\u7387\uff0c\u5e76\u4e14\u4e0d\u4f1a\u76f4\u63a5\u4e22\u5f03\u3002\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u5b83\u662f argmax \u51fd\u6570\u7684\u6982\u7387\u7248\u672c\u6216\u300csoft\u300d\u7248\u672c\u3002<\/p>\n<p>Softmax \u51fd\u6570\u7684\u5206\u6bcd\u7ed3\u5408\u4e86\u539f\u59cb\u8f93\u51fa\u503c\u7684\u6240\u6709\u56e0\u5b50\uff0c\u8fd9\u610f\u5473\u7740 Softmax \u51fd\u6570\u83b7\u5f97\u7684\u5404\u79cd\u6982\u7387\u5f7c\u6b64\u76f8\u5173\u3002<\/p>\n<p>Softmax \u6fc0\u6d3b\u51fd\u6570\u7684\u4e3b\u8981\u7f3a\u70b9\u662f\uff1a<\/p>\n<ol>\n<li>\u5728\u96f6\u70b9\u4e0d\u53ef\u5fae\uff1b<\/li>\n<li>\u8d1f\u8f93\u5165\u7684\u68af\u5ea6\u4e3a\u96f6\uff0c\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u8be5\u533a\u57df\u7684\u6fc0\u6d3b\uff0c\u6743\u91cd\u4e0d\u4f1a\u5728\u53cd\u5411 \u4f20\u64ad\u671f\u95f4\u66f4\u65b0\uff0c\u56e0\u6b64\u4f1a\u4ea7\u751f\u6c38\u4e0d\u6fc0\u6d3b\u7684\u6b7b\u4ea1\u795e\u7ecf\u5143\u3002<\/li>\n<\/ol>\n<h3><strong>8. Swish<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/267178dae5204b3a97a8002558cf19b8.png\" alt=\"img\" \/><\/p>\n<p>\u51fd\u6570\u8868\u8fbe\u5f0f\uff1ay = x * sigmoid (x)<\/p>\n<p>Swish \u7684\u8bbe\u8ba1\u53d7\u5230\u4e86 LSTM \u548c\u9ad8\u901f\u7f51\u7edc\u4e2d gating \u7684 sigmoid \u51fd\u6570\u4f7f\u7528\u7684\u542f\u53d1\u3002\u6211\u4eec\u4f7f\u7528\u76f8\u540c\u7684 gating \u503c\u6765\u7b80\u5316 gating \u673a\u5236\uff0c\u8fd9\u79f0\u4e3a self-gating\u3002<\/p>\n<p>self-gating \u7684\u4f18\u70b9\u5728\u4e8e\u5b83\u53ea\u9700\u8981\u7b80\u5355\u7684\u6807\u91cf\u8f93\u5165\uff0c\u800c\u666e\u901a\u7684 gating \u5219\u9700\u8981\u591a\u4e2a\u6807\u91cf\u8f93\u5165\u3002\u8fd9\u4f7f\u5f97\u8bf8\u5982 Swish \u4e4b\u7c7b\u7684 self-gated \u6fc0\u6d3b\u51fd\u6570\u80fd\u591f\u8f7b\u677e\u66ff\u6362\u4ee5\u5355\u4e2a\u6807\u91cf\u4e3a\u8f93\u5165\u7684\u6fc0\u6d3b\u51fd\u6570\uff08\u4f8b\u5982 ReLU\uff09\uff0c\u800c\u65e0\u9700\u66f4\u6539\u9690\u85cf\u5bb9\u91cf\u6216\u53c2\u6570\u6570\u91cf\u3002<\/p>\n<p>Swish \u6fc0\u6d3b\u51fd\u6570\u7684\u4e3b\u8981\u4f18\u70b9\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u300c\u65e0\u754c\u6027\u300d\u6709\u52a9\u4e8e\u9632\u6b62\u6162\u901f\u8bad\u7ec3\u671f\u95f4\uff0c\u68af\u5ea6\u9010\u6e10\u63a5\u8fd1 0 \u5e76\u5bfc\u81f4\u9971\u548c\uff1b \uff08\u540c\u65f6\uff0c\u6709\u754c\u6027\u4e5f\u662f\u6709\u4f18\u52bf\u7684\uff0c\u56e0\u4e3a\u6709\u754c\u6fc0\u6d3b\u51fd\u6570\u53ef\u4ee5\u5177\u6709\u5f88\u5f3a\u7684\u6b63\u5219\u5316\uff0c\u5e76\u4e14\u8f83\u5927\u7684\u8d1f\u8f93\u5165\u95ee\u9898\u4e5f \u80fd\u89e3\u51b3\uff09\uff1b<\/li>\n<li>\u5bfc\u6570\u6052 &gt; 0\uff1b<\/li>\n<li>\u5e73\u6ed1\u5ea6\u5728\u4f18\u5316\u548c\u6cdb\u5316\u4e2d\u8d77\u4e86\u91cd\u8981\u4f5c\u7528\u3002<\/li>\n<\/ul>\n<h3><strong>9. Maxout<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/2eaff51f03944b4cb3adca6b50d1ac59.png\" alt=\"img\" \/><\/p>\n<p>\u5728 Maxout \u5c42\uff0c\u6fc0\u6d3b\u51fd\u6570\u662f\u8f93\u5165\u7684\u6700\u5927\u503c\uff0c\u56e0\u6b64\u53ea\u6709 2 \u4e2a maxout \u8282\u70b9\u7684\u591a\u5c42\u611f\u77e5\u673a\u5c31\u53ef\u4ee5\u62df\u5408\u4efb\u610f\u7684\u51f8\u51fd\u6570\u3002<\/p>\n<p>\u5355\u4e2a Maxout \u8282\u70b9\u53ef\u4ee5\u89e3\u91ca\u4e3a\u5bf9\u4e00\u4e2a\u5b9e\u503c\u51fd\u6570\u8fdb\u884c\u5206\u6bb5\u7ebf\u6027\u8fd1\u4f3c (PWL) \uff0c\u5176\u4e2d\u51fd\u6570\u56fe\u4e0a\u4efb\u610f\u4e24\u70b9\u4e4b\u95f4\u7684\u7ebf\u6bb5\u4f4d\u4e8e\u56fe\uff08\u51f8\u51fd\u6570\uff09\u7684\u4e0a\u65b9\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/95235289a0f04a75ad98d0106afc00f9.png\" alt=\"img\" \/><\/p>\n<p>Maxout \u4e5f\u53ef\u4ee5\u5bf9 d \u7ef4\u5411\u91cf\uff08V\uff09\u5b9e\u73b0\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f44fe02e4cfd4dd1ab258d5c2e6b3e57.png\" alt=\"img\" \/><\/p>\n<p>\u5047\u8bbe\u4e24\u4e2a\u51f8\u51fd\u6570 h_1(x) \u548c h_2(x)\uff0c\u7531\u4e24\u4e2a Maxout \u8282\u70b9\u8fd1\u4f3c\u5316\uff0c\u51fd\u6570 g(x) \u662f\u8fde\u7eed\u7684 PWL \u51fd\u6570\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/acfcb9e675534bd9805ac3a06551ecde.png\" alt=\"img\" \/><\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e24\u4e2a Maxout \u8282\u70b9\u7ec4\u6210\u7684 Maxout \u5c42\u53ef\u4ee5\u5f88\u597d\u5730\u8fd1\u4f3c\u4efb\u4f55\u8fde\u7eed\u51fd\u6570\u3002<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/d0a4c435118547578bb63bfb5713e6b4.png\" alt=\"img\" \/><\/p>\n<h3><strong>10. Softplus<\/strong><\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/39ede8518279404390342917df9ea5d9.png\" alt=\"img\" \/><\/p>\n<p>Softplus \u51fd\u6570\uff1af\uff08x\uff09= ln\uff081 + exp x\uff09<\/p>\n<p>Softplus \u7684\u5bfc\u6570\u4e3a<\/p>\n<p>f \u2032(x)=exp(x) \/ ( 1+exp\u2061 x )<\/p>\n<p>= 1\/ (1 +exp(\u2212x ))<\/p>\n<p>\uff0c\u4e5f\u79f0\u4e3a logistic \/ sigmoid \u51fd\u6570\u3002<\/p>\n<p>Softplus \u51fd\u6570\u7c7b\u4f3c\u4e8e ReLU \u51fd\u6570\uff0c\u4f46\u662f\u76f8\u5bf9\u8f83\u5e73\u6ed1\uff0c\u50cf ReLU \u4e00\u6837\u662f\u5355\u4fa7\u6291\u5236\u3002\u5b83\u7684\u63a5\u53d7\u8303\u56f4\u5f88\u5e7f\uff1a(0, + inf)\u3002<\/p>\n<h2>\u5b9e\u73b0\u591a\u5206\u7c7b<\/h2>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u5c24\u5176\u662f\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u4e2d\uff0c\u7ecf\u5e38\u9700\u8981\u628a\u4e00\u4e9b\u8f93\u5165\u6620\u5c04\u52300-1\u4e4b\u95f4\u7684\u6982\u7387\u503c\u3002\u8fd9\u4e2a\u65f6\u5019\u6700\u5148\u60f3\u5230\u7684\u5c31\u662fsigmoid\u548csoftmax\u4e86\uff0csoftmax\u662f\u4e8c\u5206\u7c7b\u51fd\u6570sigmoid\u5728\u591a\u5206\u7c7b\u4e0a\u7684\u63a8\u5e7f\uff0c\u76ee\u7684\u5c31\u662f\u5c06\u591a\u5206\u7c7b\u7ed3\u679c\u4ee5\u6982\u7387\u7684\u5f62\u5f0f\u5c55\u73b0\u51fa\u6765\u3002\u5728\u6570\u5b66\uff0c\u5c24\u5176\u662f\u6982\u7387\u8bba\u548c\u76f8\u5173\u9886\u57df\u4e2d\uff0csoftmax\u51fd\u6570\u53c8\u79f0\u5f52\u4e00\u5316\u6307\u6570\u51fd\u6570\uff0c\u662f\u903b\u8f91\u51fd\u6570\u7684\u4e00\u79cd\u63a8\u5e7f\u3002Softmax\u51fd\u6570\u5b9e\u9645\u4e0a\u662f\u6709\u9650\u9879\u79bb\u6563\u6982\u7387\u5206\u5e03\u7684\u68af\u5ea6\u5bf9\u6570\u5f52\u4e00\u5316\u3002\u56e0\u6b64\uff0cSoftmax\u51fd\u6570\u5728\u5305\u62ec 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