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class=\"wp-block-heading\">1\u3001\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5<\/h3>\n\n\n\n<p>\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u4f7f\u7528\u7684\u4f18\u5316\u7b97\u6cd5\u4e00\u822c\u662f\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\uff0c\u5177\u4f53\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\u4ece\u67d0\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u8bfb\u8005\u53ef\u4ee5\u628a\u68af\u5ea6\u7406\u89e3\u6210\u67d0\u51fd\u6570\u504f\u5bfc\u6570\u7684\u96c6\u5408\uff0c\u4f8b\u5982\u51fd\u6570\\(f(x,y)\\)\u7684\u68af\u5ea6\u4e3a\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\mathrm{grad}f(x,y)=\\left(\\frac{\\partial f}{\\partial x},\\frac{\\partial f}{\\partial y}\\right)\\)<\/p>\n\n\n<p>\u5f53\u67d0\u51fd\u6570\u53ea\u6709\u4e00\u4e2a\u81ea\u53d8\u91cf\u65f6\uff0c\u68af\u5ea6\u5b9e\u9645\u4e0a\u5c31\u662f\u5bfc\u6570\u7684\u6982\u5ff5\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u68af\u5ea6\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u65e2\u6709\u5927\u5c0f\u53c8\u6709\u65b9\u5411\u3002\u68af\u5ea6\u7684\u65b9\u5411\u662f\u6700\u5927\u65b9\u5411\u5bfc\u6570\u7684\u65b9\u5411\uff0c\u800c\u68af\u5ea6\u7684\u6a21\u662f\u6700\u5927\u65b9\u5411\u5bfc\u6570\u7684\u503c\u3002\u53e6\u5916\uff0c\u68af\u5ea6\u5728\u51e0\u4f55\u4e0a\u7684\u542b\u4e49\u662f\u51fd\u6570\u53d8\u5316\u7387\u6700\u5927\u7684\u65b9\u5411\u3002\u6cbf\u7740\u68af\u5ea6\u5411\u91cf\u7684\u65b9\u5411\u524d\u8fdb\uff0c\u66f4\u5bb9\u6613\u627e\u5230\u51fd\u6570\u7684\u6700\u5927\u503c\uff0c\u53cd\u8fc7\u6765\u8bf4\uff0c\u6cbf\u7740\u68af\u5ea6\u5411\u91cf\u76f8\u53cd\u7684\u65b9\u5411\u524d\u8fdb\u662f\u68af\u5ea6\u51cf\u5c11\u6700\u5feb\u7684\u65b9\u5411\uff0c\u4e5f\u5c31\u662f\u8bf4\u66f4\u5bb9\u6613\u627e\u5230\u51fd\u6570\u7684\u6700\u5c0f\u503c\u3002 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class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"369\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306213742694.png\" alt=\"\" class=\"wp-image-2799\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306213742694.png 481w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306213742694-300x230.png 300w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><figcaption class=\"wp-element-caption\">\u56fe1 \u68af\u5ea6<\/figcaption><\/figure><\/div>\n\n\n<p>\u73b0\u5728\u56de\u5230\u635f\u5931\\(\\ell\\)\u7684\u6982\u5ff5\uff0c\\(\\ell\\)\u4e5f\u662f\u4e00\u79cd\u51fd\u6570\uff08\u4f8b\u5982\u5e73\u65b9\u5dee\u635f\u5931\u51fd\u6570\uff09\uff0c\u56e0\u6b64\u8981\u6c42\\(\\ell\\)\u7684\u6700\u5c0f\u503c\uff0c\u5b9e\u9645\u4e0a\u53ea\u9700\u8981\u6cbf\u7740\\(\\ell\\)\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u5bfb\u627e\u5373\u53ef\uff0c\u8fd9\u5c31\u662f\u68af\u5ea6\u4e0b\u964d\u7684\u6982\u5ff5\u3002\u5176\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\mathrm{grad}=\\frac{\\partial\\ell}{\\partial\\boldsymbol{\\omega}_{t-1}}\\)<\/p>\n<p style=\"text-align: center;\">\\(\\omega_t=\\omega_{t\\cdot1}-\\eta\\times\\mathrm{grad}\\)<\/p>\n\n\n<p>\u4e0a\u5f0f\u4e2d-grad\u8868\u793a\u68af\u5ea6\u7684\u53cd\u65b9\u5411\uff0c\u65b0\u7684\u6743\u91cd\\(\\boldsymbol{\\omega}_{t}\\)\u7b49\u4e8e\u4e4b\u524d\u7684\u6743\u91cd\\(\\boldsymbol{\\omega}_{t-1}\\)\u5411\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u524d\u8fdb\\(\\eta\\times\\mathrm{grad}\\)\u7684\u91cf\u3002\u56fe1\u4e2d\u7684\u51fd\u6570\u5e73\u9762\u5316\u540e\u8868\u793a\u7684\u68af\u5ea6\u4e0b\u964d\u8fc7\u7a0b\u5982\u56fe2\u6240\u793a\u3002<\/p>\n\n\n\n<p>\uff081\uff09\u968f\u673a\u521d\u59cb\u5316\u4e00\u4e2a\u521d\u59cb\u503c\\(\\omega_{_0}\\)\u3002<\/p>\n\n\n\n<p>\uff082\uff09\u91cd\u590d\u8fed\u4ee3\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\uff0c\u5373\\(\\boldsymbol{\\omega}_{t}=\\boldsymbol{\\omega}_{t-1}-\\eta\\times\\mathrm{grad}(t=1,2,3)\\)\u3002<\/p>\n\n\n\n<p>\uff083\uff09\u6b64\u65f6\uff0c\u66f4\u65b0\u540e\u7684\u6743\u91cd\u4f1a\u6bd4\u4e4b\u524d\u7684\u6743\u91cd\u5f97\u5230\u4e00\u4e2a\u66f4\u5c0f\u7684\u51fd\u6570\u503c\uff0c\u5373\\(\\ell(\\omega_0)&gt;\\ell(\\omega_1)&gt;\\ell(\\omega_2)\\cdots\\approx\\ell_{\\min}\\)\u3002<\/p>\n\n\n\n<p>\uff084\uff09\\(\\eta\\)\u662f\u5b66\u4e60\u7387\u7684\u610f\u601d\uff0c\u8868\u5f81\u53c2\u6570\u66f4\u65b0\u7684\u5feb\u6162\uff0c\u901a\u8fc7\\(\\eta\\times\\mathrm{grad}\\)\u76f4\u63a5\u5f71\u54cd\u53c2\u6570\u7684\u66f4\u65b0\u901f\u5ea6\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"244\" height=\"250\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306214902319.png\" alt=\"\" class=\"wp-image-2801\"\/><figcaption class=\"wp-element-caption\">\u56fe2 \u68af\u5ea6\u4e0b\u964d<\/figcaption><\/figure><\/div>\n\n\n<p>\u5f53\u5b66\u4e60\u7387\u8fc7\u5c0f\u65f6\uff0c\u66f4\u65b0\u901f\u5ea6\u592a\u6162\uff0c\u5982\u56fe3(a)\u6240\u793a\uff1b\u5f53\u5b66\u4e60\u7387\u8fc7\u5927\u65f6\uff0c\u5bb9\u6613\u51fa\u73b0\u68af\u5ea6\u9707\u8361\uff0c\u5982\u56fe3(b)\u6240\u793a\uff0c\u8fd9\u4e9b\u90fd\u662f\u4e0d\u597d\u7684\u5f71\u54cd\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"316\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306214937993.png\" alt=\"\" class=\"wp-image-2802\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306214937993.png 567w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306214937993-300x167.png 300w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><figcaption class=\"wp-element-caption\">\u56fe3 \u5b66\u4e60\u7387\u5bf9\u68af\u5ea6\u4e0b\u964d\u7684\u5f71\u54cd<\/figcaption><\/figure><\/div>\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5b66\u4e60\u7387\u662f\u76f4\u63a5\u51b3\u5b9a\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u8bad\u7ec3\u6210\u529f\u4e0e\u5426\u7684\u5173\u952e\u56e0\u7d20\u3002\u5f53\u4e00\u4e2a\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u6548\u679c\u4e0d\u597d\u6216\u8005\u8bad\u7ec3\u5931\u8d25\u65f6\uff0c\u4e0d\u4e00\u5b9a\u662f\u6a21\u578b\u8bbe\u8ba1\u7684\u539f\u56e0\uff0c\u4e5f\u53ef\u80fd\u662f\u8bad\u7ec3\u7b56\u7565\u6240\u5bfc\u81f4\uff0c\u5176\u4e2d\u5b66\u4e60\u7387\u5c31\u662f\u8bad\u7ec3\u7b56\u7565\u7684\u4e3b\u8981\u56e0\u7d20\u4e4b\u4e00\u3002\u5728\u8bad\u7ec3\u65f6\u5f80\u5f80\u4f1a\u5148\u9009\u62e9\u4e00\u4e2a\u8f83\u5c0f\u7684\u5b66\u4e60\u7387\uff08\u4f8b\u59820.0001\uff09\u8fdb\u884c\u8bad\u7ec3\uff0c\u518d\u9010\u6b65\u8c03\u5927\u5b66\u4e60\u7387\u6765\u89c2\u5bdf\u6a21\u578b\u7684\u8bad\u7ec3\u7ed3\u679c\u3002\u6b64\u5916\uff0c\u8bad\u7ec3\u6570\u636e\u96c6\u4e5f\u4f1a\u76f4\u63a5\u5f71\u54cd\u6a21\u578b\u7684\u6548\u679c\uff0c\u5373\u6a21\u578b\u7684\u6548\u679c=\u8bad\u7ec3\u96c6+\u6a21\u578b\u8bbe\u8ba1+\u8bad\u7ec3\u7b56\u7565\u3002<\/p>\n\n\n\n<p>\u6700\u540e\uff0c\u5728\u6709\u76d1\u7763\u8bad\u7ec3\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u65f6\uff0c\u5f80\u5f80\u4e0d\u4f1a\u5728\u4e00\u6b21\u8ba1\u7b97\u4e2d\u4f7f\u7528\u5168\u90e8\u7684\u6570\u636e\u96c6\uff0c\u56e0\u4e3a\u8bad\u7ec3\u6570\u636e\u96c6\u5f80\u5f80\u5f88\u5927\uff0c\u5168\u90e8\u4f7f\u7528\u65f6\u8ba1\u7b97\u8d44\u6e90\u548c\u5185\u5b58\u4f1a\u4e0d\u591f\u7528\u3002\u56e0\u6b64\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u4f1a\u91c7\u7528\u4e00\u79cd\u88ab\u79f0\u4e3a\u5c0f\u6279\u91cf\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u7b97\u6cd5\u3002\u5177\u4f53\u7684\u65b9\u6cd5\u662f\u4ece\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u968f\u673a\u91c7\u7528\\(\\text{b}\\)\u4e2a\u6837\u672c\\(i_{1},i_{2},\\cdots,i_{b}\\)\u6765\u8fd1\u4f3c\u635f\u5931\uff0c\u6b64\u65f6\u635f\u5931\u7684\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\frac{1}{b}\\sum_{i\\in I_b}\\ell(x_i,y_i,\\omega)\\)<\/p>\n\n\n<p>\u5176\u4e2d\\(\\text{b}\\)\u4ee3\u8868\u6279\u91cf\u5927\u5c0f\uff0c\u662f\u4e00\u4e2a\u6df1\u5ea6\u5b66\u4e60\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u91cd\u8981\u7684\u8d85\u53c2\u6570\u3002\u5f53\\(\\text{b}\\)\u592a\u5c0f\u65f6\uff0c\u6bcf\u6b21\u8ba1\u7b97\u91cf\u592a\u5c0f\uff0c\u4e0d\u9002\u5408\u6700\u5927\u7a0b\u5ea6\u5229\u7528\u5e76\u884c\u8d44\u6e90\uff1b\u66f4\u91cd\u8981\u7684\u662f\uff0c\\(\\text{b}\\)\u592a\u5c0f\u610f\u5473\u7740\u4ece\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u62bd\u6837\u7684\u6837\u672c\u5b50\u96c6\u6570\u91cf\u5c11\uff0c\u6b64\u65f6\u5b50\u96c6\u7684\u6570\u636e\u5206\u5e03\u53ef\u80fd\u4e0e\u539f\u59cb\u6570\u636e\u96c6\u76f8\u5dee\u8f83\u5927\uff0c\u5e76\u4e0d\u80fd\u5f88\u597d\u5730\u4ee3\u66ff\u539f\u59cb\u6570\u636e\u96c6\u3002\u5f53\\(\\text{b}\\)\u592a\u5927\u65f6\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u5b58\u50a8\u6216\u8ba1\u7b97\u8d44\u6e90\u4e0d\u8db3\u3002\u6839\u636e\\(\\text{b}\\)\u7684\u5927\u5c0f\uff0c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u53ef\u4ee5\u5206\u4e3a\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Batch Gradient Descent\uff0cBGD\uff09\u3001\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Stochastic Gradient Descent\uff0cSGD\uff09, \u4ee5\u53ca\u5c0f\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\uff08Mini-batch Gradient Descent\uff0cMBGD\uff09\u3002<\/p>\n\n\n\n<p>\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u662f\u68af\u5ea6\u4e0b\u964d\u6cd5\u5e38\u7528\u7684\u5f62\u5f0f\uff0c\u5177\u4f53\u505a\u6cd5\u662f\u5728\u66f4\u65b0\u53c2\u6570\u65f6\u4f7f\u7528\u6240\u6709\u7684\u6837\u672c\u6765\u8fdb\u884c\u66f4\u65b0\u3002\u7531\u4e8e\u9700\u8981\u8ba1\u7b97\u6574\u4e2a\u6570\u636e\u96c6\u7684\u68af\u5ea6\uff0c\u5c06\u5bfc\u81f4\u68af\u5ea6\u4e0b\u964d\u6cd5\u7684\u901f\u5ea6\u53ef\u80fd\u975e\u5e38\u7f13\u6162\uff0c\u4e14\u5bf9\u4e8e\u5185\u5b58\u5c0f\u800c\u6570\u636e\u96c6\u5e9e\u5927\u7684\u60c5\u51b5\u5341\u5206\u68d8\u624b\u3002\u800c\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u7684\u4f18\u70b9\u662f\u7406\u60f3\u72b6\u6001\u4e0b\uff0c\u7ecf\u8fc7\u8db3\u591f\u591a\u7684\u8fed\u4ee3\u540e\u53ef\u4ee5\u8fbe\u5230\u5168\u5c40\u6700\u4f18\u3002<\/p>\n\n\n\n<p>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u548c\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u539f\u7406\u7c7b\u4f3c,\u533a\u522b\u5728\u4e8e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u5728\u6c42\u68af\u5ea6\u65f6\u6ca1\u6709\u7528\u6240\u6709\u7684\u6837\u672c\u6570\u636e\uff0c\u800c\u662f\u4ec5\u4ec5\u9009\u53d6\u4e00\u4e2a\u6837\u672c\u6765\u6c42\u68af\u5ea6\u3002\u6b63\u662f\u4e3a\u4e86\u52a0\u5feb\u6536\u655b\u901f\u5ea6\uff0c\u5e76\u4e14\u89e3\u51b3\u5927\u6570\u636e\u91cf\u65e0\u6cd5\u4e00\u6b21\u6027\u585e\u5165\u5185\u5b58\u7684\u95ee\u9898\u3002\u4f46\u662f\u7531\u4e8e\u6bcf\u6b21\u53ea\u7528\u4e00\u4e2a\u6837\u672c\u6765\u66f4\u65b0\u53c2\u6570\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u4f1a\u5bfc\u81f4\u4e0d\u7a33\u5b9a\u3002\u6bcf\u6b21\u66f4\u65b0\u7684\u65b9\u5411\uff0c\u4e0d\u50cf\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u90a3\u6837\u6bcf\u6b21\u90fd\u671d\u7740\u6700\u4f18\u70b9\u7684\u65b9\u5411\u903c\u8fd1\uff0c\u800c\u662f\u4f1a\u5728\u6700\u4f18\u70b9\u9644\u8fd1\u9707\u8361\u3002<\/p>\n\n\n\n<p>\u5176\u5b9e\uff0c\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u4e0e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u662f\u4e24\u4e2a\u6781\u7aef\uff0c\u524d\u8005\u91c7\u7528\u6240\u6709\u6570\u636e\u6765\u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\uff0c\u5982\u56fe4(a)\u6240\u793a\uff1b\u540e\u8005\u91c7\u7528\u4e00\u4e2a\u6837\u672c\u6765\u8fdb\u884c\u68af\u5ea6\u4e0b\u964d\uff0c\u5982\u56fe4(b)\u6240\u793a\u3002\u4e24\u79cd\u65b9\u6cd5\u7684\u4f18\u7f3a\u70b9\u90fd\u975e\u5e38\u7a81\u51fa\uff0c\u5bf9\u4e8e\u8bad\u7ec3\u901f\u5ea6\u6765\u8bf4\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u7531\u4e8e\u6bcf\u6b21\u4ec5\u4ec5\u91c7\u7528\u4e00\u4e2a\u6837\u672c\u6765\u8fed\u4ee3\uff0c\u8bad\u7ec3\u901f\u5ea6\u5f88\u5feb;\u800c\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\u5728\u6837\u672c\u91cf\u5f88\u5927\u7684\u65f6\u5019\uff0c\u8bad\u7ec3\u901f\u5ea6\u4e0d\u80fd\u8ba9\u4eba\u6ee1\u610f\u3002\u5bf9\u4e8e\u51c6\u786e\u5ea6\u6765\u8bf4\uff0c\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u4ec5\u4ec5\u7528\u4e00\u4e2a\u6837\u672c\u51b3\u5b9a\u68af\u5ea6\u65b9\u5411\uff0c\u5bfc\u81f4\u6709\u53ef\u80fd\u4e0d\u662f\u6700\u4f18\u89e3\u3002\u5bf9\u4e8e\u6536\u655b\u901f\u5ea6\u6765\u8bf4\uff0c\u7531\u4e8e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u4e00\u6b21\u8fed\u4ee3\u4e00\u4e2a\u6837\u672c\uff0c\u5bfc\u81f4\u8fed\u4ee3\u65b9\u5411\u53d8\u5316\u5f88\u5927\uff0c\u4e0d\u80fd\u5f88\u5feb\u5730\u6536\u655b\u5230\u5c40\u90e8\u6700\u4f18\u89e3\u3002\u90a3\u4e48\uff0c\u6709\u6ca1\u6709\u4e00\u4e2a\u529e\u6cd5\u80fd\u591f\u7ed3\u5408\u4e24\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u5462\uff1f<\/p>\n\n\n\n<p>\u8fd9\u5c31\u662f\u5c0f\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u6cd5\uff0c\u5982\u56fe4(c)\u6240\u793a\u3002\u5373\u6bcf\u6b21\u8bad\u7ec3\u4ece\u6574\u4e2a\u6570\u636e\u96c6\u4e2d\u968f\u673a\u9009\u53d6\u4e00\u4e2a\u5c0f\u6279\u91cf\u6837\u672c\u7528\u4e8e\u6a21\u578b\u8bad\u7ec3\uff0c\u8fd9\u4e2a\u5c0f\u6279\u91cf\u6837\u672c\u7684\u5927\u5c0f\u662f\u8d85\u53c2\u6570\uff0c\u4e00\u822c\u6765\u8bf4\u8d8a\u5927\u8d8a\u51c6\uff0c\u5f53\u7136\u8bad\u7ec3\u4e5f\u4f1a\u8d8a\u6162\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"379\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220756710.png\" alt=\"\" class=\"wp-image-2803\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220756710.png 934w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220756710-300x122.png 300w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220756710-768x312.png 768w\" sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><figcaption class=\"wp-element-caption\">\u56fe4 \u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6536\u655b\u8d8b\u52bf\u5bf9\u6bd4<\/figcaption><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">2\u3001\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5<\/h3>\n\n\n\n<p>\u68af\u5ea6\u4e0b\u964d\u548c\u53cd\u5411\u4f20\u64ad\u662f\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u4e24\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u4eec\u5bc6\u5207\u76f8\u5173\u3002\u68af\u5ea6\u4e0b\u964d\u662f\u4e00\u79cd\u5e38\u7528\u7684\u4f18\u5316\u7b97\u6cd5\uff0c\u5b83\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u51fd\u6570\u7684\u6700\u5c0f\u503c\u6216\u6700\u5927\u503c\u3002\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u901a\u8fc7\u8c03\u6574\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u6743\u91cd\uff0c\u4ee5\u6700\u5c0f\u5316\u7f51\u7edc\u7684\u635f\u5931\u51fd\u6570\u3002\u635f\u5931\u51fd\u6570\u662f\u7528\u6765\u8861\u91cf\u7f51\u7edc\u7684\u8f93\u51fa\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u8bef\u5dee\u3002\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5bf9\u6743\u91cd\u7684\u504f\u5bfc\u6570\uff0c\u7136\u540e\u6309\u7167\u8fd9\u4e2a\u504f\u5bfc\u6570\u7684\u53cd\u65b9\u5411\u8c03\u6574\u6743\u91cd\u3002<\/p>\n\n\n\n<p>\u53cd\u5411\u4f20\u64ad\u662f\u4e00\u79cd\u6709\u6548\u7684\u8ba1\u7b97\u68af\u5ea6\u7684\u65b9\u6cd5\uff0c\u5b83\u53ef\u4ee5\u5feb\u901f\u8ba1\u7b97\u7f51\u7edc\u4e2d\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u504f\u5bfc\u6570\u3002\u53cd\u5411\u4f20\u64ad\u901a\u8fc7\u5148\u6b63\u5411\u4f20\u64ad\u8ba1\u7b97\u7f51\u7edc\u7684\u8f93\u51fa\uff0c\u7136\u540e\u4ece\u8f93\u51fa\u5c42\u5230\u8f93\u5165\u5c42\u53cd\u5411\u4f20\u64ad\u8bef\u5dee\uff0c\u6700\u540e\u6839\u636e\u8bef\u5dee\u8ba1\u7b97\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u504f\u5bfc\u6570\u3002\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u94fe\u5f0f\u6cd5\u5219\u5c06\u8bef\u5dee\u5411\u540e\u4f20\u9012\uff0c\u8ba1\u7b97\u6bcf\u4e2a\u795e\u7ecf\u5143\u5bf9\u8bef\u5dee\u7684\u8d21\u732e\u3002<\/p>\n\n\n\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u68af\u5ea6\u4e0b\u964d\u548c\u53cd\u5411\u4f20\u64ad\u662f\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u4e24\u4e2a\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7528\u4e8e\u4f18\u5316\u7f51\u7edc\u7684\u6743\u91cd\uff0c\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7528\u4e8e\u8ba1\u7b97\u6bcf\u4e2a\u795e\u7ecf\u5143\u7684\u504f\u5bfc\u6570\u3002\u5b83\u4eec\u5bc6\u5207\u76f8\u5173\uff0c\u5e76\u5728\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u4e2d\u8d77\u7740\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/p>\n\n\n\n<p>\u3010\u4f8b2\u3011\u795e\u7ecf\u7f51\u7edc\u5c42\u53c2\u6570\u66f4\u65b0\u7684\u5b8c\u6574\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\uff081\uff09\u521d\u59cb\u5316\u7f51\u7edc\uff0c\u6784\u5efa\u4e00\u4e2a\u53ea\u6709\u4e00\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5982\u56fe5\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"387\" height=\"191\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220927454.png\" alt=\"\" class=\"wp-image-2804\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220927454.png 387w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306220927454-300x148.png 300w\" sizes=\"auto, (max-width: 387px) 100vw, 387px\" \/><figcaption class=\"wp-element-caption\">\u56fe5 \u795e\u7ecf\u7f51\u7edc\u56fe<\/figcaption><\/figure><\/div>\n\n\n<p>\u5047\u8bbe\u56fe5\u4e2d\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u548c\u8f93\u51fa\u7684\u521d\u59cb\u5316\u4e3a\uff1a\\(x_{1}=0.5,x_{2}=1.0,y=0.8\\)\u3002\u53c2\u6570\u7684\u521d\u59cb\u5316\u4e3a\uff1a\\(w_{1}=1.0,w_{2}=0.5,w_{3}=0.5,w_{4}=0.7,w_{5}=1.0,w_{6}=2.0\\)\u3002<\/p>\n\n\n\n<p>\uff082\uff09\u524d\u5411\u8ba1\u7b97\uff0c\u5982\u56fe6\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"186\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221103601.png\" alt=\"\" class=\"wp-image-2805\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221103601.png 384w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221103601-300x145.png 300w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221103601-382x186.png 382w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><figcaption class=\"wp-element-caption\">\u56fe6 \u524d\u5411\u8ba1\u7b97<\/figcaption><\/figure><\/div>\n\n\n<p>\u6839\u636e\u8f93\u5165\u548c\u6743\u91cd\u8ba1\u7b97\\(h_{1}\\)\u5f97\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}h_{1}^{(1)}&amp;=w_1\\cdot x_1+w_2\\cdot x_2\\\\&amp;=1.0\\cdot0.5+0.5\\cdot1.0\\\\&amp;=1.0\\end{aligned}\\)<\/p>\n\n\n<p>\u540c\u7406\uff0c\u8ba1\u7b97\\(h_{2}\\)\u7b49\u4e8e0.95\u3002\u5c06\\(h_{1}\\)\u548c\\(h_{2}\\)\u76f8\u4e58\u6c42\u548c\u5230\u524d\u5411\u4f20\u64ad\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u5982\u56fe7\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"165\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221243535.png\" alt=\"\" class=\"wp-image-2806\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221243535.png 366w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221243535-300x135.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><figcaption class=\"wp-element-caption\">\u56fe7 \u76f8\u4e58\u6c42\u548c<\/figcaption><\/figure><\/div>\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}y^{\\prime}&amp;=w_{5}\\cdot h_{1}^{(1)}+w_{6}\\cdot h_{2}^{(1)}\\\\&amp;=1.0\\cdot1.0+2.0\\cdot0.95\\\\&amp;=2.9\\end{aligned}\\)<\/p>\n\n\n<p>\uff083\uff09\u8ba1\u7b97\u635f\u5931\uff1a\u6839\u636e\u6570\u636e\u771f\u5b9e\u503c\\(y=0.8\\)\u548c\u5e73\u65b9\u5dee\u635f\u5931\u51fd\u6570\u6765\u8ba1\u7b97\u635f\u5931\uff0c\u5982\u56fe8\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"198\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221352610.png\" alt=\"\" class=\"wp-image-2807\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221352610.png 424w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221352610-300x140.png 300w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><figcaption class=\"wp-element-caption\">\u56fe8 \u635f\u5931\u8ba1\u7b97<\/figcaption><\/figure><\/div>\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\delta&amp;=\\frac{1}{2}(y-y^{\\prime})^{2}\\\\&amp;=0.5(0.8-2.9)^{2}\\\\&amp;=2.205\\end{aligned}\\)<\/p>\n\n\n<p>\uff084\uff09\u8ba1\u7b97\u68af\u5ea6\uff1a\u6b64\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u5c31\u662f\u8ba1\u7b97\u504f\u5fae\u5206\u7684\u8fc7\u7a0b\uff0c\u4ee5\u53c2\u6570\\(w_{5}\\)\u7684\u504f\u5fae\u5206\u8ba1\u7b97\u4e3a\u4f8b\uff0c\u5982\u56fe9\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"441\" height=\"206\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221508163.png\" alt=\"\" class=\"wp-image-2808\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221508163.png 441w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306221508163-300x140.png 300w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><figcaption class=\"wp-element-caption\">\u56fe9 \u68af\u5ea6\u8ba1\u7b97<\/figcaption><\/figure><\/div>\n\n\n<p>    \u6839\u636e\u94fe\u5f0f\u6cd5\u5219\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\frac{\\partial\\delta}{\\partial w_5}=\\frac{\\partial\\delta}{\\partial y^{\\prime}}\\cdot\\frac{\\partial y^{\\prime}}{\\partial w_5}\\)<\/p>\n\n\n<p>     \u5176\u4e2d\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\frac{\\partial\\delta}{\\partial y^{\\prime}}&amp;=2\\cdot\\frac{1}{2}\\cdot(y-y^{\\prime})(-1)\\\\&amp;=y^{\\prime}-y\\\\&amp;=2.9-0.8\\\\&amp;=\\begin{array}{c}{2.1}\\end{array}\\end{aligned}\\)<\/p>\n<p style=\"text-align: center;\">\\(y^{\\prime}=w_5\\cdot h_1^{(1)}+w_6\\cdot h_2^{(1)}\\)<\/p>\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\frac{\\partial y^{\\prime}}{\\partial w_{5}}&amp;=h_{1}^{(1)}+0\\\\&amp;=1.0\\end{aligned}\\)<\/p>\n\n\n<p>    \u6240\u4ee5\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\frac{\\partial\\delta}{\\partial w_5}=\\frac{\\partial\\delta}{\\partial y^{\\prime}}\\cdot\\frac{\\partial y^{\\prime}}{\\partial w_5}=2.1\\times1.0=2.1\\)<\/p>\n\n\n<p>\uff085\uff09\u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u68af\u5ea6\uff1a\u5728\u7b2c4\u6b65\u4e2d\u662f\u4ee5\u53c2\u6570\\(w_{5}\\)\u4e3a\u4f8b\u5b50\u6765\u8ba1\u7b97\u504f\u5fae\u5206\u7684\u3002\u5982\u679c\u4ee5\u53c2\u6570\\(w_{1}\\)\u4e3a\u4f8b\u5b50\uff0c\u5b83\u7684\u504f\u5fae\u5206\u8ba1\u7b97\u5c31\u9700\u8981\u7528\u5230\u94fe\u5f0f\u6cd5\u5219\uff0c\u8fc7\u7a0b\u5982\u56fe10\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"490\" height=\"204\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306222018958.png\" alt=\"\" class=\"wp-image-2810\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306222018958.png 490w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250306222018958-300x125.png 300w\" sizes=\"auto, (max-width: 490px) 100vw, 490px\" \/><figcaption class=\"wp-element-caption\">\u56fe10 &nbsp;\u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u68af\u5ea6<\/figcaption><\/figure><\/div>\n\n<p style=\"text-align: center;\">\\(\\frac{\\partial\\delta}{\\partial w_{1}}=\\frac{\\partial\\delta}{\\partial y^{\\prime}}\\cdot\\frac{\\partial y^{\\prime}}{\\partial h_{1}^{(1)}}\\cdot\\frac{\\partial h_{1}^{(1)}}{\\partial w_{1}}\\)<\/p>\n<p style=\"text-align: center;\">\\(y^{\\prime}=w_5\\cdot h_1^{(1)}+w_6\\cdot h_2^{(1)}\\)<\/p>\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\frac{\\partial y^{\\prime}}{\\partial h_1^{(1)}}&amp;=w_5+0\\\\&amp;=1.0\\end{aligned}\\)<\/p>\n<p style=\"text-align: center;\">\\(h_1^{(1)}=w_1\\cdot x_1+w_2\\cdot x_2\\)<\/p>\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\frac{\\partial h_1^{(1)}}{\\partial w_1}&amp;=x_1+0\\\\&amp;=0.5\\end{aligned}\\)<\/p>\n<p style=\"text-align: center;\">\\(\\frac{\\partial\\delta}{\\partial w_1}=\\frac{\\partial\\delta}{\\partial y^{\\prime}}\\cdot\\frac{\\partial y^{\\prime}}{\\partial h_1^{(1)}}\\cdot\\frac{\\partial h_1^{(1)}}{\\partial w_1}=2.1\\times1.0\\times0.5=1.05\\)<\/p>\n\n\n<p>\uff086\uff09\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0\u7f51\u7edc\u53c2\u6570<\/p>\n\n\n\n<p>\u5047\u8bbe\u8fd9\u91cc\u7684\u8d85\u53c2\u6570\u201c\u5b66\u4e60\u901f\u7387\u201d\u7684\u521d\u59cb\u503c\u4e3a0.1\uff0c\u6839\u636e\u68af\u5ea6\u4e0b\u964d\u7684\u66f4\u65b0\u516c\u5f0f\uff0c\\(w_{1}\\)\u53c2\u6570\u7684\u66f4\u65b0\u8ba1\u7b97\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(w_1^{(\\mathrm{update})}=w_1-\\eta\\cdot\\frac{\\partial\\delta}{\\partial w_1}=1.0-0.1\\times1.05=0.895\\)<\/p>\n\n\n<p>\u540c\u7406\uff0c\u53ef\u4ee5\u8ba1\u7b97\u5f97\u5230\u5176\u4ed6\u7684\u66f4\u65b0\u540e\u7684\u53c2\u6570\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(w_1=0.895,w_2=0.895,w_3=0.29,w_4=0.28,w_5=0.79,w_6=1.8005\\)<\/p>\n\n\n<p>\u5230\u6b64\u4e3a\u6b62\uff0c\u6211\u4eec\u5c31\u5b8c\u6210\u4e86\u53c2\u6570\u8fed\u4ee3\u7684\u5168\u90e8\u8fc7\u7a0b\u3002\u53ef\u4ee5\u8ba1\u7b97\u4e00\u4e0b\u635f\u5931\u770b\u770b\u662f\u5426\u6709\u51cf\u5c0f\uff0c\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\delta=&amp;\\frac{1}{2}(y-y^{\\prime})^{2}\\\\&amp;=0.5(0.8-1.3478)^{2}\\\\&amp;=0.15\\end{aligned}\\)<\/p>\n\n\n<p>\u6b64\u7ed3\u679c\u76f8\u6bd4\u8f83\u4e8e\u4e4b\u524d\u8ba1\u7b97\u7684\u524d\u5411\u4f20\u64ad\u7684\u7ed3\u679c2.205\uff0c\u662f\u6709\u660e\u663e\u7684\u51cf\u5c0f\u7684\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">SGD\u4f18\u5316\u5668<\/h3>\n\n\n\n<p>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08SGD\uff09\u662f\u4e00\u79cd\u5e7f\u6cdb\u7528\u4e8e\u8bad\u7ec3\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u4f18\u5316\u7b97\u6cd5\uff0c\u5176\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5173\u4e8e\u6a21\u578b\u53c2\u6570\u7684\u68af\u5ea6\uff0c\u5e76\u6cbf\u7740\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u66f4\u65b0\u53c2\u6570\uff0c\u4ee5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u3002SGD\u6bcf\u6b21\u66f4\u65b0\u4ec5\u4f7f\u7528\u4e00\u4e2a\u6216\u4e00\u5c0f\u6279\u6837\u672c\uff0c\u8ba1\u7b97\u6548\u7387\u9ad8\uff0c\u4f46\u53ef\u80fd\u9762\u4e34\u6536\u655b\u6162\u548c\u632f\u8361\u95ee\u9898\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\uff0c<strong>\u52a8\u91cf\uff08Momentum\uff09<\/strong>\u6210\u4e3aSGD\u7684\u5173\u952e\u6280\u672f\u70b9\u4e4b\u4e00\u3002\u52a8\u91cf\u901a\u8fc7\u5f15\u5165\u5386\u53f2\u68af\u5ea6\u4fe1\u606f\uff0c\u7d2f\u79ef\u4e4b\u524d\u7684\u66f4\u65b0\u65b9\u5411\uff0c\u4ece\u800c\u52a0\u901f\u6536\u655b\u5e76\u51cf\u5c11\u632f\u8361\uff0c\u4f7f\u4f18\u5316\u8fc7\u7a0b\u66f4\u52a0\u7a33\u5b9a\u548c\u9ad8\u6548\u3002<\/p>\n\n\n\n<p>\u68af\u5ea6\u4e0b\u964d\u8fc7\u7a0b\u4e2d\uff0c\u7528\u6307\u6570\u79fb\u52a8\u5e73\u5747\u878d\u5408\u5386\u53f2\u7684\u68af\u5ea6\uff0c\u6536\u655b\u901f\u5ea6\u548c\u7a33\u5b9a\u6027\u90fd\u6709\u663e\u8457\u6536\u76ca\uff0c\u5176\u4e2d\u5386\u53f2\u68af\u5ea6\u88ab\u79f0\u4e3a\u52a8\u91cf\u9879\uff08Momentum\uff09\u3002\u5e26\u52a8\u91cf\u7684SGD\u4f18\u5316\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(m_t=\\beta m_{t-1}+(1-\\beta)g_t\\)<\/p>\n<p style=\"text-align: center;\">\\(\\omega_{t}=\\omega_{t-1}-\\eta m_{t}\\)<\/p>\n\n\n<p>\u5176\u4e2d\uff0c\\(m_{_{t-1}}\\)\u662f\u4e0a\u4e00\u65f6\u523b\u7684\u68af\u5ea6\uff0c\\(m_{_{t}}\\)\u662f\u7528EMA\u878d\u5408\u5386\u53f2\u68af\u5ea6\u540e\u7684\u68af\u5ea6\uff0c\\(\\mathbf{g}_{t}\\)\u662f\u5f53\u524d\u65f6\u523b\u7684\u68af\u5ea6\u3002\\(\\mathrm{\u03b2}\\)\u662f\u4e00\u4e2a\u8d85\u53c2\u6570\uff0c\\(\\beta m_{_{t-1}}\\)\u88ab\u79f0\u4e3a\u52a8\u91cf\u9879\u3002\u7531EMA\u7684\u539f\u7406\u53ef\u77e5\uff0c\u867d\u7136\u4e0a\u5f0f\u91cc\u53ea\u7528\u5230\u4e86\u4e0a\u4e00\u65f6\u523b\u7684\u68af\u5ea6\uff0c\u4f46\u5176\u5b9e\u662f\u5f53\u524d\u65f6\u523b\u4e4b\u524d\u7684\u6240\u6709\u5386\u53f2\u68af\u5ea6\u7684\u6307\u6570\u5e73\u5747\u3002<\/p>\n\n\n\n<p>\u52a0\u5165\u52a8\u91cf\u9879\u540e\u8fdb\u884c\u6a21\u578b\u6743\u91cd\u7684\u66f4\u65b0\uff0c\u6bd4\u76f4\u63a5\u7528\u539f\u59cb\u68af\u5ea6\u503c\uff0c\u6296\u52a8\u66f4\u5c0f\u66f4\u52a0\u7a33\u5b9a\uff0c\u4e5f\u53ef\u4ee5\u5feb\u901f\u51b2\u8fc7\u8bef\u5dee\u66f2\u9762\uff08Error Surface\uff09\u4e0a\u7684\u978d\u70b9\u7b49\u6bd4\u8f83\u5e73\u5766\u7684\u533a\u57df\u3002\u5176\u539f\u7406\u53ef\u4ee5\u60f3\u8c61\u6210\u6ed1\u96ea\u8fd0\u52a8\uff0c\u5f53\u524d\u7684\u8fd0\u52a8\u8d8b\u52bf\u603b\u4f1a\u53d7\u5230\u4e4b\u524d\u52a8\u80fd\u7684\u5f71\u54cd\uff0c\u6240\u4ee5\u6ed1\u96ea\u7684\u66f2\u7ebf\u624d\u6bd4\u8f83\u4f18\u7f8e\u5e73\u6ed1\uff0c\u4e0d\u53ef\u80fd\u5212\u51fa90\u00b0\u8fd9\u6837\u9661\u5ced\u7684\u76f4\u89d2\u5f2f\uff1b\u5f53\u6ed1\u5230\u8c37\u5e95\u65f6\uff0c\u867d\u7136\u5730\u52bf\u5e73\u5766\uff0c\u4f46\u662f\u7531\u4e8e\u4e4b\u524d\u52a8\u80fd\u7684\u5f71\u54cd\uff0c\u4e5f\u4f1a\u7ee7\u7eed\u5f80\u524d\u6ed1\uff0c\u6709\u53ef\u80fd\u501f\u52a9\u52a8\u91cf\u51b2\u51fa\u8c37\u5e95\u3002<\/p>\n\n\n\n<p>\u5c0f\u7ed3\u4e00\u4e0b\uff0c\u52a0\u5165\u52a8\u91cf\u9879\u7684\u597d\u5904\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\uff081\uff09\u5728\u4e0b\u964d\u521d\u671f\u65f6\uff0c\u52a8\u91cf\u65b9\u5411\u4e0e\u5f53\u524d\u68af\u5ea6\u65b9\u5411\u4e00\u81f4\uff0c\u80fd\u591f\u8fdb\u884c\u5f88\u597d\u7684\u6536\u655b\u52a0\u901f\u6548\u679c\u3002<\/p>\n\n\n\n<p>\uff082\uff09\u5728\u4e0b\u964d\u540e\u671f\u65f6\uff0c\u68af\u5ea6\u53ef\u80fd\u5728\u5c40\u90e8\u6700\u5c0f\u503c\u9644\u8fd1\u9707\u8361\uff0c\u52a8\u91cf\u53ef\u80fd\u5e2e\u52a9\u8df3\u51fa\u5c40\u90e8\u6700\u5c0f\u503c\u3002 <\/p>\n\n\n\n<p>\uff083\uff09\u5728\u68af\u5ea6\u6539\u53d8\u65b9\u5411\u65f6\uff0c\u52a8\u91cf\u80fd\u591f\u62b5\u6d88\u65b9\u5411\u76f8\u5bf9\u7684\u68af\u5ea6\uff0c\u6291\u5236\u632f\u8361\uff0c\u4ece\u800c\u52a0\u5feb\u6536\u655b\u3002<\/p>\n\n\n\n<p>\u52a0\u5165\u52a8\u91cf\u7684\u68af\u5ea6\u4e0b\u964d\u516c\u5f0f\u8fd8\u6709\u53e6\u4e00\u79cd\u7b80\u5355\u7684\u5b9e\u73b0\uff0c\u5373\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(g_{i}=\\beta g_{i-1}+g(\\theta_{i-1})\\)<\/p>\n<p style=\"text-align: center;\">\\(\\theta_i=\\theta_{i-1}-\\alpha\\boldsymbol{g}_i\\)<\/p>\n\n\n<h2 class=\"wp-block-heading\">AdaGrad\u4f18\u5316\u5668<\/h2>\n\n\n\n<p>\u52a8\u91cf\u662f\u4f18\u5316\u5c0f\u6279\u91cf\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u53e6\u4e00\u4e2a\u65b9\u6cd5\u88ab\u79f0\u4e3aAdaGrad\u7b97\u6cd5\uff0c\u4e3b\u8981\u662f\u5bf9\u5b66\u4e60\u7387\u505a\u4e86\u8fdb\u4e00\u6b65\u7684\u4f18\u5316\u3002\u5176\u53c2\u6570\u66f4\u65b0\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(r_{_k}\\leftarrow r_{_{k-1}}+g\\odot g\\)<\/p>\n<p style=\"text-align: center;\">\\(\\theta_{_k}\\leftarrow\\theta_{_{k-1}}-\\frac{\\eta}{\\sqrt{r_{_k}+\\sigma}}\\odot g\\)<\/p>\n\n\n<p>\u4ece\u4e0a\u5f0f\u53ef\u4ee5\u770b\u51fa\uff0c\u4e0e\u666e\u901a\u7684\u68af\u5ea6\u4e0b\u964d\u516c\u5f0f\u76f8\u6bd4\uff0c$\\eta$ \u53d8\u6210\u4e86\\(\\frac{\\eta}{\\sqrt{r_i+\\sigma}}\\)\uff0c\u5176\u4e2d\\(\\sigma\\)\u662f\u4e00\u4e2a\u503c\u6781\u5c0f\u7684\u5b9e\u6570\uff0c\u9632\u6b62\u9664\u96f6\u7684\u60c5\u51b5\u3002\u800c\\(r_{k}\\)\u662f\u4e4b\u524d\u65f6\u523b\u68af\u5ea6\u5e73\u65b9\u7684\u7d2f\u52a0\u503c\uff0c\u8fd9\u91cc\u8003\u8651\u4e24\u4e2a\u95ee\u9898:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u68af\u5ea6\u4e3a\u4ec0\u4e48\u8981\u5e73\u65b9\uff1f<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ee5\u53ca\u4e3a\u4ec0\u4e48\u8981\u505a\u7d2f\u52a0\uff1f<\/li>\n<\/ul>\n\n\n\n<p>\u68af\u5ea6\u5e73\u65b9\u7684\u4f5c\u7528\u662f\u4e3a\u4e86\u5e73\u6ed1\u5f53\u524d\u7684\u68af\u5ea6\uff0c\u5982\u679c\\(\\mathrm{g}\\)\u6bd4\u8f83\u5c0f\uff0c\\(g\\odot g\\)\u5c31\u4f1a\u66f4\u5c0f\uff0c\\(r_{k}\\)\u5c31\u4f1a\u5c0f\uff0c \\(\\frac{1}{\\sqrt{r_{i}+\\sigma}}\\)\u5c31\u4f1a\u76f8\u5bf9\u8f83\u5927\uff0c\u8fd9\u65f6\u5019\u8d77\u5230\u4e86\u653e\u5927\u5b66\u4e60\u7387\\(\\eta\\)\u7684\u4f5c\u7528\u3002\u53cd\u4e4b\uff0c\u5982\u679c\\(\\mathrm{g}\\)\u6bd4\u8f83\u5927\uff0c\u5b66\u4e60\u7387\\(\\eta\\)\u5c31\u4f1a\u51cf\u5c0f\u3002<\/p>\n\n\n\n<p>\u7d2f\u52a0\u5386\u53f2\u68af\u5ea6\u662f\u4e3a\u4e86\u8ba9\u5b66\u4e60\u7387\u968f\u7740\u8bad\u7ec3\u7684\u8fdb\u884c\u9010\u6e10\u51cf\u5c0f\u3002\u7531\u4e8e\u7d2f\u52a0\u7684\u4f5c\u7528\uff0c\\(r_{k}\\)\u4f1a\u8d8a\u6765\u8d8a\u5927\uff0c\\(\\frac{\\eta}{\\sqrt{r_k+\\sigma}}\\)\u5c31\u4f1a\u968f\u7740\u8bad\u7ec3\u8d8a\u6765\u8d8a\u5c0f\u3002\u8fd9\u662f\u4e00\u4e2a\u5408\u9002\u7684\u5b66\u4e60\u7387\u8c03\u8282\u7b56\u7565\uff0c\u5c31\u50cf\u6253\u9ad8\u5c14\u592b\u7403\u4e00\u6837\uff0c\u53ef\u4ee5\u628a\u5b66\u4e60\u7387\u770b\u4f5c\u6325\u7403\u6746\u7684\u529b\u5ea6\uff0c\u521a\u5f00\u59cb\u6253\u7403\u7684\u65f6\u5019\u80af\u5b9a\u662f\u5927\u529b\uff0c\u5e0c\u671b\u5feb\u901f\u63a5\u8fd1\u7403\u6d1e\uff1b\u6253\u7403\u540e\u671f\u7684\u65f6\u5019\u9700\u8981\u7528\u5c0f\u529b\uff0c\u5c06\u7403\u6162\u6162\u6253\u8fdb\u6d1e\u3002<\/p>\n\n\n\n<p>\u5f53\u7136\uff0cAdaGrad\u7b97\u6cd5\u4e5f\u6709\u7f3a\u70b9\u3002\u9996\u5148\u7531\u516c\u5f0f\u53ef\u4ee5\u770b\u51fa\uff0c\u5b83\u4ecd\u4f9d\u8d56\u4e8e\u4eba\u5de5\u8bbe\u7f6e\u4e00\u4e2a\u5168\u5c40\u5b66\u4e60\u7387\u3002\u5176\u6b21\\(\\eta\\)\u8bbe\u7f6e\u8fc7\u5927\u7684\u8bdd\uff0c\u4f1a\u4f7f\\(\\sqrt{r_{k}+\\sigma}\\)\u8fc7\u4e8e\u654f\u611f\uff0c\u5bf9\u68af\u5ea6\u7684\u8c03\u8282\u592a\u5927\u3002\u6700\u540e\u5728\u8bad\u7ec3\u4e2d\u540e\u671f\uff0c\u5206\u6bcd\u4e0a\u68af\u5ea6\u5e73\u65b9\u7684\u7d2f\u52a0\u5c06\u4f1a\u8d8a\u6765\u8d8a\u5927\uff0c\u4f7f\\(\\mathrm{gradient}\\to0\\)\uff0c\u53ef\u80fd\u4f1a\u4f7f\u8bad\u7ec3\u63d0\u524d\u7ed3\u675f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">RMSprop\u4f18\u5316\u5668<\/h2>\n\n\n\n<p>RMSprop\u7b97\u6cd5\u662fAdaGrad\u7b97\u6cd5\u7684\u4e00\u79cd\u53d1\u5c55\uff0c\u5bf9\u4e8e\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u6548\u679c\u5f88\u597d\uff0c\u672c\u8d28\u4e0a\u5c31\u662f\u5728\\(r_{k}\\)\u4e2d\u878d\u5165EMA\u7684\u601d\u60f3\uff0c\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(r_{_k}\\leftarrow\\beta r_{_{k-1}}+(1-\\beta)g\\odot g\\)<\/p>\n<p style=\"text-align: center;\">\\(\\theta_{_k}\\leftarrow\\theta_{_{k-1}}-\\frac{\\eta}{\\sqrt{r_{_k}+\\sigma}}\\odot g\\)<\/p>\n\n\n<p>\u76ee\u7684\u662f\u5728\u7d2f\u52a0\u5386\u53f2\u68af\u5ea6\u5e73\u65b9\u65f6\uff0c\u7ed9\u8fd1\u671f\u7684\u68af\u5ea6\u4ee5\u66f4\u5927\u7684\u6743\u91cd\uff0c\u800c\u4e0d\u662f\u4e00\u5473\u5730\u7d2f\u79ef\uff0c\u6700\u540e\u5bfc\u81f4\u68af\u5ea6\u4e3a0\u3002\u867d\u7136RMSprop\u53ef\u4ee5\u66f4\u597d\u5730\u81ea\u52a8\u8c03\u8282\u5b66\u4e60\u7387\uff0c\u4f46\u5176\u5b9e\u4f9d\u7136\u4f9d\u8d56\u4e8e\u5168\u5c40\u5b66\u4e60\u7387\u7684\u521d\u503c\u8bbe\u7f6e\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Adam\u4f18\u5316\u5668<\/h2>\n\n\n\n<p>\u6700\u540e\uff0cAdam\u7b97\u6cd5\u53ef\u4ee5\u8bf4\u662f\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u4e2d\u6700\u5e38\u7528\u7684\u4f18\u5316\u7b97\u6cd5\uff0c\u56e0\u4e3a\u5b83\u878d\u5408\u4e86\u5176\u4ed6\u4f18\u5316\u7b97\u6cd5\u7684\u4f18\u70b9\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u5e26\u6709\u52a8\u91cf\u9879\u7684RMSprop\u4f18\u5316\u5668\uff0c\u5e76\u5728\u6b64\u57fa\u7840\u4e0a\u8fd8\u505a\u4e86\u8fdb\u4e00\u6b65\u7684\u4f18\u5316\uff0c\u907f\u514d\u4e86\u51b7\u542f\u52a8\u7684\u95ee\u9898\u3002\u5b83\u7684\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\u8f93\u5165\uff1a\u5b66\u4e60\u7387\\(\\varepsilon\\)\uff0c\u521d\u59cb\u53c2\u6570\\(\\theta\\)\uff0c\u5c0f\u5e38\u6570\\(\\mathrm{\u03c3}\\)\uff0c\u7d2f\u8ba1\u68af\u5ea6\\(_{\\nu}\\)\uff0c\u7d2f\u8ba1\u5e73\u65b9\u68af\u5ea6\\(\\mathrm{r}\\)\uff0c\u8870\u51cf\u7cfb\u6570\\(\\rho\\)\uff0c\u52a8\u91cf\u53c2\u6570\\(\\alpha\\)\u3002<\/p>\n\n\n\n<p>\u4ece\u8bad\u7ec3\u96c6\u4e2d\u91c7\u96c6\\(\\mathrm{m}\\)\u4e2a\u6837\u672c$\\lbrace{x^1, x^2, \\ldots, x^m} \\rbrace$&nbsp;\uff0c\u5176\u4e2d\u6570\u636e\\(x^{(i)}\\)\u548c\u5bf9\u5e94\u76ee\u6807\\(y^{(i)}\\)\u8ba1\u7b97\u68af\u5ea6\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(g\\leftarrow\\frac{1}{m}\\nabla_{\\theta_{k-1}}L(f(x^{(i)},\\theta_{_{k-1}}),y^{(i)})\\)<\/p>\n\n\n<p>\u8ba1\u7b97\u7d2f\u8ba1\u68af\u5ea6\uff1a\\(v_{t}=\\alpha v{_{t-1}}+(1-\\alpha)g\\)\uff08\u5373\uff0c\u52a0\u5165\u52a8\u91cf\u9879\uff09\uff1b<\/p>\n\n\n\n<p>\u8ba1\u7b97\u7d2f\u8ba1\u5e73\u65b9\u68af\u5ea6\uff1a\\(r_{t}=\\rho r_{t-1}+(1-\\rho)g\\odot g\\)\uff08\u5373\uff0c\u901a\u8fc7RMSprop\u7b97\u6cd5\u5b9e\u73b0\u5b66\u4e60\u7387\u7684\u8c03\u8282\uff09\uff1b<\/p>\n\n\n\n<p>\u4fee\u6b63\uff1a\\(\\hat{\\nu}{t}=\\frac{\\nu{t}}{1-\\alpha}\\)\uff0c\\(\\hat{r}{t}=\\frac{r{t}}{1-\\rho}\\)\u3002<\/p>\n\n\n\n<p>\u66f4\u65b0\u53c2\u6570\uff1a\\(\\theta_{k}\\leftarrow\\theta{{k-1}}-\\varepsilon\\frac{\\hat{v}{t}}{\\sqrt{\\hat{r}{_t}+\\sigma}}\\)<\/p>\n\n\n\n<p>\u8fd9\u91cc\u89e3\u91ca\u4e00\u4e0b\u4ec0\u4e48\u53eb\u51b7\u542f\u52a8\uff0c\u5047\u8bbe\uff1a\u8870\u51cf\u7cfb\u6570= 0.999\uff0c\u52a8\u91cf\u53c2\u6570= 0.9\u3002<\/p>\n\n\n\n<p>\u90a3\u4e48\uff0c\u5f53\u8bad\u7ec3\u521a\u5f00\u59cb\u7684\u65f6\u5019\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(v=0.9\\times0+0.1\\times g=0.1g\\)<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(r=0.999\\times0+0.001\\times g^2=0.001g^2\\)<\/p>\n\n\n\n<p><br><br>\\(\\text{r}\\)\u548c\\(\\nu\\)\u5728\u521d\u59cb\u8bad\u7ec3\u65f6\u90fd\u5f88\u5c0f\uff0c\u610f\u5473\u7740\u521d\u59cb\u8bad\u7ec3\u65f6\u68af\u5ea6\u5f88\u5c0f\uff0c\u53c2\u6570\u66f4\u65b0\u5f88\u6162\u3002\u800c\u4fee\u6b63\u540e\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(V=\\frac{v}{1-0.9}=\\frac{0.1\\boldsymbol{g}}{0.1}=\\boldsymbol{g}\\)<\/p>\n<p style=\"text-align: center;\">\\(R=\\frac{r}{1-0.999}=\\frac{0.001\\boldsymbol{g}^2}{0.001}=\\boldsymbol{g}^2\\)<\/p>\n\n\n<p>\u901a\u8fc7\u8fd9\u6837\u7684\u65b9\u6cd5\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u7684\u907f\u514d\u51b7\u542f\u52a8\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5f53\u89e3\u51b3\u623f\u4ef7\u9884\u6d4b\u95ee\u9898\u65f6\uff0c\u9996\u5148\u5236\u4f5c\u4e00\u4e2a\u8bad\u7ec3\u6570\u636e\u96c6\uff0c\u5728\u623f\u4ef7\u7684\u4f8b\u5b50\u4e2d\uff0c\u6536\u96c6\u4e86\u8fc7\u53bb\u4e24\u5e74\u7684\u623f\u5b50\u4ea4\u6613\u8bb0\u5f55\u3002\u623f\u5b50\u7684\u6570\u636e\uff08\u9762\u79ef\u3001 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2803,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,28],"tags":[19],"class_list":["post-2798","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-18","category-28","tag-19"],"_links":{"self":[{"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2798","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2798"}],"version-history":[{"count":14,"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2798\/revisions"}],"predecessor-version":[{"id":2905,"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2798\/revisions\/2905"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.gnn.club\/index.php?rest_route=\/wp\/v2\/media\/2803"}],"wp:attachment":[{"href":"http:\/\/www.gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2798"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2798"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2798"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}