{"id":2053,"date":"2024-09-19T09:40:40","date_gmt":"2024-09-19T01:40:40","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2053"},"modified":"2025-03-12T15:05:40","modified_gmt":"2025-03-12T07:05:40","slug":"generative-adversarial-networks-gan","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2053","title":{"rendered":"\u751f\u6210\u5bf9\u6297\u7f51\u7edc                 \uff08GAN\uff09"},"content":{"rendered":"<h1><img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919094139612.png\" style=\"height:50px;display:inline\"> Deep Learning<\/h1>\n<hr \/>\n<p>create by Arwin Yu<\/p>\n<h2>Tutorial 06 - Generative Adversarial Networks - GAN<\/h2>\n<hr \/>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919094219759.png\" style=\"height:300px\">\n<\/p>\n<h3><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/bubbles\/50\/000000\/checklist.png\" style=\"height:50px;display:inline\"> Agenda<\/h3>\n<hr \/>\n<ul>\n<li>Generative Adversarial Networks\n<ul>\n<li>\u5bf9\u6297\u673a\u5236<\/li>\n<li>\u635f\u5931\u51fd\u6570<\/li>\n<li>\u8bad\u7ec3\u7b56\u7565<\/li>\n<li>\u624b\u5199\u6570\u5b57\u793a\u4f8b<\/li>\n<\/ul>\n<\/li>\n<li>Improved GAN\n<ul>\n<li>\u7279\u5f81\u5339\u914d<\/li>\n<li>\u5c0f\u6279\u91cf\u5224\u522b\u5668<\/li>\n<li>\u5355\u4fa7\u6807\u7b7e\u5e73\u6ed1<\/li>\n<li>\u865a\u62df\u6279\u89c4\u8303\u5316<\/li>\n<\/ul>\n<\/li>\n<li>f-GAN\n<ul>\n<li>\u635f\u5931\u63a8\u5bfc<\/li>\n<li>\u635f\u5931\u4e0e\u6563\u5ea6\u6846\u67b6<\/li>\n<\/ul>\n<\/li>\n<li>W-GAN\n<ul>\n<li>\u68af\u5ea6\u5f25\u6563<\/li>\n<li>Wasserstein \u8ddd\u79bb<\/li>\n<li>Wasserstein \u635f\u5931<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/cute-clipart\/64\/000000\/alarm.png\" style=\"height:50px;display:inline\"> The Adversarial Mechanism<\/h2>\n<hr \/>\n<p>\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GAN\uff09\u662f\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u7684\u4e00\u4e2a\u9769\u547d\u6027\u6982\u5ff5\uff0c\u4e3a\u6570\u636e\u751f\u6210\u63d0\u4f9b\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u65b9\u5f0f\u3002\u5176\u540d\u79f0\u4e2d\u7684<strong>\u5bf9\u6297<\/strong>\u4f53\u73b0\u4e86\u6838\u5fc3\u601d\u60f3\uff1a\u901a\u8fc7\u4e24\u4e2a\u795e\u7ecf\u7f51\u7edc\u4e4b\u95f4\u7684\u76f8\u4e92\u7ade\u4e89\u6765\u751f\u6210\u6570\u636e\u3002<\/p>\n<p>\u8fd9\u4e24\u4e2a\u7f51\u7edc\u5206\u522b\u662f\uff1a\u751f\u6210\u5668 (Generator) \u548c\u5224\u522b\u5668 (Discriminator)\u3002<\/p>\n<p>\u60f3\u8c61\u4e00\u4e2a\u4f8b\u5b50\uff0c\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u5982\u540c\u4e00\u573a\u7cbe\u5fc3\u7f16\u6392\u7684\u827a\u672f\u8868\u6f14\u3002\u821e\u53f0\u4e0a\u6709\u4e24\u4f4d\u4e3b\u8981\u7684\u827a\u672f\u5bb6\uff1a\u751f\u6210\u5668\u548c\u5224\u522b\u5668\u3002<\/p>\n<ul>\n<li>\n<p>\u751f\u6210\u5668\u5145\u6ee1\u521b\u610f\u548c\u9b54\u6cd5\uff0c\u4ece\u65e0\u4e2d\u521b\u9020\uff0c\u6325\u52a8\u753b\u7b14\uff0c\u5c1d\u8bd5\u5236\u4f5c\u6700\u7f8e\u7684\u753b\u4f5c\u3002\u5b83\u4ece\u4e00\u4e2a\u968f\u673a\u7684\u7075\u611f\uff08\u566a\u58f0\u5411\u91cf\uff09\u51fa\u53d1\uff0c\u8bd5\u56fe\u521b\u4f5c\u4ee4\u4eba\u4fe1\u670d\u7684\u4f5c\u54c1\u3002<\/p>\n<\/li>\n<li>\n<p>\u800c\u5728\u821e\u53f0\u7684\u53e6\u4e00\u4fa7\uff0c\u5224\u522b\u5668\u5219\u626e\u6f14\u7740\u6279\u8bc4\u5bb6\u7684\u89d2\u8272\uff0c\u76ee\u5149\u9510\u5229\uff0c\u4e0d\u653e\u8fc7\u4efb\u4f55\u7455\u75b5\u3002\u5f53\u5b83\u9762\u524d\u5c55\u793a\u7684\u4f5c\u54c1\u6765\u6e90\u4e8e\u771f\u5b9e\u4e16\u754c\u65f6\uff0c\u5b83\u6b23\u7136\u70b9\u5934\uff1b\u4f46\u5f53\u4f5c\u54c1\u51fa\u81ea\u751f\u6210\u5668\u4e4b\u624b\uff0c\u5b83\u4fbf\u7ec6\u7ec6\u5ba1\u67e5\uff0c\u51b3\u5b9a\u8fd9\u662f\u771f\u54c1\u8fd8\u662f\u8d5d\u54c1\u3002\u8fd9\u4e2a\u5224\u522b\u8fc7\u7a0b\u4e0d\u65ad\u5730\u53cd\u9988\u7ed9\u751f\u6210\u5668\uff0c\u544a\u8bc9\u5b83\u5728\u54ea\u91cc\u505a\u5f97\u4e0d\u591f\u597d\uff0c\u9700\u8981\u6539\u8fdb\u3002<\/p>\n<\/li>\n<li>\n<p>\u8fd9\u573a\u821e\u8e48\u662f\u4e00\u4e2a\u6301\u7eed\u7684\u8fed\u4ee3\u8fc7\u7a0b\uff0c\u53cc\u65b9\u4e92\u76f8\u6311\u6218\uff0c\u5171\u540c\u6210\u957f\u3002<\/p>\n<\/li>\n<li>\n<p>\u968f\u7740\u65f6\u95f4\u7684\u6d41\u901d\uff0c\u751f\u6210\u5668\u7684\u6280\u5de7\u53d8\u5f97\u8d8a\u6765\u8d8a\u7eaf\u719f\uff0c\u800c\u5224\u522b\u5668\u7684\u9274\u8d4f\u80fd\u529b\u4e5f\u65e5\u76ca\u63d0\u9ad8\u3002\u6700\u7ec8\uff0c\u6211\u4eec\u5e0c\u671b\u5728\u8fd9\u573a\u821e\u8e48\u4e2d\uff0c\u751f\u6210\u5668\u80fd\u591f\u521b\u4f5c\u51fa\u5982\u6b64\u9ad8\u8d28\u91cf\u7684\u4f5c\u54c1\uff0c\u4ee5\u81f3\u4e8e\u5373\u4f7f\u662f\u6700\u5c16\u9510\u7684\u6279\u8bc4\u5bb6\u2014\u2014\u5224\u522b\u5668\uff0c\u4e5f\u65e0\u6cd5\u533a\u5206\u5176\u771f\u4f2a\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u5177\u4f53\u6765\u8bf4\uff1a<\/p>\n<p>\u5728\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u7684\u821e\u53f0\u4e0a\uff0c\u751f\u6210\u5668\u626e\u6f14\u7740\u4e00\u4e2a\u5145\u6ee1\u521b\u610f\u7684\u827a\u672f\u5bb6\u89d2\u8272\u3002\u8fd9\u4f4d\u201c\u827a\u672f\u5bb6\u201d\u4ece\u4e00\u4e2a\u968f\u673a\u5411\u91cf\u4e2d\u6c72\u53d6\u7075\u611f\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u795e\u7ecf\u7f51\u7edc\u5c42\uff08\u5982\u5377\u79ef\u6216\u5168\u8fde\u63a5\u5c42\uff09\u5c06\u5176\u8f6c\u5316\u4e3a\u6709\u5f62\u7684\u4f5c\u54c1\u3002\u4e0e\u771f\u5b9e\u4e16\u754c\u7684\u827a\u672f\u5bb6\uff08\u771f\u5b9e\u7684\u6570\u636e\uff09\u4e0d\u65ad\u7ec3\u4e60\u548c\u4fee\u6b63\u6280\u5de7\u4ee5\u5b8c\u5584\u4f5c\u54c1\u7684\u8fc7\u7a0b\u76f8\u4f3c\uff0c\u751f\u6210\u5668\u4e5f\u4e0d\u65ad\u5730\u8c03\u6574\u81ea\u5df1\u7684\u53c2\u6570\uff0c\u4ee5\u4f7f\u5176\u4ea7\u751f\u7684\u4f5c\u54c1\u66f4\u52a0\u903c\u771f\u3002\u5176\u76ee\u6807\u662f\u521b\u4f5c\u51fa\u4ee4\u4eba\u4fe1\u670d\u7684\u6570\u636e\uff0c\u4ee5\u81f3\u4e8e\u5224\u522b\u5668\u2014\u2014\u8fd9\u4f4d\u4e25\u683c\u7684\u827a\u672f\u8bc4\u8bba\u5bb6\uff0c\u96be\u4ee5\u533a\u5206\u5176\u771f\u4f2a\u3002\u56e0\u6b64\uff0c<strong>\u751f\u6210\u5668\u4e0d\u4ec5\u662f\u4e00\u4e2a\u521b\u4f5c\u8005\uff0c\u66f4\u662f\u4e00\u4e2a\u7ec8\u8eab\u5b66\u4e60\u8005\uff0c\u4e0d\u65ad\u5730\u901a\u8fc7\u5224\u522b\u5668\u7684\u53cd\u9988\u6765\u5b8c\u5584\u81ea\u5df1\u7684\u201c\u827a\u672f\u6280\u5de7\u201d<\/strong>\u3002<\/p>\n<p>\u800c\u5224\u522b\u5668\u662f\u90a3\u4f4d\u6279\u5224\u773c\u5149\u7280\u5229\u7684\u827a\u672f\u8bc4\u8bba\u5bb6\u3002\u5b83\u5bf9\u6bcf\u4e00\u4ef6\u4f5c\u54c1\u90fd\u8fdb\u884c\u4e25\u683c\u7684\u5ba1\u67e5\uff0c\u901a\u8fc7\u5176\u5185\u90e8\u7531\u591a\u4e2a\u795e\u7ecf\u7f51\u7edc\u5c42\uff08\u4f8b\u5982\u5377\u79ef\u5c42\u6216\u5168\u8fde\u63a5\u5c42\uff09\u7ec4\u6210\u7684\u590d\u6742\u673a\u5236\uff0c\u5224\u5b9a\u8fd9\u4ef6\u4f5c\u54c1\u662f\u5426\u4e3a\u771f\u5b9e\u4e16\u754c\u7684\u4f73\u4f5c\uff0c\u8fd8\u662f\u751f\u6210\u5668\u6240\u521b\u4f5c\u7684\u6a21\u4eff\u54c1\u3002\u5224\u522b\u5668\u5728\u63a5\u6536\u5230\u6570\u636e\u540e\uff0c\u901a\u8fc7\u5176\u7f51\u7edc\u7ed3\u6784\u8f93\u51fa\u4e00\u4e2a\u8bc4\u5206\uff0c\u8868\u793a\u8fd9\u4efd\u6570\u636e\u7684\u771f\u5b9e\u6027\u6982\u7387\u3002\u5176\u6838\u5fc3\u4efb\u52a1\u662f\u6b63\u786e\u5730\u8bc6\u522b\u51fa\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u6570\u636e\uff0c\u5e76\u901a\u8fc7\u5176\u5224\u65ad\u4e3a\u751f\u6210\u5668\u63d0\u4f9b\u5b9d\u8d35\u7684\u53cd\u9988\uff0c\u4f7f\u5176\u6709\u673a\u4f1a\u66f4\u8fdb\u4e00\u6b65\u5730\u5b8c\u5584\u81ea\u5df1\u7684\u521b\u4f5c\u6280\u80fd\u3002\u56e0\u6b64\uff0c<strong>\u5224\u522b\u5668\u65e2\u662f\u4e00\u4e2a\u4e25\u82db\u7684\u8bc4\u5ba1\uff0c\u4e5f\u662f\u751f\u6210\u5668\u6210\u957f\u9053\u8def\u4e0a\u7684\u5173\u952e\u5f15\u5bfc\u8005<\/strong>\u3002<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919095858526.png\" style=\"height:300px\">\n<\/p>\n<p>\u5f53\u8c08\u8bba\u4f20\u7edf\u7684 GAN \u65f6, \u5b83\u7684\u76ee\u6807\u51fd\u6570\u662f\u4e00\u4e2a\u4e24\u4eba\u96f6\u548c\u535a\u5f08, \u5176\u4e2d\u751f\u6210\u5668 ( $G$ ) \u548c\u5224\u522b\u5668 ( $D$ ) \u6709\u5bf9\u7acb\u7684\u76ee\u6807\u3002\u535a\u5f08\u8fc7\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3a:<br \/>\n$$<br \/>\n\\min _G \\max _D \\mathcal{L}(D, G)=\\mathrm{E}_{x \\sim p_{\\text {dat }}(x)}[\\log D(x)]+\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]<br \/>\n$$<\/p>\n<ul>\n<li>\u5916\u90e8\u7684\u6700\u5c0f\u5316 (min) \u4ee3\u8868\u751f\u6210\u5668 $G$ \u7684\u76ee\u6807\u3002\u751f\u6210\u5668\u5e0c\u671b\u6700\u5c0f\u5316\u5224\u522b\u5668\u5bf9\u5176\u751f\u6210\u7684\u6837\u672c\u4ea7\u751f\u7684\u6b63\u786e\u5206\u7c7b\u6982\u7387\u3002\u6362\u53e5\u8bdd\u8bf4, \u751f\u6210\u5668\u8bd5\u56fe\u9a97\u8fc7\u5224\u522b\u5668, \u8ba9\u5176\u8ba4\u4e3a\u751f\u6210\u7684\u6837\u672c\u662f\u771f\u5b9e\u7684\u3002<\/li>\n<li>\u5185\u90e8\u7684\u6700\u5927\u5316 (max)\u4ee3\u8868\u5224\u522b\u5668 $D$ \u7684\u76ee\u6807\u3002\u5224\u522b\u5668\u5e0c\u671b\u6700\u5927\u5316\u5176\u5bf9\u771f\u5b9e\u548c\u751f\u6210\u6837\u672c\u7684\u5206\u7c7b\u80fd\u529b\u3002<\/li>\n<\/ul>\n<p>\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5728\u751f\u6210\u5668\uff08Generator\uff09\u548c\u5224\u522b\u5668\uff08Discriminator\uff09\u4e4b\u95f4\u5efa\u7acb\u4e00\u4e2a\u7ade\u4e89\u5173\u7cfb\u3002\u4e3a\u4e86\u4f7f\u8fd9\u79cd\u7ade\u4e89\u6709\u6548\uff0c\u9700\u8981\u4e3a\u8fd9\u4e24\u4e2a\u7f51\u7edc\u5b9a\u4e49\u9002\u5f53\u7684\u635f\u5931\u51fd\u6570\u3002\u5728\u6700\u57fa\u672c\u7684GAN\u4e2d\uff0c\u751f\u6210\u5668\u7684\u4efb\u52a1\u662f\u751f\u6210\u80fd\u591f\u6b3a\u9a97\u5224\u522b\u5668\u7684\u6570\u636e\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u751f\u6210\u5668\u5e0c\u671b\u5224\u522b\u5668\u8ba4\u4e3a\u5176\u751f\u6210\u7684\u6570\u636e\u5c3d\u53ef\u80fd\u5730\u63a5\u8fd1\u771f\u5b9e\u6570\u636e\u3002\u56e0\u6b64\uff0c\u751f\u6210\u5668\u7684\u635f\u5931\u51fd\u6570\u901a\u5e38\u57fa\u4e8e\u5224\u522b\u5668\u5bf9\u751f\u6210\u6570\u636e\u7684\u8bc4\u4f30\u3002<\/p>\n<pre><code class=\"language-python\">\nimport torch as t\nfrom torch import nn\nfrom torch.autograd import Variable\nfrom torch.optim import Adam\nfrom torchvision import transforms\nfrom torchvision.utils import make_grid\nfrom torchvision.datasets import CIFAR10, MNIST\nfrom pylab import plt\n%matplotlib inline\n\nclass Config:\n    lr = 0.0002\n    nz = 100 # noise dimension\n    image_size = 64\n    image_size2 = 64\n    nc = 1 # chanel of img \n    ngf = 64 # generate channel\n    ndf = 64 # discriminative channel\n    beta1 = 0.5\n    batch_size = 32\n    max_epoch = 10 # =1 when debug\n    workers = 2\n    gpu = True # use gpu or not\n\nopt=Config()\n\n# data preprocess\ntransform=transforms.Compose([\n                transforms.Resize(opt.image_size),\n                transforms.ToTensor(),\n                transforms.Normalize([0.5], [0.5])\n                ])\n\ndataset=MNIST(root=&#039;data&#039;, transform=transform, download=True)\n# dataloader with multiprocessing\ndataloader=t.utils.data.DataLoader(dataset,\n                                   opt.batch_size,\n                                   shuffle=True,\n                                   num_workers=opt.workers)\n# define model\nnetg = nn.Sequential(\n    nn.ConvTranspose2d(opt.nz,opt.ngf*8,4,1,0,bias=False),\n    nn.BatchNorm2d(opt.ngf*8),\n    nn.ReLU(True),\n\n    nn.ConvTranspose2d(opt.ngf*8,opt.ngf*4,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ngf*4),\n    nn.ReLU(True),\n\n    nn.ConvTranspose2d(opt.ngf*4,opt.ngf*2,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ngf*2),\n    nn.ReLU(True),\n\n    nn.ConvTranspose2d(opt.ngf*2,opt.ngf,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ngf),\n    nn.ReLU(True),\n\n    nn.ConvTranspose2d(opt.ngf,opt.nc,4,2,1,bias=False),\n    nn.Tanh()\n)\n\nnetd = nn.Sequential(\n    nn.Conv2d(opt.nc,opt.ndf,4,2,1,bias=False),\n    nn.LeakyReLU(0.2,inplace=True),\n\n    nn.Conv2d(opt.ndf,opt.ndf*2,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ndf*2),\n    nn.LeakyReLU(0.2,inplace=True),\n\n    nn.Conv2d(opt.ndf*2,opt.ndf*4,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ndf*4),\n    nn.LeakyReLU(0.2,inplace=True),\n\n    nn.Conv2d(opt.ndf*4,opt.ndf*8,4,2,1,bias=False),\n    nn.BatchNorm2d(opt.ndf*8),\n    nn.LeakyReLU(0.2,inplace=True),\n\n    nn.Conv2d(opt.ndf*8,1,4,1,0,bias=False),\n    nn.Sigmoid()\n)<\/code><\/pre>\n<h2><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/?size=100&id=bJclkWKA0ENc&format=png&color=000000\" style=\"height:50px;display:inline\">GAN\u6a21\u578b\u4e0e\u635f\u5931\u8be6\u89e3<\/h2>\n<hr \/>\n<p>\u5047\u8bbe $G$ \u662f\u751f\u6210\u5668, $D$ \u662f\u5224\u522b\u5668\u3002\u5f53\u7ed9\u5b9a\u4e00\u4e2a\u968f\u673a\u566a\u58f0\u5411\u91cf $z$ \u65f6, \u751f\u6210\u5668 $G$ \u751f\u6210\u4e00\u4e2a\u6570\u636e $G(z)$ \u3002<\/p>\n<p>\u5224\u522b\u5668 $D$ \u8bc4\u4f30\u8fd9\u4e2a\u6570\u636e\u5e76\u7ed9\u51fa\u4e00\u4e2a\u6982\u7387 $D(G(z))$, \u8868\u793a\u5b83\u8ba4\u4e3a $G(z)$ \u662f\u771f\u5b9e\u6570\u636e\u7684\u6982\u7387\u3002<\/p>\n<p>\u751f\u6210\u5668\u5e0c\u671b $D(G(z))$ \u5c3d\u53ef\u80fd\u5730\u63a5\u8fd1 1, \u5373\u5224\u522b\u5668\u88ab\u6b3a\u9a97\u5e76\u8ba4\u4e3a\u751f\u6210\u6570\u636e\u662f\u771f\u5b9e\u7684\u3002<\/p>\n<p><strong>\u5355\u72ec\u8003\u8651\u751f\u6210\u5668\uff1a<\/strong><\/p>\n<p>\u5982\u679c\u53ea\u8003\u8651\u4ece\u751f\u6210\u5668\u4ea7\u751f\u7684\u56fe\u7247, \u800c\u5ffd\u7565\u771f\u5b9e\u6570\u636e\u7684\u5f71\u54cd $\\left(\\mathrm{E}_{x \\sim p_{d: 18}(x)}[\\log D(x)]=0\\right)$, \u539f\u59cb\u7684GAN\u635f\u5931\u53ef\u4ee5\u7b80\u5199\u4e3a:<br \/>\n$$<br \/>\nL_G=\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]<br \/>\n$$<\/p>\n<p>\u516c\u5f0f\u89e3\u91ca: <\/p>\n<ul>\n<li>\u5f53 $D(G(z))$ \u63a5\u8fd1 1 \u65f6, \u610f\u5473\u7740\u5224\u522b\u5668\u51e0\u4e4e\u5b8c\u5168\u786e\u4fe1\u751f\u6210\u7684\u6570\u636e\u662f\u771f\u5b9e\u7684\u3002\u6b64\u65f6, $1-D(G(z))$ \u63a5\u8fd1 0 , \u800c $\\log (1-D(G(z)))$ \u7684\u503c\u4f1a\u662f\u4e00\u4e2a\u5f88\u5927\u7684\u8d1f\u6570\u3002\u8fd9\u6b63\u662f\u6211\u4eec\u6240\u671f\u671b\u7684\u6700\u5c0f\u5316\u751f\u6210\u5668\u635f\u5931\u3002<\/li>\n<li>\u5f53 $D(G(z))$ \u63a5\u8fd1 0 \u65f6, \u610f\u5473\u7740\u5224\u522b\u5668\u8ba4\u4e3a\u751f\u6210\u7684\u6570\u636e\u662f\u5047\u7684\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b, $1-D(G(z))$ \u63a5\u8fd1 1, \u56e0\u6b64 $\\log (1-D(G(z)))$ \u63a5\u8fd1 0 \u3002\u751f\u6210\u5668\u4f1a\u5c3d\u91cf\u907f\u514d\u8fd9\u79cd\u60c5\u51b5, \u56e0\u4e3a\u751f\u6210\u5668\u7684\u76ee\u6807\u662f\u6700\u5c0f\u5316 $\\log (1-D(G(z)))$, \u8fd9\u5b9e\u9645\u4e0a\u662f\u9f13\u52b1\u751f\u6210\u5668\u4ea7\u751f\u80fd\u591f\u6b3a\u9a97\u5224\u522b\u5668\u7684\u6570\u636e\u3002<\/li>\n<\/ul>\n<p><strong>\u4e3a\u4ec0\u4e48\u635f\u5931\u516c\u5f0f\u4e2d\u4f1a\u5b58\u5728\u4e00\u4e2alog\uff1f<\/strong><\/p>\n<p>\u4e00\u65b9\u9762\uff0cGAN\u4e2d\u6d89\u53ca\u5230\u7684\u635f\u5931\u51fd\u6570\u5e38\u5e38\u4e0e\u6982\u7387\u6709\u5173\uff0c\u8fd9\u4e9b\u6982\u7387\u56e0\u4e3a\u5c42\u7ea7\u7ed3\u6784\u7684\u539f\u56e0\u7ecf\u5e38\u9700\u8981\u8fdb\u884c\u4e58\u6cd5\u64cd\u4f5c\u3002\u5f53\u5904\u7406\u5f88\u5c0f\u7684\u6982\u7387\u503c\u65f6\uff0c\u5b83\u4eec\u7684\u4e58\u79ef\u53ef\u80fd\u4f1a\u53d8\u5f97\u975e\u5e38\u5c0f\uff0c\u63a5\u8fd1\u4e8e\u673a\u5668\u7684\u6570\u503c\u4e0b\u9650\uff0c\u8fd9\u53ef\u80fd\u5bfc\u81f4\u6570\u503c\u4e0d\u7a33\u5b9a\uff0c\u5373\u6240\u8c13\u7684\u201c\u4e0b\u6ea2\u201d\u95ee\u9898\u3002\u4e0b\u6ea2\u4f1a\u5bfc\u81f4\u8fd9\u4e9b\u975e\u5e38\u5c0f\u7684\u503c\u88ab\u56db\u820d\u4e94\u5165\u4e3a\u96f6\u3002\u901a\u8fc7\u91c7\u7528\u5bf9\u6570\uff0c\u53ef\u4ee5\u5c06\u4e58\u6cd5\u64cd\u4f5c\u8f6c\u5316\u4e3a\u52a0\u6cd5\u64cd\u4f5c\uff0c\u8fd9\u6709\u52a9\u4e8e\u63d0\u9ad8\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0clog\u6709\u653e\u5927\u7f5a\u5206\u7684\u6548\u5e94\u3002\u5177\u4f53\u6765\u8bf4, \u5f53 $D(G(z)$ )\u5f88\u5c0f (\u8868\u793a\u5224\u522b\u5668\u51e0\u4e4e\u786e\u5b9a\u751f\u6210\u7684\u6837\u672c\u662f\u5047\u7684) \u65f6, $1-D(G(z))$ \u4ecd\u7136\u63a5\u8fd1 1\u3002\u6b64\u65f6, $\\log (1-D(G(z)))$ \u7684\u503c\u63a5\u8fd1\u4e8e 0 \u3002\u7136\u800c, \u968f\u7740 $D(G(z))$ \u7684\u589e\u52a0, \u5373\u751f\u6210\u7684\u6837\u672c\u5f00\u59cb\u83b7\u5f97\u67d0\u79cd\u7a0b\u5ea6\u7684\u903c\u771f\u5ea6, \u4f46\u4ecd\u7136\u53ef\u4ee5\u88ab\u5224\u522b\u5668\u533a\u5206\u51fa\u6765, $1-D(G(z))$ \u5f00\u59cb\u8fc5\u901f\u51cf\u5c0f\u3002\u5bf9\u6570\u51fd\u6570\u5bf9\u8fd9\u4e9b\u503c\u7684\u653e\u5927\u6548\u5e94\u660e\u663e\u3002\u4f8b\u5982, $\\log (1-0.5)=-0.693$ \u548c $\\log (1-0.9)=-2.302$, \u53ef\u4ee5\u770b\u5230, \u5f53\u7531\u751f\u6210\u5668\u751f\u6210\u7684\u6837\u672c\u4ece\u88ab\u5224\u522b\u5668\u8bc4\u4f30\u4e3a $50 \\%$ \u771f\u5b9e\u5230 $90 \\%$ \u771f\u5b9e\u65f6, \u635f\u5931\u503c\u6709\u4e86\u663e\u8457\u7684\u4e0b\u964d\u3002\u8fd9\u79cd\u653e\u5927\u6548\u5e94\u786e\u4fdd\u4e86\uff0c\u5f53\u751f\u6210\u5668\u7a0d\u5fae\u63d0\u9ad8\u5176\u751f\u6210\u6837\u672c\u7684\u903c\u771f\u5ea6\u65f6\uff0c\u5b83\u4f1a\u53d7\u5230\u4e00\u4e2a\u5927\u7684\u7f5a\u5206\uff0c\u9f13\u52b1\u5b83\u66f4\u8fdb\u4e00\u6b65\u5730\u6539\u8fdb\u3002\u8fd9\u79cd\u653e\u5927\u7f5a\u5206\u6548\u5e94\u786e\u4fdd\u751f\u6210\u5668\u4e0d\u6ee1\u8db3\u4e8e\u4ec5\u4ec5\u4ea7\u751f\u7a0d\u597d\u7684\u6837\u672c\uff1b\u76f8\u53cd\uff0c\u5b83\u88ab\u6fc0\u52b1\u8981\u4ea7\u751f\u5c3d\u53ef\u80fd\u903c\u771f\u7684\u6837\u672c\uff0c\u4ee5\u964d\u4f4e\u5176\u635f\u5931\u3002<\/p>\n<p><strong>\u5355\u72ec\u8003\u8651\u5224\u522b\u5668\uff1a<\/strong><\/p>\n<p>\u5982\u679c\u53ea\u8003\u8651\u5224\u522b\u5668\u7684\u89d2\u5ea6\uff0cGAN\u7684\u635f\u5931\u51fd\u6570\u4e3b\u8981\u5173\u6ce8\u4e8e\u5224\u522b\u5668\u5982\u4f55\u533a\u5206\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u7684\u6570\u636e\u3002\u5bf9\u4e8e\u5224\u522b\u5668 $D$, \u635f\u5931\u51fd\u6570\u4e3a:<br \/>\n$$<br \/>\nL_D=\\mathrm{E}_{x \\sim p_{\\text {data }}(x)}[\\log D(x)]+\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]<br \/>\n$$<\/p>\n<p>\u635f\u5931\u51fd\u6570\u7531\u4e24\u90e8\u5206\u7ec4\u6210:<\/p>\n<p>(1) $\\mathrm{E}_{x \\sim p_{\\text {data}}(x)}[\\log D(x)]$ : \u8fd9\u90e8\u5206\u662f\u5173\u4e8e\u771f\u5b9e\u6570\u636e\u7684\u3002\u5224\u522b\u5668 $D$ \u8bd5\u56fe\u6700\u5927\u5316\u5bf9\u771f\u5b9e\u6570\u636e\u6837\u672c $x$ \u7684\u6b63\u786e\u5206\u7c7b\u6982\u7387\u3002\u6362\u53e5\u8bdd\u8bf4, \u5b83\u5e0c\u671b\u5bf9\u4e8e\u6765\u81ea\u771f\u5b9e\u6570\u636e\u5206\u5e03\u7684\u6837\u672c $x$, \u8f93\u51fa\u5c3d\u53ef\u80fd\u63a5\u8fd1 1 \u3002<\/p>\n<p>(2) $\\mathrm{E}_{z \\sim p_(z)}[\\log (1-D(G(z)))]$ : \u8fd9\u90e8\u5206\u662f\u5173\u4e8e\u751f\u6210\u7684\u6570\u636e\u7684\u3002\u5224\u522b\u5668 $D$ \u8bd5\u56fe\u6700\u5927\u5316\u5176\u5bf9\u751f\u6210\u6570\u636e\u7684\u6b63\u786e\u5206\u7c7b\u6982\u7387, \u5373\u5c06\u5176\u5206\u7c7b\u4e3a\u5047\u7684\u3002\u8fd9\u610f\u5473\u7740, \u5bf9\u4e8e\u4ece\u5148\u9a8c\u566a\u58f0\u5206\u5e03 $p_z$ \u4e2d\u91c7\u6837\u7136\u540e\u901a\u8fc7\u751f\u6210\u5668 $G$ \u751f\u6210\u7684\u5047\u6837\u672c, \u5224\u522b\u5668\u7684\u8f93\u51fa\u5e94\u8be5\u5c3d\u53ef\u80fd\u63a5\u8fd1 0 \u3002<\/p>\n<p>\u5224\u522b\u5668 $D$ \u7684<strong>\u76ee\u6807\u662f\u6700\u5927\u5316\u635f\u5931\u51fd\u6570<\/strong>\u3002\u8fd9\u610f\u5473\u7740, \u4e3a\u4e86\u8fbe\u5230\u6700\u4f73\u6548\u679c, \u5224\u522b\u5668\u5e0c\u671b\u80fd\u591f\u51c6\u786e\u5730\u533a\u5206\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u7684\u6570\u636e\u3002\u5728\u6700\u7406\u60f3\u7684\u60c5\u51b5\u4e0b, \u5bf9\u4e8e\u771f\u5b9e\u6570\u636e, $D(x)=1$; \u800c\u5bf9\u4e8e\u751f\u6210\u7684\u6570\u636e\uff0c $D(G(x))=0$\u3002<\/p>\n<p>\u4f46\u5728\u5b9e\u9645\u8bad\u7ec3\u4e2d\uff0c\u8fd9\u79cd\u7406\u60f3\u60c5\u51b5\u5f88\u5c11\u8fbe\u5230\uff0c\u56e0\u4e3a\u751f\u6210\u5668\u4e5f\u5728\u5c1d\u8bd5\u6539\u8fdb\u81ea\u5df1\uff0c\u751f\u6210\u66f4\u903c\u771f\u7684\u6837\u672c\u6765\u6b3a\u9a97\u5224\u522b\u5668\u3002<\/p>\n<pre><code class=\"language-python\"># optimizer\noptimizerD = Adam(netd.parameters(),lr=opt.lr,betas=(opt.beta1,0.999))\noptimizerG = Adam(netg.parameters(),lr=opt.lr,betas=(opt.beta1,0.999))\n\n# criterion\ncriterion = nn.BCELoss()\n\nfix_noise = Variable(t.FloatTensor(opt.batch_size,opt.nz,1,1).normal_(0,1))\nif opt.gpu:\n    fix_noise = fix_noise.cuda()\n    netd.cuda()\n    netg.cuda()\n    criterion.cuda()  <\/code><\/pre>\n<h3>GAN\u6a21\u578b\u7684\u8bad\u7ec3<\/h3>\n<hr \/>\n<p>GAN \u6a21\u578b\u5728\u5f00\u59cb\u8bad\u7ec3\u4e4b\u524d, \u9996\u5148\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u5408\u9002\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002\u4f8b\u5982, \u5bf9\u4e8e\u56fe\u50cf\u751f\u6210, \u4e00\u822c\u57fa\u4e8e\u5377\u79ef\u7684\u7ed3\u6784\u504f\u591a\u3002\u521d\u59cb\u5316\u751f\u6210\u5668 $G$ \u548c\u5224\u522b\u5668 $D$ \u7684\u6743\u91cd, \u901a\u5e38\u4f7f\u7528\u5c0f\u7684\u968f\u673a\u503c\u3002 GAN \u5305\u62ec\u4e24\u4e2a\u7f51\u7edc: \u751f\u6210\u5668\u548c\u5224\u522b\u5668, \u5b83\u4eec\u9700\u8981\u4ea4\u66ff\u6216\u540c\u65f6\u8bad\u7ec3\u3002GAN \u7684\u5faa\u73af\u8bad\u7ec3\u5927\u81f4\u5982\u4e0b:<\/p>\n<ul>\n<li>\u9996\u5148\u8bad\u7ec3\u5224\u522b\u5668\uff0c\u4f7f\u7528\u5f53\u524d\u7684\u751f\u6210\u5668\u751f\u6210\u5047\u6570\u636e\u548c\u771f\u5b9e\u6570\u636e\u8bad\u7ec3\u5224\u522b\u5668\uff0c\u5224\u522b\u5668\u7684\u76ee\u6807\u662f\u6b63\u786e\u5730\u533a\u5206\u771f\u5b9e\u6570\u636e\u548c\u5047\u6570\u636e\u3002<\/li>\n<\/ul>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u4e00\u65b9\u9762\u4ece\u771f\u5b9e\u6570\u636e\u5206\u5e03\u4e2d\u62bd\u53d6\u4e00\u4e2a\u6279\u91cf\u7684\u6570\u636e $x$, \u8ba1\u7b97\u5224\u522b\u5668 $D$ \u5728\u771f\u5b9e\u6570\u636e\u4e0a\u7684\u8f93\u51fa $D(x)$, \u8ba1\u7b97\u635f\u5931 $\\mathrm{E}_{x \\sim p_{\\text {deta }}(x)}[\\log D(x)]$\u3002\u53e6\u4e00\u65b9\u9762\u4ece\u968f\u673a\u566a\u58f0\u5206\u5e03\u4e2d\u62bd\u53d6\u4e00\u4e2a\u6279\u91cf\u7684\u566a\u58f0 $z$ \u3002\u4f7f\u7528\u751f\u6210\u5668 $G$ \u751f\u6210\u4e00\u4e2a\u6279\u91cf\u7684\u5047\u6570\u636e $G(z)$ \u3002\u8ba1\u7b97\u5224\u522b\u5668 $D$ \u5728\u5047\u6570\u636e\u4e0a\u7684\u8f93\u51fa $D(G(z))$, \u8ba1\u7b97\u635f\u5931 $\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]$ \u3002\u5408\u5e76\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u6570\u636e\u7684\u635f\u5931\uff0c\u4f7f\u7528\u8fd9\u4e2a\u603b\u635f\u5931\u6765\u66f4\u65b0\u5224\u522b\u5668 $D$ \u7684\u6743\u91cd\uff0c\u901a\u5e38\u4f7f\u7528\u4f18\u5316\u5668\u5982Adam\u6216RMSProp\u3002<\/p>\n<ul>\n<li>\u7136\u540e\u8bad\u7ec3\u751f\u6210\u5668\uff0c\u8bd5\u56fe\u6b3a\u9a97\u5224\u522b\u5668\uff0c\u4f7f\u5176\u8ba4\u4e3a\u751f\u6210\u7684\u6570\u636e\u662f\u771f\u5b9e\u7684\uff0c\u751f\u6210\u5668\u7684\u76ee\u6807\u662f\u751f\u6210\u80fd\u591f\u88ab\u5224\u522b\u5668\u8bef\u5224\u4e3a\u771f\u5b9e\u6570\u636e\u7684\u6570\u636e\u3002<\/li>\n<\/ul>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u4ece\u968f\u673a\u566a\u58f0\u5206\u5e03\u4e2d\u518d\u6b21\u62bd\u53d6\u4e00\u4e2a\u6279\u91cf\u7684\u566a\u58f0 $Z$, \u901a\u8fc7\u5224\u522b\u5668 $D$ \u8bc4\u4f30\u751f\u6210\u5668 $G$ \u4ea7\u751f\u7684\u5047\u6570\u636e, \u8ba1\u7b97\u635f\u5931 $\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]$,\u4f7f\u7528\u8be5\u635f\u5931\u66f4\u65b0\u751f\u6210\u5668 $G$ \u7684\u6743\u91cd\u3002<\/p>\n<p>\u6bcf\u9694\u51e0\u4e2a\u8f6e\u6b21\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9b\u6307\u6807\u6765\u8bc4\u4f30\u751f\u6210\u5668\u7684\u8f93\u51fa\u3002\u91cd\u590d\u4e0a\u8ff0\u8bad\u7ec3\u6b65\u9aa4\u76f4\u5230\u6ee1\u8db3\u7ec8\u6b62\u6761\u4ef6\uff0c\u8fd9\u53ef\u4ee5\u662f\u9884\u5b9a\u7684\u8bad\u7ec3\u8f6e\u6570\u3001\u6a21\u578b\u6027\u80fd\u8fbe\u5230\u67d0\u4e2a\u9608\u503c\u6216\u5176\u5b83\u6761\u4ef6\u3002\u5982\u679c\u672a\u6ee1\u8db3\u6761\u4ef6\uff0c\u8fd4\u56de\u5e76\u5f00\u59cb\u65b0\u7684\u8bad\u7ec3\u5faa\u73af\u3002<\/p>\n<p>\u5728\u5faa\u73af\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u751f\u6210\u5668\u548c\u5224\u522b\u5668\u90fd\u4f1a\u9010\u6e10\u6539\u8fdb\uff0c\u4e89\u53d6\u66f4\u597d\u5730\u6267\u884c\u5176\u4efb\u52a1\u3002\u6700\u7ec8\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u5e73\u8861\u70b9\uff0c\u751f\u6210\u5668\u751f\u6210\u7684\u6570\u636e\u4e0e\u771f\u5b9e\u6570\u636e\u51e0\u4e4e\u65e0\u6cd5\u533a\u5206\u3002<strong>\u8fd9\u79cd\u9010\u6b65\u7684\u3001\u53cd\u590d\u7684\u8bad\u7ec3\u65b9\u6cd5\u5141\u8bb8\u6a21\u578b\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u548c\u9002\u5e94\uff0c\u8fd9\u662f\u8bb8\u591a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u6210\u529f\u7684\u5173\u952e\u3002<\/strong><\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919100721598.png\" style=\"height:300px\">\n<\/p>\n<pre><code class=\"language-python\">import matplotlib.pyplot as plt\n\n# \u5b58\u50a8\u6bcf\u4e2a\u8fed\u4ee3\u7684\u635f\u5931\nlosses_D = []\nlosses_G = []\n\nfor epoch in range(opt.max_epoch):\n    for ii, data in enumerate(dataloader, 0):\n        real, _ = data\n        input = Variable(real)  # \u5c06\u771f\u5b9e\u56fe\u50cf\u5305\u88c5\u4e3aPyTorch\u53d8\u91cf\uff0c\u7528\u4e8e\u8ba1\u7b97\u56fe\u4e2d\n        label = Variable(t.ones(input.size(0)))  # \u521b\u5efa\u4e0e\u771f\u5b9e\u56fe\u50cf\u6570\u91cf\u76f8\u540c\u7684\u6807\u7b7e\u53d8\u91cf\uff0c\u6240\u6709\u503c\u4e3a1\uff0c\u8868\u793a\u771f\u5b9e\u6570\u636e\n        noise = t.randn(input.size(0), opt.nz, 1, 1)  # \u751f\u6210\u4e0e\u771f\u5b9e\u56fe\u50cf\u6570\u91cf\u76f8\u540c\u7684\u968f\u673a\u566a\u58f0\uff0c\u7528\u4e8e\u751f\u6210\u5047\u56fe\u50cf\n        noise = Variable(noise)  # \u5c06\u968f\u673a\u566a\u58f0\u5305\u88c5\u4e3aPyTorch\u53d8\u91cf\uff0c\u7528\u4e8e\u8ba1\u7b97\u56fe\u4e2d\n\n        if opt.gpu:\n            noise = noise.cuda()\n            input = input.cuda()\n            label = label.cuda()\n\n        # ----- train netd -----\n        netd.zero_grad()\n        ## train netd with real img\n        output = netd(input)\n        error_real = criterion(output.squeeze(), label)\n        error_real.backward()\n        D_x = output.data.mean()\n        ## train netd with fake img\n        fake_pic = netg(noise).detach()\n        output2 = netd(fake_pic)\n        label.data.fill_(0)  # 0 for fake\n        error_fake = criterion(output2.squeeze(), label)\n        error_fake.backward()\n        D_x2 = output2.data.mean()\n        error_D = error_real + error_fake\n        optimizerD.step()\n\n        # ------ train netg -------\n        netg.zero_grad()\n        label.data.fill_(1)\n        noise.data.normal_(0, 1)\n        fake_pic = netg(noise)\n        output = netd(fake_pic)\n        error_G = criterion(output.squeeze(), label)\n        error_G.backward()\n        optimizerG.step()\n        D_G_z2 = output.data.mean()\n\n        # \u5b58\u50a8\u635f\u5931\u503c\n        losses_D.append(error_D.item())\n        losses_G.append(error_G.item())\n\n        if ii % 500 == 0:\n            print(f&quot;Iteration {ii}\/{epoch}: &quot;\n                  f&quot;Discriminator Loss: {error_D.item():.4f}, &quot;\n                  f&quot;Generator Loss: {error_G.item():.4f}, &quot;\n                  f&quot;D(x): {D_x:.4f}, &quot;\n                  f&quot;D(G(z)) (on fake data): {D_G_z2:.4f}, &quot;\n                  f&quot;D(G(z)) (on real data): {D_x2:.4f}&quot;)\n    if epoch % 2 == 0:\n        fake_u = netg(fix_noise)\n        imgs = make_grid(fake_u.data * 0.5 + 0.5).cpu()  # CHW\n        plt.imshow(imgs.permute(1, 2, 0).numpy())  # HWC\n        plt.show()\n\n# \u7ed8\u5236\u635f\u5931\u56fe\u50cf\nplt.figure(figsize=(10, 5))\nplt.title(&quot;Generator and Discriminator Loss During Training&quot;)\nplt.plot(losses_G, label=&quot;G&quot;)\nplt.plot(losses_D, label=&quot;D&quot;)\nplt.xlabel(&quot;iterations&quot;)\nplt.ylabel(&quot;Loss&quot;)\nplt.legend()\nplt.show()\n<\/code><\/pre>\n<pre><code>Iteration 0\/0: Discriminator Loss: 1.4153, Generator Loss: 2.2284, D(x): 0.5435, D(G(z)) (on fake data): 0.1137, D(G(z)) (on real data): 0.5437\nIteration 500\/0: Discriminator Loss: 0.1514, Generator Loss: 3.0821, D(x): 0.9358, D(G(z)) (on fake data): 0.0631, D(G(z)) (on real data): 0.0774\nIteration 1000\/0: Discriminator Loss: 0.4804, Generator Loss: 3.4960, D(x): 0.9392, D(G(z)) (on fake data): 0.0401, D(G(z)) (on real data): 0.3090\nIteration 1500\/0: Discriminator Loss: 0.5928, Generator Loss: 0.9506, D(x): 0.6448, D(G(z)) (on fake data): 0.4395, D(G(z)) (on real data): 0.0816<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919100852576.png\" style=\"height:300px\">\n<\/p>\n<pre><code>Iteration 0\/1: Discriminator Loss: 0.0247, Generator Loss: 5.7162, D(x): 0.9912, D(G(z)) (on fake data): 0.0073, D(G(z)) (on real data): 0.0153\nIteration 500\/1: Discriminator Loss: 1.0094, Generator Loss: 0.9566, D(x): 0.4293, D(G(z)) (on fake data): 0.5299, D(G(z)) (on real data): 0.0001\nIteration 1000\/1: Discriminator Loss: 0.6532, Generator Loss: 1.8176, D(x): 0.6847, D(G(z)) (on fake data): 0.2071, D(G(z)) (on real data): 0.1556\nIteration 1500\/1: Discriminator Loss: 0.1293, Generator Loss: 3.3530, D(x): 0.9577, D(G(z)) (on fake data): 0.0606, D(G(z)) (on real data): 0.0757\nIteration 0\/2: Discriminator Loss: 0.3889, Generator Loss: 3.1383, D(x): 0.7578, D(G(z)) (on fake data): 0.0593, D(G(z)) (on real data): 0.0695\nIteration 500\/2: Discriminator Loss: 0.0038, Generator Loss: 7.2360, D(x): 0.9991, D(G(z)) (on fake data): 0.0008, D(G(z)) (on real data): 0.0029\nIteration 1000\/2: Discriminator Loss: 0.0003, Generator Loss: 8.2740, D(x): 1.0000, D(G(z)) (on fake data): 0.0003, D(G(z)) (on real data): 0.0003\nIteration 1500\/2: Discriminator Loss: 0.0004, Generator Loss: 8.2971, D(x): 0.9999, D(G(z)) (on fake data): 0.0003, D(G(z)) (on real data): 0.0003<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919100910389.png\" style=\"height:300px\">\n<\/p>\n<pre><code>Iteration 0\/3: Discriminator Loss: 45.9291, Generator Loss: 57.0330, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 500\/3: Discriminator Loss: 46.7132, Generator Loss: 57.0013, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 1000\/3: Discriminator Loss: 45.3573, Generator Loss: 56.9371, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 1500\/3: Discriminator Loss: 45.8882, Generator Loss: 56.7955, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 0\/4: Discriminator Loss: 45.8601, Generator Loss: 56.6574, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 500\/4: Discriminator Loss: 44.3233, Generator Loss: 56.2416, D(x): 0.0000, D(G(z)) (on fake data): 0.0000, D(G(z)) (on real data): 0.0000\nIteration 1000\/4: Discriminator Loss: 1.1467, Generator Loss: 6.4441, D(x): 0.9674, D(G(z)) (on fake data): 0.0028, D(G(z)) (on real data): 0.5383\nIteration 1500\/4: Discriminator Loss: 0.9613, Generator Loss: 0.6755, D(x): 0.5275, D(G(z)) (on fake data): 0.5707, D(G(z)) (on real data): 0.1398<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919100953359.png\" style=\"height:300px\">\n<\/p>\n<pre><code>Iteration 0\/5: Discriminator Loss: 0.2203, Generator Loss: 4.7817, D(x): 0.9162, D(G(z)) (on fake data): 0.0125, D(G(z)) (on real data): 0.1106\nIteration 500\/5: Discriminator Loss: 0.0109, Generator Loss: 6.2570, D(x): 0.9943, D(G(z)) (on fake data): 0.0037, D(G(z)) (on real data): 0.0051\nIteration 1000\/5: Discriminator Loss: 0.6208, Generator Loss: 1.0894, D(x): 0.6850, D(G(z)) (on fake data): 0.4199, D(G(z)) (on real data): 0.1146\nIteration 1500\/5: Discriminator Loss: 0.0145, Generator Loss: 7.2275, D(x): 0.9875, D(G(z)) (on fake data): 0.0015, D(G(z)) (on real data): 0.0017\nIteration 0\/6: Discriminator Loss: 0.1797, Generator Loss: 3.4921, D(x): 0.8830, D(G(z)) (on fake data): 0.0603, D(G(z)) (on real data): 0.0432\nIteration 500\/6: Discriminator Loss: 0.0832, Generator Loss: 4.9905, D(x): 0.9758, D(G(z)) (on fake data): 0.0134, D(G(z)) (on real data): 0.0556\nIteration 1000\/6: Discriminator Loss: 0.0076, Generator Loss: 5.4778, D(x): 0.9961, D(G(z)) (on fake data): 0.0072, D(G(z)) (on real data): 0.0037\nIteration 1500\/6: Discriminator Loss: 0.0284, Generator Loss: 5.3925, D(x): 0.9894, D(G(z)) (on fake data): 0.0145, D(G(z)) (on real data): 0.0173<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919101016476.png\" style=\"height:300px\">\n<\/p>\n<pre><code>Iteration 0\/7: Discriminator Loss: 0.3365, Generator Loss: 5.0217, D(x): 0.9900, D(G(z)) (on fake data): 0.0175, D(G(z)) (on real data): 0.2437\nIteration 500\/7: Discriminator Loss: 0.0115, Generator Loss: 5.7578, D(x): 0.9984, D(G(z)) (on fake data): 0.0054, D(G(z)) (on real data): 0.0098\nIteration 1000\/7: Discriminator Loss: 0.0230, Generator Loss: 7.0461, D(x): 0.9833, D(G(z)) (on fake data): 0.0015, D(G(z)) (on real data): 0.0059\nIteration 1500\/7: Discriminator Loss: 0.2590, Generator Loss: 3.4847, D(x): 0.8923, D(G(z)) (on fake data): 0.0504, D(G(z)) (on real data): 0.1185\nIteration 0\/8: Discriminator Loss: 0.0319, Generator Loss: 5.4885, D(x): 0.9725, D(G(z)) (on fake data): 0.0072, D(G(z)) (on real data): 0.0033\nIteration 500\/8: Discriminator Loss: 0.0042, Generator Loss: 7.1622, D(x): 0.9984, D(G(z)) (on fake data): 0.0014, D(G(z)) (on real data): 0.0026\nIteration 1000\/8: Discriminator Loss: 0.0657, Generator Loss: 2.7716, D(x): 0.9879, D(G(z)) (on fake data): 0.0956, D(G(z)) (on real data): 0.0487\nIteration 1500\/8: Discriminator Loss: 0.0198, Generator Loss: 5.2304, D(x): 0.9981, D(G(z)) (on fake data): 0.0076, D(G(z)) (on real data): 0.0175<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919101041120.png\" style=\"height:300px\">\n<\/p>\n<pre><code>Iteration 0\/9: Discriminator Loss: 0.0542, Generator Loss: 6.2787, D(x): 0.9919, D(G(z)) (on fake data): 0.0035, D(G(z)) (on real data): 0.0441\nIteration 500\/9: Discriminator Loss: 0.0059, Generator Loss: 5.9002, D(x): 0.9951, D(G(z)) (on fake data): 0.0046, D(G(z)) (on real data): 0.0009\nIteration 1000\/9: Discriminator Loss: 1.5574, Generator Loss: 7.5224, D(x): 0.9998, D(G(z)) (on fake data): 0.0009, D(G(z)) (on real data): 0.7207\nIteration 1500\/9: Discriminator Loss: 0.0035, Generator Loss: 7.3944, D(x): 0.9983, D(G(z)) (on fake data): 0.0009, D(G(z)) (on real data): 0.0018<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919101057478.png\" style=\"height:300px\">\n<\/p>\n<h2><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/?size=100&id=tlQgjxHobhnD&format=png&color=000000\" style=\"height:50px;display:inline\">Improved GAN<\/h2>\n<hr \/>\n<p>\u201cImproved Techniques for Training GANs\u201d\u662f\u4e00\u7bc7\u7531Ian J. Goodfellow \u548c\u4ed6\u7684\u540c\u4e8b\u5728 2016 \u5e74\u53d1\u8868\u7684\u8bba\u6587\uff0c\u8fd9\u7bc7\u8bba\u6587\u5bf9\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GANs\uff09\u7684\u8bad\u7ec3\u8fc7\u7a0b\u505a\u51fa\u4e86\u91cd\u8981\u7684\u6539\u8fdb\u548c\u63d0\u8bae\u3002\u8fd9\u4e9b\u6539\u8fdb\u4e3b\u8981\u96c6\u4e2d\u5728\u63d0\u9ad8GANs\u7684\u7a33\u5b9a\u6027\u548c\u6027\u80fd\u4e0a\uff0c\u89e3\u51b3\u4e86\u4e00\u4e9b\u65e9\u671fGANs\u8bad\u7ec3\u4e2d\u7684\u5e38\u89c1\u95ee\u9898\uff0c\u4f8b\u5982<strong>\u6a21\u5f0f\u5d29\u6e83\uff08mode collapse\uff09<\/strong>\u3002<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919101209612.png\" style=\"height:300px\">\n<\/p>\n<p>\u5f53\u8bad\u7ec3GAN\u65f6\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u5e0c\u671b\u751f\u6210\u5668\u80fd\u591f\u5b66\u4e60\u5230\u6570\u636e\u5206\u5e03\u7684\u5404\u4e2a\u65b9\u9762\uff0c\u4ee5\u4ea7\u751f\u591a\u6837\u6027\u4e14\u903c\u771f\u7684\u6570\u636e\u3002\u7136\u800c\uff0c\u6a21\u5f0f\u5d29\u6e83\u6307\u7684\u662f\u751f\u6210\u5668\u5f00\u59cb\u751f\u6210\u6781\u5176\u6709\u9650\u7684\u6837\u672c\u79cd\u7c7b\uff0c\u5373\u4fbf\u8fd9\u4e9b\u6837\u672c\u80fd\u591f\u4ee5\u5f88\u9ad8\u7684\u6210\u529f\u7387\u6b3a\u9a97\u5224\u522b\u5668\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u751f\u6210\u5668\u627e\u5230\u4e86\u4e00\u79cd\u201c\u6377\u5f84\u201d\uff0c\u53ea\u751f\u6210\u67d0\u4e9b\u7279\u5b9a\u7684\u6837\u672c\uff08\u8fd9\u4e9b\u6837\u672c\u53ef\u80fd\u5728\u5224\u522b\u5668\u5f53\u524d\u72b6\u6001\u4e0b\u96be\u4ee5\u88ab\u8bc6\u522b\u4e3a\u5047\u7684\uff09\uff0c\u800c\u5ffd\u89c6\u4e86\u6570\u636e\u7684\u5176\u5b83\u7279\u5f81\u548c\u591a\u6837\u6027\u3002\u8fd9\u5bfc\u81f4\u751f\u6210\u7684\u6570\u636e\u867d\u7136\u903c\u771f\uff0c\u4f46\u591a\u6837\u6027\u4e25\u91cd\u4e0d\u8db3\u3002<\/p>\n<p>\u53d1\u751f\u6a21\u5f0f\u5d29\u6e83\u7684\u4e3b\u8981\u539f\u56e0\u662fGANs\u6a21\u578b\u7684\u4e0d\u7a33\u5b9a\u6027\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5224\u522b\u5668\u5b66\u4e60\u5f97\u592a\u5feb\uff0c\u751f\u6210\u5668\u53ef\u80fd\u4f1a\u627e\u5230\u5e76\u91cd\u590d\u4f7f\u7528\u80fd\u591f\u901a\u8fc7\u5224\u522b\u5668\u7684\u67d0\u4e9b\u7279\u5b9a\u6a21\u5f0f\uff0c\u800c\u4e0d\u662f\u5b66\u4e60\u66f4\u591a\u6837\u5316\u7684\u6570\u636e\u751f\u6210\u7b56\u7565\u3002\u5373\uff0c<strong>\u5982\u679c\u751f\u6210\u5668\u548c\u5224\u522b\u5668\u4e4b\u95f4\u7684\u8bad\u7ec3\u4e0d\u591f\u5e73\u8861\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4e00\u65b9\u8fc7\u4e8e\u5f3a\u5927\uff0c\u4ece\u800c\u4fc3\u4f7f\u53e6\u4e00\u65b9\u91c7\u53d6\u6781\u7aef\u7b56\u7565\u3002<\/strong><\/p>\n<p>\u4e0d\u7a33\u5b9a\u6027\u7684\u6839\u6e90\u662f\u7531\u4e8eGANs\u7684\u8bad\u7ec3\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u4e24\u4e2a\u7f51\u7edc\uff08\u751f\u6210\u5668\u548c\u5224\u522b\u5668\uff09\u4e4b\u95f4\u7684\u535a\u5f08\u8fc7\u7a0b\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u80fd\u4f1a\u975e\u5e38\u4e0d\u7a33\u5b9a\u3002<strong>\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u4e24\u8005\u5e94\u8be5\u8fbe\u5230\u7eb3\u4ec0\u5747\u8861\uff0c\u4f46\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u5f80\u5f80\u5f88\u96be\u5b9e\u73b0<\/strong>\u3002\u4f8b\u5982\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u5224\u522b\u5668\u592a\u5f3a\uff0c\u5b83\u5c06\u8fc7\u4e8e\u5bb9\u6613\u5730\u533a\u5206\u51fa\u751f\u6210\u5668\u7684\u8f93\u51fa\uff0c\u5bfc\u81f4\u751f\u6210\u5668\u6536\u5230\u7684\u68af\u5ea6\u4fe1\u53f7\u8fc7\u4e8e\u5f3a\u70c8\u548c\u5c16\u9510\u3002\u8fd9\u53ef\u80fd\u4f7f\u5f97\u751f\u6210\u5668\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u627e\u4e0d\u5230\u63d0\u5347\u5176\u751f\u6210\u8d28\u91cf\u7684\u65b9\u5411\uff0c\u8fdb\u800c\u9677\u5165\u56f0\u5883\uff0c\u65e0\u6cd5\u4ea7\u751f\u8db3\u591f\u903c\u771f\u7684\u6570\u636e\u3002<\/li>\n<li>\u5982\u679c\u5224\u522b\u5668\u592a\u5f31\uff0c\u5b83\u4e0d\u80fd\u63d0\u4f9b\u8db3\u591f\u7684\u51c6\u786e\u53cd\u9988\u7ed9\u751f\u6210\u5668\u3002\u8fd9\u6837\u751f\u6210\u5668\u5373\u4f7f\u4ea7\u751f\u4f4e\u8d28\u91cf\u7684\u8f93\u51fa\u4e5f\u80fd\u201c\u8499\u6df7\u8fc7\u5173\u201d\uff0c\u4f7f\u5f97\u5176\u6ca1\u6709\u8db3\u591f\u7684\u6fc0\u52b1\u53bb\u6539\u8fdb\u548c\u5b66\u4e60\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u6570\u636e\u3002<\/li>\n<\/ul>\n<p>\u60f3\u8c61\u4e00\u4e2a\u573a\u666f\uff0c\u5728\u8fd9\u4e2a\u573a\u666f\u4e2d\uff0c\u5b66\u751f\u7684\u4efb\u52a1\u662f\u5b66\u4e60\u5982\u4f55\u7ed8\u5236\u975e\u5e38\u903c\u771f\u7684\u98ce\u666f\u753b\u6765\u201c\u6b3a\u9a97\u201d\u8001\u5e08\uff0c\u800c\u8001\u5e08\u7684\u4efb\u52a1\u662f\u8981\u5206\u8fa8\u51fa\u8fd9\u4e9b\u753b\u4f5c\u662f\u5b66\u751f\u7ed8\u5236\u7684\uff0c\u8fd8\u662f\u7531\u771f\u6b63\u7684\u827a\u672f\u5bb6\u521b\u4f5c\u7684\u3002\u5982\u679c\u8001\u5e08\u975e\u5e38\u6709\u7ecf\u9a8c\uff08\u5373\u5224\u522b\u5668\u592a\u5f3a\uff09\uff0c\u80fd\u591f\u8f7b\u6613\u5730\u8bc6\u522b\u51fa\u6240\u6709\u5b66\u751f\u7684\u753b\u4f5c\uff0c\u4e0d\u7ba1\u4ed6\u4eec\u7684\u8d28\u91cf\u5982\u4f55\u3002\u8fd9\u4f1a\u5bfc\u81f4\u4ee5\u4e0b\u51e0\u4e2a\u95ee\u9898\uff1a<\/p>\n<ul>\n<li>\u5b66\u751f\uff08\u751f\u6210\u5668\uff09\u611f\u5230\u7070\u5fc3\uff0c\u5b66\u751f\u53ef\u80fd\u4f1a\u56e0\u4e3a\u81ea\u5df1\u7684\u4f5c\u54c1\u603b\u662f\u88ab\u8f7b\u6613\u8fa8\u8bc6\u51fa\u6765\u800c\u611f\u5230\u6cae\u4e27\uff0c\u9010\u6e10\u5931\u53bb\u6539\u8fdb\u4f5c\u54c1\u7684\u52a8\u529b\u6216\u65b9\u5411\uff0c\u4e0d\u77e5\u9053\u5e94\u8be5\u5982\u4f55\u8fdb\u6b65\u3002\u5176\u6b21\uff0c\u7f3a\u4e4f\u6709\u6548\u53cd\u9988\uff0c\u8001\u5e08\u53ef\u80fd\u4ec5\u4ec5\u544a\u8bc9\u5b66\u751f\u201c\u8fd9\u662f\u9519\u8bef\u7684\u201d\uff0c\u800c\u6ca1\u6709\u7ed9\u51fa\u5177\u4f53\u7684\u6539\u8fdb\u5efa\u8bae\uff0c\u4f7f\u5f97\u5b66\u751f\u96be\u4ee5\u4ece\u4e2d\u5b66\u5230\u5982\u4f55\u6539\u8fdb\u4ed6\u4eec\u7684\u7ed8\u753b\u6280\u5de7\u3002<\/li>\n<li>\u5982\u679c\u8001\u5e08\u7684\u5224\u65ad\u80fd\u529b\u8f83\u5f31\uff08\u5373\u5224\u522b\u5668\u592a\u5f31\uff09\uff0c\u5219\u4f1a\u51fa\u73b0\u5b66\u751f\u7f3a\u4e4f\u6311\u6218\uff0c\u5982\u679c\u8001\u5e08\u51e0\u4e4e\u603b\u662f\u8ba4\u4e3a\u5b66\u751f\u7684\u4f5c\u54c1\u662f\u771f\u6b63\u827a\u672f\u5bb6\u7684\u4f5c\u54c1\uff0c\u5b66\u751f\u53ef\u80fd\u4f1a\u89c9\u5f97\u81ea\u5df1\u5df2\u7ecf\u201c\u638c\u63e1\u201d\u4e86\u7ed8\u753b\u6280\u5de7\uff0c\u800c\u5b9e\u9645\u4e0a\u4ed6\u4eec\u7684\u4f5c\u54c1\u8d28\u91cf\u5e76\u4e0d\u9ad8\u3002\u7531\u4e8e\u7f3a\u4e4f\u9002\u5f53\u7684\u6311\u6218\u548c\u51c6\u786e\u7684\u53cd\u9988\uff0c\u5b66\u751f\u53ef\u80fd\u5728\u81ea\u6ee1\u4e2d\u505c\u6b62\u8fdb\u6b65\uff0c\u6216\u4e0d\u77e5\u9053\u81ea\u5df1\u9700\u8981\u5728\u54ea\u4e9b\u65b9\u9762\u8fdb\u884c\u63d0\u5347\u3002<\/li>\n<\/ul>\n<p><strong>\u6a21\u5f0f\u5d29\u6e83\u7684\u89e3\u51b3\u65b9\u6cd5\uff1a<\/strong><\/p>\n<pre><code>\u7279\u5f81\u5339\u914d\n\u5c0f\u6279\u91cf\u5224\u522b\u5668\n\u5355\u4fa7\u6807\u7b7e\u5e73\u6ed1\n\u865a\u62df\u6279\u89c4\u8303\u5316<\/code><\/pre>\n<p><strong>\u7279\u5f81\u5339\u914d\uff08Feature Matching\uff09\u65e8\u5728\u901a\u8fc7\u6539\u53d8\u751f\u6210\u5668\uff08G\uff09\u7684\u8bad\u7ec3\u76ee\u6807\u6765\u63d0\u9ad8\u751f\u6210\u6837\u672c\u7684\u8d28\u91cf\u548c\u591a\u6837\u6027\u3002<\/strong><\/p>\n<ul>\n<li>\u5728\u4f20\u7edf\u7684\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u4e2d\uff0c\u751f\u6210\u5668\u7684\u6838\u5fc3\u4efb\u52a1\u662f\u5236\u9020\u51fa\u80fd\u591f\u6b3a\u9a97\u5224\u522b\u5668\uff08D\uff09\u7684\u6837\u672c\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u751f\u6210\u5668\u52aa\u529b\u521b\u5efa\u770b\u8d77\u6765\u8db3\u591f\u771f\u5b9e\uff0c\u4ee5\u81f3\u4e8e\u5224\u522b\u5668\u96be\u4ee5\u533a\u5206\u771f\u4f2a\u7684\u56fe\u50cf\u3002<\/li>\n<li>\u7136\u800c\uff0c\u8fd9\u79cd\u65b9\u6cd5\u6709\u4e00\u4e2a\u5f0a\u7aef\uff1a\u751f\u6210\u5668\u53ef\u80fd\u8fc7\u5206\u4e13\u6ce8\u4e8e\u90a3\u4e9b\u5f53\u524d\u80fd\u6700\u5bb9\u6613\u6b3a\u9a97\u5224\u522b\u5668\u7684\u7279\u5f81\uff0c\u5ffd\u89c6\u4e86\u5176\u5b83\u91cd\u8981\u7279\u5f81\uff0c\u5bfc\u81f4\u8f93\u51fa\u7684\u6837\u672c\u591a\u6837\u6027\u53d7\u9650\u3002<\/li>\n<li>\u7279\u5f81\u5339\u914d\u6280\u672f\u5e94\u8fd0\u800c\u751f\uff0c\u5b83\u8c03\u6574\u4e86\u751f\u6210\u5668\u7684\u76ee\u6807\uff0c\u4f7f\u4e4b\u4e0d\u518d\u4ec5\u4ec5\u662f\u6b3a\u9a97\u5224\u522b\u5668\uff0c\u800c\u662f\u5c3d\u53ef\u80fd\u5730\u7f29\u5c0f\u751f\u6210\u6837\u672c\u548c\u771f\u5b9e\u6837\u672c\u5728\u5224\u522b\u5668\u7f51\u7edc\u7684\u4e2d\u95f4\u5c42\u6240\u63d0\u53d6\u7279\u5f81\u7684\u8ddd\u79bb\u3002<\/li>\n<\/ul>\n<p>\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u7279\u5f81\u5339\u914d\u4fc3\u4f7f\u751f\u6210\u5668\u751f\u6210\u5728\u66f4\u591a\u7ef4\u5ea6\u4e0a\u4e0e\u771f\u5b9e\u6570\u636e\u76f8\u4f3c\u7684\u6837\u672c\u3002\u5b83\u4e0d\u53ea\u662f\u8ffd\u6c42\u8868\u9762\u4e0a\u7684\u903c\u771f\u5ea6\uff0c\u800c\u662f\u6df1\u5165\u5230\u6570\u636e\u7684\u672c\u8d28\u7279\u5f81\uff0c\u4ece\u800c\u589e\u52a0\u4e86\u751f\u6210\u6837\u672c\u7684\u771f\u5b9e\u6027\u548c\u591a\u6837\u6027\u3002\u8fd9\u79cd\u7efc\u5408\u6027\u7684\u8bad\u7ec3\u76ee\u6807\u6709\u52a9\u4e8e\u63d0\u5347\u751f\u6210\u5668\u7684\u7efc\u5408\u6027\u80fd\uff0c\u907f\u514d\u4e86\u8fc7\u5ea6\u4e13\u6ce8\u4e8e\u67d0\u4e9b\u7279\u5b9a\u7279\u5f81\u7684\u9677\u9631\uff0c\u540c\u65f6\u4e5f\u95f4\u63a5\u5730\u51cf\u5c11\u4e86\u6a21\u5f0f\u5d29\u6e83\u73b0\u8c61\u7684\u53d1\u751f\u3002<\/p>\n<pre><code class=\"language-python\"># Define a helper class for Feature Matching\nclass FeatureMatchingLoss(nn.Module):\n    def __init__(self, discriminator, layer_idx=-1):\n        super(FeatureMatchingLoss, self).__init__()\n        self.discriminator = discriminator\n        self.layer_idx = layer_idx\n        self.criterion = nn.L1Loss()\n\n    def forward(self, real_data, fake_data):\n        real_features = self.discriminator.forward_features(real_data, layer_idx=self.layer_idx)\n        fake_features = self.discriminator.forward_features(fake_data, layer_idx=self.layer_idx)\n        return self.criterion(real_features, fake_features)\n\n# Modify the discriminator to extract features from intermediate layers\nclass DiscriminatorWithFeatures(nn.Module):\n    def __init__(self):\n        super(DiscriminatorWithFeatures, self).__init__()\n        # Define the layers as before\n        self.layers = nn.Sequential(\n            nn.Conv2d(opt.nc, opt.ndf, 4, 2, 1, bias=False),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf, opt.ndf*2, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*2),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf*2, opt.ndf*4, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*4),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf*4, opt.ndf*8, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*8),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf*8, 1, 4, 1, 0, bias=False),\n            nn.Sigmoid()\n        )\n\n    def forward(self, x):\n        return self.layers(x)\n\n    def forward_features(self, x, layer_idx):\n        for i, layer in enumerate(self.layers):\n            x = layer(x)\n            if i == layer_idx:\n                break\n        return x\n\n# Update the discriminator initialization\nnetd = DiscriminatorWithFeatures()\n\n# Initialize Feature Matching loss\nfeature_matching_loss = FeatureMatchingLoss(netd, layer_idx=3)\n<\/code><\/pre>\n<p><strong>\u5c0f\u6279\u91cf\u5224\u522b\u5668\uff08Mini-batch Discrimination\uff09\u7684\u6838\u5fc3\u76ee\u6807\u662f\u589e\u5f3a\u6a21\u578b\u5bf9\u6837\u672c\u591a\u6837\u6027\u7684\u5173\u6ce8<\/strong><\/p>\n<ul>\n<li>\u8fd9\u79cd\u6280\u672f\u901a\u8fc7\u5728\u5224\u522b\u5668\u7f51\u7edc\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u7279\u6b8a\u7684\u5c42\u6765\u5b9e\u73b0\uff0c\u8fd9\u4e2a\u5c42\u7684\u529f\u80fd\u662f\u8bc4\u4f30\u4e00\u4e2a\u5c0f\u6279\u6b21\uff08mini-batch\uff09\u4e2d\u5404\u4e2a\u6837\u672c\u4e4b\u95f4\u7684\u5dee\u5f02\u6027\u3002<\/li>\n<li>\u5177\u4f53\u6765\u8bf4\uff0c\u5f53\u4e00\u4e2a\u6279\u6b21\u7684\u6570\u636e\u8f93\u5165\u5230\u5224\u522b\u5668\u4e2d\u65f6\uff0c\u8fd9\u4e2a\u65b0\u589e\u7684\u5c42\u4f1a\u8ba1\u7b97\u5e76\u6bd4\u8f83\u6279\u6b21\u4e2d\u5404\u4e2a\u6837\u672c\u7684\u7279\u5f81\u3002\u8fd9\u4e9b\u7279\u5f81\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\u6837\u672c\u95f4\u7684\u76f8\u4f3c\u5ea6\u6216\u5dee\u5f02\u5ea6\u7b49\u7edf\u8ba1\u91cf\u3002\u5982\u679c\u751f\u6210\u5668\u5f00\u59cb\u4ea7\u751f\u5927\u91cf\u76f8\u540c\u6216\u76f8\u4f3c\u7684\u6837\u672c\uff0c\u8fd9\u4e9b\u6837\u672c\u4e4b\u95f4\u7684\u9ad8\u5ea6\u76f8\u4f3c\u6027\u5c31\u4f1a\u5728\u8fd9\u4e2a\u65b0\u5c42\u4e2d\u88ab\u660e\u663e\u6355\u6349\u5230\u3002<\/li>\n<\/ul>\n<p>\u7531\u4e8e\u8fd9\u79cd\u9ad8\u5ea6\u7684\u76f8\u4f3c\u6027\u901a\u5e38\u4e0d\u662f\u771f\u5b9e\u6570\u636e\u96c6\u6240\u8868\u73b0\u51fa\u7684\u7279\u70b9\uff0c\u56e0\u6b64\u5c0f\u6279\u91cf\u5224\u522b\u5c42\u80fd\u591f\u5e2e\u52a9\u5224\u522b\u5668\u66f4\u5bb9\u6613\u5730\u8fa8\u8bc6\u51fa\u8fd9\u4e9b\u91cd\u590d\u6216\u76f8\u4f3c\u7684\u6837\u672c\u662f\u7531\u751f\u6210\u5668\u751f\u6210\u7684\uff0c\u800c\u4e0d\u662f\u6765\u81ea\u771f\u5b9e\u6570\u636e\u96c6\u3002\u8fd9\u79cd\u8bc6\u522b\u7ed3\u679c\u5c06\u53cd\u9988\u7ed9\u751f\u6210\u5668\uff0c\u4f7f\u5f97\u751f\u6210\u5668\u5728\u540e\u7eed\u7684\u8bad\u7ec3\u4e2d\u53d7\u5230\u60e9\u7f5a\uff0c\u56e0\u4e3a\u5b83\u672a\u80fd\u4ea7\u751f\u8db3\u591f\u591a\u6837\u5316\u7684\u8f93\u51fa\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5c0f\u6279\u91cf\u5224\u522b\u5668\u5b9e\u9645\u4e0a\u662f\u5728\u9f13\u52b1\u751f\u6210\u5668\u521b\u9020\u51fa\u66f4\u591a\u6837\u5316\u548c\u72ec\u7279\u7684\u6837\u672c\u3002\u5b83\u901a\u8fc7\u5bf9\u6837\u672c\u95f4\u76f8\u4f3c\u5ea6\u7684\u76d1\u63a7\uff0c\u8feb\u4f7f\u751f\u6210\u5668\u4e0d\u65ad\u63a2\u7d22\u65b0\u7684\u3001\u591a\u6837\u5316\u7684\u751f\u6210\u8def\u5f84\uff0c\u800c\u4e0d\u662f\u505c\u7559\u5728\u4ea7\u751f\u5c11\u6570\u51e0\u79cd\u6a21\u5f0f\u7684\u5b89\u5168\u533a\u57df\u3002\u8fd9\u6837\uff0c\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u751f\u6210\u6837\u672c\u7684\u8d28\u91cf\u548c\u591a\u6837\u6027\uff0c\u8fd8\u6709\u6548\u5730\u7f13\u89e3\u4e86\u6a21\u5f0f\u5d29\u6e83\u7684\u95ee\u9898\uff0c\u4f7f\u5f97\u751f\u6210\u7684\u56fe\u50cf\u66f4\u52a0\u4e30\u5bcc\u548c\u591a\u53d8\u3002<\/p>\n<pre><code class=\"language-python\">class MinibatchDiscrimination(nn.Module):\n    def __init__(self, in_features, out_features, kernel_dims):\n        super(MinibatchDiscrimination, self).__init__()\n        self.T = nn.Parameter(t.Tensor(in_features, out_features, kernel_dims))\n        nn.init.normal_(self.T, 0, 1)\n\n    def forward(self, x):\n        M = x.mm(self.T.view(self.T.shape[0], -1))\n        M = M.view(-1, self.T.shape[1], self.T.shape[2])\n        out = []\n        for i in range(M.size(0)):\n            out.append(t.sum(t.exp(-t.sum((M[i] - M) ** 2, 2)), 0))\n        out = t.cat(out).view(M.size(0), -1)\n        return t.cat([x, out], 1)\n\nclass DiscriminatorWithMinibatchDiscrimination(nn.Module):\n    def __init__(self):\n        super(DiscriminatorWithMinibatchDiscrimination, self).__init__()\n        self.main = nn.Sequential(\n            nn.Conv2d(opt.nc, opt.ndf, 4, 2, 1, bias=False),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf, opt.ndf*2, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*2),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf*2, opt.ndf*4, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*4),\n            nn.LeakyReLU(0.2, inplace=True),\n            MinibatchDiscrimination(opt.ndf*4*4*4, 100, 5), # Minibatch discrimination layer\n            nn.Conv2d(opt.ndf*4, opt.ndf*8, 4, 2, 1, bias=False),\n            nn.BatchNorm2d(opt.ndf*8),\n            nn.LeakyReLU(0.2, inplace=True),\n            nn.Conv2d(opt.ndf*8, 1, 4, 1, 0, bias=False),\n            nn.Sigmoid()\n        )\n\n    def forward(self, x):\n        return self.main(x)\n\nnetd = DiscriminatorWithMinibatchDiscrimination().cuda()\n<\/code><\/pre>\n<p><strong>\u5355\u4fa7\u6807\u7b7e\u5e73\u6ed1\uff08One-Sided Label Smoothing\uff09\u662f\u4e00\u79cd\u6709\u6548\u7684\u6b63\u5219\u5316\u6280\u672f<\/strong><\/p>\n<p>\u5728\u4f20\u7edf\u7684GAN\u8bad\u7ec3\u6846\u67b6\u4e2d\uff0c\u5224\u522b\u5668\u7684\u4efb\u52a1\u662f\u533a\u5206\u771f\u5b9e\u6837\u672c\u548c\u751f\u6210\u5668\u4ea7\u751f\u7684\u5047\u6837\u672c\u3002\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\uff0c\u771f\u5b9e\u6837\u672c\u901a\u5e38\u88ab\u6807\u8bb0\u4e3a1\uff08\u4ee3\u8868\u201c\u771f\u5b9e\u201d\uff09\uff0c\u800c\u5047\u6837\u672c\u88ab\u6807\u8bb0\u4e3a0\uff08\u4ee3\u8868\u201c\u5047\u201d\uff09\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u660e\u786e\u7684\u3001\u4e8c\u5143\u5316\u7684\u6807\u8bb0\u65b9\u5f0f\u6709\u65f6\u4f1a\u5bfc\u81f4\u5224\u522b\u5668\u8fc7\u5ea6\u81ea\u4fe1\u3002<br \/>\n\u8fc7\u5ea6\u81ea\u4fe1\u7684\u5224\u522b\u5668\u610f\u5473\u7740\u5b83\u5bf9\u4e8e\u5176\u5206\u7c7b\u7684\u51c6\u786e\u6027\u8fc7\u4e8e\u786e\u5b9a\uff0c\u8fd9\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4e24\u4e2a\u4e3b\u8981\u7684\u95ee\u9898\uff1a<\/p>\n<ul>\n<li>\u5728\u9762\u5bf9\u7a0d\u6709\u4e0d\u540c\u7684\u6216\u672a\u89c1\u8fc7\u7684\u6837\u672c\u65f6\uff0c\u5224\u522b\u5668\u7684\u6027\u80fd\u53ef\u80fd\u6025\u5267\u4e0b\u964d\uff0c\u56e0\u4e3a\u5b83\u672a\u80fd\u5b66\u4e60\u5230\u8db3\u591f\u7684\u6cdb\u5316\u80fd\u529b<\/li>\n<li>\u5224\u522b\u5668\u53ef\u80fd\u4f1a\u8fc7\u5ea6\u5f3a\u5316\u751f\u6210\u5668\u7684\u67d0\u4e9b\u7279\u5b9a\u7f3a\u9677\uff0c\u5bfc\u81f4\u751f\u6210\u5668\u5728\u8ffd\u6c42\u6b3a\u9a97\u5224\u522b\u5668\u7684\u8fc7\u7a0b\u4e2d\u504f\u79bb\u5b9e\u9645\u7684\u6570\u636e\u5206\u5e03\uff0c\u4ece\u800c\u53ef\u80fd\u52a0\u5267\u6a21\u5f0f\u5d29\u6e83\u7684\u98ce\u9669\u3002<\/li>\n<\/ul>\n<p>\u5355\u4fa7\u6807\u7b7e\u5e73\u6ed1\u6b63\u662f\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\u3002\u5728\u8fd9\u79cd\u6280\u672f\u4e2d\uff0c<strong>\u771f\u5b9e\u6837\u672c\u7684\u6807\u7b7e\u4e0d\u518d\u662f\u56fa\u5b9a\u76841\uff0c\u800c\u662f\u88ab\u8bbe\u7f6e\u4e3a\u7565\u5c0f\u4e8e1\u7684\u503c<\/strong>\uff0c\u4f8b\u59820.9\u62160.95\u3002<\/p>\n<p>\u8fd9\u6837\u7684\u505a\u6cd5\u51cf\u8f7b\u4e86\u5224\u522b\u5668\u5bf9\u6bcf\u4e2a\u6837\u672c\u7684\u7edd\u5bf9\u5206\u7c7b\uff08\u5b8c\u5168\u662f\u771f\u6216\u5b8c\u5168\u662f\u5047\uff09\uff0c\u4ece\u800c\u6291\u5236\u4e86\u5176\u8fc7\u5ea6\u81ea\u4fe1\u7684\u503e\u5411\u3002<\/p>\n<p>\u7ed3\u679c\u5c31\u662f\u4e00\u4e2a\u6cdb\u5316\u80fd\u529b\u66f4\u5f3a\u7684\u5224\u522b\u5668\uff0c\u5b83\u5bf9\u4e8e\u771f\u5b9e\u6837\u672c\u7684\u8bc6\u522b\u4e0d\u518d\u662f\u5b8c\u5168\u80af\u5b9a\u7684\uff0c\u800c\u662f\u7ed9\u4e88\u4e86\u4e00\u5b9a\u7684\u5bb9\u9519\u7a7a\u95f4\uff0c\u4f7f\u5f97\u5224\u522b\u5668\u5728\u5224\u65ad\u65b0\u7684\u6216\u7565\u6709\u5dee\u5f02\u7684\u771f\u5b9e\u6837\u672c\u65f6\u8868\u73b0\u5f97\u66f4\u4e3a\u7a33\u5065\u3002 <\/p>\n<pre><code class=\"language-python\">label = Variable(t.ones(input.size(0)) * 0.9)  # Smooth real labels to 0.9\n<\/code><\/pre>\n<p><strong>\u865a\u62df\u6279\u89c4\u8303\u5316\uff08Virtual Batch Normalization, VBN\uff09\u662f\u4e00\u79cd\u6539\u8fdb\u7684\u89c4\u8303\u5316\u6280\u672f<\/strong><\/p>\n<ul>\n<li>\n<p>VBN\u5b83\u5728\u4f20\u7edf\u6279\u89c4\u8303\u5316\uff08Batch Normalization, BN\uff09\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u4e86\u5173\u952e\u7684\u4f18\u5316\uff0c\u7279\u522b\u9002\u7528\u4e8e\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u7b49\u590d\u6742\u6a21\u578b\u7684\u8bad\u7ec3\u3002BN\u4f5c\u4e3a\u4e00\u79cd\u5e7f\u6cdb\u5e94\u7528\u7684\u6280\u672f\uff0c\u901a\u8fc7\u89c4\u8303\u5316\u795e\u7ecf\u7f51\u7edc\u4e2d\u5404\u5c42\u7684\u8f93\u5165\uff0c\u6709\u52a9\u4e8e\u52a0\u5feb\u8bad\u7ec3\u901f\u5ea6\uff0c\u51cf\u5c11\u6a21\u578b\u5bf9\u521d\u59cb\u5316\u6743\u91cd\u7684\u654f\u611f\u5ea6\uff0c\u5e76\u80fd\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u6291\u5236\u8fc7\u62df\u5408\u3002\u7136\u800c\uff0c\u5728\u8bad\u7ec3\u9ad8\u5ea6\u590d\u6742\u7684\u7f51\u7edc\u65f6\uff0c\u5c24\u5176\u662fGANs\u4e2d\u7684\u751f\u6210\u5668\u65f6\uff0cBN\u9762\u4e34\u7740\u4e00\u4e2a\u6311\u6218\uff1a<strong>\u4e0d\u540c\u6279\u6b21\u95f4\u7684\u534f\u65b9\u5dee\u504f\u79fb<\/strong>\u3002<\/p>\n<\/li>\n<li>\n<p>\u534f\u65b9\u5dee\u504f\u79fb\u662f\u6307\u5f53\u7f51\u7edc\u5728\u4e0d\u540c\u6279\u6b21\u7684\u6570\u636e\u4e0a\u8bad\u7ec3\u65f6\uff0c\u5373\u4f7f\u662f\u540c\u4e00\u8f93\u5165\uff0c\u5728\u7f51\u7edc\u5185\u90e8\u7684\u8868\u793a\u53ef\u80fd\u4f1a\u7531\u4e8e\u6bcf\u4e2a\u6279\u6b21\u6570\u636e\u7684\u7edf\u8ba1\u5c5e\u6027\uff08\u5982\u5747\u503c\u3001\u65b9\u5dee\uff09\u7684\u5dee\u5f02\u800c\u4ea7\u751f\u53d8\u5316\u3002\u8fd9\u79cd\u53d8\u5316\u53ef\u80fd\u5bfc\u81f4\u7f51\u7edc\u7684\u8bad\u7ec3\u8fc7\u7a0b\u53d8\u5f97\u4e0d\u7a33\u5b9a\uff0c\u7279\u522b\u662f\u5728GANs\u4e2d\uff0c\u751f\u6210\u5668\u7684\u8f93\u51fa\u6781\u6613\u53d7\u5230\u8f93\u5165\u6570\u636e\u6279\u6b21\u5dee\u5f02\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u5f71\u54cd\u6574\u4e2a\u7f51\u7edc\u7684\u5b66\u4e60\u548c\u751f\u6210\u8d28\u91cf\u3002<\/p>\n<\/li>\n<li>\n<p>\u4e0e\u4f20\u7edf\u7684BN\u4e0d\u540c\uff0cVBN\u5f15\u5165\u4e86\u4e00\u4e2a\u56fa\u5b9a\u7684\u201c\u53c2\u8003\u6279\u6b21\u201d\uff08reference batch\uff09\u3002\u8fd9\u4e2a\u53c2\u8003\u6279\u6b21\u5728\u8bad\u7ec3\u5f00\u59cb\u65f6\u88ab\u9009\u53d6\uff0c\u5e76\u5728\u6574\u4e2a\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u4e0d\u53d8\u3002\u5f53\u8fdb\u884c\u6279\u89c4\u8303\u5316\u65f6\uff0cVBN\u4e0d\u4ec5\u8003\u8651\u5f53\u524d\u6279\u6b21\u7684\u6837\u672c\u7edf\u8ba1\u7279\u6027\uff08\u4f8b\u5982\u5747\u503c\u548c\u65b9\u5dee\uff09\uff0c\u8fd8\u540c\u65f6\u53c2\u7167\u8fd9\u4e2a\u56fa\u5b9a\u6279\u6b21\u7684\u7edf\u8ba1\u7279\u6027\u8fdb\u884c\u89c4\u8303\u5316\u3002\u8fd9\u79cd\u65b9\u6cd5\u6709\u6548\u5730\u51cf\u5c11\u4e86\u7531\u4e8e\u6279\u6b21\u4e4b\u95f4\u7684\u7edf\u8ba1\u5c5e\u6027\u5dee\u5f02\u6240\u5bfc\u81f4\u7684\u5185\u90e8\u534f\u53d8\u91cf\u504f\u79fb\uff0c\u4f7f\u5f97\u751f\u6210\u5668\u7684\u8bad\u7ec3\u8fc7\u7a0b\u66f4\u4e3a\u7a33\u5b9a\u3002<\/p>\n<\/li>\n<li>\n<p>\u901a\u8fc7\u8fd9\u79cd\u7ed3\u5408\u5f53\u524d\u6279\u6b21\u548c\u56fa\u5b9a\u53c2\u8003\u6279\u6b21\u7684\u7edf\u8ba1\u6570\u636e\u7684\u89c4\u8303\u5316\u65b9\u6cd5\uff0cVBN\u6709\u52a9\u4e8e\u63d0\u9ad8\u6a21\u578b\u5728\u5904\u7406\u4e0d\u540c\u6570\u636e\u6279\u6b21\u65f6\u7684\u7a33\u5b9a\u6027\u548c\u4e00\u81f4\u6027\u3002\u5bf9\u4e8eGANs\u800c\u8a00\uff0c\u8fd9\u610f\u5473\u7740\u751f\u6210\u5668\u80fd\u591f\u66f4\u52a0\u5e73\u7a33\u5730\u5b66\u4e60\u548c\u9002\u5e94\uff0c\u907f\u514d\u56e0\u4e3a\u8f93\u5165\u6570\u636e\u7684\u8f7b\u5fae\u53d8\u5316\u800c\u4ea7\u751f\u8f83\u5927\u7684\u8f93\u51fa\u6ce2\u52a8\uff0c\u4ece\u800c\u5728\u6574\u4e2a\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5b9e\u73b0\u66f4\u9ad8\u7684\u6027\u80fd\u548c\u66f4\u597d\u7684\u7ed3\u679c\u3002\u865a\u62df\u6279\u89c4\u8303\u5316\u56e0\u6b64\u6210\u4e3a\u4e86\u63d0\u9ad8\u590d\u6742\u7f51\u7edc\u7a33\u5b9a\u6027\u548c\u6027\u80fd\u7684\u4e00\u4e2a\u91cd\u8981\u5de5\u5177\uff0c\u5c24\u5176\u5728GANs\u7684\u8bad\u7ec3\u4e2d\u663e\u793a\u51fa\u5176\u72ec\u7279\u7684\u4ef7\u503c\u3002<\/p>\n<\/li>\n<\/ul>\n<p><a href=\"https:\/\/github.com\/openai\/improved-gan\">\u53c2\u8003\uff1aopenai--improved-gan<\/a><\/p>\n<h2><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/?size=100&id=tm3mvGuLwRlx&format=png&color=000000\" style=\"height:50px;display:inline\"> f-GAN<\/h2>\n<hr \/>\n<p>2016\u5e74\u7684\u8bba\u6587\u300af-GAN: Training Generative Neural Samplers using Variational Divergence Minimization\u300b\u5f15\u5165\u4e86\u4e00\u79cd\u65b0\u7684\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GAN\uff09\u6846\u67b6\uff0c\u540d\u4e3af-GAN\u3002\u8fd9\u7bc7\u8bba\u6587\u901a\u8fc7\u5c06\u4f20\u7edf\u7684GAN\u8bad\u7ec3\u6846\u67b6\u6269\u5c55\u5230\u4e00\u7cfb\u5217\u57fa\u4e8ef\u6563\u5ea6\u7684\u66f4\u5e7f\u6cdb\u7684\u8ddd\u79bb\u6216\u6563\u5ea6\u63aa\u65bd\u4e0a\uff0c\u4e3a\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u548c\u65b9\u6cd5\u3002<\/p>\n<h3>GAN\u6a21\u578b\u635f\u5931\u4e0e\u6563\u5ea6<\/h3>\n<p>\u7b80\u5355\u56de\u5fc6\u4e00\u4e0bGAN\u6a21\u578b\u7684\u76ee\u6807\u51fd\u6570\uff0c\u5728\u6807\u51c6GAN\u8bbe\u7f6e\u4e2d\uff0c\u751f\u6210\u5668\u7684\u76ee\u6807\u662f\u6700\u5927\u5316\u5224\u522b\u5668\u505a\u51fa\u9519\u8bef\u5224\u65ad\u7684\u6982\u7387\uff0c\u800c\u5224\u522b\u5668\u7684\u76ee\u6807\u662f\u51c6\u786e\u533a\u5206\u771f\u5b9e\u6570\u636e\u548c\u5047\u6570\u636e\u3002\u8fd9\u53ef\u4ee5\u5f62\u5f0f\u5316\u4e3a\u4ee5\u4e0b\u7684\u6781\u5c0f\u6781\u5927\u95ee\u9898:<\/p>\n<p>$$<br \/>\n\\min _G \\max _D V(D, G)=\\mathrm{E}_{x \\sim p_{\\text {dtas }}(x)}[\\log D(x)]+\\mathrm{E}_{z \\sim p_z(z)}[\\log (1-D(G(z)))]<br \/>\n$$<\/p>\n<p>\u5176\u4e2d, $\\mathrm{E}$ \u8868\u793a\u671f\u671b\u64cd\u4f5c; $p_{\\text {data }}$ \u662f\u771f\u5b9e\u6570\u636e\u7684\u5206\u5e03; $x$ \u662f\u4ece\u771f\u5b9e\u6570\u636e\u4e2d\u62bd\u6837\u7684\u6837\u672c;  $p_z$ \u662f\u751f\u6210\u5668\u7684\u8f93\u5165\u566a\u58f0\u5206\u5e03, \u901a\u5e38\u5047\u5b9a\u4e3a\u9ad8\u65af\u6216\u5747\u5300\u5206\u5e03; $z$ \u662f\u4ece $p_z$ \u4e2d\u62bd\u6837\u7684\u566a\u58f0\u5411\u91cf; $G(z)$ \u662f\u751f\u6210\u5668 $G$ \u4f7f\u7528\u566a\u58f0 $z$ \u751f\u6210\u7684\u6570\u636e\u6837\u672c\u3002<\/p>\n<p>\u5f53\u5224\u522b\u5668 $D$ \u548c\u751f\u6210\u5668 $G$ \u90fd\u8fbe\u5230\u5176\u5404\u81ea\u7684\u6700\u4f18\u65f6, GAN \u8bad\u7ec3\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u5728\u6700\u5c0f\u5316\u751f\u6210\u6570\u636e\u5206\u5e03 $p_g$ \u548c\u771f\u5b9e\u6570\u636e\u5206\u5e03 $p_{\\text {data }}$ \u4e4b\u95f4\u7684 Jensen-Shannon \u6563\u5ea6\uff08JS \u6563\u5ea6\uff09\u3002JS \u6563\u5ea6\u662f\u8861\u91cf\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u5dee\u5f02\u7684\u4e00\u79cd\u65b9\u6cd5, \u5b9a\u4e49\u4e3a:<br \/>\n$$<br \/>\nJ S(P | Q)=\\frac{1}{2} K L(P | M)+\\frac{1}{2} K L(Q | M)<br \/>\n$$<\/p>\n<p>\u5176\u4e2d, $M=\\frac{1}{2}(P+Q)$ \u662f $P$ \u548c $Q$ \u7684\u5e73\u5747\u5206\u5e03\u3002 $K L(P | Q)$ \u662f\u4e24\u4e2a\u6982\u7387\u5206\u5e03 $P$ \u548c $Q$ \u4e4b\u95f4\u7684 Kullback-Leibler \u6563\u5ea6, \u5177\u4f53\u6765\u8bf4 KL \u6563\u5ea6\u5b9a\u4e49\u4e3a:<br \/>\n$$<br \/>\n\\mathrm{KL}(P | Q)=\\sum_x P(x) \\log \\frac{P(x)}{Q(x)}<br \/>\n$$<\/p>\n<p><strong>\u4e0b\u9762\u6765\u4ed4\u7ec6\u63a8\u5bfc\u4e00\u4e0b\u4e0a\u8ff0\u7ed3\u8bba\u3002<\/strong><\/p>\n<p>\u5224\u522b\u5668 $D$ \u7684\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a:<br \/>\n$$<br \/>\nV(D, G)=\\mathrm{E}_{x \\sim p_{\\text {data }}}[\\log D(x)]+\\mathrm{E}_{x \\sim p_g}[\\log (1-D(x))]<br \/>\n$$<\/p>\n<p>\u6211\u4eec\u8981\u627e\u5230 $D$ \u7684\u5f62\u5f0f, \u4f7f\u5f97 $V(D, G)$ \u6700\u5927\u5316\u3002\u4e3a\u6b64,\u53ef\u4ee5\u5c06\u671f\u671b\u8f6c\u6362\u6210\u79ef\u5206\u7684\u5f62\u5f0f,\u5e76\u5206\u522b\u9488\u5bf9 $p_{\\text {data }}$ \u548c $p_g$ \u8fdb\u884c\u8ba1\u7b97, \u516c\u5f0f\u5982\u4e0b:<\/p>\n<p>$$<br \/>\nV(D, G)=\\int_x p_{\\text {data }}(x) \\log D(x) d x+\\int_x p_g(x) \\log (1-D(x)) d x<br \/>\n$$<\/p>\n<p>\u4e3a\u4e86\u6700\u5927\u5316 $V(D, G)$, \u5bf9 $D$ \u6c42\u5bfc\u5e76\u4ee4\u5176\u4e3a 0 , \u516c\u5f0f\u5982\u4e0b:<br \/>\n$$<br \/>\n\\frac{\\delta V}{\\delta D}=\\frac{p_{\\text {data }}(x)}{D(x)}-\\frac{p_g(x)}{1-D(x)}=0<br \/>\n$$<\/p>\n<p>\u5c06\u4e0a\u8ff0\u7684\u5bfc\u6570\u8bbe\u7f6e\u4e3a 0 , \u6c42\u89e3 $D$ \u5f97\u5230:<\/p>\n<p>$$<br \/>\n\\begin{gathered}<br \/>\n\\frac{p_{\\text {data }}(x)}{D(x)}=\\frac{p_g(x)}{1-D(x)} \\\\<br \/>\np_{\\text {data }}(x)(1-D(x))=p_g(x) D(x) \\\\<br \/>\np_{\\text {data }}(x)-p_{\\text {data }}(x) D(x)=p_g(x) D(x) \\\\<br \/>\np_{\\text {data }}(x)=D(x)\\left(p_{\\text {data }}(x)+p_g(x)\\right) \\\\<br \/>\nD(x)=\\frac{p_{\\text {data }}(x)}{p_{\\text {data }}(x)+p_g(x)}<br \/>\n\\end{gathered}<br \/>\n$$<\/p>\n<p>\u8fd9\u5c31\u662f\u6700\u4f18\u5224\u522b\u5668$D^*$\u7684\u5f62\u5f0f\u3002\u76f4\u89c2\u5730\u8bf4, \u8fd9\u4e2a\u5f62\u5f0f\u8868\u793a\u4e86 $x$ \u6765\u81ea\u771f\u5b9e\u6570\u636e\u7684\u6982\u7387, \u4e0e $x$\u6765\u81ea\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u6570\u636e\u7684\u603b\u6982\u7387\u4e4b\u6bd4\u3002\u5f53\u751f\u6210\u5668 $G$ \u5b8c\u7f8e\u5730\u6a21\u4eff\u4e86\u771f\u5b9e\u6570\u636e\u5206\u5e03 $p_{\\text {data }}$ \u65f6, \u5373$p_g(x)=p_{\\text {data }}(x)$ \u3002\u6b64\u65f6, $D^*(x)$ \u5c06\u8f93\u51fa 0.5 , \u8868\u793a\u5b83\u65e0\u6cd5\u533a\u5206\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u6570\u636e, \u8fd9\u4e5f\u662f GAN \u8bad\u7ec3\u7684\u7406\u60f3\u72b6\u6001\u3002<\/p>\n<p>\u5f53\u5224\u522b\u5668 $D$ \u662f\u6700\u4f18\u7684, \u5373$D^*(x)=\\frac{p_{\\text {data }}(x)}{p_g(x)+p_{\\text {data }}(x)}$  \u65f6, \u8003\u8651\u751f\u6210\u5668 $G$ \u7684\u6700\u4f18\u60c5\u51b5\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b, \u53ef\u4ee5\u91cd\u65b0\u5ba1\u89c6 GAN \u7684\u503c\u51fd\u6570 $V(D, G)$, \u5b83\u5728 $D$ \u6700\u4f18\u7684\u60c5\u51b5\u4e0b\u8f6c\u5316\u4e3a:<\/p>\n<p>$$<br \/>\nV\\left(G, D^*\\right)=\\mathrm{E}_{x \\sim p_{\\text {data }}}\\left[\\log D^*(x)\\right]+\\mathrm{E}_{x \\sim p_s}\\left[\\log \\left(1-D^*(x)\\right)\\right]<br \/>\n$$<\/p>\n<p>\u5c06 $D^*$ \u7684\u6700\u4f18\u5f62\u5f0f\u4ee3\u5165\u4e0a\u8ff0\u7b49\u5f0f\u4e2d, \u53ef\u4ee5\u5f97\u5230:<br \/>\n$$<br \/>\nV\\left(G, D^*\\right)=\\mathrm{E}_{x \\sim p \\text { data }}\\left[\\log \\frac{p_{\\text {data }}(x)}{p_{\\text {data }}(x)+p_g(x)}\\right]+\\mathrm{E}_{x \\sim p_g}\\left[\\log \\frac{p_g(x)}{p_{\\text {data }}(x)+p_g(x)}\\right]<br \/>\n$$<\/p>\n<p>\u7406\u8bba\u4e0a, \u6c42 $G^*$ \u7b49\u4ef7\u4e8e $p_g(x)$ \u53ef\u4ee5\u51c6\u786e\u5730\u6a21\u4eff  $p_{\\text {data }}(x)$, \u5373 $p_g(x)=p_{\\text {data }}(x)$, \u6b64\u65f6,  $\\frac{p_{\\text {data }}(x)}{p_g(x)+p_{\\text {data }}(x)}$ \u548c $\\frac{p_g(x)}{p_g(x)+p_{\\text {data }}(x)}$ \u90fd\u8d8b\u8fd1\u4e8e $\\frac{1}{2}$ \u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b, \u7531\u4e8e $\\log \\frac{1}{2}=-\\log 2$, \u5f53  $p_{\\text {data }}=p_g$ \u65f6, \u8fd9\u4e24\u4e2a\u671f\u671b\u503c\u52a0\u5728\u4e00\u8d77\u5c31\u662f $-\\log 2-\\log 2=-2 \\log 2$ \u3002\u5373<strong>\u6700\u4f18\u7684\u751f\u6210\u5668\u5c06\u8d8b\u5411\u4e8e\u5176\u6700\u5c0f\u503c $-2 \\log 2$ \u3002<\/strong><\/p>\n<p><strong>\u7ee7\u7eed\u63a8\u5bfc GAN \u635f\u5931\u51fd\u6570\u4e0e\u6563\u5ea6\u7684\u5173\u7cfb<\/strong>\u3002\u53ef\u4ee5\u5bf9\u5e26\u5165\u6700\u4f18 $D^*$ \u7684\u635f\u5931\u51fd\u6570\u8fdb\u884c\u8fdb\u4e00\u6b65\u7684\u63a8\u5bfc, \u5177\u4f53\u5982\u4e0b:<\/p>\n<p>$$\\begin{aligned}<br \/>\n\\mathrm{Loss}&amp; =\\mathrm{E}_{x\\sim p\\mathrm{data}}\\left[\\log\\frac{p_{\\mathrm{data}}\\left(x\\right)}{p_{\\mathrm{data}}\\left(x\\right)+p_{g}\\left(x\\right)}\\right]+\\mathrm{E}_{x\\sim p_{g}}\\left[\\log\\frac{p_{g}\\left(x\\right)}{p_{\\mathrm{data}}\\left(x\\right)+p_{g}\\left(x\\right)}\\right] \\\\<br \/>\n&amp;=\\mathbb{E}_{x\\sim p\\textbf{data}}\\left[\\log\\left(\\frac12\\cdot\\frac{2p_\\text{data}\\left(x\\right)}{p_\\text{data}\\left(x\\right)+p_g\\left(x\\right)}\\right)\\right]+\\mathbb{E}_{x\\sim p_g}\\left[\\log\\left(\\frac12\\cdot\\frac{2p_g\\left(x\\right)}{p_\\text{data}\\left(x\\right)+p_g\\left(x\\right)}\\right)\\right] \\\\<br \/>\n&amp;=\\mathbb{E}_{x\\sim p\\mathrm{data}}\\left[\\log\\frac12\\right]+\\mathbb{E}_{x\\sim p\\mathrm{data}}\\left[\\log\\frac{2p_{\\mathrm{data}}\\left(x\\right)}{p_{\\mathrm{data}}\\left(x\\right)+p_{g}\\left(x\\right)}\\right]+\\mathbb{E}_{x\\sim p_{g}}\\left[\\log\\frac12\\right]+\\mathbb{E}_{x\\sim p_{g}}\\left[\\log\\frac{2p_{g}\\left(x\\right)}{p_{\\mathrm{data}}\\left(x\\right)+p_{g}\\left(x\\right)}\\right] \\\\<br \/>\n&amp;=-\\log4+\\mathbb{E}_{x\\sim p\\mathrm{data}}\\left\\lceil\\log\\frac{2p_\\mathrm{data}\\left(x\\right)}{p_\\mathrm{data}\\left(x\\right)+p_\\mathrm{g}\\left(x\\right)}\\right\\rceil+\\mathbb{E}_{x\\sim p_\\mathrm{g}}\\left\\lceil\\log\\frac{2p_\\mathrm{g}\\left(x\\right)}{p_\\mathrm{data}\\left(x\\right)+p_\\mathrm{g}\\left(x\\right)}\\right\\rceil<br \/>\n\\end{aligned}$$<\/p>\n<p>\u4e0b\u9762, \u5c06 $V\\left(G, D^*\\right)$ \u4e0e KL \u548c JS \u6563\u5ea6\u8054\u7cfb\u8d77\u6765, \u5148\u770b $V\\left(G, D^*\\right)$ \u7684\u540e\u4e24\u9879\u3002\u9996\u5148, \u89c2\u5bdf\u5230 $\\frac{2 p_{\\text {data }}(x)}{p_{\\text {data }}(x)+p_g(x)}$ \u548c $\\frac{2 p_g(x)}{p_{\\text {dta }}(x)+p_g(x)}$  \u5206\u522b\u662f\u4ee5  $p_{\\text {data }}$ \u548c $p_{\\mathrm{g}}$  \u4e3a\u57fa\u7840\u7684\u4e24\u4e2a\u6982\u7387\u5206\u5e03, \u5176\u4e2d\u6bcf\u4e2a\u90fd\u4e0e\u4e2d\u95f4\u5206\u5e03 $M=\\frac{p_{\\text {data }}+p_g}{2}$  \u6709\u5173\u3002\u8fd9\u6837\u53ef\u4ee5\u91cd\u5199 $V\\left(G, D^*\\right)$ :<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nV\\left(G, D^*\\right) &amp; =-\\log 4+\\mathrm{E}_{x \\sim p \\text { data }}\\left[\\log \\frac{2 p_{\\text {data }}(x)}{p_{\\text {data }}(x)+p_g(x)}\\right]+\\mathrm{E}_{x \\sim p_g}\\left[\\log \\frac{2 p_g(x)}{p_{\\text {data }}(x)+p_g(x)}\\right] \\\\<br \/>\n&amp; =-\\log 4+K L\\left(p_{\\text {data }} | \\frac{p_{\\text {data }}+p_g}{2}\\right)+K L\\left(p_g | \\frac{p_{\\text {data }}+p_g}{2}\\right) \\\\<br \/>\n&amp; =-\\log 4+2 \\cdot J S\\left(p_{\\text {data }} | p_g\\right)<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u56e0\u6b64, \u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba: <strong>\u5728\u6700\u4f18\u5224\u522b\u5668 $D^*$ \u7684\u6761\u4ef6\u4e0b, GAN \u7684\u4ef7\u503c\u51fd\u6570 $V\\left(G, D^*\\right)$ \u5b9e\u9645\u4e0a\u7b49\u4e8e $-\\log 4$ \u52a0\u4e0a $p_{\\text {data }}$ \u548c $p_g$ \u4e4b\u95f4\u7684\u4e24\u500d JS \u6563\u5ea6<\/strong>\u3002\u8fd9\u8868\u660e GAN \u7684\u8bad\u7ec3\u8fc7\u7a0b\u672c\u8d28\u4e0a\u662f\u8bd5\u56fe\u6700\u5c0f\u5316$p_{\\text {data }}$ \u548c $p_g$\u4e4b\u95f4\u7684 $\\mathrm{JS}$ \u6563\u5ea6, \u4f7f\u751f\u6210\u7684\u6570\u636e\u5206\u5e03\u5c3d\u53ef\u80fd\u5730\u63a5\u8fd1\u771f\u5b9e\u6570\u636e\u5206\u5e03\u3002\u5f53 $\\mathrm{JS}$ \u6563\u5ea6\u6563\u5ea6\u6700\u5c0f\u65f6, \u610f\u5473\u7740 $p_{\\text {data }}$ \u548c $p_g$ \u4e0d\u53ef\u533a\u5206, \u8fd9\u662f GAN \u8bad\u7ec3\u7684\u7406\u60f3\u76ee\u6807\u3002<\/p>\n<h3>GAN\u635f\u5931\u7684\u901a\u7528\u6846\u67b6f-\u6563\u5ea6<\/h3>\n<ul>\n<li>\n<p>f-divergence: f-divergence\u662f\u4e00\u7c7b\u5e7f\u4e49\u7684\u8ddd\u79bb\u5ea6\u91cf\uff0c\u7528\u6765\u8861\u91cf\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u7684\u5dee\u5f02\u3002KL\u6563\u5ea6\u3001Jensen-Shannon\u6563\u5ea6\u3001\u603b\u53d8\u5dee\u8ddd\u79bb\u7b49\u90fd\u662ff-divergence\u7684\u7279\u4f8b\u3002f-GAN\u901a\u8fc7\u6700\u5c0f\u5316\u751f\u6210\u5206\u5e03\u4e0e\u771f\u5b9e\u6570\u636e\u5206\u5e03\u4e4b\u95f4\u7684f-divergence\u6765\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u3002<\/p>\n<\/li>\n<li>\n<p>\u5bf9\u6297\u8bad\u7ec3: \u4e0e\u4f20\u7edf\u7684GAN\u7c7b\u4f3c\uff0cf-GAN\u5305\u542b\u4e24\u4e2a\u7f51\u7edc\uff1a\u751f\u6210\u5668\uff08G\uff09\u548c\u5224\u522b\u5668\uff08D\uff09\u3002\u751f\u6210\u5668\u8d1f\u8d23\u751f\u6210\u5047\u6837\u672c\uff0c\u5224\u522b\u5668\u5219\u5c1d\u8bd5\u533a\u5206\u771f\u5b9e\u6837\u672c\u548c\u5047\u6837\u672c\u3002<\/p>\n<\/li>\n<li>\n<p>\u76ee\u6807\u51fd\u6570: f-GAN\u901a\u8fc7\u5bf9\u6297\u8bad\u7ec3\u6765\u4f18\u5316f-divergence\u3002\u5177\u4f53\u6765\u8bf4\uff0cf-GAN\u7684\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n<\/li>\n<\/ul>\n<p>$$<br \/>\n\\min _G \\max _D V(D, G)=\\mathbb{E}_{x \\sim p_{\\text {data }}}[D(x)]-\\mathbb{E}_{z \\sim p_z}\\left[f^*(D(G(z)))\\right]<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\uff0c $f^*$ \u662f $\\mathrm{f}$-divergence\u7684\u5bf9\u5076\u51fd\u6570\uff0c $p_{\\text {data }}$ \u662f\u771f\u5b9e\u6570\u636e\u5206\u5e03\uff0c $p_z$ \u662f\u751f\u6210\u5668\u7684\u8f93\u5165\u566a\u58f0\u5206\u5e03\u3002<\/p>\n<p><strong>f-GAN\u7684\u7279\u70b9<\/strong><\/p>\n<ul>\n<li>\n<p>\u7075\u6d3b\u6027: f-GAN\u901a\u8fc7\u9009\u62e9\u4e0d\u540c\u7684f-divergence\uff0c\u53ef\u4ee5\u7075\u6d3b\u5730\u9002\u5e94\u4e0d\u540c\u7684\u4efb\u52a1\u9700\u6c42\u3002\u4f8b\u5982\uff0c\u901a\u8fc7\u9009\u62e9KL\u6563\u5ea6\u53ef\u4ee5\u66f4\u597d\u5730\u5339\u914d\u7a00\u758f\u6570\u636e\u5206\u5e03\uff0c\u901a\u8fc7\u9009\u62e9Jensen-Shannon\u6563\u5ea6\u53ef\u4ee5\u63d0\u5347\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\u3002<\/p>\n<\/li>\n<li>\n<p>\u7a33\u5b9a\u6027: \u901a\u8fc7\u4f18\u5316\u5e7f\u4e49\u7684f-divergence\uff0cf-GAN\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u66f4\u7a33\u5b9a\uff0c\u907f\u514d\u4e86\u4f20\u7edfGAN\u4e2d\u5e38\u89c1\u7684\u6a21\u5f0f\u5d29\u6e83\u548c\u8bad\u7ec3\u4e0d\u6536\u655b\u95ee\u9898\u3002<\/p>\n<\/li>\n<li>\n<p>\u6cdb\u5316\u6027: f-GAN\u7684\u6846\u67b6\u5177\u5907\u5f88\u5f3a\u7684\u6cdb\u5316\u6027\uff0c\u80fd\u591f\u9002\u7528\u4e8e\u591a\u79cd\u751f\u6210\u4efb\u52a1\uff0c\u5305\u62ec\u56fe\u50cf\u751f\u6210\u3001\u6587\u672c\u751f\u6210\u7b49\u3002<\/p>\n<\/li>\n<\/ul>\n<h3><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/?size=100&id=fXN7M1okR9HL&format=png&color=000000\" style=\"height:50px;display:inline\"> Wasserstein GAN\uff08W-GAN\uff09<\/h3>\n<hr \/>\n<ul>\n<li>WGAN\uff0c\u5373Wasserstein GAN\uff0c\u65e8\u5728\u89e3\u51b3\u4f20\u7edfGAN\u8bad\u7ec3\u4e2d\u7684\u4e00\u4e9b\u95ee\u9898\uff0c\u5c24\u5176\u662f\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u548c\u68af\u5ea6\u6d88\u5931\u3002<\/li>\n<li>WGAN\u901a\u8fc7\u4f7f\u7528Wasserstein\u8ddd\u79bb\uff08Earth-Mover\u8ddd\u79bb\u6216EM\u8ddd\u79bb\uff09\u6765\u8861\u91cf\u771f\u5b9e\u6570\u636e\u5206\u5e03\u548c\u751f\u6210\u6570\u636e\u5206\u5e03\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u6539\u8fdb\u4e86GAN\u7684\u8bad\u7ec3\u8fc7\u7a0b\u3002<\/li>\n<\/ul>\n<p><strong>\u4ece\u635f\u5931\u89d2\u5ea6\uff0c\u4f20\u7edfGAN\u6a21\u578b\u8bad\u7ec3\u4e0d\u7a33\u5b9a\u7684\u539f\u56e0\u5982\u4e0b<\/strong><\/p>\n<ul>\n<li>\n<p>\u5728\u4f20\u7edf\u7684 GAN \u4e2d, \u901a\u5e38\u4f7f\u7528 $\\mathrm{JS}$ \u6563\u5ea6\u6216 $\\mathrm{KL}$ \u6563\u5ea6\u6765\u8861\u91cf\u771f\u5b9e\u6570\u636e\u5206\u5e03  $P_{\\text {data }}$ \u548c\u751f\u6210\u6570\u636e\u5206\u5e03 $P_g$ \u4e4b\u95f4\u7684\u5dee\u5f02\u3002\u5f53\u4e24\u4e2a\u5206\u5e03  $P_{\\text {data }}$ \u548c $P_g$ \u6ca1\u6709\u91cd\u53e0\u65f6, \u5b58\u5728\u4e0b\u5217\u95ee\u9898:<\/p>\n<ul>\n<li>\u5728 KL \u6563\u5ea6\u7684\u60c5\u51b5\u4e0b, \u5982\u679c\u5b58\u5728\u4efb\u4f55 $x$ \u4f7f\u5f97 $P_{\\text {data }}(x)&gt;0$ \u800c $P_g(x)=0$, \u90a3\u4e48 $D_{\\mathrm{KL}}\\left(P_{\\text {data }} | P_{\\mathrm{g}}\\right)$ \u4f1a\u53d8\u4e3a\u65e0\u7a77\u5927\u3002\u8fd9\u5728\u6570\u5b66\u4e0a\u662f\u56e0\u4e3a $\\log (0)$ \u672a\u5b9a\u4e49, \u5e76\u4e14\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u8fd9\u901a\u5e38\u610f\u5473\u7740\u65e0\u6cd5\u8ba1\u7b97\u68af\u5ea6\u3002<\/li>\n<li>\u5bf9\u4e8e $\\mathrm{JS}$ \u6563\u5ea6, \u5f53 $P_{\\text {data }}$ \u548c $P_g$ \u5b8c\u5168\u4e0d\u91cd\u53e0\u65f6, $D_{\\mathrm{JS}}\\left(P_{\\text {data }} | P_g\\right)$  \u4f1a\u662f\u4e00\u4e2a\u5e38\u6570 $(\\log 2)$ \u3002\u8fd9\u610f\u5473\u7740 GAN \u7684\u751f\u6210\u5668\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u5c06\u65e0\u6cd5\u5f97\u5230\u4efb\u4f55\u6307\u5bfc\u68af\u5ea6\u6765\u8c03\u6574\u5176\u53c2\u6570, \u56e0\u4e3a\u4e0d\u8bba\u751f\u6210\u5668\u5982\u4f55\u6539\u53d8, JS \u6563\u5ea6\u90fd\u4fdd\u6301\u4e0d\u53d8, \u8fd9\u5c31\u662f\u6240\u8c13\u7684 \u201c\u68af\u5ea6\u6d88\u5931\u201d \u95ee\u9898\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u7b80\u5355\u8bf4\uff0c\u5f53GAN\u6a21\u578b\u7684\u751f\u6210\u5668\u56e0\u4e3a\u521d\u59cb\u5316\u7b49\u56e0\u7d20\u5bfc\u81f4\u751f\u6210\u7684\u6570\u636e\u5206\u5e03\u4e0e\u771f\u5b9e\u6570\u636e\u7684\u5206\u5e03\u76f8\u5dee\u5f88\u5927\u65f6\uff08\u6ca1\u6709\u91cd\u53e0\uff09\uff0cGAN\u6a21\u578b\u7684\u8bad\u7ec3\u68af\u5ea6\u662f\u5f97\u4e0d\u5230\u66f4\u65b0\u7684\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>Wasserstein\u8ddd\u79bb<\/strong><\/p>\n<p>Wasserstein\u8ddd\u79bb\uff0c\u4e5f\u88ab\u79f0\u4e3aEarth Mover\u2019s Distance\uff08EMD\uff09\uff0c\u662f\u4e00\u79cd\u8861\u91cf\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u5dee\u5f02\u7684\u65b9\u6cd5\uff0c\u5177\u4f53\u7528\u4e8e\u5ea6\u91cf\u5c06\u4e00\u4e2a\u5206\u5e03\u8f6c\u6362\u6210\u53e6\u4e00\u4e2a\u5206\u5e03\u6240\u9700\u7684\u201c\u6700\u5c0f\u5de5\u4f5c\u91cf\u201d\u3002\u5728\u7406\u89e3Wasserstein\u8ddd\u79bb\u4e4b\u524d\uff0c\u9700\u8981\u9996\u5148\u7406\u89e3\u51e0\u4e2a\u5173\u952e\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u6982\u7387\u5206\u5e03\uff1a\u5c06\u6982\u7387\u5206\u5e03\u60f3\u8c61\u4e3a\u4e00\u5b9a\u91cf\u7684\u201c\u571f\u5806\u201d\uff0c\u5728\u8fd9\u4e2a\u6bd4\u55bb\u4e2d\uff0c\u6bcf\u4e2a\u4f4d\u7f6e\u7684\u571f\u5806\u5927\u5c0f\u8868\u793a\u6982\u7387\u7684\u503c\u3002<\/li>\n<li>\u79fb\u52a8\u571f\u5806\u7684\u201c\u5de5\u4f5c\u91cf\u201d\uff1a\u5982\u679c\u60f3\u628a\u4e00\u4e2a\u4f4d\u7f6e\u4e0a\u7684\u571f\u5806\u79fb\u52a8\u5230\u53e6\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u90a3\u4e48\u6240\u9700\u7684\u5de5\u4f5c\u91cf\u4e0e\u571f\u5806\u7684\u5927\u5c0f\u548c\u79fb\u52a8\u8ddd\u79bb\u6210\u6b63\u6bd4\u3002<\/li>\n<\/ul>\n<p>Wasserstein \u8ddd\u79bb\u7684\u6570\u5b66\u5b9a\u4e49\u662f:<br \/>\n$$<br \/>\nW(P, Q)=\\inf _{\\gamma \\in \\Pi(P, Q)} \\mathrm{E}_{(x, y) \\sim \\gamma}[|x-y|]<br \/>\n$$<br \/>\n\u5176\u4e2d:<\/p>\n<ul>\n<li>$P$ \u548c $Q$ \u662f\u4e24\u4e2a\u6982\u7387\u5206\u5e03;<\/li>\n<li>$\\Pi(P, Q)$ \u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u8054\u5408\u5206\u5e03 $\\gamma$, \u8fd9\u4e9b\u8054\u5408\u5206\u5e03\u7684\u8fb9\u7f18\u5206\u5e03\u5206\u522b\u662f $P$ \u548c $Q$ \u3002<\/li>\n<li>inf \u8868\u793a\u6c42\u53d6\u4e0b\u786e\u754c, \u5373\u6240\u6709\u53ef\u80fd\u65b9\u6848\u4e2d\u7684\u6700\u5c0f\u503c\u3002<\/li>\n<li>$\\mathrm{E}_{(x, y) \\sim \\gamma}[|x-y|]$ \u8868\u793a\u5728\u8054\u5408\u5206\u5e03 $\\gamma$ \u4e0b\uff0c\u4ece $P$ \u5230 $Q$ \u7684\u70b9\u5bf9 $(x, y)$ \u4e4b\u95f4\u8ddd\u79bb\u7684\u671f\u671b\u503c\u3002<\/li>\n<\/ul>\n<p>\u4ece\u76f4\u89c2\u4e0a\u7406\u89e3\uff0c\u5c06\u4e24\u4e2a\u6982\u7387\u5206\u5e03P\u548cQ\u60f3\u8c61\u6210\u4e24\u5806\u5f62\u72b6\u548c\u4f53\u79ef\u4e0d\u540c\u7684\u571f\u5806\uff0cWasserstein\u8ddd\u79bb\u76f8\u5f53\u4e8e\u5c06\u4e00\u5806\u571f\u5806\u7684\u5f62\u72b6\u5b8c\u5168\u6539\u53d8\u6210\u53e6\u4e00\u5806\u571f\u5806\u6240\u9700\u7684\u6700\u5c0f\u201c\u5de5\u4f5c\u91cf\u201d\u3002\u8fd9\u91cc\u7684\u201c\u5de5\u4f5c\u91cf\u201d\u53ef\u4ee5\u7406\u89e3\u4e3a\u571f\u7684\u79fb\u52a8\u8ddd\u79bb\u548c\u79fb\u52a8\u7684\u91cf\u7684\u4e58\u79ef\u4e4b\u548c\u3002\u6240\u4ee5\uff0c\u5373\u4f7f\u4e24\u4e2a\u5206\u5e03\u5b8c\u5168\u4e0d\u91cd\u53e0\uff08\u6ca1\u6709\u5171\u540c\u7684\u652f\u6301\uff09\uff0cWasserstein\u8ddd\u79bb\u4ecd\u7136\u80fd\u7ed9\u51fa\u4e00\u4e2a\u6709\u610f\u4e49\u7684\u503c\uff0c\u8fd9\u4e2a\u503c\u53cd\u6620\u4e86\u5b83\u4eec\u4e4b\u95f4\u7684\u201c\u8ddd\u79bb\u201d\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u63a8\u5bfc: <\/p>\n<ul>\n<li>\n<p>\u8054\u5408\u5206\u5e03 $\\gamma$ \u4ee3\u8868\u4e86\u4ece\u5206\u5e03 $P$ \u5230\u5206\u5e03 $Q$ \u7684\u4e00\u4e2a \u201c\u8f6c\u79fb\u8ba1\u5212\u201d \u3002<\/p>\n<\/li>\n<li>\n<p>\u8981\u8ba1\u7b97\u79fb\u52a8\u603b\u7684 \u201c\u5de5\u4f5c\u91cf\u201d, \u9700\u8981\u8ba1\u7b97\u6240\u6709\u8fd9\u4e9b\u79fb\u52a8\u7684 \u201c\u8d28\u91cf\u201d \u4e58\u4ee5\u5176\u79fb\u52a8\u7684\u8ddd\u79bb $|x-y|$ \u3002<\/p>\n<\/li>\n<li>\n<p>\u8fd9\u5c31\u662f\u79ef\u5206 $\\int_{X \\times X}|x-y| d \\gamma(x, y)$ \u7684\u542b\u4e49\u3002<\/p>\n<\/li>\n<li>\n<p>\u4e0a\u8ff0\u79ef\u5206\u5728\u6240\u6709\u53ef\u80fd\u7684 $x$ \u548c $y$ \u5bf9\u4e0a\u8fdb\u884c, \u8868\u793a\u6574\u4e2a\u8f6c\u79fb\u8ba1\u5212\u7684\u603b\u5de5\u4f5c\u91cf\u3002\u7531\u4e8e\u53ef\u80fd\u6709\u8bb8\u591a\u79cd\u5c06 $P$ \u8f6c\u6362\u4e3a $Q$ \u7684\u65b9\u5f0f, \u9700\u8981\u5bfb\u627e\u4f7f\u5f97\u603b\u5de5\u4f5c\u91cf\u6700\u5c0f\u7684\u8ba1\u5212\u3002\u8fd9\u5c31\u662f  $\\inf _{\\gamma \\in \\Pi(P, Q)}$ \u6240\u8868\u8fbe\u7684\u542b\u4e49\u3002<strong>\u5728\u6240\u6709\u53ef\u80fd\u7684\u8054\u5408\u5206\u5e03 $\\gamma$ \u4e2d\u5bfb\u627e\u4e00\u4e2a\u4f7f\u5f97\u603b\u5de5\u4f5c\u91cf\u6700\u5c0f\u7684\u5206\u5e03\u3002<\/strong><\/p>\n<\/li>\n<li>\n<p>\u5728GAN\u8bad\u7ec3\u4e2d\uff0cWasserstein\u8ddd\u79bb\u7684\u8fd9\u79cd\u7279\u6027\u4f7f\u5176\u5373\u4f7f\u5728\u6982\u7387\u5206\u5e03\u4e0d\u91cd\u53e0\u7684\u60c5\u51b5\u4e0b\uff0c\u4e5f\u80fd\u63d0\u4f9b\u7a33\u5b9a\u6709\u6548\u7684\u68af\u5ea6\uff0c\u8fd9\u89e3\u51b3\u4e86\u4f20\u7edfGAN\u4f7f\u7528JS\u6563\u5ea6\u6216KL\u6563\u5ea6\u65f6\u9762\u4e34\u7684\u68af\u5ea6\u6d88\u5931\u95ee\u9898\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>WGAN\u7684\u635f\u5931\u5b9a\u4e49<\/strong><\/p>\n<p>\u7531\u4e8eKantorovich-Rubinstein\u5bf9\u5076\u6027\uff0c\u56e0\u6b64\u53ef\u4ee5\u7528\u53e6\u4e00\u79cd\u65b9\u5f0f\u8868\u8fbeWasserstein\u8ddd\u79bb\uff1a<\/p>\n<p>$$<br \/>\nW\\left(\\mathrm{P}_{\\text {real }}, \\mathrm{P}_{\\mathrm{gen}}\\right)=\\sup _{|f|_L \\leq 1}\\left[\\mathrm{E}_{x \\sim \\mathrm{P}_{\\text {real }}}[f(x)]-\\mathrm{E}_{x \\sim \\mathrm{P}_{\\mathrm{gen}}}[f(x)]\\right]<br \/>\n$$<\/p>\n<p>\u5176\u4e2d sup \u8868\u793a\u4e0a\u786e\u754c, \u786e\u4fdd\u51fd\u6570 $f$ \u904d\u5386\u6240\u6709 1 -\u5229\u666e\u5e0c\u8328\u8fde\u7eed\u7684\u51fd\u6570\u3002<\/p>\n<p>\u5173\u4e8e\u5bf9\u5076\u6027\u63a8\u8bba\u5177\u4f53\u7684\u6570\u5b66\u539f\u7406\u5728\u8fd9\u91cc\u4e0d\u505a\u8be6\u7ec6\u63a8\u5bfc, \u6ce8\u610f\u6b64\u63a8\u8bba\u5fc5\u987b\u8981\u6c42\u786e\u4fdd\u51fd\u6570 $f$ \u904d\u5386\u6240\u6709 1 -\u5229\u666e\u5e0c\u8328\u8fde\u7eed\u7684\u51fd\u6570\u3002<\/p>\n<p>1-\u5229\u666e\u5e0c\u8328\u8fde\u7eed\u51fd\u6570\u662f\u4e00\u7c7b\u5728\u6570\u5b66\u5206\u6790\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u51fd\u6570, \u5b83\u4eec\u6ee1\u8db3\u7279\u5b9a\u7684 \u201c\u7a33\u5b9a\u6027\u201d\u6216 \u201c\u5e73\u6ed1\u6027\u201d \u6761\u4ef6\u3002\u4e00\u4e2a\u51fd\u6570\u88ab\u79f0\u4e3a 1-\u5229\u666e\u5e0c\u8328\u8fde\u7eed, \u5982\u679c\u5bf9\u4e8e\u5176\u5b9a\u4e49\u57df\u5185\u7684\u4efb\u610f\u4e24\u70b9,\u51fd\u6570\u503c\u7684\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc7\u8fd9\u4e24\u70b9\u95f4\u8ddd\u79bb\u7684\u7edd\u5bf9\u503c\u3002\u5f62\u5f0f\u5316\u5730, \u4e00\u4e2a\u51fd\u6570 $f: \\mathrm{R}^n \\rightarrow \\mathrm{R}$ \u88ab\u79f0\u4e3a 1-\u5229\u666e\u5e0c\u8328\u8fde\u7eed, \u5982\u679c\u5bf9\u4e8e\u6240\u6709 $x, y \\in \\mathrm{R}^n$, \u6709:$|f(x)-f(y)| \\leq|x-y|$ \u3002\u5176\u4e2d, $|x-y|$ \u8868\u793a $x$ \u548c $y$ \u4e4b\u95f4\u7684\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u30021-\u5229\u666e\u5e0c\u8328\u8fde\u7eed\u6027\u8d28\u4fdd\u8bc1\u4e86\u51fd\u6570\u7684\u8f93\u51fa\u5bf9\u8f93\u5165\u7684\u5fae\u5c0f\u53d8\u5316\u53ea\u6709\u6709\u9650\u7684\u54cd\u5e94\u3002\u8fd9\u610f\u5473\u7740\u51fd\u6570\u56fe\u5f62\u6ca1\u6709\u5267\u70c8\u7684\u6ce2\u52a8, \u8868\u73b0\u51fa\u4e00\u5b9a\u7684\u5e73\u6ed1\u6027\u3002<\/p>\n<p><strong>\u5728 WGAN \u4e2d, \u4f7f\u7528\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u5224\u522b\u5668 $D$, \u5b83\u5c1d\u8bd5\u6a21\u62df\u4e0a\u8ff0\u5bf9\u5076\u6027\u4e2d\u7684\u6700\u4f18 1-\u5229\u666e\u5e0c\u8328\u8fde\u7eed\u51fd\u6570 $f$ \u3002<\/strong> \u8fd9\u5c31\u610f\u5473\u7740\u9700\u8981\u8bad\u7ec3 $D$ \u6765\u6700\u5927\u5316 $\\mathrm{E}_{x \\sim \\mathrm{P}_{x=1}}[D(x)]-\\mathrm{E}_{x \\sim \\mathrm{P}_{\\mathrm{g} m}}[D(x)]$ \u3002\u56e0\u6b64, \u5224\u522b\u5668 $D$ \u7684\u635f\u5931\u51fd\u6570\u5728 WGAN \u4e2d\u53ef\u4ee5\u8868\u793a\u4e3a:<br \/>\n$$<br \/>\nL_D=-\\left(\\mathrm{E}_{x \\sim \\mathrm{P}_{\\text {est }}}[D(x)]-\\mathrm{E}_{z \\sim \\mathrm{P}_z}[D(G(z))]\\right)<br \/>\n$$<\/p>\n<ul>\n<li>\n<p>$\\mathrm{E}_{x \\sim \\mathrm{P}_{\\mathrm{Rax}}}[D(x)]$ \u662f\u5bf9\u4e8e\u771f\u5b9e\u6570\u636e\u6837\u672c $x$ \u7684\u5224\u522b\u5668\u8f93\u51fa\u7684\u671f\u671b\u503c<\/p>\n<\/li>\n<li>\n<p>$\\mathrm{E}_{z \\sim P_Z}[D(G(z))]$  \u662f\u5bf9\u4e8e\u751f\u6210\u5668 $G$ \u751f\u6210\u7684\u5047\u6570\u636e\u6837\u672c\u7684\u5224\u522b\u5668\u8f93\u51fa\u7684\u671f\u671b\u503c\u3002<\/p>\n<\/li>\n<li>\n<p>\u5bf9\u4e8e\u751f\u6210\u5668 $G L_G=-\\mathrm{E}_{z \\sim \\mathcal{E}}[D(G(z))]$, \u751f\u6210\u5668 $G$ \u7684\u76ee\u6807\u662f\u6700\u5927\u5316\u5224\u522b\u5668 $D$ \u5bf9\u5176\u751f\u6210\u7684\u5047\u6837\u672c\u7684\u8bc4\u5206\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u786e\u4fdd\u8ba1\u7b97\u51fa\u7684Wasserstein\u8ddd\u79bb\u6709\u6548\uff0cWGAN\u8981\u6c42\u5224\u522b\u5668\u662f\u4e00\u4e2a1-\u5229\u666e\u5e0c\u8328\u51fd\u6570\u3002<\/p>\n<ul>\n<li>\n<p>\u5728WGAN\u7684\u521d\u59cb\u7248\u672c\u4e2d\uff0c\u901a\u5e38\u901a\u8fc7\u526a\u88c1\u8bc4\u4ef7\u5668\u7684\u6743\u91cd\u5230\u4e00\u4e2a\u56fa\u5b9a\u8303\u56f4\uff08\u4f8b\u5982[\u22120.01,0.01]\uff09\u6765\u5b9e\u73b0\u3002<\/p>\n<\/li>\n<li>\n<p>\u5728\u540e\u7eed\u7684\u7814\u7a76\u4e2d\uff0c\u5229\u7528\u68af\u5ea6\u60e9\u7f5a\u6765\u4ee3\u66ff\u6743\u91cd\u526a\u88c1\uff0c\u4ee5\u4fbf\u66f4\u6709\u6548\u5730\u5b9e\u65bd1-\u5229\u666e\u5e0c\u8328\u7ea6\u675f\u5e76\u63d0\u9ad8\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u68af\u5ea6\u60e9\u7f5a\u7684\u57fa\u672c\u601d\u60f3\u662f\u76f4\u63a5\u7ea6\u675f\u5224\u522b\u5668\u7684\u68af\u5ea6, \u800c\u4e0d\u662f\u901a\u8fc7\u526a\u88c1\u5176\u6743\u91cd\u3002\u8fd9\u6837\u505a\u7684\u539f\u7406\u662f\u57fa\u4e8e 1-\u5229\u666e\u5e0c\u8328\u51fd\u6570\u7684\u4e00\u4e2a\u7279\u6027\uff1a\u5bf9\u4e8e 1-\u5229\u666e\u5e0c\u8328\u51fd\u6570 $f$, \u5728\u5176\u5b9a\u4e49\u57df\u4e2d\u7684\u4efb\u610f\u4e00\u70b9 $x$,\u5176\u68af\u5ea6\u7684\u8303\u6570\u4e0d\u4f1a\u8d85\u8fc7 1 , \u5373 $|\\nabla f(x)| \\leq 1$ \u3002<\/p>\n<p>\u5728WGAN-GP\uff08Wasserstein GAN with Gradient Penalty\uff09\u4e2d\uff0c\u4e3a\u4e86\u5f3a\u5236\u5b9e\u73b0\u8fd9\u4e00\u7ea6\u675f\uff0c\u7814\u7a76\u8005\u4eec\u63d0\u51fa\u4e86\u5728\u5224\u522b\u5668\u7684\u635f\u5931\u51fd\u6570\u4e2d\u52a0\u5165\u4e00\u4e2a\u68af\u5ea6\u60e9\u7f5a\u9879\u3002\u8fd9\u4e2a\u60e9\u7f5a\u9879\u57fa\u4e8e\u968f\u673a\u91c7\u6837\u7684\u70b9\u4e0a\u5224\u522b\u5668\u68af\u5ea6\u7684\u4e8c\u8303\u6570\uff0c\u76ee\u7684\u662f\u4f7f\u8fd9\u4e2a\u68af\u5ea6\u7684\u4e8c\u8303\u6570\u5c3d\u53ef\u80fd\u5730\u63a5\u8fd11\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4, WGAN-GP \u4e2d\u5224\u522b\u5668\u7684\u635f\u5931\u51fd\u6570 $L_D$ \u88ab\u4fee\u6539\u4e3a\u5305\u542b\u4ee5\u4e0b\u68af\u5ea6\u60e9\u7f5a\u9879:<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240922093004323.png\" style=\"height:60px\">\n<\/p>\n<p>\u5176\u4e2d:<\/p>\n<ul>\n<li>$\\mathrm{P}_r$ \u662f\u771f\u5b9e\u6570\u636e\u5206\u5e03;<\/li>\n<li>$\\mathrm{P}_g$\u662f\u751f\u6210\u5668\u7684\u6570\u636e\u5206\u5e03;<\/li>\n<li>$\\hat{x}$ \u662f\u4ece\u771f\u5b9e\u6570\u636e\u548c\u751f\u6210\u6570\u636e\u4e4b\u95f4\u7684\u63d2\u503c\uff08\u4f8b\u5982, $\\hat{x}=\\epsilon x+(1-\\epsilon) \\tilde{x}$, \u5176\u4e2d $\\epsilon$ \u662f\u4e00\u4e2a\u968f\u673a\u6570, \u901a\u5e38\u5728 0 \u5230 1 \u4e4b\u95f4\u5747\u5300\u91c7\u6837\uff09;<\/li>\n<li>$\\lambda$ \u662f\u68af\u5ea6\u60e9\u7f5a\u7684\u6743\u91cd, \u662f\u4e00\u4e2a\u8d85\u53c2\u6570, \u9700\u8981\u6839\u636e\u5177\u4f53\u5e94\u7528\u8fdb\u884c\u8c03\u6574\u3002<\/li>\n<\/ul>\n<pre><code class=\"language-python\">import torch as t\nfrom torch import nn\nfrom torch.autograd import Variable\nfrom torch.optim import RMSprop\nfrom torchvision.utils import make_grid\nfrom pylab import plt\n%matplotlib inline\n\nimport os\nos.environ[&#039;CUDA_VISIBLE_DEVICES&#039;]=&#039;1&#039;\nclass Config:\n    lr = 0.00005\n    nz = 100 # noise dimension\n    image_size = 64\n    image_size2 = 64\n    nc = 1 # chanel of img \n    ngf = 64 # generate channel\n    ndf = 64 # discriminative channel\n    beta1 = 0.5\n    batch_size = 32\n    max_epoch = 40 # =1 when debug\n    workers = 2\n    gpu = True # use gpu or not\n    clamp_num=0.01# WGAN clip gradient\n\nopt=Config()\n\nnetg = nn.Sequential(\n            nn.ConvTranspose2d(opt.nz,opt.ngf*8,4,1,0,bias=False),\n            nn.BatchNorm2d(opt.ngf*8),\n            nn.ReLU(True),\n\n            nn.ConvTranspose2d(opt.ngf*8,opt.ngf*4,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ngf*4),\n            nn.ReLU(True),\n\n            nn.ConvTranspose2d(opt.ngf*4,opt.ngf*2,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ngf*2),\n            nn.ReLU(True),\n\n            nn.ConvTranspose2d(opt.ngf*2,opt.ngf,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ngf),\n            nn.ReLU(True),\n\n            nn.ConvTranspose2d(opt.ngf,opt.nc,4,2,1,bias=False),\n            nn.Tanh()\n        )\n\nnetd = nn.Sequential(\n            nn.Conv2d(opt.nc,opt.ndf,4,2,1,bias=False),\n            nn.LeakyReLU(0.2,inplace=True),\n\n            nn.Conv2d(opt.ndf,opt.ndf*2,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ndf*2),\n            nn.LeakyReLU(0.2,inplace=True),\n\n            nn.Conv2d(opt.ndf*2,opt.ndf*4,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ndf*4),\n            nn.LeakyReLU(0.2,inplace=True),\n\n            nn.Conv2d(opt.ndf*4,opt.ndf*8,4,2,1,bias=False),\n            nn.BatchNorm2d(opt.ndf*8),\n            nn.LeakyReLU(0.2,inplace=True),\n\n            nn.Conv2d(opt.ndf*8,1,4,1,0,bias=False),\n            # Modification 1: remove sigmoid\n            # nn.Sigmoid()\n        )\ndef weight_init(m):\n    # weight_initialization: important for wgan\n    class_name=m.__class__.__name__\n    if class_name.find(&#039;Conv&#039;)!=-1:\n        m.weight.data.normal_(0,0.02)\n    elif class_name.find(&#039;Norm&#039;)!=-1:\n        m.weight.data.normal_(1.0,0.02)\n#     else:print(class_name)\n\nnetd.apply(weight_init)\nnetg.apply(weight_init)\n\n# modification 2: Use RMSprop instead of Adam\n# optimizer\noptimizerD = RMSprop(netd.parameters(),lr=opt.lr ) \noptimizerG = RMSprop(netg.parameters(),lr=opt.lr )  \n\n# modification3: No Log in loss\n# criterion\n# criterion = nn.BCELoss()\n\nfix_noise = Variable(t.FloatTensor(opt.batch_size,opt.nz,1,1).normal_(0,1))\nif opt.gpu:\n    fix_noise = fix_noise.cuda()\n    netd.cuda()\n    netg.cuda()\n\n# begin training\none=t.FloatTensor([1])\nmone=-1*one\n\nfor epoch in range(opt.max_epoch):\n    for ii, data in enumerate(dataloader, 0):\n        real, _ = data\n        input = Variable(real)\n        noise = t.randn(input.size(0), opt.nz, 1, 1)\n        noise = Variable(noise)\n\n        if opt.gpu:\n            one = one.cuda()\n            mone = mone.cuda()\n            noise = noise.cuda()\n            input = input.cuda()\n\n        # \u88c1\u526a\u5224\u522b\u5668\u53c2\u6570\n        for parm in netd.parameters():\n            parm.data.clamp_(-opt.clamp_num, opt.clamp_num)\n\n        # \u8bad\u7ec3\u5224\u522b\u5668\n        netd.zero_grad()\n        ## \u4f7f\u7528\u771f\u5b9e\u56fe\u7247\u8bad\u7ec3\u5224\u522b\u5668\n        output = netd(input)\n        output.backward(one.expand_as(output))  # \u4fee\u6539\u70b9\uff1a\u5bf9\u4e8e\u771f\u5b9e\u6837\u672c\uff0c\u68af\u5ea6\u4e3a\u6b63\uff0c\u5373\u589e\u52a0\u5224\u522b\u5668\u8f93\u51fa\u7684\u503c\u3002\n        ## \u4f7f\u7528\u751f\u6210\u7684\u5047\u56fe\u7247\u8bad\u7ec3\u5224\u522b\u5668\n        fake_pic = netg(noise).detach()\n        output2 = netd(fake_pic)\n        output2.backward(mone.expand_as(output2))  # \u4fee\u6539\u70b9\uff1a\u4f7f\u68af\u5ea6\u5f20\u91cf\u5f62\u72b6\u5339\u914d\n        optimizerD.step()\n\n        # \u8bad\u7ec3\u751f\u6210\u5668\n        if (ii + 1) % 5 == 0:\n            netg.zero_grad()\n            noise.data.normal_(0, 1)\n            fake_pic = netg(noise)\n            output = netd(fake_pic)\n            output.backward(one.expand_as(output))  # \u4fee\u6539\u70b9\uff1a\u5bf9\u4e8e\u751f\u6210\u6837\u672c\uff0c\u68af\u5ea6\u4e3a\u8d1f\uff0c\u5373\u51cf\u5c11\u5224\u522b\u5668\u8f93\u51fa\u7684\u503c\u3002\n            optimizerG.step()\n\n    if epoch % 4 ==0:            \n        fake_u = netg(fix_noise)\n        imgs = make_grid(fake_u.data * 0.5 + 0.5).cpu()  # CHW\n        plt.imshow(imgs.permute(1, 2, 0).numpy())  # HWC\n        plt.show()\n<\/code><\/pre>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919102925956.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919102946913.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103003747.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103017190.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103033868.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103049548.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103104222.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103119549.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103134497.png\" style=\"height:300px\">\n<\/p>\n<p align=\"center\">\n  <img decoding=\"async\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/09\/20240919103147528.png\" style=\"height:300px\">\n<\/p>\n<h2><img decoding=\"async\" src=\"https:\/\/img.icons8.com\/dusk\/64\/000000\/prize.png\" style=\"height:50px;display:inline\"> Credits<\/h2>\n<hr \/>\n<ul>\n<li>Icons made by <a href=\"https:\/\/www.flaticon.com\/authors\/becris\" title=\"Becris\">Becris<\/a> from <a href=\"https:\/\/www.flaticon.com\/\" title=\"Flaticon\">www.flaticon.com<\/a><\/li>\n<li>Icons from <a href=\"https:\/\/icons8.com\/\">Icons8.com<\/a> - <a href=\"https:\/\/icons8.com\">https:\/\/icons8.com<\/a><\/li>\n<li><a href=\"https:\/\/d2l.ai\/chapter_recurrent-neural-networks\/index.html\">Dive Into Deep Learning - Recurrent Neural Networks<\/a><\/li>\n<li><a href=\"https:\/\/atcold.github.io\/pytorch-Deep-Learning\/en\/week12\/12-1\/\">DS-GA 1008 - NYU CENTER FOR DATA SCIENCE - Deep Sequence Modeling<\/a><\/li>\n<li><a href=\"https:\/\/pytorch.org\/tutorials\/beginner\/text_sentiment_ngrams_tutorial.html\">Text classification with the torchtext library<br \/>\n<\/a><\/li>\n<li><a href=\"https:\/\/www.borealisai.com\/research-blogs\/tutorial-17-transformers-iii-training\/\">Tricks For Training Transformers - Borealis AI - P. Xu, S. Prince<\/a><\/li>\n<li><a href=\"https:\/\/taldatech.github.io\">Tal Daniel<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Deep Learning create by Arwin Yu Tutorial 06 &#8211; Generati [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2058,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,24],"tags":[19],"class_list":["post-2053","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-18","category-24","tag-19"],"_links":{"self":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2053"}],"version-history":[{"count":26,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2053\/revisions"}],"predecessor-version":[{"id":2116,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2053\/revisions\/2116"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/media\/2058"}],"wp:attachment":[{"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2053"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}